Ganitsara Sangrah

Author(s): Mahaviracharya, A N Upadhye, Hiralal Jain, L C Jain
Publisher: Jain Sanskriti Samrakshak Sangh
Catalog link: https://jainqq.org/explore/090174/1

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jIvarAja jaina graMthamAlA-12 mahAvIrAcArya-viracita gaNitasAra-saMgraha sva. bra, jIvarAja gautamacandrajI prakAzaka jaina saMskRti saMrakSaka saMgha, solApUra vi. saM. 2020 [ kiMmata

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Jivaraja Jaina Granthamala, No. 12 General Editors : Dr. A. N. UPADHYE & Dr. H. L. Jain Mahaviracharya's Ganitasara-Sangraha (An Ancient Treatise on Mathematics ) Authentically Edited with a Hindi Translation and Introduction etc. by L. C. Jain JABALPUR Published by Gulabchand Hirachand Doshi Jajna Samskrti Samrakshaka Sangha, Sholapur 1963 All Rights Reserved Price Rupees Twelve only

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First Edition : 750 Copies Copies of this book can be had direct from Jaina Samskrti Samrakshaka Samgha, Santosha Bhavana, Phaltan Galli, Sholapur ( India ) Price Rs. 12/- per copy, exclusive of postage jIvarAja jaina graMthamAlA kA paricaya solApura nivAsI brahmacArI jIvarAja gautamacaMdajI dozI kaI varSoM se saMsAra se udAsIna hokara dharmakArya meM apanI vRtti lagA rahe the| san 1940 meM unakI yaha prabala icchA ho uThI ki apanI nyAyopArjita saMpatti kA upayoga vizeSa rUpa se dharma aura samAja kI unnati ke kArya meM kareM / tadanusAra unhoMne samasta deza kA paribhramaNa kara jaina vidvAnoM se sAkSAt aura likhita sammatiyA~ isa bAta kI saMgraha kI ki kauna se kArya meM saMpatti kA upayoga kiyA jAya / sphuTa mata saMcaya kara lene ke pazcAt san 1941 ke grISma kAla meM brahmacArIjI ne tIrthakSetra gajapaMthA ( nAsikA ) ke zItala vAtAvaraNa meM vidvAnoM kI samAja ekatra kI aura UhApoha pUrvaka nirNaya ke lie ukta viSaya prastuta kiyA / vidvatsammelana ke phalasvarUpa brahmacArIjI ne jaina saMskRti tathA sAhitya ke samasta aMgoM ke saMrakSaNa, uddhAra aura pracAra ke hetu se 'jaina saMskRti saMrakSaka saMgha' kI sthApanA kI aura usake lie 30,000) tIsa hajAra ke dAna kI ghoSaNA kara dii| unakI parigrahanivRtti bar3hatI gaI, aura san 1944 meM unhoMne lagabhaga 2,00,000) do lAkha kI apanI saMpUrNa saMpatti saMgha ko TrasTa rUpa se arpaNa kara dii| isa taraha Apane apane sarvasva kA tyAga kara di. 16-1-57 ko atyanta sAvadhAnI aura samAdhAna se samAdhimaraNakI ArAdhanA kii| isI saMgha ke antargata 'jIvarAja jaina graMthamAlA' kA saMcAlana ho rahA hai| prastuta graMtha isI graMthamAlA kA bArahavA~ puSpa hai| prakAzaka gulAbacaMda hirAcaMda dozI, jaina saMskRti saMrakSaka saMgha, solApura mudraka bAlakRSNa zAstrI jyotiSa prakAza presa, kAlabhairava mArga, vArANasI

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sva. brahmacArI jIvarAja gautamacaMdajI dozI, saMsthApaka jaina saMskRti saMrakSaka saMgha, zolApUra

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jIvarAja jaina granthamAlA, grantha 12 granthamAlA-saMpAdaka DaoN. A. ne. upAdhye va DaoN0 hIrAlAla jaina mahAvIrAcArya-viracita gaNita sAra-saMgraha (gaNita zAstra viSayaka prAcIna grantha ) saMskRta mUla, hindI anuvAda va prastAvanA, pariziSTa Adi sahita prAmANika rUpa se saMpAdita saMpAdaka lakSmIcandra jaina jabalapura prakAzaka zrI gulAbacanda hirAcanda dozI jaina saMskRti saMrakSaka saMgha solApura vI. ni. saMvat 2490 san 1963 vikrama saMvat 2020 mUlya ru. 12 mAtra

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FOREWORD I have had the privilege of going through this edition of Mahaviracharya's Ganitasara-Samgraha, prepared with critical annotations and an introduction by Prof. L. C. Jain of the Department of Mathematics, Govt. Science College, Jabalpur, under the general editorship of the renowned orientalists, Dr. A. N. Upadhye and Dr. H. L. Jain. Apart from the extreme care which the learned editor has exercised in the choice of technical expressions and terminology in Hindi throughout this edition, what struck me the most is his sympathetic and erudite understanding of the highly intricate interactions among various schools of mathematical thought that must have gone into the making of a background for a classic like the Ganitasara-Samgraha. And this, I am sure, places the present edition on a distinctly higher-than-ever-attained plane of excellence. I hail the appearance of this work of Prof. L. C. Jain in the world of learning. JABALPUR November 4, 1963 T. PATI Head of the Department of Mathematics University of Jabalpur

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viSaya-sUcI (1) DA. tri. pati kA prAkkathana ( Foreword) (2) granthamAlA saMpAdakIya (3) pro0 bAgIjI kA prAstAvika ( Introductory ) (4) saMpAdakIya ( Editorial ) (5) prastAvanA gaNita itihAsa kA sAmAnya avalokana ... gaNita itihAsa kA viziSTa avalokana ... (6) gaNitasArasaMgraha-mUla aura anuvAda 1. saMjJA (pAribhASika zabda) adhikAra maGgalAcaraNa gaNitazAstra prazaMsA kSetra-paribhASA (kSetramApa sambandhI pAribhASika zabdAvali) kAla-paribhASA ( kAlamApa sambandhI pAribhASika zabdAvali) ... dhAnya-paribhASA (dhAnyamApa sambandhI pAribhASika zabdAvali) ... suvarNa-paribhASA (svarNamApa sambandhI pAribhASika zabdAvali) ... rajata-paribhASA ( rajatamApa sambandhI pAribhASika zabdAvali) ... loha-paribhASA ( loha dhAtumApa sambandhI pAribhASika zabdAvali)... parikarma nAmAvali (gaNita kI mukhya kriyAoM ke nAma ) zUnya tathA dhanAtmaka evaM RNAtmaka rAzi sambandhI sAmAnya niyama saMkhyA saMjJA sthAna nAmAvali ( saMketanAtmaka sthAnoM ke nAma ) gaNaka guNa nirUpaNa 2. parikarma vyavahAra ( aGkagaNita sambandhI kriyAe~) pratyutpanna (guNana) bhAgahAra (bhAga) varga vargamUla ghana ghanamUla saMkalita (zreDhiyoM kA saMkalana) vyutkalita 3. kalAsavarNa vyavahAra ( bhinna) bhinna pratyutpanna (bhinnoM kA guNana)

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bhinna bhAgahAra ( bhinnoM kA bhAga) bhinna sambandhI varga, vargamUla, ghana, ghanamUla bhinna saMkalita ( bhinnAtmaka zreDhiyoM kA yogakaraNa ) bhinna vyutkalita (zreDhirUpa bhinnoM kA vyutkalana) ... kalAsavarNa SaD jAti (chaH prakAra ke bhinna ) ... bhAgajAti (sAdhAraNa bhinnoM kA jor3a aura ghaTAnA)- -- prabhAga aura bhAgabhAga jAti (saMyuta aura jaTila bhinna ) bhAgAnubandha jAti (saMyava bhinna) - bhAgApavAha jAti (viyavita bhinna) bhAgamAtR jAti (do yA adhika prakAra ke bhinnoM se saMyukta bhinna ) ... 4. prakIrNaka vyavahAra (bhinnoM para vividha prazna ) bhAga aura zeSa jAti mUla jAti zeSamUla jAti dviragra zeSamUla jAti aMzamUla jAti bhAga saMvarga jAti UnAdhika aMzavarga jAti mUlamizra jAti bhinna dRzya jAti 5. trairAzika vyavahAra anukrama trairAzika vyasta trairAzika vyasta paMcarAzika vyasta saptarAzika vyasta navarAzika gati nivRtti paMcarAzika, saptarAzika, navarAzika bhANDapratibhANDa ( vinimaya) kraya vikraya mizraka vyavahAra saMkramaNa aura viSama saMkramaNa paMcarAzika vidhi vRddhi vidhAna (byAja) prakSepaka kuTTIkAra ( samAnupAtI bhAga) vallikA kuTTIkAra

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vii 124 135 145 165 l 204 213 251 251 viSama kuTTIkAra sakala kuTTIkAra suvarNa kuTTIkAra vicitra kuTTIkAra zreDhIbaddha saMkalita (zreNiyoM kA saMkalana) 7. kSetragaNita vyavahAra (kSetraphala ke mApa sambandhI gaNanA) vyAvahArika gaNita ( anumAnataH mApasambandhI gaNanA) sUkSma gaNita janya vyavahAra paizAcika vyavahAra 8. khAta vyavahAra (khoha athavA gar3hA sambandhI gaNanAe~) sUkSma gaNita citi gaNita (IToM ke Dhera sambandhI gaNita) krakacikA vyavahAra 9. chAyA vyavahAra ( chAyA sambandhI gaNita) pariziSTa 1 saMkhyA nirUpaka zabdAvali 2 anuvAda meM avatarita saMskRta zabda 2 a graMtha meM prayukta saMskRta pAribhASika zabdAvali 3 uttara-mAlA 4 mApa-sAraNI 5 kAraMjA jaina-bhaNDAra prati-paricaya 6 prophesara raMgAcArya aura DeviDa Aijina smitha kI prastAvanAe~ prastAvanA kI anumakraNikA zuddhi-patra ... 262 ... 267 (aMtima)1

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granthamAlA saMpAdakIya par3hanA, likhanA aura ginanA ye manuSya kI maulika vidyAyeM mAnI gaI haiN| jaina-zAstroM meM jina bahattara kalAoM kA ullekha milatA hai unameM sarvaprathama sthAna lekha kA aura dUsarA gaNita kA hai / tathApi AgamoM meM prAyaH ina kalAoM ko 'lehAiyAo gaNiyappahANAo' arthAt lekhAdika, kintu gaNita pradhAna kahA gayA hai| isase siddha hotA hai ki bAlaka kI zikSA meM evaM mAnavIya vyavahAra meM gaNita kA bar3A mahattva thaa| jaina-sAhitya yadyapi dharma va darzana pradhAna hai, tathApi usameM gaNita-zAstra kA upayoga va vyAkhyAna pada pada para pAyA jAtA hai| vizeSataH isa sAhitya ke cAra anuyoga-prathama, karaNa, caraNa aura dravya mAne gaye haiN| unameM karaNAnuyoga meM loka kA svarUpa varNita pAyA jAtA hai; aura usa nimitta se sUrya, candra va nakSatra tathA dvIpa, samudra Adi ke vivaraNoM meM gaNita kI nAnA prakriyAoM kA pracuratA se upayoga kiyA gayA hai / sUryaprajJapti, candraprajJapti evaM jambUdvIpaprajJapti nAmaka upAGgoM meM tathA tiloyapaNNatti, SaTkhaMDAgama kI dhavala TIkA evaM gommaTasAra va trilokasAra tathA unakI TIkAoM meM pracuratA se gaNita kA prayoga pAyA jAta hai; aura vaha bhAratIya prAcIna gaNita ke vikAsa ko samajhane ke liye bar3A mahattvapUrNa hai| sUryaprajJapti ko to gaNitAnuyoga bhI kahA gayA hai| vaidika paramparA meM gaNita kA viSaya vedAGga jyotiSa Adi jyotiSa ke graMthoM meM prayukta pAyA jAtA hai| pA~cavIM zatI meM hue AryabhaTa hI eka sarvaprathama jyotiSI pAye jAte haiM jinhoMne apane AryASTazata nAmaka kRti meM 33 zlokAtmaka gaNita kA eka prakaraNa svataMtra rUpa se jor3A hai| unake pazcAt hae brahmagupta ne bhI apane brAhma sphuTa siddhAnta nAmaka graMtha meM gaNita kA eka adhyAya jor3A hai| isa samasta paramparA meM eka bhI aisA graMtha nahIM dikhAI detA jo pUrNataH gaNita-viSayaka kahA jA sake / aisA sarvaprathama graMtha mahAvIrAcArya kRta gaNitasAra-saMgraha hI hai jisakI racanA rASTrakUTa nareza amoghavarSa ke rAjyakAla meM huI thI jo san 813 se 880 IsvI taka pAyA jAtA hai| yaha rAjA jainadharma kA bar3A anurAgI thA aura usake saMrakSaNa meM bahuta se jaina sAhitya kI racanA huii| rAjA svayaM eka kavi thA aura praznottara-ratna-mAlikA nAmaka prakhyAta subhASita kavitA usI kI banAI siddha hotI hai| prastuta graMtha kI utthA nikA meM hI amoghavarSa kI bar3I prazaMsA kI gaI hai| yahA~ jo unheM mahAn yathAkhyAta-cAritra-jaladhi Adi vizeSaNa diye gaye haiM unapara se aisA anumAna hotA hai ki unhoMne rAjyatyAga kara munidharma dhAraNa kiyA thA / ratnamAlikA ke anta meM jo unheM 'vivekAt tyaktarAjyena' kahA hai usase bhI isI bAta kA samarthana hotA hai| (dekhiye DaoN0 hI0 lA0 jaina, rASTrakUTa nareza amoghavarSa kI jaina-dIkSA, jaina siddhAnta bhAskara, ArA, 1943 ) / eka pUrNataH gaNita viSayaka graMtha aisA bhI milA hai jo Azcarya nahIM mahAvIrAcArya se

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pUrvakAlIna ho| pezAvara ke samIpa bakSAlI nAmaka grAma meM bhUmi ke bhItara se eka bhUrja patra para likhe hue graMtha ke khaMDa san 1881 meM prApta hue| inakI chAnabIna se patA calA ki inameM bhinna, vargamUla, samAntara aura guNottara zreDhiyAM Adi gaNita kI prakriyAoM kA varNana hai| kucha vidvAn isa graMtha ko tIsarI cauthI zatI kI racanA kA anumAna karate haiM aura kucha ise bArahavIM zatI ke lagabhaga rakhane ke bhI pakSa meM haiN| ( dekhiye Bibhutibhusan Datta, The Bakhshali Mathematics, Bul. Cal. Math. Soc., XXI, 1 ( 1929 ), pp. 1-60 ). prastuta sarvAMgapUrNa gaNita graMtha ke mahattva ko samajha kara isakA sampAdana prophesara raMgAcArya ne aMgrejI anuvAda sahita san 1912 meM kiyA thA jisakA prakAzana madrAsa gavanmeMTa kI ora se huA thA / idhara aneka varSoM se vaha prakAzana alabhya hai jisake kAraNa prAcIna gaNita ke vidvAnoM va zodhakoM ko bar3I asuvidhA pratIta hotI thii| isI kAraNa yaha Avazyaka samajhA gayA ki isa graMtha kA punaH saMzodhana, anuvAda va prakAzana karAyA jAya / yaha kArya gaNita ke prAdhyApaka zrI lakSmIcandra jaina ne apane hAtha meM liyA aura unhoMne apane hindI anuvAda tathA prastAvanA meM viSaya ko suspaSTa karane meM bar3A parizrama kiyA hai jisake liye hama unake bahuta kRtajJa haiN| prastuta graMthamAlA ke adhikAriyoM ne isa graMtha ko prakAzita karanA saharSa svIkAra kiyA isake liye ve dhanyavAda ke pAtra haiM / isa graMtha ke lie pro0 bhUpAla bALappA bAgI ( dhAravADa ) ne mahattvapUrNa prAstAvika likhA hai, jisake lie hama unake AbhArI haiM / aneka sampAdana va mudraNa sambandhI kaThinAiyoM ke kAraNa graMtha ke prakAzana meM bahuta vilamba huA isakA hameM dukha hai| vidvAnoM se hamArI prArthanA hai ki ve isa mahattvapUrNa zAstra ke sambandha meM apane abhimata va sujhAva nissaMkoca bhejane kI kRpA kareM, jisase viSaya kA uttarottara parimArjana hotA rhe| hI. lA. jaina A. ne. upAdhye pradhAna sampAdaka

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IN TRODUCTORY Aryabhata, the elder ( c. 510 A, D.), Brahmagupta ( c. 628 A. D.), Mahaviracharya (c. 850 A. D.) and Bha karacharya (c. 1150 A. D.) are the most eminent mathematicians of ancient India. Mahaviracharya, the author of the Ganitasara Samgraha, lived in a period well-known, in the history of South India, for its prosperity, political stability and academic fertility. He was a contemporary and enjoyed the patronage of Nrpatunga, or Amoghavarsha ( 815877 A, D.) of the Rashtrakuta dynasty. Nrpatunga was ruling at Manyakheta, but his kingdom.extended far northwards, His capital was a centre of learning. He was not only a mighty ruler, but also a patron of poets and himself a man of literary aptitude and attainments. A Kannada work, Kavirajamarga, on poetics is attributed to him He was a great devotee of Jinasena (the author of Adipurana and Parsvabhyudaya) whose ascetic practices and literary gifts must have captivated his mind. He soon became a pious Jaina and renounced the kingdom in preference to religious life as mentioned by him in his Sanskrit work, the Prasnottara-ratnamala and as graphically described by his contemporary Mahaviracharya in his Ganitasara Samgraha. Mahaviracharya combines the discipline of seasoned mathematician with the warm and vivid imagination of a creative poet. He skilfully summarizes all the known mathematics of his time into a perfect textbook which was used for centuries in the whole of Southern India. He states rules clearly and precisely. He simplifies and sharpens many processes. He generalises many a theorem shedding light on new aspects by apt iliustrations, Ganitasara-Samgraha is a veritable treasury of problems many of which are characterised by mathematical subtiety, poetic beauty and delicate hint of refind humour, qualities so rare in a mathematical text book. It is difficult to decide, in a textbook, what is old and what is the original contribution of the author.

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xi Here is a brief survey of the contents of the book : Chapter I opens with the salutation to Lord Mahavira, the twentyfourth Tirthankara of the Jainas, who by his knowledge of the science of the numbers illuminates the three worlds. This is follwed by a warm and handsome tribute of gratitude paid to his royal patron, Amoghavarsha. After this, comes the most enthusiastic and unique panegyric ever bestowed on the science of Mathematics. Then we have measures used, names of operations and numerals. Rules governing the use of negative numbers are correctly stated; those regarding the use of zero may be stated in modern notation thus: a+-0 = a; a x0 = 0; a/0=a. The last part is obviously wrong. As regards the square root of a negative number, the author observes that since squares of positive and negative numbers are positive, square root of a negative number cannot exist. Considering the limitations of his time, Mahaviracharya could not have reached a more sensible conclusion. We may note, in this context, that the necessary extension of the concept of number which assimilates square roots of negative numbers into the number system, was achieved as late as in 1797 by C. Wessel a Norwegian surveyor (Bell's "The Development of Mathematics' page 177). Chapter II deals, in respect of integers, with operations of multiplication, division, squaring and its inverse, cubing and its inverse, arithmetic and geometric series. Problem II 17. In this problem, put down in order (from the unit's place upwards) 1, 1, 0, 1, 1, 0, 1 and 1, which (figures so placed) give the measure of a number and (then) if this number is multiplied by 91, there results that necklace which is worthy of a prince. The 'Necklace' referred to, may be displayed thus: 11011011 x 91-1002002001. Two more 'garlands worthy of a prince' are: (II 11, 15): 333333666667 x 33 = 11000011000011; and 752207 x 73=11, 111, 111.

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Chapters III and IV are devoted to elementary operations with fractions, Mahaviracharya has paid considerable a tention to the problem of expression of a unit fraction as the sum of unit fraction. This problem has interested mathematicians from remote antiquity (Abmes Papyrus 1650 B, C.). Here are three relevant problems ( II 75, 77, 78 ) set in modern notation. (1)] = 3 + + 20+ + 3n 2 +21-23; (271-231+ 5***** +(2n-1)2n-+ 2mg (3)==n(n't enjtentan) n+84 +87) **** (n + a + ag + *** + 2,-2) (n + a, +2, + *** + ar-1) ar * a, ( n + a2 + a, + *** + a,) Problem IV 4: One third of a herd of elephants and three times the square root of the remaining part of the herd) were seen on the mountain slope; and in a lake was seen a male elephant along with three female elephants. How many were the elephants there? Here is a sample of monkish humour ! Chapter V treats 'Rule of Three' and its generalised forms. Chapter VI. Having created the arithmetical apparatus in the earlier chapters, in this long chapter, Mahaviracharya applies it to solving many problems which one encounters in life such as money. lending, number of combinations of given things, indeterminate equations of first degree, etc. Problem (VI 1281): In relation to twelve (numerically equal ) heaps of pomegranates which having been put together and combined with five of those same fruits) were distributed equally among 19 travellers. Give out the numerical measure of any one heap. Problem (VI 218 ): The number of combinations of n different things taken r at a time is n(n-1)(n-2) (n-r+1) 12 3. ***** r! (n-r)! lor n!

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xiii It is interesting to note that this general formula was discovered in Europe as late as in 1634 by Herigone (Smith's History of Mathematics Vol. II). We may also recall here that the number 7 which occurs in Saptabhangi provides a simple example in the theory of Permutations and Combinations. A layman can verify that he can form seven and only seven different combinations of three distinct objects. Jainas have been using mathematics freely in their sacred literature from very remote antiquity. The above example supports this fact. Problem ( VI 220 ): 0 friend, tell me quickly how many varieties there may be, owing to variation in combination of a single-string necklace made up of diamonds, supphires, emeralds, corals and pearls ? Problem (VI 287 ) : What is that quantity which when divided by 7, (then ) multiplied by 3, ( then ) squared, ( then ) increased by 5, (then) divided by 3/5, (then ) halved and ( then ) reduced to its square root, happens to be 59. Note the sheer devilry of it! In chapters VII and VIII problems on mensuration are treated, Some of the formulas used are noted here : (1) The Pythargorean formula for the sides of a right angled triangle is a: = b + 0% where a is the hypotenuse. (2). Area of A ABC is Vs (s-a) (8-b) (8-c) where 2 s= a + b + c. (3). The area and the diagonals of a quadrilateral ABCD are : v (s-a ) (8 - b) (8-0) (s-d) where 2 g = a + b +c+d; (ac+bd) (ab+cd). a c+bd) (ad + bc). ad + b c a b+cd It is unfortunate that both Mahaviracharya and his predecessor Brahmagupta made the common mistake of not mentioning the fact that these formulas hold for oyclic quadrilaterals only. (4). T = 3 or 10. (5). The circumference of an ellipse whose major and minor axes are of lengths 2 a and 2 b is 24 b2 + 16 ao which reduces to 2 av 1- 2 where e is the eccentricity. It is difficult to imagine.

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xiv how Mahaviracharya could attain such a close approximation without the help of the powerful tools available to us. Chapter IX treats the so called "Shadow Problems." Raobahadur Rangacharya's edition of Ganitasara-Samgraha with English translation has been out of print for over thirty five years. Thanks to the zeal and labours of Prof. L. C. Jain, the present edition with Hindi translation goes some way to meet a long felt need. It is, however, felt that a new edition with English translation by an experienced Mathematician who knows Sanskrit well is an urgent need. The writer is thankful to his learned friends Dr. Hiralalji Jain and Dr. A. N. Upadhye for assigning to him the pleasant task of writing this foreword. DHARWAR, October 1963 B. B. BAGI

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EDITORIAL The work of Hindi translation of Ganitasara-Samgraha was entrusted to me by Dr. H. L. Jain in 1951, soon after I had joined the College of Science at Nagpur. It took nearly twelve years for its publication. During this period, while in his contact, I became interested in the study of mathematical contents of the old Prakrit texts (Dhavala and Tiloyapannatti) recently brought to light and edited with Hindi translation by him. It was easy to mark out the difference between the treatment in Ganitasara Samgraha and the mathematical contents of the Prakrit texts. The former is a work on Indian logistics or Laukiki, a few portions of which could be useful for the study of the latter which we may call Indian arithmetica. Artha, in Prakrit texts, implies the measure of substance, field, time and beings' becomings in terms of monads. The Prakrit texts, made known to the Hindi world by Dr. H. L. Jain and others, form important sources of Indian arithmetica which throw light on the darkest period of Indian history of mathematics. It is regretted that certain articles of Dr. A. N. Singh on these topics are not known to historians of mathematics, for they were not published in recognized mathematical magazines. A reference to these was made by Sinvhal in an article on Dr. Singh in Ganita, Vol. 5, No. 2, (1954). In the present work, I have based the translation mainly on the English translation of Professor Rangacharya, taking liberty of Hindi expressions and keeping his notes intact. In the introduction I have tried to give a general observation on the history of mathematics upto the time of Mahaviracharya, This is chiefly based on Bell's Development of Mathematics and History of Hindu Mathematics by Datta and Singh. Then I have given a specific observation on the history of mathematics of the Pythagorean era. In this I have given relevant references of the works which form important sources of Indian arithmetica, and have tried to correlate certain similarities in Greek, Egyptian, Babylonian, Indian and Chinese arithmetica etc. I have concluded therein that the mathematics developed in the school of Vardhamana Mahavira

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xvi is one of the connecting and missing links in the history of Mathematics. I have traced these developments in a systematic form in the Jiva Tatva Pradipika commentary on Gommatasara, It abounds in symbolism for place value, logarithms, transfinite and finite cardinals, sets and operators. One may be confused to see that a single symbol has been used in various texts to denote various measures or operations. For example, zero as a circle stands for a negative sign, for one-sensed soul, for the agrihita stage of soul ( for a void ), for filling up gaps, and for a place value. Sets are of varying. oscillating and constant types. A kind of well ordering concept seems to have been used in formation of sequences from the greatest transfinite set. Comparability also plays an important role in the treatment Thus Mahaviracharya had before him, the works of his predecessors, both in logistics and in arithmetica. He made a clear remark in this congestion, is verse 70, Chapter 1, for a study of Agama for further details. His work contains other elementary descriptions on series etc., found in details in Prakrit texts, referred above. It seems that his acquaintance with proper infinities in which monads alone played the role of division etc., made him to think of division by zero as a distribution in a logical way. If a sum is to be distributed to none, the sum would remain unaffeced. The first four appendices contain practically the same matter as appeared in Rangacharya's translation. The fifth appendix contains new collation material compiled at the instance of Dr H, I, Jain from certain manuscripts from Karanja. In the sixth appendix it has been thought useful to reproduce the preface of Professor Rargacharya and introduction of Professor David Eugene Smith. Thanks are due to Professor B. D. Dube for his kindness to give valuable suggestions. Thanks are also due to the proprietor of the Press for his kind co-operation. I am grateful to my Principal, Shri G. R. Inamdar, and to my senior colleague, Prof. K. S. Rathore, for their affectionate patronage. My gratitude is also due to Prof. S. B. Gour for his close assistance, JABALPUR, NOVEMBER 1963 L. C. JAIN

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samarpaNa zrI 105 pU0 kSu0 manohara varNI 'sahajAnanda' jinhoMne nirantara jJAna tapa sAdhanA rata ho "syAM svasmai sve sukhI svayam" udghoSa gIta se saMtapta jaga jIvana meM candra sitArA maya zItala samyaktva-prabhAta utArA hai tathA jIvana bandhu vinobA bhAve - jinhoMne sarvodaya aura bhUmidAnAdi ratna dIpoM se kRSNa kSubdha tama jaladhi taToM para supta prANoM ke prANoM ko jAgRta rakhA hai ko sAdara sasneha

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prastAvanA bhAratIya gaNita itihAsa ke jagataprasiddha gaNitajJa mahAvIrAcArya ke gaNitasAra saMgraha grantha kA punaruddhAra prophesara raMgAcArya dvArA san 1912 meM huaa| isa grantha ke tIna apUrNa hastalekha unhoMne gavharnameMTa orieMTala menaskripTasa lAyabrerI, madrAsa meM, usa samaya ke DI. pI. AI. zrI jI. eca. sTuarTa kI preraNA se prApta kiye| una tIna hastalipiyoM meM se eka to' graMtha kI lipi meM kAgaja para hai, jisameM saMskRta TIkA sahita prathama pAMca adhyAya haiN| bAkI do hastalipiyAMretADapatroM para kanaDI lipi meM haiN| eka tADapatra meM prathama pAMca adhyAya haiM, aura dUsare meM sAta adhyAya haiM, jinameM kSetraphaloM kA jyAmitIya vidhi se nirUpaNa hai| ina donoM hastalipiyoM meM saMskRta meM likhA huA mUla graMtha hai, aura kanar3I bhASA meM kucha vividha udAharaNArtha prazna tathA unhIM praznoM ke uttara diye gaye haiN| isa graMtha kA pUrNarUpeNa aMgrejI meM anuvAda karane ke liye prophesara raMgAcArya ne kaI jagaha khoja karavAI, jisake phala svarUpa unheM kucha aura hastalipiyAM prApta hii| cauthI hastalipi gavharnameMTa) orieMTala lAyabrerI, maisUra meM prApta huI / yaha hastalipi mUla rUpa meM tAr3a patra para kisI jaina paMDita ke pAsa thI, jise kAgaja para kanar3I meM utArA gayA thA / isa lipi meM pUrA grantha hai, sAtha meM, vallabha dvArA kanaDI bhASA meM kI gaI TIkA bhI hai / vallabha ne usI meM likhA hai ki isI grantha kI TIkA unhoMne telagU meM bhI kii| pAMcavIM hastalipi,4) dakSiNa kanar3a, mUDabidrI meM eka jaina maMdira ke bhAMDAra meM tADapatra para kanar3I meM likhita prApta huI / isameM bhI pUrNa graMtha hai tathA kanar3I meM prazna aura unake uttara diye gaye haiM / gyArahavIM sadI meM rAjamuMdrI ke rAjarAjendra ke zAsana kAla meM isa graMtha kA anuvAda pAvaluri mallaNa dvArA telagU meM huA, jisakI kucha hastalipiyAM madrAsa kI gavharnameMTa orieMTala menaskripTsa lAyabrerI meM haiN| ___ grantha par3hane se jJAta hotA hai ki granthakAra sambhavataH IsA kI navIM sadI meM maisUra prAMta ke kisI kanar3I bhAga meM hue hoMge, jahAM rASTrakUTa vaMza ke cakrikA bhaMjana rAjA amoghavarSa nRpatuMga') kA zAsana thA / mahAvIrAcArya ke kArya kA mahatva samajhane ke liye gaNita ke vikAsa ke itihAsa para vihaMgama dRSTi DAlanA Avazyaka pratIta hotA hai| gaNita ke vikAsa meM bhAratIyoM kA kitanA aMzadAna thA yaha bhI isase spaSTa ho jAvegA / isa vikAsa vivaraNa kohama kevala mahAvIra ke kAla tathA pazcima ke dezoM taka sImita rkheNge| 1. isa hastalipi ko prophesara raMgAcArya ne "P" dvArA abhidhAnita kiyA hai| hama bhI inhIM saMketoM ko upayoga meM laaveNge| 2. donoM hastalipiyoM meM sAdhAraNa lakSaNa hone evaM viSaya avichAdI (overlapping) na hone ke kAraNa inheM "K" dvArA abhidhAnita kiyA gayA hai| 3. isakA abhidhAna "M" dvArA kiyA gayA hai| . 4. isa hastalipi ko "B" dvArA abhidhAnita kiyA gayA hai| 5. amoghavarSa nRpatuMga ke viSaya meM itihAsakAroM kA mata hai ki ve IsA kI navIM sadI ke pUrvArddha meM rAjagaddI para baitthe| inake vizeSa paricaya ke liye nAthUrAma premI kA "jaina sAhitya aura itihAsa" 1942, pR0 517 Adi dekhiye|

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gaNitasArasaMgraha gaNita itihAsa kA sAmAnya avalokana yaha jJAta nahIM ki vizva ke kisa pradeza meM, kaba aura kisane yaha socA ki saMkhyA aura AkRti kA jJAna sabhya jIvana ke liye utamA upayogI siddha hogA jitanI ki bhASA / saMkhyA aura AkRti, ina do mukhya dhArAoM dvArA gaNita vartamAna rUpa meM AI / prathama dhArA aMkagaNita aura bIjagaNita ko lAI, tathA dUsarI dhArA jyAmiti ko| satrahavIM sadI meM ye donoM milakara gaNitIya vizleSaNa ( mathematical analysis ) rUpI agamya nadI ke rUpa meM badala gii| / IsA masIha se saikar3oM sadiyoM pahile vizva ke jo pradeza sabhyatA kI carama sImA taka pahu~ca sake unameM prAyaH sabakA itihAsa ajJAta hai, kevala vahI deza itihAsa ko banA sake jahAM aitihAsika sAmagriyAM abhI taka hajAroM varSoM ke vinAzakArI vAtAvaraNa se lohA lekara surakSita calI aaii| ina dezoM meM bibIloniyA ( bAbula ), misra aura bhArata vizeSa rUpa se prasiddha haiN| dajalA aura pharAta nadiyoM ke kachAra ke pazcimI bhAga meM sthita jhUlane vAle bagIcoM ke deza bebIlona (Babylon) meM lagabhaga IsA se prAyaH 5700 varSa pUrva ke abhilekha vahAM kI sabhyatA kA pradarzana karate haiN| usa kAla meM isa deza ke nivAsI apane jJAna ko miTTI kI cakrikAoM, rambhoM (belanoM) aura trisamapAzvoM meM aMkita kara unheM pakAkara surakSita rakhate the| unake adhyayana se jJAta hotA hai ki unakI sabhyatA kA AdhAra kRSi thA, jisake lie unheM paMcAMga (calendar) kI AvazyakatA hotI thii| usa sadI meM unhoMne apane varSe kA Arambha viSuvata bindu ( vernal equinox ) se kiyA thaa| yaha jJAna unhoMne apane pUrva ke deza sumera (Sumer) vAsiyoM se sIkhA hogaa| IsA se prAyaH 2500 varSa pUrva sumera ke vyApArI vajana aura mApoM se paricita the / unhIM kI gaNanA kA mAna bebIlona phuNcaa| vaha mAna SASThikA (60 ko AdhAra lekara ) thA, jisameM dazamalava (10 ko AdhAra lekara prApta huI ) paddhati kA kucha mizraNa thaa| yaha anumAna lagAyA jAtA hai ki 10, aMguliyoM ko ginane se aura 60, 10 meM 1 gayA hogaa| 6 isalie cunA gayA ki usase upayogI bhinnoM ko saralatA pUrvaka vyakta kiyA jA sakatA thaa| IsA se prAyaH 2000 varSa pUrva kI aMkagaNiti kI sAriNiyoM meM guNana ke sivAya vargamUla tathA varga aura ghana kI sAriNiyA~ bhI thiiN| na+nara kI sAriNI kA bhI ve upayoga karate the, jahA~ na kA mAna 1 se lekara 30 taka thaa| isa prakAra unakI naisargika pravRtti phalanIyatA (functionality) kI ora thii| usa samaya yahA~ kI bIjagaNita meM nirIkSaNa aura upapatti dRSTigata nahIM hai, para samIkaraNoM kA AMzika hala diyA gayA hai| Ajakala kI pAribhASika zabdAvali (terminology) meM unhoMne kSa+akSa+ba= . ko ya + ya =sa ke rUpa meM badalakara hala kiyA, jisameM unhoMne ya= tathA sa = - a rakhakara aba se pUrva samIkaraNa ko guNita kiyA / yadi pariNAmI sa dhanAtmaka hai to ya ke aura kSa ke mAna ( values )na+na kI sAriNI se prApta ho sakate haiN| usa samaya ke bAda isa kriyA kI paddhati iTalI kI solahavIM sadI kI bIjagaNita meM milatI hai| kucha samIkaraNoM ke sivAya, unhoMne dasa ajJAta vAle dasa ekaghAtIya samIkaraNoM yukta praznoM ke rUpoM kA hala bhI kiyA hai| usa kAla kI zAMkava gaNita meM Ayata, samakoNa tribhuja, samadvibAhu tribhuja Adi kA kSetraphala nikAlA jA cukA thA, aura paridhi vyAsa kI niSpatti 3 mAnI jA cukI thii| saMbhavataH yahA~ ke nivAsI siMcAI aura naharoM sambandhI samasyAoM meM Ayatana, lamba vRttIya belana aura lamba samapAzvoM ke ThIka taraha sAdhita kiye gaye udAharaNoM ko upayoga meM

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prastAvanA lAte the / yahA~ kI rekhA gaNita kI tIna bAteM ullekhanIya haiN| prathama to yaha ki arddhavRtta kA koNa samakoNa hotA hai| dUsarI yaha ki ve sAdhya (karNa)2 (lamba) + (AdhAra)2, kA upayoga 20 16, 12 aura 17, 15, 8 jaisI rAziyoM meM kara cuke the| tIsarI yaha ki gaNitIya vizleSaNake udmoM ke cinha, jaise. samakoNika tribhujoM ke barAbara koNoM kI saMvAdI bhujAe~ samAnupAtI hotI haiN| yaha huI bebIlona kI pragati jisake pazcAt vahA~ ke pragati cinha nahIM milate / aba sthala mArga se araba deza ko pArakara nIla nadI ke kinAre base misra deza meM cliye| yaha piremiDoM (stUpoM) kA vicitra deza IsA se prAyaH 4000 varSa pUrva se lekara 2781 varSa pUrva taka ke purAtatva kI sAmagrI kA bhaMDAra hai| bebIlona kI taraha isa deza kI sabhyatA kA AdhAra kRSi thaa| isakA patA saMbhavataH 4241 varSa pUrva ke vahA~ ke eka tithipatra se calatA hai jisameM 30 dina vAle 12 mAha haiM, jinameM 5 dina jor3ane se 365 dina pUre kiye jAte haiN| isa jyotirvijJAna hetu vahA~ aMkagaNita bhI vikasita kI gii| bebIlona kI taraha isa deza ke abhilekha surakSita rahe Aye; kyoMki eka to yahA~ kI jalavAyu marusthalI thI, aura dUsare yahA~ mRtakoM (baila, magara, billI aura mAnavoM) ke liye bahuta mAnyatA dI jAtI thii| isI kAraNa mistriyoM ne AvazyakatAnusAra yaha khoja nikAlA ki nirarthaka "kalama ke gUde" (papyri ) se pavitra magaroM kI lAzoM ko DhUMsa-ThUsa kara bharane se unheM jIvita avasthA kA rUpa dekara surakSita rakhA jA sakatA hai| inhIM pepIriyoM ( papy ri) dvArA jJAta hotA hai ki misrI IsA se prAyaH 3500 varSa parva kI aMkagaNita meM karor3oM kI saMkhyA kA ullekha karate the| isa tithi kI unakI citralipi ( hieroglyphics) meM varNana hai ki 1,20,000 mAnava, 400,000 baila aura 1,422,000 bakare kaidI banAye gaye / gaNanA ke bAda unhoMne dazamalavapaddhati kA anusaraNa kiyA, para vaha sthAna-mAna ( place value) rahita thii| isake pazcAt, IsA se 1650 varSa pUrva kI aMkagaNita meM guNana bhAga hai| minnoM meM 3 ko vizeSa pratIka dvArA prarUpita kiyA gayA hai, anya bhinnoM ko = sadRza rUpa vAle bhinnoM ke yoga meM hAsita na kiyA gayA hai / prAyaH isI samaya kI riMDa pepirasa (Rhind papyrus) meM 25 + + 1 aMkita hai| Amisa ( Ahmes ) ne - ke saba bhinnoM ko ( jahA~ na kA mAna 5 se lekara 101 taka hai ) pUrvavat likhA hai| Age ( IsA se sambhavataH 2000 varSa pUrva ke eka prazna se ) bIjagaNita ke udgama kA AbhAsa milatA hai, jo Ajakala ke pratIkoM meM kara + kha = 100; kha = ka ko hala karane ke samAna hai| misrI logoM ne ise hala karane ke liye kUTa sthiti kI rIti (rule of false position) kA upayoga kiyA hai, jo IsA kI prAyaH 15 vIM sadI taka upayoga meM AtI rahI hai| unheM samAnupAta (proportion) jJAna bhI thA, jo gaNitIya vizleSaNa kA eka mukhya AdhAra hai| prAyaH isI samaya unhoMne paridhi aura vyA sa kI sUkSma niSpatti ko aura 316 batalAyA hai / yadyapi isa deza meM paithegorasa ke sAdhya (52 = 42+32 ) kA koI likhita pramANa nahIM milatA; tathApi unake avastarI rajjuoM ( rope stret chers ) meM 5, 4, 3 kA anupAta rahatA thA / vyAvahArika mApoM ke viSaya meM kahA jAtA hai ki IsA se prAyaH3000 varSa pUrva bhI misravAsI paryApta unnati kara cuke the| isake kaI udAharaNa haiN| eka to yaha ki nadI ke cAroM ora kI 700 mIla jagaha meM unake jala pramApI (water gauges) eka sataha meM the| dUsarA yaha ki unheM tribhuja kA kSetraphala tathA belana Adi ke zuddha Ayatana nikAlanA

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gaNitasArasaMgraha jJAta thaa| inake sivAya eka aura bAta ullekhanIya hai ki vizva prasiddha greTa piremiDa ke atirikta eka aura sabase mahAn piremiDa, misra ke kisI ajJAta gaNitajJa ke mastiSka meM thA, jisakI khoja 1930 meM mAsko pepirasa ( Moscow papyrus) ke anuvAda ke pazcAt huI hai| isa mahAna gaNitajJa ne usameM eka sahI sUtra diyA hai, jisake dvArA varga AdhAra vAle stUpa ke lambachinnaka kA Ayatana nikAlA jA sakatA hai| sUtra yaha hai : Ayatana = 3 u (a+aba+ba2), jahA~ a, ba, kramazaH Urdhva tala tathA adhotala ke AdhAroM kI bhujAoM ke mApa haiM, aura u usakI UrdhvAdhara U~cAI ( vertical height) hai| isakA samaya lagabhaga IsA se 1850 varSa pUrva hai / isa sUtra meM grIka logoM kI nizzeSaNa vidhi' (method of exhaustion), aura 17vIM sadI ke keveliyara (Cavelieri) kI "avibhAjyoM kI rIti" (method of indivisibles) nihita hai| apane liye vaha sImA (limit) kA siddhAnta hai aura bAda meM anukala kalana (integral calculus) / inakA kiMcit aura sAmAnya rUpa (generalised form) ArkimiDIz2a ne IsA se prAyaH 500 varSa pUrva batalAyA hai| gaNita ko misravAsI bhI isa hada taka bar3hAkara Age na bar3ha ske| misra ke isa gaNitIya itihAsa ke pazcAt hama bhArata na pahu~cakara pahile bhUmadhyasAgara ke rAste grIsa deza (yUnAna ) pahu~cate haiM, jo IsA se prAyaH 600 varSa pUrva ke pazcAt rekhA aura zAMkava gaNita meM advitIya pragati karane ke liye prasiddha hai| grIsa kI gaNita ke itihAsa meM IsA se prAyaH 650 varSa pUrva hae thelsa tathA (IsA se prAyaH 600 varSa pUrva 1 527 varSa pUrva ? utpanna hae ) paithegorasa ne gaNita ko tarka para AdhArita kiyA, aura prAkRtika ghaTanAoM ko aMka gaNita dvArA pradarzita kiyA / paithegorasa ke samaya se prArambha huI grIsa deza kI pragati ko dekhakara yaha anumAna lagAnA svAbhAvika hai ki yaha pragati pUrvIya dezoM ke jJAna kA AdhAra lekara sambhava ho sakI hogii| yaha mAnyatA hai ki usakA sabase mahAn AviSkAra "samAna Atati bala (tension) vAle dhAgoM kI lambAiyoM ke aMkagaNitIya kucha anupAtoM (ratios) para saMgIta-aMtarAloM kI nirbharatA" ke viSaya meM thaa| usake raikhikIya sAdhya se sabhI paricita haiM / isI sAdhya ke dvArA paithegorasa ne V2 kI aparimeyatA ko batalAyA, aura "bhujA" tathA "vikarNa" saMkhyAoM kI zreDhi saMracanA ke viSaya meM niyama nikaalaa| inake sivAya paithegorIya vagoM ne vAstavika mUla vAle varga samIkAroM kA raikhikIya hala nikAlA, anupAta kA siddhAnta nikAlA, pAMca niyamita sAMdroM kI racanA batalAI, aura diye gaye kSetraphala kI AkRti ke tulya anya AkRtiyA~ banAkara btlaaii| unake dvArA praNIta rUpaka ( figurate) saMkhyAyeM Aja kI aMkagaNita ke lie bar3I sujhAvapUrNa siddha hii| jaise, tribhujIya saMkhyAoM kA prayoga enapiDokliyana rasAyanazAstra meM karane para yaha sAra nikalatA hai ki samasta dravya vAstava meM tribhuja haiN| paithegorasa ke samaya se aMka jyotiSa kA Arambha honA bhI mAnA jAtA hai| kAlAntara meM iTalI ke eliyA nagara nivAsI z2Ino (Zeno-4951-435 ? IsvI pUrva) ke cAra asadbhAsoM ( paradoxes ) meM gaNitIya ananta kI avadhAraNA ke pariSkRta karane kA prayAsa parilakSita hotA hai| isake sivAya yUDo (Eudous-IsA se 408 pUrva se 355 taka)ne anupAta kA siddhAnta nikAlakara misra ke Ayatana nikAlane ke sUtroM ko siddha kiyA, tathA gaNitIya vizleSaNa kI vAstavika saMkhyA paddhati system of real numbers) kI sthApanA kii| sambhavataH isI siddhAnta ke AdhAra para nizzeSaNa vidhi aura DeDIkaeNnDa ke bAda anukalakalana kA upayoga huaa| kahA jAtA hai ki yUDone bhI pUrva ke dezoM kA bhramaNa kiyA thaa| yUkiDa (IsA se 365 varSa pUrva se 275 pUrva) ne aMkagaNitIya vibhAjana para AdhArabhUta sAdhyoM ko siddha kiyaa| usane rekhAgaNita ko tarka paddhati para bunA aura arthamiti kI

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prastAvanA (arithmetica) ko vyavasthita kiyA, tathA raikhikIya kAzikI para vivecana diyaa| isa taraha paithemosta aura yUkliDa ne zAMkava gaNita ko chor3akara zeSa prAthamika rekhAgaNita ko ThosarUpa se sampUrNa banA diyA / inake pazcAt ArkamiDIz2a kA nAma AtA hai, jo vizva kA dUsarA gaNitIya bhautikazAstrI kahalAtA hai| yaha gaNitajJa IsA se 287 varSa pUrva se 212 varSa pUrva taka rhaa| isane sthaitikI aura usthatikI ( hydrostatics) ke gaNitIyavijJAnoM kI jar3a jamAI, anukela kalana kA anumAna lagAyA aura apane nAma kI samAnakoNika kuntala (equiangular spiral "p=ag") kI sparza rekhAkhIMcakara calana kalana (differential calculus) kA sthUla rUpa meM prayoga kiyaa| inake sivAya, usane vizleSaNa vidhi kA prayoga gola, rambha, zaMku, golIya khaMDoM, paribhramaNa se prApta golaja, atiparavalaja ( hyperboloid ) Adi kI zAMkava gaNanA meM kiyaa| inameM se kucha ko yadi Ajakala ke pratIkoM meM likhA jAya to agralikhita ko anukalita karanA hogAH / " Sinx dx; J(ax + x2) dx. inake sivAya isane paravalayaja ( paraboloid ) ke khaMDa kA kSetraphala nikAlate samaya phala kI raikhikIya upapatti dI, aura uso kI ananta zreDhi kA yoga, abhilekha baddha itihAsa ke anusAra, sarvaprathama . nikAlA / vaha zreDhi hai / (4) na jisameM isa tathya kA upayoga kiyA gayA ki sImA / / isa prakAra Aja kI gaNita ArkamiDIz2a ke sAtha utpanna hokara usI ke sAtha mRta hokara dosahasra varSoM ke pazcAt dekArte (Descartes) aura nyuTana dvArA punarjIvita kI gii| isake pazcAt , (IsA se 150 varSa pUrva) hiparakasa (Hipparchus ) ne grahoM kI gatiyoM kA rekhAgaNita dvArA nirUpaNa kiyaa| isameM 15 vIM sadI meM kAparanikasa aura 16 vIM sadI meM kepalara ne parivardhana kiyaa| kahA jAtA hai ki herana ( san 200 IsvI) ne tribhuja kA kSetraphala nikAlane ke liye nimnalikhita niyama diyA: A- [sA (sA-kA) (sA-khA.) (sA-gA) peppasa ( Pappus) ne 250 IsvI meM tIna mahatvapUrNa sAdhya khoje| usane dIrghavRttaja (ellipsoid ) Adi kI nAbhi ( focus ), niyatA (directrix) ke guNoM ko siddha kiyA aura isa prakAra vizleSakIya rekhAgaNita meM zaMkucchedoM ke liye sAdhAraNa dvighAta samIkAra kA AbhAsa prakaTa kiyA / usane prakSepI jyAmiti kA eka sAdhya khojA, aura anukala kalana se (paribhramaNa se prApta na honevAle ) sAMdroM kI parimA (Ayatana) ko nikAlane ke liye sAdhya khoje / prAyaH isI kAla meM DAyopheMTasa ( Diophantus) ne ekaghAtIya, do aura tIna ajJAta vAle, samIkaraNoM ko sAdhita kiyaa| grIka gamita kA tIvra vikAsa prAyaH usa samaya se dekhA jAtA hai, jaba ki IsA se 480 varSa pUrva huI mairathAna ( Marathon ) Adi kI lar3AiyoM meM ina logoM ne phArasa deza para adhikAra jamAkara vahA~ kI gaNita siikhii| yaha kahanA kaThina hai ki phArasa ko yaha gaNita jJAna bhArata se prApta huA yA bebIlona, sumera aura phainIkiyA ( Phoenicia) se| vizva sabhyatA ke prAcIna kendra bhArata meM ( IsA se prAyaH 3000 varSa pUrva ke ) ucca sabhyatA ke cihna siMdhu nadI kI ghATI meM milate haiM / usa samaya ke bhAratIya IMTa ke makAna banAte the, zahara kI bandiza karate the aura svarNa, rajat , tAmra, kAMsa Adi dhAtuoM kA upayoga kara ucca zreNI kA jIvana vyatIta karate the /

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gaNitasArasaMgraha mohenajo-dar3o ke lekhoM tathA muharoM ko pUrNa rUpa se par3hA nahIM jA sakA hai| unameM kaI aise cihna haiM, jo sambhavataH bar3I saMkhyAoM ko darzAne ke liye aMkita kiye gaye hoMge, para unake vAstavika mAna kA patA pAne kA koI upAya nahIM dikhAI detA / vedoM meM bhI sabhyatA kI uccAvasthA spaSTa rUpa se dikhAI detI hai / 'brAhmaNa sAhitya' ( prAyaH 2000 - 000 pU0 ) meM dhArmika aura dArzanika tatva to haiM hI, inake atirikta usameM aMkagaNita, rekhAgaNita, bIjagaNita aura jyotirvijJAna kI jhalaka bhI dikhAI detI hai / vyAkaraNa tathA svara vidyA sambandhI khojoM se pratIta hotA hai ki brAhmI lipi, IsA se pUrva paripUrNa kI gaI hogI, aura sambhavataH usake pahile brAhmI saMkhyAoM kA AviSkAra huA hogA / brAhmaNa sAhitya kAla meM bIjagaNita mukhyataH raikhikIya thI / kisI diye gaye varga ko dI gaI bhujA vAle Ayata meM badalane kI raikhikIya vidhi jo zulba ( prAyaH 800-500 I0 pU0 ) meM varNita kI gaI hai, eka ajJAta vAle eka ghAtIya samIkAra ko hala karane ke samAna hai / yathA, aya = sara, jahA~ ya ajJAta pada hai / jaba diye gaye kSetra ko kisI dUsare adhika yA kama kSetraphala vAle kSetra meM badalanA hotA thA, taba usa kriyA meM varga samIkaraNa kA upayoga hotA thA / vaidika AhutiyoM kI sabase mahatvapUrNa mahAvedI, samadvibAhu sama caturbhuja ( trapezium) ke AkAra kI thI, jisakA AdhAra 30, sAmane kI bhujA 24 aura U~cAI (lamba) 36 ekaka ( units ) thii| vedI ke kSetra ko ma ekaka se bar3hAne ke liye ajJAta bhujA kSa mAnane para ya kA nimnalikhita mAna prApta hotA hai : yA ( 24 ya + 30 ya 36 ya X = 36x. 2 972 ya e = 972 + ma, ma 972 yA = +- 1+ 1 yadi ma ko 972 (na - 1 ) rakhA jAya tAki bar3hI huI vedI kA kSetraphala, pUrva kSetra se 'na' gunA to kSa = V na prApta hotA hai / isa prakAra ke kucha vizeSa prakaraNa, zulba meM varNita haiM / na = 14 ho jAya, 6 yA 14 ya evaM, 24+30 2 + ma, vAle prakaraNa brAhmaNa sAhitya meM pAye jAte haiN| isI meM zine sita ( bAja pakSI ke AkAra kI 7 8 bedI) kA kSetraphala bar3hAne ke liye [ka* = 12 = ( sannikaTataH ) 14 ] varga samIkaraNa kA upayoga kiyA gayA hai / inake sivAya, nimnalikhita prakAra ke anirdhArita ( undetermined ) samIkaraNa bhI vediyoM kI racanA meM upayoga meM lAye gaye haiM : kare + khadeg = gare ( ka, kha, ga tInoM ajJAta haiM ); ka' + a = ga e ( ka aura ga ajJAta haiM ); aka + bakha + saga + dadha = pa ka + kha + ga + gha= pha }, jahA~ ka, kha, ga aura gha ajJAta 1 isake bAda, eka jyotiSa kA choTA sA graMtha vedAMga jyotiSa mahAtmA lagadha dvArA kisI svataMtra jyotiSa graMtha ke AdhAra para yajJa kI suvidhA ke liye saMgrahIta kiyA gayA pratIta hotA hai / yaha graMtha sambhavataH kAzmIra ke zrInagara se bhI uttara meM, kAbula ke akSAMza ke AsapAsa, kahIM racita huI jJAta hotA hai * dekhiye DA0 gorakha prasAda dvArA sampAdita 'sarala vijJAna sAgara' pRSTha 410, ( ilAhAbAda vijJAna pariSad ), bhAga 1, aMka 1 - 4, ( 1946 )

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prastAvanA vedAMga jyotiSa kA eka yuga 5 saura varSa kA hotA thA, jisameM 60 saura mAsa, 2 adhimAsa, 62 cAMdra mAsa aura 1830 ahorAtra yA sAvana dina samajhe jAte the| eka yuga meM 124 pakSa aura eka pakSa meM 15 tithiyA~ mAnI gaI thiiN| isa graMtha ke atirikta triloka prajJapti, sUrya prajJapti, caMdraprajJapti aura jyotiSa karaNDaka graMthoM meM grIkapUrva jaina-jyotiSa gaNitIya vicAra-dhArA dRSTigata hotI hai| __ prophesara vebara ( Weber ) ke kathanAnusAra sUrya prajJapti graMtha, vedAMga jyotiSa ke samAna kevala dhArmika kRtyoM ke sampAdana ke liye hI racita nahIM huA, varan isake dvArA jyotiSa kI aneka samasyAe~ sulajhAkara prakhara pratibhA kA paricaya diyA gyaa| IsA se 400 varSa pUrva ke pazcAt hindU gaNita punaruddhAra huaa| usa samaya sUrya siddhAnta aura paitAmaha siddhAnta likhe gye| gaNita do bhAgoM meM vibhakta huI. eka to aMkagaNita tathA bIjagaNita aura dUsarI jyotiSa tathA kSetragaNita / vaise to, bahuta pahile se bhAratIya gaNanA kA AdhAra 10 thaa| jaba grIka 104 taka aura romana 10 taka ke Upara kI gaNanA jAnate na the, taba bhArata meM aneka saMketanA sthAnoM kA jJAna thaa| IsA se 500 varSa pUrva se hI zatakamAna para AdhArita saMkhyAoM ke nAmoM kI zreNI ko jArI rakhane ke prayatna ho cuke the / IsA se 100 varSa pUrva ke graMtha anuyoga sUtra meM (2)16 taka kI saMkhyA kA upayoga ho cukA thaa| isameM spaSTa rUpa se 2 ko AdhAra cunA gayA thaa| jaba sthAna-mAna kA vikAsa huA taba ikAI se lekara dazamalava mAna para saMkhyA ko likhane ke liye saMketanA sthAna diye gye| zUnya pratIka* kA upayoga piMgala ne ( IsA se 200 varSa pUrva 1) apane cA~dA sUtra ke chandoM meM kiyA hai| IsA ke kucha sadiyoM pazcAt kI ( bakSAlI gA~va kI khudAI se prApta ) bhoja patroM para likhita eka pothI meM bhI aMka zailI kA prayoga dekhA gayA hai| isameM gaNanA meM zUnya kA upayoga huA hai| zUnya pratIka sahita sthAna-mAna saMketanA paddhati, gaNita ke sabhI AviSkArakoM dvArA buddhi kI pragati ke liye diye gaye aMzadAna meM uccatama koTi kI hai| yaha abhI taka ajJAta hai ki dazamalava sthAna-mAna paddhati kA janmadAtA kauna vidvAn-vizeSa athavA RSi-maNDala thA / sAhityaka tathA purAlekha-sambandhI pramANoM se yaha nizcita kiyA gayA hai ki yaha paddhati 200 I0 pU0 ke lagabhaga bhAratavarSa meM jJAta thii| isa navIna paddhati ke prayoga kA prAcInatama likhita pralekha 594 I0 kA gurjara kA dAna patra hai| yahA~ yaha ullekha karanA Avazyaka pratIta hotA hai ki senTrala amerikA ke mAyA logoM kI tithipatrI meM bhI zUnya AyA hai / ye 20 ko AdhAra lekara koI sthAna-mAna paddhati kA upayoga karate the| yaha mAyA gaNanA IsA se 200 se lekara 600 varSa bAda kI mAnI gaI hai| IsA kI pA~cavI sadI meM jagat prasiddha gaNitajJa AryabhaTa paTanA meM hue| inake pahile pauliza, romaka, vAziSTha, saura aura paitAmaha nAma se jyotiSa ke pA~ca sampradAya pracalita the / romaka sampradAya yUnAnI bhAratIya zUnya ke AviSkAra ke vistAra ke viSaya meM Encyclopaedia Britannica, vol. 23, p. 947, (1929) para ullikhita lekha dekhiye| .. sthAna-mAna saMketanA ke saMbaMdha meM nyugebAera (Neugebauer) kA abhimata ullekhanIya hai. It seem to me rather plausible to explain the decimal place value notation as a modification of the sexagesimal place yalue notation with which the Hindus became familiar through Hellenistic astronomy."-The exact Sciences in Antiquity. Provi. dence ( 1957), p. 189.

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gaNitasArasaMgraha gaNanA zailI kA dyotaka hai / inake graMtha AryabhaTIya se jJAta hotA hai ki inhone saba graMthoM kA sAra grahaNakara apane samaya ke jyotiSa jJAna ko bar3hAne meM abhUtapUrva kArya kiyA / inhoMne sUrya tAroM ko sthira batalAyA, pRthvI kI paridhi nizcita kI ora sUrya, caMdra grahaNa ke kAraNoM kA vaijJAnika DhaMga se spaSTIkaraNa kiyaa| isa graMtha ke gaNita pAda adhyAya meM aMkagaNita, bIjagaNita aura rekhAgaNita ke bahuta se kaThina praznoM ko 30 zlokoM meM bhara diyA gayA hai| usameM unhoMne kSetraphala, ghanaphala, trikoNamiti, chAyA sambandhI prazna, vRtta kI jIvA aura zarI kA sambandha, do rAziyoM kA guNanaphala aura antara jAna kara rAziyoM ko alaga karane kI rIti, varga samIkaraNa kA eka udAharaNa, trairAzika, mitroM ke guNana bhAga kI rIti, kucha kaThina samIkaraNoM ko hala karane ke niyama, do grahoM kA yutikAla jAnane kA niyama, aura kuhaka niyamAdi kA kathana kiyA hai| jyA kA vAcaka zabda sAina, jyA kI saMskRta paryAya 'ziMjanI' ke rUpAMtara kA apabhraMza hai| sAtavIM sadI meM gaNita kA prazaMsanIya vikAsa brahmagupta dvArA huaa| 21 adhyAya ke graMtha brAhmasphuTa ke gaNitAdhyAya meM inhoMne vizeSataH vyasta trairAzika, bhANDa pratibhANDa, mizraka vyavahAra, byAja, zreNiyoM, chAyA mApa Adi meM aMkagaNita kA prayoga kiyA, aura kuTTaka gaNita meM RgAtmaka saMkhyAoM ke liye niyama nikAle, anirvRta (indeterminate) samIkaraNoM para kArya kiyA, aura sUrya ghar3I meM trikoNamiti kA prayoga kiyaa| a + 1 =ya, ( jisameM kSa aura ya azAta hai) jaise anirdhRta samIkaraNoM kA vivecana bhI graMthakAra ne kiyaa| isa samIkaraNa kA nAma bhUla se peliyana (Peleian) samIkaraNa par3a gayA hai / yaha dvighAtIya varga rUpoM aura varga kSetroM ke aMkagaNitIya siddhAntoM kA mUlabhUta AdhAra hai / inake sivAya kSetra vyavahAra, vRttakSetra gaNita, khAta vyavahAra, citi vyavahAra, RkacikA vyavahAra, rAzi, chAyA vyavahAra Adi kA vivecana bhI kiyA gayA hai / * isa sadI meM musalamAnoM kI saMskRti ke sahasA utthAna tathA 12 vIM sadI meM usake sahasA patana ke sambandha meM itihAsa bar3A rocaka hai / san 622 meM paigambara muhammada sAhiba ke anuyAyI apanI yAtrAoM para hare jhaMDe ke nIce saMgaThita hokara cala pdd'e| san 635 meM damaska (Damascus) para vijaya prApta kara san 637 meM jerusalama ( yarUzalama ) jItA gayA / cAra varSa pazcAt sikandariyA kA pustakAlaya naSTa kiyA gyaa| misra ko adhikAra meM lekara 642 IsvI meM phArasa para Adhipatya jamAyA gyaa| 100 varSa pazcAt vijetAgaNa 711 IsvI meM spena meM pahu~ce, jahA~ unhoMne sabhyatA ko 8 zatAbdiyoM taka bddh'aayaa| isI kAla meM ve bhArata kI aMkaNita tathA prIsa kI rekhAgaNita ko yUropa le Aye pUrva meM abbAsIda Abbasid ) khalIphAoM ke Adhipatya meM bagadAda pUrva kI sabhyatA kA kendra 750 se 1258 IsvI taka rahA, aura spena meM kAraDovA ( Cordova ) pazcima kI bauddhika rAnI ( the intellectual queen of the west) bnaa| isa antarAla meM vijJAna ke AdAna-pradAna ke sambandha meM Encyclopaedia Britannica meM nimnalikhita ullekha hai - "The muslim civilization, particularly as represented at Baghdad, e 800. e 1000, developed a type of mathematics which combined the characteristic features of the Greek and Hindu treatment of the science. Eastern faith in astrology and skill in number met with Western faith in philosophy and skill in geometry, and the Baghdad scholars, absorbing each, produced text books In general algebra, elementary number, astronomy and trigonometry which, through the efforts of Latin translators, gave new life to mathematics in Europe"-vol. 15, p 84, (1929)

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prastAvanA isake pahile ki hama dakSiNa meM gaNita kI pragati mahAvIrAcArya ke graMtha se pradarzita kareM, eka aura navIna khoja hameM AkarSita kara letI hai| mahAvIrAcArya ke sambhavataH pUrvakAlIna, suprasiddha dhavalAkAra vIrasenAcArya ne IsA kI sambhavataH dvitIya sadI ke udbhaTa AcArya zrI puSpadaMta aura bhUtabali dvArA racita SaTakhaMDAgama graMthoM kI dhavalA nAmaka TokA pUrNa karane meM apanA sArA jIvana arpita kiyaa| yaha graMthamAlA gata bIsa varSoM meM hI DAkTara hIrA lAla jaina prabhRti vidvAnoM dvArA prakAza meM lAI gaI hai| TIkAkAra ne sthAna sthAna para kinhIM gaNita graMthoM se, sUtroM ko uddhRta kiyA hai / DA. avadhezanArAyaNa siMha dvArA isa graMtha ke zAMkava gaNita ke atirikta gaNita kI navIna nimnalikhita khojeM prakAza meM lAI gaI haiM, jinakA upayoga jaina darzana ke adhyayana hetu saMbhavataH IsA kI prArambhika 'zatAbdiyoM meM pracalita ho gayA hogaa| prathama to baDI baDI saMkhyAoM kA upayoga jinako vyakta karane ke liye pratIka saMketanA anya granthoM meM upalabdha hai| jaise,2 kI tIsarI vargita sambArgata rAzi vaha hai jo 256 meM usIkA 256 bAra guNana karane para prApta hotI hai| dUsare salAgAgaNana athavA laghugaNaka (logarithm) kA bRhat upayoga, jisake AviSkAraka 17 vIM sado ke 'jAna nepiyara' evaM 'justa barjI' mAne jAte haiN| tIsare, ananta rAziyoM kA gaNita, jisake vikAsa ke liye 19 vIM sadI meM hue jArja keMTara ke prayatna suprasiddha haiN| jahA~ taka rekhAgaNita kA sambandha hai, yativRSabha (4001, 600 1 IsvI pazcAt ) kI tiloya paNatI meM evaM vIrasena kI dhavalA TIkA (DA. hIrAlAla jaina dvArA sampAdita, pustaka 4) meM sambhavataH IsA pUrva ke graMtha aggayaNiya, didvivAda, parikamma, loyaviNicchaya, loya vibhAga, logAiNi Adi meM se udhRta gAthAyeM evaM ullekha mahatvapUrNa haiM / ina do graMthoM ke aitihAsika mahatvapUrNa prakaraNoM meM se kucha ye haiM : dRSTi vAda se jambUdvIpa kI paridhi kA mApa, upamA pramANa, vividha kSetroM kA ghanaphala nikAlane kI vidhiyA~; bANa, jIvA, dhanuSa pRSTha Adi meM sambandha, dhanuSakSetra kA kSetraphala, sajAtIya tathA samakSetra ghanaphala vAlI AkRtiyoM kA rUpAntara evaM unakI bhujAoM ke bIca sambandha Adi / isa prakAra dhavalAdi siddhAnta graMthoM meM alaukika gaNita kA AdhAra liyA gayA hai. jisa para abhI koI graMtha prakAza meM nahIM AyA hai| laukika gaNita ke sambandha meM sarvaprathama mahAvIrAcArya kA yaha gaNita sArasaMgraha nAmaka graMtha sam 1912 meM suprasiddha huaa| mahAvIrAcArya kA yaha 9 adhyAya vAlA graMtha aitihAsika dRSTi se mahatvapUrNa siddha huaa| isakI khoja ne yaha siddha kara diyA ki bhArata ke sadara dakSiNa meM bhI uttara ke vidyA kendroM kI taraha, vidyA ke kendra the| isa sudUra dakSiNa meM, gaNita ke vijJAna ko bar3hAne meM usa samaya prayatna kiyA gayA, jaba ki uttarIya bhArata meM brahmagupta aura bhAskara ke samaya ke + inake vistRta vivaraNa ke liye nimnalikhita lekha dekhiyeSingh. A. N., History of Mathematics in India from Jain Sources; The Jain Antiquary Vol. XV, No. II. (1949), pp. 46-53; Vol. XVI, No. II, (1950) pp. 54-69. dekhiye(1) lakSmIcaMdra jaina, tiloyapaNNattI kA gaNita, prastAvanA lekha ( jambUdovapaNNattIsaMgaho ), zolApura ( 1958) / (2) ToDaramala, artha saMdRSTi (gommaTasAra), gAMdhI hari bhAI devakaraNa jainagraMthamAlA, kalakattA (prakAzana varSa ullikhita nahIM)

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10 gaNitasArasaMgraha bIca zrIdharAcArya ko chor3akara koI prakAMDa gaNitajJa na huA / mahAvIrAcArya ne apane samaya ke nRpatuMga amoghavarSa ke Azraya meM rahakara, pUrvavarttI gaNitajJoM ke kArya meM kucha sudhAra kiyA, navIna prazna diye, dIrghavRtta ( ellipse) kA kSetraphala nikAlA tathA mUlabaddha aura dvighAtIya samIkaraNa Adi meM suMdara DhaMga se pahu~ca kI / inake grantha meM brahmadatta kuTTaka se eka aura adhyAya adhika hai, para isake adhyAyoM ke viSaya ekase nahIM haiN| sabase pahile, isa graMtha kI 49 vIM gAthA par3hane se mAlUma hotA hai ki mahAvIrAcArya ne zUnya ke viSaya meM sabase pahile bhAga karane kI kriyA darzAne kA sAhasapUrNa prayatna kiyA / kisI saMkhyA meM zUnya dvArA vibhAjana ke lie, unhoMne likhA ki saMkhyA zUnya dvArA vibhAjita hone para badalatI nahIM hai / jisa dRSTikoNa ko lekara yaha likhA gayA vaha isalie ThIka hai ki jaba kucha vastuoM ko lekara unheM kucha vyaktiyoM meM bA~TA jAya to ve vastue~ vibhAjita ho jAyeMgI / jaba unheM zUnya vyaktiyoM meM vitarita karanA ho, arthAt bA~TanA ho to vastue~ jyoM kI tyoM baca rheNgii| para, gaNitIya vizleSaNa ke dRSTikoNa se sImA ka -= Oc na 0 na hotI hai jahAM ka eka parimita ( finite ) saMkhyA hai / isake pazcAt, gAthA 63 se lekara 68 taka saMketanAtmaka sthAnoM ke nAma diye gaye haiM / unake pahile 19 veM sthAna taka saMkhyA kI gaNanA ke nAma diye jA cuke the / unhoMne 24 sthAna taka nAma diye jisameM 24 veM sthAna kA nAma mahAkSobha likhA hai / ye 24 sthAna, sambhavataH 24 tIrthakaroM kI saMkhyA ke AdhAra para diye gaye hoNge| isI taraha ratna zabda ko " tIna" darzAne ke lie upayoga kiyA gayA, jabaki gaNitajJoM ne usakA upayoga "pAMca" darzAne ke liye kiyA / jaina darzana meM samyakdarzana jJAna cAritra ko ratnatraya kahA gayA hai / isI prakAra tatva, pannaga, bhaya, karma Adi kaI zabdoM kA upayoga jaina darzana ke AdhAra para saMkhyAyeM darzAne ke liye kiyA gayA hai| bar3I saMkhyA ko darzAne ke lie granthakAra ne sthAnAha kA upayoga kiyA hai / jaise, 3021 likhane ke lie caMdra, akSi, AkAza, ani likhA hai / graMthakAra ne bhAga dene kI eka varttamAna vidhi kA kathana kiyA / isa suvidhAjanaka vidhi se ubhayaniSTha guNanakhaMDoM ko haTAkara vibhAjana kiyA jAtA hai| kisI bhI bhinna ko ikAI bhinnoM kI kisI saMkhyA ke yoga dvArA vyakta karane ke lie kucha niyama bhI diye gaye haiM / ye niyama sarvathA maulika haiN| mizraka vyavahAra meM bhI do naye prakAra ke praznoM ko hala karane ke lie niyama diye gaye haiM / byAja nikAlane ke prazna meM gAthA ( 38 ) meM diye gaye sUtra se patA calatA hai ki mahAvIrAcArya ko nimnalikhita sarvasamikA ( identity ) jJAta thI : a sa i a+sa + i + ... ba + da + pha+... sAtha hI, ( a + ba ) 3 = a + 3a'ba ba da pha + 3ba' a + ba', dvArA pradarzita sUtra unake pUrvavarttI gaNitajJoM dvArA diyA gayA para mahAvIra ne isa sUtra kA sAdhAraNa rUpa banAkara prastuta kiyA, jisake lie niyama bhI batalAye gaye haiM ...= ( a+ba+sa+ da +) = a + 3a ( ba+sa+ da + + 3a ( ba + sa + da +) + ( ba + sa+ da + . ..), ityAdi / graMthakAra ne kUTa sthiti dvArA bhI adhyAya 3 tathA 4 ke kaI prazna hala kiye haiM / kUTa sthiti ke niyama kA upayoga bIjagaNita ke vikAsa kI pUrvAvasthA ko darzAtA hai, jabaki ajJAta ke liye koI pratIka hotA thA / bhArata meM yaha niyama kevala aMkagaNita meM upayoga meM lAyA gayA, kyoMki bIjagaNita pahile se

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prastAvanA hI paryApta pragati kara cukI thii| bakhzAlI hastalipi meM ise yadRccha, vA~chA yA kAmikA ke nAma se abhidhAnita kiyA gayA hai| mahAvIra ke bIjagaNita tathA kAlpanika rAzi ke viSayameM unakI pratibhA kA paricaya dene ke sambandha meM I. TI. bela kI abhyukti hai "The rule of signs became common in India after their restatement by Mahavira in the ninth century....The early history of compplex numbers is much like that of negatives, a record of blind manipulations, unrelieved by any serious attempt at interpretation or understanding. The first clear recognition of imaginaries was Mahavira's extremely intelligent remark in the ninth century that, in the nature of things, a negative number has no square root. He had mathematical insight enough to leave the matter there, and not to proceed to meaningless manipulations of unintelligible symbols." + isake atirikta graMthakAra ne vyApakIkRta (generallized) paddhati vAle ekaghAtIya samIkaraNoM ko hala karane ke niyama diye haiM, aura aneka ajJAta vAle yugapat dvighAta samIkaraNoM ko hala kiyA hai / unheM jJAta thA ki varga samIkaraNa ke do mUla hote haiM / jahA~ DAophenTasa ne ma, na bhujAe~ lekara samakoNa tribhuja banAyA, vahA~ mahAvIra ne ma, na bhujAe~ lekara Ayata kI racanA kI hai| adhyAya 7 kI 953, 971, 1123 vIM gAthAoM meM mahAbIra ne diye gaye karNa (a) ko lekara sabhI sambhava samakoNoM ko prApta karane ke liye, arthAt ka +kha = a ko lekara hala karane ke liye tIna niyama diye haiN| prathama do niyama eka dRSTi se ThIka nahIM haiM, kyoMki a2-14 yA a2-2 parimeya ( rational) taba taka nahIM ho sakate, jaba taka ki pa ko ThIka taraha na cunA jAya / tIsarA niyama bar3e mahatva kA hai| yaha rIti, bAda meM yUropa meM, pIz2e ( Pisa) ke lena? phIbonAci ( Leonardo Fibonacoi) ne 1202 IsvI meM phira se khojI gii| isa vidhi kA udgama zulva sUtroM meM hai| brahmagupta aura mahAvIra donoM ne caturbhuja kSetra kA kSetraphala nikAlane ke liye nimnalikhita sUtra diyA hai:- (sA-phA) (sA - khA) (sA- gA) (sA - ghA) jahAM sA, ardhaparimApa hai aura kA, khA, gA, ghA bhujAoM ke mApa haiN| para yaha sUtra kevala cakrIya caturbhujoM ke lie ThIka utaratA hai| isI prakAra, viSama tribhuja ke kSetraphala ke sambandha meM niyama diye gaye haiN| * dekhiye, mUla gAthA 52, prathama adhyAya / Development of Mathematics,pp. 173,175 1945) 1 uparyukta varNana se kahA jA sakatA hai ki bhAratIyoM ne bIjagaNita ke vijJAna ko do mukhya bhAgoM meM vibhakta kiyaa| eka bhAga to bIja (vizleSaNa analysis) kA vivecana karatA hai, aura dUsarA bhAga aise viSayoM kA jo bIja ke liye Avazyaka haiN| ve viSaya, cihnoM ke niyama, zUnya aura anantI kI aMkagaNita, ajJAtoM ke sAtha kriyAe~, karaNI, kuTTaka aura peliyana samIkaraNa ( Pellian equation ) haiM /

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gaNitasArasaMgraha mahAvIrAcArya aura brahmagupta Adi ke praznoM tathA anya prakaraNoM kI bhinnatA ke sambandha meM DeviDa yUjena smitha kA nimnalikhita vaktavya dRSTavya hai: "......For example, all of these writers treat of the areas of polygons, but Mahaviracarya is the only one to make any point of those that are reentrant. All of them touch upon area of a segment of a circle, but all give different rules. The so called janya operation is akin to work found in Brahmagupta and yet none of the problems is the same. The shadow problems, primitive cases of trigonometry and gnomonics, suggest a similarity among these three great writers, and yet those of Mahaviracarya are much better than the one to be found in either Brahmgupta or Bhasker, and no question is duplicated."* mahAvIrAcArya dvArA gaNitagraMtha ke sivAya 'jyotiSa paTala' graMtha bhI racita kie jAne kI sambhAvanA "bhAratIya jyotiSa ke lekhaka paM0 nemicaMdra zAstrI ne prakaTa kI hai| abhI taka isake liye puSTa pramANa prApta nahIM ho sake haiN| gaNita itihAsa kA uparyata sAmAnya avalokana hamane mukhyataH I. TI. bela ke "Develop ment of Mathematics". aura vibhUtibhUSaNa datta tathA avadhezanArAyaNa siMha ke, "History of Hindu Mathematics" nAmaka graMthoM kA AdhAra lekara diyA hai| cIna ke sambandha meM abhI hameM yatheSTa sAmragI nahIM mila sakI hai| gaNita itihAsa kA viziSTa avalokana aba hama bhAratIya gaNita itihAsa ke aMdhatama kAla meM praveza karane kA prayatna kreNge| isa kAla meM, vizeSakara yUnAna aura bhArata meM sambhavataH bebilana, misra aura bhArata kI prAcIna mRtaprAyaH gaNita meM akasmAt gati aaii| gaNita dvArA alaukikIya viSayoM ko bAMdhane ke abhUtapUrva prayAsa hone lge| isa prayAsa ke cihna yUnAna meM mukhyataH pithegorasa ke vargoM meM aura vizeSa rUpa se bhArata meM tIrthakara mahAvIra ke tIrtha meM parilakSita kie gaye haiN| AtmA ko satya kI ora AkarSita karane ke lie kevala inhIM vargoM meM darzana, dharma kI dhArAoM meM gaNita kA prayoga advitIya hai| yaha nizcita hai ki isa kAla meM vizva kI prAcIna gaNita meM isa prayojana se bIja boyA gayA, ki bIjagaNita ke dvArA prasphuTita pAramArthika bodha, upAdeya meM ekAgratA kI siddhi de ske| eka ora yUnAna meM pithegorasa dvArA pratipAdita ahiMsA ke sAtha hI sAtha saMkhyA siddhAnta se puSTa darzana janma maraNa ke cakra * Introduction to English Translation & Notes of gaNatasAra saMgraha by M. Rangacharya, (1912). bhAratIya jJAnapITha, kaashii| cIna meM tatsambandhita prayAsoM kI khoja ke liye abhI hameM upayukta sAmagrI prApta nahIM huI hai| phira bhI, jo kucha hameM mila sakA hai use aMta meM prastuta kiyA hai|

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prastAvanA 13 se vimukta hone kA sAdhana pratIta hotA hai, vahAM bhArata meM "sukhI raheM saba jIva jagata ke" jaisI bhAvanAoM se prerita tatvoM ke sAmAnyakaraNa kI sImA "khammAmi savva jIvANaM, savve jIvA khamantu me / mettI me savva bhUdesu, bairaM majhaM Na keNavi // " meM parilakSita hokara rAzi siddhAnta kI prayukti se anantatva ko prApta huI dikhAI detI hai / hamArA yaha saMketa hai ki yUnAna aura bhArata ke gaNita kI tulanA kA ukta AdhAra sambhavataH upayogI siddha hogA / isa tulanA kA abhiprAya kisI deza kI mahAnatA Adi dikhAne kA nahIM hai, varan yaha batalAne kA hai ki satya aura ahiMsA ke tatva vizva ke gurutA kendra ko zAMti ke prAMgaNa meM khIMcakara le jAte haiM, aura isa khiMcAva meM jo AdAna pradAna hotA hai vahAM sApekSatA kRta parivAda vizvabaMdhutva ke aMcala meM vilIna ho jAte haiN| yahI kAraNa hai ki aise samaya meM ukta tatvoM se abhiprerita khojoM ke itihAsa ko mahatva nahIM diyA jAtA, jisase itihAsa kAla kA mauna aura aMdha rahanA svabhAvika pratIta hotA hai / punarjAgaraNa ke itihAsa ke tatvoM kI khoja karane ke lie hama pithegorasa kA bhramaNa patha apanAveMge / isa bhramaNa patha ke viSaya meM abhyukti prasiddha hai ki "Like many others of the sages in that Kingdom (Egypt), he was carried captive to Babylon, where he conversed with the Persian and Chaldean Magi; and travelled as far as India, and visited the Gymnosophists." * tadanusAra hama sarva prathama misra deza ke varddhamAna mahAvIra kAlIna punarjAgaraNa ke itihAsa para prakAza DAleMge / thelIz2a (640 I.pU.) aura pithegorasa, donoM kA bhramaNa misra meM seiTika yuga (Saitic Period) 663-525 IsvI pUrva meM huA hogA / isa samaya misra meM kUphU (Khufu) kAlIna siddhAntoM kI jo punarjAgRti huI vaha (kSitija meM udaya hone vAle 'ajJAna aMdhakAra vinAzaka' sUrya-Horus em akhet ke paramparAgata pratIka) gIz2A (Giza) ke sphiMksa (Sphinx) se sahasambandhita thii| kUphU ke sambandha meM navIna mata yaha hai ki isa parAkramI nRpa ne I. pUrva 2600 ke lagabhaga bali prathA kA aMta kara janatA ke hita meM unheM vibhinna kAryoM meM saMlagna kiyA thaa| madhyapUrva kI prAyaH sabhI prAcIna sabhyatAoM vAle dezoM meM sphiMksa kI vibhinna mudrAeM rUr3hi rUpa se pUjA kI pAtra rahI haiN| jisake mukha ko chor3a kara zeSa aMga siMha kA hai aise sphiMksa ke misrI nAma kramazaH samastAvatAroM meM sUrya ( Horem-akhet-Kheperi-Ra-Atum 14201441 B. C.), jIvita mUrti ( Seshepankh ), siMha ( Sinuhe), Adi rahe haiM / isa sphiMksa mUrti meM mAnava vadana dekara, itihAsakAroM ke matAnusAra, siMha ke AtaGka meM buddhi, zakti aura dayA kA sammizraNa kiyA gayA hai| TAlemIya ( Ptolemaic) kAlIna lekha meM isa mUrti ko tIna mukuTa yukta batalAkara mAnoM tInoM lokoM ke nAtha kI upAdhi se vibhUSita kiyA hai "And Horus of Edfu transformed himself into lion which had the face of a man, and which was crowned with the Triple Crown (')."+ sambhavataH 26 ve rAjavaMza kAla ( IsvI pUrva 588-569 ?) kI mahatvapUrNa invenTarI sTIle ( Inventory Stela ) meM aMkita lekha * Encyclopedia Americana, vol. 23, p. 47, (1944) + Salem Hossan : Tne sphinx, p, 80,Cairo ( 1949)

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14 gaNitasArasaMgraha ahiMsA kI pravartanA ke saMvAda ko prakAza meM lAtA huA sphiMksa kI kahAnI meM varddhamAna mahAvIra kI jIva dayA kI sadRzatA prakaTa karatA pratIta hotA hai: - "......The plans of the Image of Hor-em-akhet were brought in order to bring to revision the sayings of the disposition of the Image of the very Redoubtadle............He came to make a tour, in order to see the thunderbolt, which stands in the Place of the Sycamore, so named because of a great sycamore, whose branches were struok when the Lord of Heaven descended upon the place of Hor-em-akhet, and also this image retracing the erasure according to the above mentioned disposition, which is written......of all the animals killed at Rostaw. It is a table for the vases full of these animals which, except for the thighs, were eaten near these 7 gods, demanding......( The God gave) the thought in his heart, of a written decree on the side of this Sphinx, in an hour of the night ("). The figure of this God, being cut in stone, is solid, and will exist to eternity, having always its face regarding the orient."* uparyukta lekha kA mukhya bhAga pavitra mUrtiyoM evaM pratIkoM ke prarUpaNa se pUrNa hai jo kUphU dvArA prApta huI mAnI jAtI haiM / nimnatama koTi ke jIvoM ke prati misra meM pracalita dayA kA ullekha Arcabizapa vhetalI ne kiyA hai, "In Egypt there are hospitals for superannuated cats, and the most loathsome insects are regarded with tenderness;...... . ," tathA vahA~ mAMsabhakSaNa niSedha evaM brahmacarya pUjA ke mahatvapUrNa lakSaNa mAne jAte haiM, "Chastity, abstinence from animal food, ablutions, long and mysterious ceremonies of preparations of initiation, were the most prominent features of worship........." kuphU dvArA nirmita mahAstUpa ke sphiksa kA sthala seiTika kAla ( Saitic Period) meM jIva dayA kI preraka pazu pUjA kA kendra rahA hai| isakI puSTi, salIma hasana ke zabdoM meM yaha hai, "At the time when this stela was inscribed, there was a great revival of the worship of the A pis bull at Memphis, and that animal may also have been venerated in the Giza district at least during the Saitic Period and later............." isake prAyaH 300 varSa uparAnta kA itihAsa aMdhakAramaya hai| yahAM "itihAsa pitA" hiraoNDoTasa bhI mauna hai| 300 I.pU. se lekara 300 I. pa. taka kA kAla helenIya ( Hellenism) yuga hai| isa samaya sikaMdariyA yUnAnI kalA aura vijJAna kA kendra rahatA hai| phalita jyotiSa kA udaya hotA hai| * The Sphinx, pp. 222-224, (1949), + W. E. H. Lecky, History of European Morals, Vol. I., pp 289, 325 ( 1899).

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prastAvanA 15 yUnAnI vijJAna kA uccatama vikAsa hotA hai, para aMkagaNita aura jyotiSa ( astronomy ) vahI AdikAlIna rahate haiN| misra meM pracalita aMkagaNita se yUnAniyoM ne kyA sIkhA ? isa prazna para vAeDena kA mata hai ki yUnAniyoM ne misra kI guNana vidhi tathA bhinnoM kA kalana sIkhA hogaa| isa prakAra ke kalana ko ucca bIjagaNita ke vikasita karane kA AdhAra nahIM banAyA jA sakatA hai| yUnAniyoM ne jyAmiti ko bhI svataMtra rUpa se vikasita kiyaa| misra kI jyAmiti ke kucha phala avazya hI prazaMsanIya rahe hoM, para yUnAniyoM ke lie vaha kevala prayukta aMkagaNita hI tho / romana yuga meM bhI, jaba ki phalita jyotiSa kA vikAsa huA, misra kI gaNita jyotiSa yUnAna aura bebilana kI gaNita jyotiSa se bahuta pIche rahI / yahAM misra aura bhArata kI abhilekhabaddha sAmagrI para dRSTipAta karanA kahAM taka upayogI siddha hogA, nahIM kahA jA sakatA: (1) na kevala mAsko pepAyarasa meM, varan riMDa pepAyarasa ( sambhavataH IsA se 1700 varSa pUrva ) meM bhI paridhi aura vyAsa ke anupAtta (T) kA mAna (3)2 athavA 3.1605......mAnA gayA hai| ThIka yahI mAna nemicaMdrAcArya ne isa prakAra ullikhita kiyA hai, "yadi kisI vRtta kI trijyA tra aura usake samAI kisI varga kI bhujA bha ho, to tra= bha hotA hai" 7 kA eka dUsarA mAna / 10 hai, jo dazamalava ke do aMkoM taka isI rUpa meM prApta hotA hai| ise yati vRSabha ne tiloya paNNattI meM dRSTivAda se avatarita ullikhita kiyA hai| (2) samalamba caturbhuja ke kSetraphala nikAlane ke sUtroM kA upayoga tiloya paNNattI kI gAthAoM. 1-165, 181 Adi meM huA hai| uparokta sUtroM se avatarita sUtra kA upayoga mistra ke yaMtriyoM ne caturbhuja kA sthUla kSetraphala nikAlane ke lie kiyaa| yaha sUtra eDaphU ke sUrya maMdira meM ( sambhavataH IsA se 100 varSa pUrva kA) prApta huA hai / x (3) misra meM 7 kA eka dUsarA mAna bIjoM kI rAziyoM athavA unase bharI jAne vAlI varimAoM ke mApa se parigaNita paridhi aura vyAsa kA anupAta (ratio) ke rUpa meM 32 prApta hotA hai| + vyAsa ko yadi ikAI liyA jAya to vIrasenAcArya dvArA ullikhita sUtra "vyAsaM SoDaza guNitaM......" se 7 kA mAna prApta hotA hai| (4) raju (Rope) jinAgama ke vividha viSayoM kA nirUpaNa karatA hai| yaha AyAma kI eka vizva ikAI hai jisakA sambandha sUcyaMgula, dvIpa samudroM kI saMkhyA, Adi se sthApita kiyA hai| kenTara ke *J.L. Coolidge: A History of Geometrical Methods, p. 11, (1940). +triloka sAra, gAthA 101 * vibhUti bhUSaNa datta, jaina siddhAnta bhAskara, bhAga 2, kiraNa 2, pR0 34 / @ti. pa. 4-50, 57 / 4 SaTkhaMDAgama, pustaka , gAthA 1, 3 Adi / +T. Health, Greek Mathematics, vol. I., p. 125, (1921). SaTkhaMDAgama, pu. 4, pR. 40, gAthA 14 / lakSmIcaMdra jaina, tiloya paNNattI kA gaNita, zolApura, pR. 99-101, ( 1959) /

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gaNitasArasaMgraha anusAra, misra ke yaMtrI, pithegorasa ke sAdhya kA upayoga rajju ke dvArA karate the, aura ve rajju bAMdhane yA khIMcane vAle kahalAte the| vAeDena kA mata hai ki kenTara kA yaha kathana ki ye loga 3:4:5 vAle raja kA upayoga karate the, aura unheM pithegorasa kA sAdhya jJAta thA, sahI nahIM hai| itanA avazya hai ki piremiDa Adi ke nirmANa meM misrI bahuta zuddha rUpa se samakoNa banAte the / * . (5) misra meM dviguNita karane kA parikalana (duplatio) aura arddhaccheda prakriyA (mediatio) prAcIna kAla se pracalita thii| yahI yUnAna meM nIopithegoriyana varga ne upayoga meM utArA, aura yahI hama SaTakhaMDAgama! jaise graMthoM meM bikhare hue pAte haiM / bhinnoM ke parigaNana misra ke ina pepAyarasoM meM tathA dhavalA TIkA meM vistRta rUpa meM dekhane milatA hai| inake sivAya 'ha' (aha) parikalana rAzi kalana kI paramparA ko sUcita karane haiN| kUTa (false) sthiti ke misrI prayoga mahAvIrAcArya ke gaNitasAra saMgraha meM dekhane meM Aye haiN| (6) varga AdhAra vAle stUpa (aura sambhavataH usake samacchinnakoM) ke ghanaphala nikAlane meM misra meM zuddha aura prasiddha sUtroM kA ullekha milatA hai| yahAM bhArata meM vIrasena dvArA yukti bala se siddha kiyA gayA varga AdhAra vAle lokAkAza kA citraNa, usake tathA vAtavalaya kI paratoM ke ghanaphala kA kalana, Adi hameM misra ke stUpoM ke vAstavika bheda ko jAnane ke lie prerita karate haiN| kuphU dvArA nirmita karAyA gayA mahAstUpa medhAvI vaijJAnikoM ke adhIkSaNa meM dharma, gaNita, jyotiSa tathA anya mahatvapUrNa aitihAsika ghaTanAoM ke saMyukta saMskAra ke phala svarUpa nirmita kiyA gayA hogaa| hiraoNDoTasa ke anusAra misra vAsI stUpa AkAra ko jIvana kA prakAra rUpa (emblem ) mAnate the / stUpa kA vistRta AdhAra hamArI vartamAna dazA ke astitva kA prArambha evaM usakA bindu meM avasAna, ( sAMsArika) astitva kA anta mAnA jAtA thaa| ho sakatA hai ki isI kAraNa unhoMne apanI samAdhiyoM meM isa AkRti kA upayoga kiyA ho / + IsA se prAyaH 484 varSa pUrva hue hiraoNDoTasa kI ukta abhyukti kI puSTi memphisa ke prAyaH uttara meM sthita piremiDa yuga se pUrva ke maMdira kI paramparA dvArA hotI hai| isa maMdira meM sabase pavitra 'piremiDa ke AkAra kA eka patthara thaa| yaha vizvAsa kiyA jAtA thA ki yaha patthara sUrya (ajJAna aMdhakAra vinAzaka) bhagavAn ko phIniksa (Gr. Phoinix ) pakSI ke rUpa meM prakaTa hone meM AdhAra rUpa thA / prAcIna kiMvadantI ke anusAra yaha pakSI 500 yA 600 varSa jIvita rahane ke pazcAt apanI citA banAkara svayaM ke paMkhoM se sulagAtA hai, aura apanI hI bhasma meM se nikala kara ur3a jAtA hai| isa prakAra vaha amaratA kA pratIka, athavA sarvotkRSTa, sampUrNa rUpa (paragon) bhI mAnA jAtA hai| yaha vivaraNa hameM karma siddhAnta kI mAnyatA kA prArUpa pratIta hotA hai, jahAM karma Idhana ko tapakI jvAlAoM meM vidagdha kara mukti yA kaivalya prApta kiyA jAtA hai| hiraoNDoTasa ne stUpa ke vistRta AdhAra ko hamArI vartamAnadazA ke astitva kA prArambha batalAyA hai| cAra mahAna bhujAe~ saMsArI jIvana kA prarUpaNa karatI haiM jo sambhavataH pithegorasa kA Tetractys hai aura jaina mAnyatA kA caturgati cakra (caducaMkamaNa) hai| isa dazA kA bindu rUpa meM prakaTa honA (aura sAMsArika) * B. L. van der Waerden, Science Awakening, Holland, p. 6, Eng. trans. (1945). + Ibid, p. 18, 1 SaTUkhaMDAgama, pu0 4, gaNita prastAvanA / x B. L. Waerden, Science Awakening, pp. 34,35. + The Encyclopedia Americana, p. 40, vol. 23, ( 1944), * I. E. S. Edwards, The Pyramids of Egypt, ( Pelican ), p. 21, ( 1947).

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prastAvanA astitva kA aMta mAnA jAnA, jaina mAnyatA kI paMcama gati, mokSa se samanvaya sthApita karanA pratIta hotA hai | yaha caMdu caMkramaNa svastika ke artha ko bhI stUpa kI bhujA prarUpaNA meM samanvita karanA dRSTigata hotA hai / karma siddhAnta kI mAnyatA kI sadRzatA kucha aMzoM meM hameM nimnalikhita uddharaNoM meM bhI dRSTigata hotI haiM-- brahmArpaNaM brahma havirbrahmAgnau brAhmaNA hutam / brahmaiva tena gaMtavyaM brahma karma samAdhinA // punaH yajJa ke isa nirvacana ko lekara yaha kathana hai gata saGgasya muktasya jJAnAvasthita cetasaH / yajJAyAcarataH karma samagraM pravilIyate // isI abhiprAya ko nimnalikhita zloka meM nidarzita kiyA hai-- yathaidhAMsi samiddho'gnirbhasmasAtkurute'rjuna / jJAnAgniH sarvakarmANi bhasma sAtkurute yathA // 17 piremiDa meM sthita anya vastuoM ke nAma dhArmika mahattA se otaprota the / "anantatva kA durga" thA, tathA sAtha meM rakhI jAnevAlI nAva sambhavataH saMsArasAgara se pratIka rUpa thii| jo kucha ho, itanA avazya hai, ki mRtyu ke uparAMta AnevAlI meM isI jIvana ke aMtarAla meM pUrI taiyAriyA~ kI jAtI thIM, sambhavataH na kevala rAjA ke lie, varan rAjyasattadvArA isa stUpa pratIka prarUpaNA ke sahAre samasta buddhi jIvI varga ke liye bhI / sabase prAcIna hIliApolisa ke maMdira ke piremiDa pratIka ko sabase vRhat rUpa meM sthApita karane kA zreya ahiMsA ke prabala samarthaka kUphU kohI hai / meM isa prakAra bane hue stUpoM ko misrI meM mera m (e) r kahA jAtA hai, jisakA nirvacana 'ArohaNa sthala' ( place of ascension ) kiyA jAtA hai / yaha nirvacana yadyapi bhASA vijJAna viSayaka niyamoM ke viruddha nahIM hai, tathApi saMzayAtmaka hai / phira bhI, piremiDa graMthoM ( texts ) meM isa prakAra kA ullekha hai ki "usa (rAjA) ke liye svarga sopAna DAlI gaI hai tAki vaha svargArohaNa kara sake |"() yaha vizvAsa na kevala prAcIna misra hI pracalita thA, varan mesopoTemiyA, esiriyA aura bebina meM bhI pracalita thA jahA~ ATha maMjiloM kI imArateM sambhavataH isI hetu nirmita kI gaI thIM / inakA nAma z2igurAta thA aura sipAra ( Sippar ) ke aise bhavana kA nAma 'ujjvala svarga kA sopAna bhavana' thA / ina stUpoM kA anya pracalita piremiDa hai, jo yUnAnI bhASA ke misrI gaNitIya grantha ke anusAra sambhavataH yaha eka jyAmitIya pada hai, jisakA artha, "vaha jo asa (us) se (sIdhA) Upara jAtA hai" bilakula aspaSTa, kintu piremiDa ( stUpa ) ke utsedha kA dyotaka hai / hama abhI nahIM kaha sakate ki tiloyapaNNattI meM varNita samavazaraNa kI vidhiyoM meM nirmita thUha kyA inhIM se sahasambandhita haiM ? piromisa zabda se utpanna huA hai / * zrImadbhagavad gItA 4- 24 + vahI, 4 - 23 + vahI, 4-37 () The Pyramids of Egypt, pp. 236, 237. ga0 sA0 saM0 pra0-3 samAdhi kA nAma pAra le jAne kI ghaTanAoM kI AzaMkA

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18 gaNitasArasaMgraha yUnAnI gaNita ke bIjIya tatvoM sambandha, Ajakala bebilana kI bIja gaNita se jor3A jAtA hai / isa prakAra o. nyugebAera (Neugebauer), o. bekera (Becker), rAiDemAisTara (Reidemeister) prabhRti vidvAnoM ne yaha dekhakara ki bIjagaNita DAophenTasa se prArambha na hokara prAyaH 2000 varSa pUrva mesopoTemiyA se prArambha hotI hai, yaha bhI saMbhAvanA vyakta kI hai ki pithegorasa ke arthamitikI siddhAnta ko bebilana kA arthamitikI siddhAMta kahanA ucita hogaa| isI prakAra bI. ela. vAerDena ne bhI nimnalikhita tathyoM ko pramANita karane kA prayAsa kiyA hai* 1-thelIz2a aura pithegorasa ne bebilana kI gaNita ko lekara prArambha kiyA parantu use bilakula bhinna, viziSTa rUpa se yUnAnI, lakSaNa diyaa| 2-pithegorIya vargoM meM aura bAhara, gaNita ko uccatara aura satata uccatara rUpa meM vikasita kiyA gayA / isa prakAra gaNita dhIre-dhIre dRr3hatara tarka kI jijJAsA kA samAdhAna karane lgaa| isa sambandha meM vAeDena kA mata hai ki gaNita itihAsa ke adhyayana meM nimnalikhita bAtoM ko anAvazyaka na samajhA jAve (1) saMskRti kA sAmAnya itihAsa, jisameM na kevala jyotiSa aura yAMtrikI varan bhavana nirmANa vidyA ( architecture ), zilpa ( technology ), darzana aura yahA~ taka ki dharma (pithegorasa) ke viSayoM ko samAviSTa kiyA jAve / (2) rAjanaitika aura sAmAjika dazAe~ / (3) vyaktigata caritra aura usakA jIvana kArya / ___ gaNita kSetra meM sabase mahatvapUrNa AdhArabhUta cAra kriyAe~ hotI haiM, jinakA upayoga saMketoM dvArA gaNita ke vikAsa ko carama sImA taka pahu~cAyA jA sakatA hai| saMketoM meM sthAnA: paddhati tathA dAzamika paddhati lAnA bar3e mahatva kI vastu hai| isake AdhAra para bar3I saMkhyAoM kA lekhana tathA anya gaNanAoM ko sugama banAyA jA sakatA hai| isameM saMdeha nahIM ki jyotiSa meM Adhunika SASThika paddhati kA itihAsa sambhavataH 4959 varSa purAnA hai| bebilana vAsiyoM ne SASThika paddhati sumeravAsiyoM (syumiariena) se lI aura isa paddhati ko yUnAnI jyotiSI TAlemI (150 I0 ) ne apanAyA tathA usameM zUnya pratIka kA upayoga kara apane kAla kI dAzamika paddhati ke samAha banAyA / / SASThika paddhati meM sthiti sambandhI pratIkoM kA upayoga to hotA thA, parantu usameM kaI doSa bhI the| 1 aura 60 ke pratIkoM, tathA 1,0,30, aura 1,30, ke pratIkoM meM aMtara na thA / bhAratIyoM dvArA yUnAnI jyotiSa ke aMzadAna lene ke AdhAra para sambhavataH vAerDena ne phrAyaTenthela ( Freudenthal) ke mata kA samarthana kiyA hai: "Freudenthal's hypothesis reduces therefore to the following: Before becoming subject to the Greek influence, the Hindus had a versified, positional system, arranged decimally and starting with * Science Awakening, p. 5.. + Science Awakening, p. 39. cIna meM bhI paJcAGga meM SASTika dAzamika paddhati upayoga meM lAI gaI thI, jisameM 60 ko uccatara ikAI athavA 'cakra' nirUpita kiyA gayA thaa| Cf. Struik. D. J., A concise History of Mathematics, Dover, ( 1948).

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prastAvanA 19 the lowest units. They had the digits 1-9 and similar symbols for, 10. 20,.... Along with Greek astronomy, the Hindus became acquainted with the Sexagesimal system and the zero, They amalgamated this positional system with their own; to their own Brahmin digits 1-9, they adjoined the Greek 0 and they adopted the Greek-Babylonian order, It is quite possible that things went in this way. This detracts in no way from the honour due to the Hindus; it is they who deve, loped the most perfect notation for numbers, known to us." vAena kA ukta samarthana, unakI nimnalikhita abhyukti para bhI AdhArita pratIta hotA hai: "In this manner Buddha continues through 23 stages. According to an arithmetic book, koti is a hundred times one hundred thousand ( sata sata sahassa), so that the largest number mentioned by Buddha is 102, 1046 = 1053. But in most arithmetics, these same words ayuta and niyuta have other values, viz, 104 and 105. But Buddha has not yet reached the end : This is only the first series, he says. Beyond this there are 8 other series. It is clear that these numerals were never used for actual counting or for calculations. They are pure fantasies which, like Indian towers, were constructed in stages to dazzling heights"'t isa sambandha meM hama ina vidvAnoM kA dhyAna tiloyapaNNattI aura dravya pramANanugama, SaTa khaMDAgama pustaka 3 kI ora AkarSita karanA cAhate haiN| tiloyapaNNattI ke jyotiSIya prakaraNoM ko dekhane se patA calatA hai ki jina svataMtra, maulika graMthoM se usameM sAmagrI lI gaI hai, unameM kAlagaNanA kA pratyakSa AdhAra yUnAnI SASThika paddhati nahIM hai| sAtha hI, dravya pramANAnugama ke adhyayana se pratIta hotA hai ki IsA ke aneka varSa pUrva, sambhavataH varddhamAna mahAvIra kAla meM hI athavA bAda meM, jIvoM ke guNasthAna, mArgaNAsthAna Adi meM saMkhyA prarUpaNa ke lie bar3I-bar3I saMkhyAoM ke lekhana, gaNana Adi kI AvazyakatA par3I hogii| isa AvazyakatA ke liye unheM koI krAMtikArI sarala paddhati ko grahaNa karanA Avazyaka ho gayA hogaa| usa samaya vizva ke yA to kisI chora se unheM zUnya ke AdhAra para sthAnAsahita dAzamika paddhati apanAnA par3I hogI, athavA unheM hI zUnya ko lekara isa paddhati kA AviSkAra karanA par3A hogaa| jaisA ki hama Age dekheMge ki yUnAna ke pithegorasa ke varga aura bhArata ke varddhamAna mahAvIra ke tIrtha meM aisI kaI bAtoM meM sadRzatAe~ haiM ki hameM yaha sambhAvanA pratIta hotI hai ki IsA se prAyaH 500 yA 600 varSa pUrva ke bIca bhI yUnAniyoM aura bhAratIyoM meM AdAna pradAna huaa| na kevala sthAnArdAsahita dAzamika paddhati hI, varan jIva dravya ke pramANa kI saMkhyA kA bodha kSetra, kAla Adi kA AdhAra lete hue aneka maulika paddhatiyoM ke AdhAra para karAyA gayA hai, jo vizva ke prAcIna gaNita graMthoM meM dikhAI nahIM detA hai| kucha aise prakaraNa haiM, jaise salAgA artha * Science Awakening, pp. 56, 57. + Ibid. p. 52.

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20 gaNitasArasaMgraha ( zalAkA pramANa, Logarithm ),* rAzi siddhAnta Adi jinake AviSkAra yUropa meM satrahavIM aura unnIsavIM sadI meM hue haiN| isa prakAra "AvazyakatA, AviSkAra kI jananI hai', ke AdhAra para hama yaha sambhAvanA bhI vyakta karate haiM ki varddhamAna mahAvIra ke tIrtha meM unake anuyAyiyoM dvArA sthAnAr2yA pratIka sahita dAzamika paddhati ke abhAva kI pUrti karane ke prayAsa avazya hI kiye gaye hoNge| yUnAniyoM dvArA bebilanavAsiyoM ke aMzadAna kA upayoga sambhavataH thelIz2a dvArA grahaNa kAla kA batalAyA jAnA puSTa karatA hai| bebilana meM grahaNoM ke avalokana kI tithiyA~ sambhavataH 747 I0 pU0 meM hue nabonasAra nRpati ke kAla meM nizcita huI pratIta hotI haiN| isake pazcAt I0 pU0 580 meM nebyukaDanez2ara (dvitIya) (Nebuchadnezzar II 605-562 B.C.) ke rAjyakAla taka kalA aura vijJAna meM unnati tathA caMdramA aura grahoM ke avalokana ke pramANa milate haiN| isake pazcAt uttarottara kAla meM jyotiSa ke vikAsa ke pramANa milate haiN| nebyakaDanez2ara ke sambandha meM eka do aise tathya hai jo hameM DA0 prANanAtha vidyAlaMkAra dvArA prApta prabhAsa pATaNa ke tAmrapatra ke lekha, "bebIlona ke nRpati nebacaMdanejAra ne raivatagiri ke sAtha nemi ke maMdira kA jIrNoddhAra karAyA thA "tt kI ora AkarSita karatA hai| ye tathya isa prakAra haiM: "From his inscriptions we gather that Nebuchadrezzar was a man of peculiarly religious character". "His peaceful energies were devoted to building magnificent palaces and temples and herein he excelled". I parantu uparyukta koI puSTa pramANa nahIM hai, jisake AdhAra para hama bhArata aura bebilana kA varddhamAna mahAvIra ke tIrtha se sambandhita punarjAgaraNa se sambandha batalA skeN| isake sambandha meM bhAratIya zilpa aura nyAya praNAlikA kI bebilana ke zilpa aura nyAya praNAlI se tulanA sambhavataH upayogI siddha ho / abhI taka upalabdha sAmagrI ke AdhAra para gaNita sambandhI tulanA Adi hama agale pRSThoM meM deNge| bebilana ke ucca rUpa se vikasita bIjagaNita kI sambhAvyatA ke viSaya meM yaha pramANa diyA jAtA hai ki unake pAsa utkRSTa SASThika pratIka prarUpaNA thI, jisase saMkhyA aura bhinnoM ko darzAyA jA sakatA thA, aura unameM samAnasaralatApUrvaka gaNanAe~ kI jA sakatI thiiN| isa prakAra unheM eka tathA do ajJAta vAle raikhIya aura varga samIkaraNoM ke hala karane kI rIti jJAta thii| inake sivAya (a+ba)2 jaise bIjIya sUtroM kA jyAmitIya prarUpaNa, samAntara rekhAoM se udayabhUta anupAta ke sambandha, pithegorasakA sAdhya, tribhuja aura samalamba caturbhuja kA kSetraphala Adi kA jJAna sambhavataH unheM pUrva pracalita paramparA se thaa| saMkhyAsiddhAnta meM zreDhiyoM kA saMkalana bhI dRSTigata hotA hai / parantu yaha saba jJAna pithegorasa ko dharma aura darzana meM gaNita ke * ToDaramala ne arthasaMdRSTi meM artha ko dravya,kSetra, kAla aura bhAva kA pramANa nirUpita kiyA hai| tt athavA nebyukaDarez2ara Cf. Encyclopaedia Britannica, vol. 16, p. 184 ( 1956 ). ___ mu. kAMtisAgara, zramaNa saMskRti aura kalA, pR. 57 (1952 ); khaMDaharoM kA vaibhava, bhAratIya jJAnapITha kAzI, pR. 11(1953); tathA Times of India, 19-3-1935. + Encyclopaedia Britannica, Vol. 16, p. 185, ( 1956). +J. B. Bury & others, The Cambridge Ancient History, P. 216, Vol. III, 1 (964).

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prastAvanA 21 prayukta karane, tathA gaNita meM gati lAne meM kahAM taka preraka rahA hogA, isa para hameM abhI vicAra karanA zeSa hai| uparyukta gaNita ke prayoga hama prAkRta graMthoM meM dekhate haiM, parantu vizeSarUpa se do tathya hameM Azcarya meM DAla dete haiM: (1) tiloya-paNNattI ke caturtha adhikAra meM gAthA 180 aura 181 meM diye gaye sUtra jIvA aura dhanuSa kA pramANa nikAlane ke lie uddhata hue haiN| gaNanA/10 ke AdhAra para ina sUtroM kI saMracanA kA pramANa milatA hai / jIvA ke viSaya meM bilakula aisA hI sUtra, jIvA = (vyAsa)2- (vyAsa - bANa )2] ke rUpa meM, bebilana ke abhilekhoM ke AdhAra para 2600 I0 pUrva (1) upasthita honA Azcarya janaka hai| jahA~ kA mAna 3 honA svIkRta ho cukA thA vahA~ pithegorasa ke sAdhya ke AdhAra para isa sUtra kA honA upayukta pratIta hotA hai| dhanuSa ke sambandha meM diyA gayA sUtra, T kA mAna /10 lene ke AdhAra para hai jo bebilana meM aprApya hai I (2) vIrasena ne kSetra prayoga vidhike AdhAra para jo bIjIya samIkaraNoM kA raikhikIya nirUpaNa diyA hai, vaha bhI kyA bebilana athavA yUnAna se liyA gayA hai, athavA pAraparimita gaNAtmaka saMkhyAoM ke nirUpaNa ke liye pracalita aneka vidhiyoM meM se eka yaha vidhi bhI jainAcAryoM kI maulika rUpa se AviSkRta vidhi hai, yaha bhI vicAraNIya hai / * (3) SASThikA paddhati kA udgama sthala bebilana mAnA jAtA hai| 60 ko AdhAra lene ke kaI kAraNa prastuta kie gaye haiN| yaha paddhati jyotiSa meM vizeSa rUpa se sthAna pAye hue hai| tiloya paNNattI meM sUrya kA eka pUrNa paribhramaNa 60 muhUrtoM meM mAnA hai| 60, mAne hue 109800 gagana khaMDoM kA eka guNanakhaMDa bhI hai / yaha gaNanA bhI bebilana aura cIna se sahasambandha khojane meM sambhavataH sahAyaka siddha ho sakatI hai| aba hama yUnAna meM praveza karate haiN| yahA~, nissaMdeha, jyotiSa gaNanA meM rAzi siddhAnta, 12 ghaMTe kA dina, chAyA mApa nirUpaNa ( sUrya ghar3I ke rUpa meM Gnomon aura Polos), candra aura grahoM kI gatiyoM kA avalokana, bebilanIya prabhAvoM se achUtA nahIM hai| parantu yaha saba prabhAva kyA pithegorasa kAlIna hai, athavA pithegorasa para jyotiSa kA bhI prabhAva kisI dUsare deza kA thA, isa para vicAra karanA hai| isa meM sandeha nahIM ki ukta prabhAva pithegorasa ke bAda dRSTigata avazya hotA hai| parantu hameM pithegorasa ke kAla kA adhyayana bar3I sAvadhAnI se karane kI AvazyakatA hai| isake viSaya meM hama sarvaprathama kucha kiMvadaMtiyA~ aura tathya pAThakoM ke sammukha rakhanA caaheNge| (1) yUnAna ke "sAta jJAniyoM meM se thelIz2a prathama thA, jinake viSaya meM kahA jAtA thA, "Sayings such as the celebrated Delphic "Know thyself, were ascribed to them"t (2) sUrya grahaNa ke viSaya meM jo phalita thelIz2a ne ghoSita kiyA thA, usake viSayameM vAerDena kA kA yaha kathana hai "Herodotus reports ( see p. 84 ) that, during the battle on the Halys, day was suddenly turned into night and that Thales had pre I J. L. Coolidge : A History of Geometrical Methods, pp. 6, 7 ( 1940 ). * SaT khaMDAgama pu., 3, pR. 42-43 / + Science Awakening, p. 85.

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22 gaNitasArasaMgraha dicted this event to the Delians for that year. According to Diogenes Laertius, Xenophanes voiced his admiration of Thales for this prediction. Thus, besides Herodotus, we have the older witness Xenophanes for this accomplishment. At present it is generally agreed that this event refers to the solar eclipse of 585 B.C. How was it possible for Thales, who according to all our sources, is the first Greek astronomer, to predict a solar .eclipse ? Such a feat requires the experience of more than forty years, no matter how one proceeds. It is not possible for one man alone to gather this experience. But Thales had no Greek predecessors. The conclusion 18 inescapable that he must have drawn upon the experience of Oriental astronomers."* (3) thelIz2a ko sambhavataH bebilana vAsiyoM (?) se nimnalikhita jyAmitIya phala prApta hue the, jinake lie usane upapatti Adi dene kA prayatna kiyA: (a) vRtta kA vyAsa use samadvibhAjita karatA hai| (ba ) sama dvibAhu tribhuja ke AdhArIya koNa samarUpa (similar ) hote haiN| (sa) yuddhImasa ke anusAra, usane yaha khojA thA ki do sarala rekhAoM ke praticchedana se prApta koNa samAna hote haiM / ityaadi| (4) thelIz2a ke kAla meM misra aura bebilana kA gaNita mRtaprAya ho cukA thA / (5) nIo-pleTonisTa ( Neo-Platonist ) proklasa (Proclus, 412-485 A. D.) ne pithegorasa kI jyAmiti ke sambandha meM yaha ullekha kiyA hai, Pythagorus, who came after him, transformed this science into a free form of education; he examined this discipline from its first principles and he endeavoured to study the propositions, without concrete representation, by purely logical thinking. He also discovered the theory of irrationals (or of proportions ) and the construction of the cosmic solids ( i.e. of the regular polyhedra)i uparyukta vivaraNa se pratIta hotA hai ki jyAmitIya aura jyotiSIya sAmagrI, yUnAna meM isa kAla meM bAharI dezoM se lAkara, sUkSmarUpa se avalokita kara, tarka para AdhArita gahana adhyayana kA viSaya banAI gii| isameM sandeha nahIM, ki ukta sAmagrI ne ina vidvAnoM ko prabhAvita kiyA hogA, kyoMki binA prabhAva ke, kisI viSaya kI ora dhyAna AkRSTa honA sAdhAraNata: sambhava pratIta nahIM hotaa| jo bAta, bIjarUpa se prabhAvaka pratIta hotI hai, vaha "gaNita dvArA pratipAdita dharma se AtmA kA utthAna karanA" dRSTigata * Ibid. p. 86. + Ibid. p. 89. + Ibid. p. 90.

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prastAvanA hotI hai / dekheM ki prabhAva kA yaha mAdhyama pithegorasa ke varga aura varddhamAna mahAvIra ke tIrtha se kahA~ taka sadRzatA rakhatA hai 1 ( 1 ) aisA pratIta hotA hai, ki IsA se prAyaH ( 582 - 500 1 ) varSa pUrva misra meM prabala svecchA se rahate hue pithegorasa ne jinake saMsarga meM svataH ko vibhinna vijJAnoM se ( a lot of knowledge without intellect ) paricita kiyA thA, unake mizana kA prabhAva usake naitika jIvana meM pazu prati ( mukti hetu ), vizuddha dayA kI chApa chor3a baiThA thA, 23 "But this crazy crank Pythagorus had made quite a fuss when he saw one of the prominent citizens taking a stick to his dog. "Stop beating that dog!" he had shouted like a madman. "In his howls of pain 1 recognize the voice of a friend who died in Memphis twelve years ago. For a sin such as you are committing he is now the dog of a harsh master. By the next turn of the Wheel of Birth, he may be the master and you the dog. May he be more merciful to you than you are to him. Only thus can he escape the Wheel. In the name of Apollo my father, stop, or I shall be compelled to lay on you the tenfold curse of the tetractys."+ ( 2 ) isa caducaMkramaNa ( tetractys ), caturgati baMdhana ( svastika prarUpaNA ? ) se vimukti hetu pithegorasa aura Age bar3hakara, hare paudhoM ke prati bhI, mamatA pradarzita karatA hai, "Then, too, there was all this talk about what he ate, or rather about what he would not eat. What could the man possibly have against beans? They were a staple of everyone's diet; and here was Pythagorus refusing to touch them because they might harbour the souls of his dead friends......... He had even deterred a cow from trampling a patch of beans by whispering some magic word in its ear"-- isI prakAra, ( ekeMdriya jIva, bAloM, se nirmita ) UnI kapar3oM se sambandhita abhyukti nimna prakAra hai, "He also tells that the Pythagoreans did not bury their dead in woollen clothing. This looks more like religious ritual than like mathematics. The Pythagoreans, who were held up to ridicule on the stage, were presented as superstitious, as filthy vegetarians, but not as mathematicians". [] * Ibid. p. 13. + E. T. Bell, The Magic of Numbers, p. 87, ( 1946 ) ++ The Magic of Numbers pp. 91, 92. [] Science Awakening p. 92.

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gaNitasArasaMgraha (3) punaH, mAMsa bhakSaNa niSedha kI zailI meM AtmA kI niyata saMkhyA ke rUpa meM gaNita kA praveza hai, "The thought of all the souls they might have left shivering in the void by devouring their own goats and swine made the good Samians extremely unhappy. A few weeks more of these upsetting suggestions, and they would all be strict vegetarians-except for beans. Equally upsetting was the ghastly thought that some of their n might be malicious little monsters with no souls to restrain their bestial instincts, For Pythagorus had assured them that the total number of souls in the universe is constant".* AtmAoM ke punarjanma tathA AtmA kI amaratA kA upadeza dene vAle pithegorasa ke varga bandhutva meM, gaNita kI mahattA darzAne vAlA ullekha nimnalikhita bhI hai: "The Pythagoreans thus have purification and initiation in common with several other mystery-rites. Ascetic, monestic living, vegetarianism, and common ownership of goods occur also in other sects. But, what distinguishes the Pythagoreans from all others, is the road along which they believe the elevation of the soul and the union with God to take place, namely by means of mathematics, Mathematics formed a part of their religion. Their doctrine proclaims that God has ordered the universe by means of numbers. God is unity, the world is plurality and it consists of contrasting elements. It is harmony which restores unity to the contrasting parts and which moulds them into a cosmos. Harmony is divine, it consists of numerical ratios. Whosoever acquires full understanding of this number-harmony, he becomes himself divine and immortal."+ abhI yaha kahanA kaThina hai ki pithegorasa ne vahI pratipAdana kiyA jo varddhamAna mahAvIra ke tIrtha meM paramparA ke AdhAra para kiyA gayA pratIta hotA hai / parantu, dhavalA graMthoM (vizeSakara, SaTakhaMDAgama pu. 3) ko dekhane para yaha avazya pratIta hotA hai ki ina donoM vargoM ke lakSya prAyaH eka se rahe haiN| isakI puSTi, punaH, nimnalikhita uddharaNa se hotI hai, "According to Heraclides of Pontus, Pythagorus said that, "Beatitude is the knowledge of the perfection of the numbers of the soul". Mathematics and number mysticism mingle fantastically in the Pythagorean dootrine. Nevertheless, it was from this mystical doctrine that the exact science of the later Pythagoreans developed."'() * The magic of Numbers, p. 92. + Science Awakening p. 93. (Ibid p. 94.

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prastAvanA 25 (4) pithegorasa ke liye "a lot of knowledge without intellect" se sambandhita abhyukti vAerDena ne isa prakAra dI hai: "This contemptuous remark cannot refer to a logically constructed theory of numbers and a geometry such as we find in the writings of the later Pythagoreans. But, if Pythagorus gathered into one lump, all kinds of half-assimilated learning about the gods and the stars, about musical scales, sacred numbers and geometrical calculations, and proclaimed such an omnium-gatherum to his followers as divine wisdom in a prophetic manner, then Heraclitus' ridicule, as well as the veneration of mystics, such as Empedocles, become entirely understandable''.* isI prakAra, eka aura aisA ullekha hai jo vicAraNIya hai: "What inspiration laid forceful hold on Pythagorus when he discovered the subtle geometry of (the heavenly) spirals and compressed in a small sphere the whole of the circle which the aether embraces."t pithegorIya varga ne grahoM ko jIvita devatAoM kI mAnyatA dI hai / eka aura mahatvapUrNa tathya hai, "candra sambandhI gaNanA meM 59 kA AdhAra', yathA, .. ___"Firmly convinced of the mystic values of numbers, Pythagorus determined to a base a brand new cycle on a primary foundation of arithmetic. Fifty-nine was a "beautiful number, since itj was a prime, When to this was added the undoubted fact that, when we count the days and nights in every one of the moon's months, the total is always 69,......" isa 59 dina aura rAtri prakaraNa se sambandhita AdhArabhUta prAkRta graMthoM meM vizeSa vistAra se varNita caMdra sambandhI gaNanA hai| yaha jJAta hai ki sUrya kI apekSA se caMdra eka muhUrta meM 62 gaganakhaMDa pIche raha jAtA hai, isaliye 109800 gaganakhaMDa athavA eka paribhramaNa pUrNa karane meM 59 3 dina lagate haiM, isa AdhAra para caMdra arddhacakra kA synodic mAsa 29.512...."dina nikalatA hai| yahA~ batalAnA Avazyaka hai ki hinda jyotiSa graMthoM kI ayana pravRtti prAkRta jyotiSa graMthoM se bhinna hai|) (5) Age, jahA~ parimita, aparimita, ekatva, anekatva, sAMta, ananta Adi ke viSaya meM ruci lene vAle pithegorasa ke varga ne aparimeya rAziyoM ko dRzyarUpa dekara parimeya banAyA aura isa prakAra * Ibid. p. 95. + Heath, Greek History of Mathematics, Vol. 1, p. 163. ( 1921) + A. T. Olmsteed, History of Persian Empire, Chicago, p. 209, (1948) () jaina-siddhAMta-bhAskara bhAga 8, kiraNa 2, pR. 77, (1941) ga0 sA0 saM0 pra0-4

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gaNitasArasaMgraha jyAmiti para AdhArita advitIya sAdhana ko prakAza meM lAyA, usI prakAra yahA~ bhArata meM SaTakhaMDAgama jaise siddhAnta granthoM meM na kevala darzana aura dharma ko, varan dravyoM (jIva aura pudgala) ke pramANoM ko dravya, kSetra, kAla, bhAva, vikalpa, alpa bahutva ke sAdhanoM se dRzya rUpa diyaa| isakA vRhada vivecana yahA~ denA sambhava nahIM hai| isake hetu tiloya paNNattI ke gaNita ke sivAya dhavala granthoM meM mukhyataH pustaka 3 aura 4, kezava varNI athavA ToDaramala kI gommaTasAra kI TIkA tathA gopAladAsa baraiyA kRta jainasiddhAntadarpaNa dRSTavya haiN| yahA~ yaha bAta batalAnA Avazyaka hai ki pithemorIya varga ne jahA~ aparimeyako parimeya banAne ke liye jyAmiti AkRtiyoM kA Azraya liyA hai, vahA~ prAkRta granthoM meM parimeya kA bodha dene ke pazcAt use aparimeya rUpa meM bhI prastuta kiyA hai| yahIM sAmAnyakaraNa kA bIja chipA hai / inake pradarzana ke liye prAkRta granthoM meM jahA~ paramANu dvArA avagAhita AkAza-pradeza (bindu) ko mUlabhUta liyA hai, vahA~ pithegorasa kA bindu bhI ullekhanIya hai, "Points are the primary elements of space for Pythagorus, and a point is that which has position only. Unlike material things & point has neither parts nor magnitude. These defects are shared by 1 when the latter is regarded as the Monad or the generative element of number. If Pythagorus thought of space as being made up of points, then points generated his space. But whatever he imagined space to be, he identified a point with 1.** (6)1 ko saMkhyA rAzi meM samanvita na karane vAle aura sambhavataH bhAratIya pagar3I ko dhAraNa karane vAle pithegorasa kA bindu hameM eliyA nivAsI z2Ino ke cAra asadbhAsoM ( virodhAbhAsoM) kI ora bhI AkRSTa karatA hai| pleTo ne ullekha kiyA hai ki vaha samajha cukA thA ki kisI vastu ko samAna aura asamAna, eka aura aneka, sthira aura gativAn kaise siddha karanA / jIno ke "sAnta kI ananta vibhAjyatA ke khaMDana" aura avibhAgI "samaya" (now) athavA "vartamAna kAla" jaisI avadhAraNAoM ( concepts) meM hama jinAgama praNIta "pradeza" aura "samaya" sambandhI mAnyatAoM kA spaSTa bimba dekhate haiN| isa sambandha meM aisA pratIta hotA hai mAno syAdvAda para AdhArita anekAntAtmaka vastu svarUpa viSayaka jJAna kA jIno ne AdhAra lekara sambhavataH ina asadbhAsoM Adi kA saMkalana kevala apane ArAdhya pArameniDIz2a (Parmenides, fl. bth century B.C.) ke siddhAntoM kI rakSA ke lie vivAdotsuka vidvAnoM ko viDambanA meM DAlane ke hetu kiyA ho| isakI puSTi nimnalikhita avataraNa se hotI pratIta hotI hai : "'Yes, Socrates', said Zeno; 'but though you are as keen as a Sparton hound, you do not quite catch the motive of the piece, which was only intended to protect Parmenides against ridicule..."[] * The Magic of Numbers, p. 161. + Science Awakening, Plate 13, p. 112. +T. Heath : Greek History of Mathematics, vol. (i). p. 273. [] The Dialogues of Plato by B. Jowett, vol. II, p 634. (1953) Oxford,

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prastAvanA 27 isake sAtha hI satya ke pujArI aura viSa pyAle ke grAhaka saoNkrATIz2a (Socrates, 469-399 B.C.) sambandhI abhyukti bhI vicAraNIya hai, "Here we have, first of all, an unmistakable attack made by the youthful Socrates on the paradoxes of Zeno. He perfectly understands their drift, and Zeno himself is supposed of to admit this. But they appear to him, as he says in the Philebus also to be rather truisms than paradoxes."* erisTATila ke zabdoM meM prathama do tarka nimnalikhita haiM: (1) DAikaoNTomI ( Dichotomy):-koI bhI gamana nahIM hotA, kyoMki jise gati kriyA rUpa meM pariNata kiyA jAtA hai use aMta meM pahu~cane ke pUrva (darI ke ) madhya meM pahu~canA par3egA' ( aura usa arddha bhAga ko taya karane ke pUrva arddha kA arddha bhAga taya karanA hogA aura isa prakAra ananta taka ) (2) AkilIz2a ( The Achilles ) 'kathana hai ki manda gativAna ko tIvra gativAn kabhI na pakar3a sakegA; kyoMki jisa sthAna ko maMda gativAna ne chor3A hai vahA~ taka tIvra gativAn ko pahu~canA par3egA aura isaliye maMda gativAn AvazyakIya rUpa se sadA kucha dUra Age hI rhegaa| spaSTa hai ki ye do tarka parimita akhaMDa mahattAoM kI ananta vibhAjyatA kA khaMDana karate haiN| jinAgama ke anusAra amUrtika AkAza dravya ko syAta akhaMDa aura syAt ananta pradezavAn mAnA gayA hai| pradeza (khaDa) kI avadhAraNA pudgala paramANu kI avibhAjyatA yA aMtya mahattA ke AdhAra para mukhya rUpa se ko gaI hai / isa prakAra amUrta dravya meM bheda (vibhAjana) kI kalpanA ko sthAna na dekara kevala mUrta dravya pudgala meM bheda kI sambhAvanA kI puSTi kara, aura pradeza kI paribhASA, "jitane AkAza ko eka avibhAgI pudgala paramANu ko vyApta kare" rUpa meM dekara, lokAkAza meM asaMkhyAta pradezoM kI mukhya rUpa se kalpanA kI gaI hai| yahA~ taka hI nahIM, varan eka sUcyaMgula meM pradezoM kI saMkhyA kA pramANa, saMkhyAmAna aura upamAmAna meM samIkaraNa sthApita karate hue, vaha pramANa batalAyA gayA hai jo palyopama kAla rAzi meM sthApita samayoM kI saMkhyA ke arddhaccheda pramANa kA paraspara guNana karane para prApta ho| isa paramparAgata samIkaraNa ke AdhAra para prathama tarka kA samAdhAna hotA pratIta hotA hai, kyoMki sRSTi meM paramANu ko aMtya mahattA prApta karA dene para, kisI parimita dUrI meM arddhacchedoM kI saMkhyA kA pramANa adhika se adhika asaMkhyAta hI hone para, ananta vibhAjyatA kA prazna uThatA pratIta nahIM hotaa| asaMkhyAta pramANa mukhyarUpa kalpanA ke AdhAra para, dvitIya taka bhI samAdhAnita hotA pratIta hotA hai, kyoMki paramANu svarUpa aMtyamahattA vAlI vastuoM ke bhI gamanasambandhI sadbhAva meM kisI dUrI ke arddhaccheda, trayaccheda, caturthaccheda Adi sabhI kI saMkhyA, pradeza kI kalpanA ke AdhAra para asaMkhyAta athavA saMkhyAta hI hogI, ananta nahIM; aura isa prakAra "kabhI nahIM" prazna bhI samAdhAnita hotA pratIta hotA hai| aisA pratIta hotA hai mAno jIno ne bhautika saMsAra meM hone vAlI ghaTanAoM ko hI vAstavika AdhAra mAnakara amUrtika AkAza kI vibhAjyatA kI kalpanA kA khaMDana kiyA hai| aisA kahA jAtA hai ki ye tarka pithegorIya siddhAntoM ke khaMDana ke liye nahIM the, * Ibid. p. 638. + T. Heath, Greek History of Mathmetics vol. I, p. 275, (1921) + Ibid. pp. 275 276.

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28 kyoMki pithegorIya varga ne bindu having position ) ke rUpa meM gaNita sArasaMgraha athavA pradeza kI paribhASA, "sthiti vAlA ekaka" ( unit sthApita kI thI / * ina do tarkoM ke AdhAra para, vIrasena kI zailI meM, "parantu aisA hai nahIM" yaha anyathA yukti khaMDana ( aniSTa pradarzana ) vidhi, jinAgama praNIta ukta tathyoM kI puSTi karane kI vidhiyoM ke samAna pratIta hotI hai / athavA aisA mAlUma par3atA hai mAno sImita kSetra meM saMkhyAta yA asaMkhyAta (parimita ) pradeza saMkhyA rAzi kI puSTi karane ke liye hI ye tarka prastuta kiye gaye haiM / Age, erisTATila ke zabdoM meM jIno ke aMtima do tarka ye haiM-(3) bAja ( The Arrow ) :- - "yadi, jInoM kA kathana hai, pratyeka vastu yA to sthira hai gati kriyA meM pariNata hai ( gamana meM hai ) jaba ki vaha ( svataH ) ke samAna AkAza ko vyApta karatI hai, jaba ki vaha gativAn vastu usI kSaNa ( in the now ) meM sadA hai, to gativAn bANa sthira hai ( gativAn nahIM hai ) ( 4 ) krIr3AMgana ( The Stadium ) : - " cauthA tarka samAna vastuoM kI samAna saMkhyA vAlI do paMktiyoM ke sambandha meM hai jo kisI daur3a kSetra meM samAna pravega se viruddha dizAoM meM eka dUsare kA atikramaNa karatI haiM, eka paMkti kSetra ke aMta se tathA dUsarI madhya se prasthAna karatI haiN| yaha, vaha socatA hai, isa upasaMhAra para pahu~cAtI hai ki datta samaya kA arddha bhAga, dviguNita ke tulya hotA hai * vIrasenAcArya ne vyavahArakAla kI aMtya mahattA ko avibhAgI samaya meM paramANu kI gamanazIlatA ke AdhAra para prastuta kiyA hai, " eka paramANu kA dUsare paramANu ke vyatikrama karane meM jitanA kAla lagatA hai, haiN| caudaha rAju AkAza pradezoM ke atikramaNa mAtra kAla se jo atikramaNa karane meM usake eka paramANu atikramaNa karane ke kAla kA nAma samaya hai / " () * Ibid. p. 278. | Ibid. p. 276. isa prakAra lokAnta se lokAgra taka pratyeka bindu para se jAne vAle paramANu ke gujarane kI ghaTanA, pratyeka pradeza para sthita ghar3I, tathA gamanazIla paramANu meM sthita aisI hI ghar3I (1), vahI "eka avibhAjya samaya, tatkSaNa," batalAvegI jisa 'eka samaya' meM vaha pudgala paramANu, gamanarUpa kriyA meM pariNata huA, lokAgra para jAkara, sthira paryAya ko prApta hotA hai| isa prakAra pratyeka pradeza se gujarane kI eka samaya kAlIna ghaTanA meM yugapatatva kA samAveza hai / vyavahAra se, kAla ke ananta samaya, vartamAna kAla ko eka samaya mAnakara batalAe gaye haiN| nizcaya naya se amUrta, apradezI kAla dravya vartanA kA kAraNa hone se, tathAprati samaya ananta vartanAe~ hone se, mukhya kAlANu ananta samaya vAlA bhI mAnA gayA hai|[] kAla kI aMtya pramANa choTI paryAya se ghire hue kAla ko samaya batalAyA gayA hai / aise avibhAgI [ kyoMki koI praryAya ke badalane meM sRSTi meM hone vAlI 'paryAyAMtarI kriyA meM ', use samaya kahate samartha paramANu hai, + Ibid. p. 276. () SaTa khaDAMgama pu0 4, pR0 318 | [] tatvArtharAjavArtika, adhyAya 5, pR0 434 ( pannAlAla, vAkalIvAla )

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prastAvanA eka samaya se kama kAla nahIM lagatA ] samaya meM Urdhvagamanatva svabhAvavAlA siddhAtmA, madhya loka se lokAma sthita siddha zilA para pahu~ca jAtA hai| isI prakAra eka hI samaya meM Iyapatha Asava meM kamoM kA AnA, AtmA se sparza karanA aura nirjarita ho jAnA tathA cAra samaya se pahile maraNAMtika samudrAta meM AtmA ke pradezoM kA anuzreNi vigraha gati se loka meM sthita kisI bhI pradeza sthita janma sthAna kA sparza karanA aura cAra samaya meM daMDa, kapATa, pratara evaM lokapUraNa kriyA kA honA, ye saba kriyAe~, athavA paryAyoM meM aMtara Adi kA eka samayavartI hone kA jJAna jIno ke ukta asadbhAsoM kA viSaya bana jAtA hai; ki kyA ina paryAyoM athavA kriyAoM se bhI koI sUkSmatara paryAyeM nahIM hotI haiM, jo jJAna meM A sakeM, kyoMki ve eka samaya ke avaktavyam bhAga (1) meM ghaTita hotI haiN| kriyA kI paribhASA zrI akalaMka deva dvArA nimna rUpa meM prastuta hai, "ubhaya nimittApekSaH paryAya vizeSo dravyasya dezAMtara prApti hetuH kriyA // " # 29 aisA samajhA jAtA hai ki uparokta tarka saMtata mahattAoM kI avibhAjya tatvoM dvArA saMracanA kI kalpanA ke viruddha haiN|, parantu aisA pratIta hotA hai mAno tRtIya asadbhAsa avibhAgI samaya ke khaMDana ke lie nahIM hai, varan usa eka samaya meM "14 rAju jo dezAntara mAti hai, vaha kevala sthiratA athavA gativAn rUpAdi aneka alaga-alaga vartanAe~ rUpa nahIM hai, varan una vartanAoM kA eka samaya meM eka paryAya parivartana rUpa honA hai", isa prakAra ke hone vAle paryAya parivartana kI sambhAvyatA kI puSTi ke lie hai / kAraNa yaha hai ki gativAn bANa kI eka samaya meM sthiratA aura gamana rUpa honA svAbhAvika pratIta hotA hai, aura eka-eka pradeza para gujarate hue usakA gamana rUpa rahate hue sthira kahanA nyAya saMgata nahIM hai; varan usa eka samaya meM sahasA 7-14 rAju pramANa pradeza rAzi kA zIghra bANa ke samAna atikramaNa karate hue lokAya para jAkara sthiratA paryAya kA grahaNa karanA asvAbhAvika isaliye pratIta ho ki samaya avibhAjya hai, para isa vartamAna kAla rUpa eka samaya meM aisA hotA hai - "nahIM to vaha bANa calatA hI nahIM", tarka se avasthita ( established ) AbhAsita hotA hai| caturtha tarka sambhavataH ukta samaya ( now ) ke AdhAra para upasthita huA pratIta hotA hai| hamArI samajha meM yahA~ yaha prazna uThAyA gayA hai ki eka paramANu kA dUsare paramANu kA vyatikramaNa karate samaya, athavA 14 rAju meM sthita pradezoM kA atikramaNa karate samaya, usa eka samaya meM pradeza kI sImA kA ullaMghana karate samaya, athavA eka sAtha asaMkhyAta pradezoM kA ullaMghana karate samaya, ukta samaya ke vibhAjita ho jAne kI kalpanA nyAyasaMgata hai, athavA nahIM? aisA pratIta hotA hai, mAno z2Ino ne 'eka samaya' kI avibhAjyatA kI kalpanA ko nyAyasaMgata batalAne ke lie yaha asadbhA ullikhita kiyA ho ki kyA koI samaya kA arddhamAna usake dviguNita pramAga ke tulya hotA hai ? jo kucha ho, varddhamAna mahAvIra ke tIrtha meM paramparAgata anugamoM meM pracura mAtrA meM prayukta ye tathya hameM vizvabaMdhutva ke prAgaNa meM hue sambhAvita AdAna-pradAna kI salakeM prastuta karate pratIta hote haiN| hama abhI yaha bhI nahIM kaha sakate ki yUnAniyoM dvArA zaMku ke cheda ( kATa) se prApta vibhinna chedoM ( sections ) ke gahana adhyayana kI preraNA sUrya, caMdrAdi ke sumeda ke paritaH samApana, asamApana * dekhiye vahI, pR0 84, a05, sUtra 7/1 + T. Hoath Greek History of Mathematics, Vol.] (1), p. 278 (1921) tatvArtha rAjavArtika, a05, 024 / 26

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30 gaNitasArasaMgraha sarpiloM (spirals) meM paribhramaNa ko A~kha para Apatita tiryaka zaMku rUpa meM parilakSita (prekSita) karane ke phalasvarUpa prApta huI ho| itanA avazya hai tiloya paNNattI jaise graMtha meM grahoM ke gamana kA vivaraNa kAlavaza vinaSTa honA hI batalAyA hai, parantu apoloniyasa ( Apollonius, circa 262-190 B. C.) aura TAlemI kI kRtiyoM se saMkalana kA prayAsa nahIM kiyA gayA hai| aba hama dekheMge ki kyA gaNita itihAsa kI zRMkhalA kI bhagna kar3iyoM meM se varddhamAna mahAvIra ke tIrtha meM pratipAdita alaukika gaNita kA vikAsa bhI eka kar3I hai| bhagnakar3iyoM ke viSaya meM ullikhita vAerDena kI abhyukti yaha hai : "We have no real proofs for the existence of such an uninterrupted tradition; too many connecting links are missing for this. It is rather a general impression of relatedness which makes itself felt when one knows the cuneiform texts and then looks through Heron or Diophantus, or the Chinese "classic of the maritime isle", or the Aryabhayta# of Aryabhata or the Algebra of Alkhwarizmi. According to all Arabic sources, Alkh warizmi was the first writer on algebra, but his algebra is so mature that we cannot assume that he discovered everything himself. The algebra of Alkhwarizmi can hardly be accounted for on the basis of the Greek and Indian sources which we know; one gets more and more the impression that he has drawn on older sources which in some way or other are connected with Babylonian algebra."t bebilana se cIna taka anya sAmagrI pahu~cane athavA bebilana aura cIna ke prayukta anupAta siddhAnta se sahasambandhita bhanna kar3I kA anurekhaNa karane meM bhI itihAsajJoM ne apanI asamarthatA prakaTa kI hai : "The oldest Chinese collection of problems on applied proportions' looks like an ancient Babylonian text, but it is next to impossible to prove their dependence or to trace the road along which they were transmitted."t isameM sandeha nahIM hai ki cIniyoM ne hajAroM varSoM se jJAna kA AdAna pradAna karate hue bhI apane lakSaNa (character) aura maulikatA (originality) ko akSuNNa rakhA hai| hama yahA~ kevala thor3e se uddharaNoM dvArA varddhamAna mahAvIra ke tIrtha se sahasambandhita satya, ahiMsA aura gaNita ke prAMgaNa meM cIna aura bhArata ke samAntara rUpa se vikasita tathyoM para prakAza DAlanA cAhate haiN| IsvI pazcAt 65 ke lagabhaga cIna meM sarvaprathama bauddha dharma prakaTa hotA pratIta hotA hai| hama isake kucha zatAbdiyoM pUrva umar3I vizvabandhutva kI laharoM se prabhAvita kSetra, kAla, bhAva kA avalokana karanA upayogI samajhate haiM: * zuddha rUpa "Arybhatiya" hai| + Science Awakening, p. 280. * Ibid. p. 278.

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prastAvanA 31 (1) eka ora jahA~ yUnAna meM paudhoM meM jIva kA astitva mAnA gayA hai, vahA~ cIna meM bhI isase sambandhita siddhAnta para jojepha nIDema dvArA prakAza DAla gayA hai : "Another case which seems to me comparable is the Aristotelian doctrine of the 'ladder of souls, in which plants were regarded as possessing a vegetative soul, animals a vegetative and a sensitive soul, and man & vegetative, a sensitive and & rational soul. I shall later show (sect. 9 ) that a very similar doctrine was taught by: Hsun Tzu ( Hsun Chhing ).2 Aristotle lived from 384 to -322, Hsun Chhing from - 298 to --238."* uparyukta kA sambandha prAkRta graMthoM meM varNita jIvoM ke guNasthAna aura mArgaNAsthAnoM se anurekhita karanA upayogI pratIta hotA hai / isa ora AkRSTa karane vAle tathya nimnalikhita haiM: "In the realm of philosophical theory and practice, determined efforts have been made to show that early Taoism owed much both to the Indian Upanishad literature for its theorya, and to Indian yogism for some of its practices; further, that Chinese Chhan Buddhism was an importation from India. These views, however, as Creel says, have never been really convincing. The Upanishadse are metaphysical commentaries on the Vedas, and date from the -8th to the -1th centuries, so that they are little earlier than the first period of elaboration of Taoist doctrine, Their strongly marked metaphysical idealism, with its conception of the unity of the brahman and the atman, the absolute and the self, is not at all characteristic of the Taoists; though the latter, as we shall see, greatly emphasised the unity of nature, and the incorporation of the individual within it. For the influence of Yoga practices, especially the breathing exercises, which are certainly very ancient in India. upon early Taoism, & better case can be made out (Filliozat, 3). Some Taoist schools, at any rate, practised self-hypnosis by concentration on the inhaling and exhaling processes (Waleyh ). butit was not universal as Chuang Tzu has a passage condemning it. In any case the aims of this samadhi or dhyana among the Taoists were entirely different from those of the Indian rishis. Both wished to master organic life and to attain 'supernatural powers, but while China, p. 155, vol. I, * J. Needham, Science and Civilization in Cambridge ( 1954).

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32 gaNitasArasaMgraha the Indians sought for an ascetic virtue which would enable them to dominate the gods themselves (cf. Wilkins' ), the Taoists sought a material immortality in a universe in which there were no gods to overcome, and asceticism was only one of the methods which they were prepared to use to attain their end.'* / uparyukta tulanA meM hama zubhacaMdrAcArya ke 'jJAnArNava' kI ora pAThakoM kA dhyAna AkarSita kareMge, jahA~ AtmA ke vyaktitva ke carama vikAsa ke liye (aMtataH mukti ke lie) prANAyAma ko vighna kA kAraNa nirUpita kiyA hai samyaka samAdhi siddhayartha pratyAhAraH prazasyate / prANAyAmena vikSiptaM manaH svAsthyaM na vindati // 4 // vAyoH saMcAra cAturya maNi mAdyaGga sAdhanam / prAyaH pratyUha bIjaM syaanmunermuktimbhiipstH||6|| prANasyAyamane pIDA tasvAM syAdA smbhvH| tena pracyAvyate nUnaM jJAta tatvo'pi lakSyataH // 9 // nAtiriktaM phalaM sUtre prANAyAmAtprakIrtitam / atastadartha masmAbhirnAtiriktaH kRtaH zramaH // 11 // (prakaraNa saMkhyA 30) ... sAtha hI varddhamAna mahAvIra ke tIrtha meM siddha pada prApta karane hetu samyak tapa ko jo pradhAnatA dI gaI thI vaha paramparA se pracalita pratikramaNa meM isa prakAra dRSTigata hotI hai / "tavasiddha jayasiddha saMjamasiddha carittasiddhe y| jANammi daMsammi ya siddhe sirasA NamaMsAmi // " (2)cIna aura bhArata ke bIca sambandha jor3ane vAlA eka tathya aura hai, "parimita kSetra kI ananta vibhAjyatA kA khaMDana / " isake sAtha hI sambandhita yugapatatva (simultaneity) aura paramANu sambandhI tathya haiM jinake liye varddhamAna mahAvIra ke tIrtha meM saMkalita sAmagrI Adi kA tulanAtmaka adhyayana kitanA upayogI hogA yaha nimnalikhita uddharaNa se spaSTa ho jAvegA, "Finally, he discusses the relation between the paradoxes of Hui Shih? and the Eleatic paradoxes, without attaining any definite conclusion - the correspondence is, indeed, another example of that extraordinary simultaneity between phenomena which we sometimes find at the two ends of the Old World. For the date of Hui Shiha is late -5th century, and Eleatic Zeno's floruit is placed about-460." * Ibid. p. 153. + Ibid. p. 154.

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prastAvamA 33 37TTT, "One might take the theories of atomism as an example. Its story in our own classical civilization, beginning with such men as Leucippus and Democritus of Abdera, of the 5th century, and culminating in Epicurus and Lucretius of the late 3rd and early -1st, is well known to us. Indian atomism seems to be later in date, the Jaina System of Umasvati showing its greatest strength about +50, and the Vaigeshika dargana ( theory ) of Kanada flourishing in the second half of the + 2nd Century. But there are reasons, as Reyi urges, for believing that the roots of the theory of paramanu (atoms ) go much further back in the history of Indian thought. Thirdly, in Chinese physics atomism never arose, as we shall seea, but the geometry of the Mo Ching' ( the Mohist Canon, which must have been put together somewhere in the neighbourhood of - 370 ) seems to define a point as a line which has been out so short that it cannot be cut any further." (3) Age yaha jAnate hue ki cIna aura bhArata meM bauddha dharma sambandhI AdAna pradAna kA prArambha IsA kI cauthI sadI se huA, hama isase pUrva kA eka aisA ullekha bhI pAte haiM jo sambhavataH bhArata se sambandhita ho, "The Huai Nan T zu book (c.-200 ) contains a remark that Yu the Great 'when he went to the country of the Nacked People, left his clothes before entering it and put them on when he came out, thus showing that wisdom adapts itself to circumstances." (4) isameM sandeha nahIM ki cInI gaNita kA pratyakSa sambandha bhAratIya gaNita ke sAtha dikhAI detA hai, para yaha kAla varddhamAna mahAvIra ke zatAbdiyoM pazcAt kA hai : "The proof of the Pythagoras Theorem used by Chao Chun-Chhing in his + 2nd-century commentary on the Chou Pei? (the oldest mathematical classic) appears again in the work of Bhaskar ( + 1150 ). The rule for the area of the segment of a cirole given in the Chiu Chang Suan Shu* (Nine Chapters on the Mathematical Art) of the + 1st-century appears again in the + 9th-century work of Mahavira. Indeterminate problems of the Sun Tzu Suan Chings (Master Sun's Mathematical Manual) of the + 3rd century are found in Brahmagupta (+7th century). Aryabhata (+5th century ) has * Ibid. p. 155. Ibid. p. 206.

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34 gaNitasArasaMgraha geometrical survey material very like that of Liu Hui of the +3rd "" ____ jahA~ taittirIya saMhitA meM kevala 27 nakSatroM ko mAnyatA dI hai, vahA~ cIna meM 28 nakSatra mAne gaye haiN| tiloya paNNattI meM bhI 1caMdra ke 28 nakSatra mAne gaye haiM (7-465 ), tathA caMdra ke kAraNabhUta zukla pakSa aura kRSNa pakSa meM pAtAloM ke pavana kA bar3hanA aura ghaTanA batalAyA gayA hai (4-2403) / yahA~ isa tathya se samAnatA rakhatA huA yUnAna aura cIna se sambandhita ullekha dhyAna dene yogya hai / jahA~ IsA pUrva sAtavIM sadI ke cInI tAo siddhAnta ke grantha kuAna na ( Kuan Tzu) meM caMdramA ke zukla aura kRSNa pakSa meM samudrI jIvoM kA bar3hanA aura ghaTanA batalAyA hai, vahA~ yUnAna meM erisTATila (Aristotle) ne bhI yahI ullikhita kiyA hai| gaNita sambandhI anya tulanAeM tiloya paNNattI ke gaNita tathA ToDaramala kI gommaTasAra TIkA Adi se kI jA sakatI haiN| isa sambandha meM ullikhita grantha ke anya bhAga (1-7) bhI draSTavya haiN| yahA~ itanA kahanA Avazyaka hai ki varddhamAna mahAvIra ke tIrtha meM anantAtmaka rAziyoM kA alpabahutva anyatra kahIM dekhane meM nahIM AyA hai / darzana meM gaNita ke prayukta karane kI anupama praNAlI "alpa bahattva" meM parilakSita hotI hai| kezavavarNI kI gommaTasAra TIkA meM isa tathA anya viSayaka prarUpaNA meM prayukta pratIkoM meM zUnya, dhana aura RNAdi ke liye eka se adhika cihna upayoga meM lAye gaye haiM, jo aitihAsika dRSTi se atyanta mahatvapUrNa haiN| uparyukta avalokana se hama isa niSkarSa para pahu~cate haiM ki pithegorasa kAlIna akhila vizva meM jo gaNita yukta darzana kA punarjAgaraNa huA, usake itihAsa kI bhagna zRMkhalA kI eka kar3I varddhamAna mahAvIra kA tIrtha kAlIna lokottara gaNita (arthamitikI) bhI hai| * Ibid. p. 213. + Ibid. p. 150. cInI n ke mAna 3, V0, 357 tathA dAzamika paddhati sahita zalAkA gaNana draSTavya haiN|

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kRtajJatA prakAzana prastuta graMtha ke hiMdI anuvAda kI preraNA mujhe DA. hIrAlAla jaina ne prAyaH gyAraha varSa pUrva nAgapura meM dI thI / isa sambandha meM samaya samaya para diye gaye unake sujhAvoM ke lie maiM unakA AbhArI huuN| saMskRta ke vidyArthI hone kA saubhAgya mujhe prApta nahIM huA, isaliye prastuta anuvAda mukhyataH prophesara ema. raMgAcArya ke saTIka AGgala bhASAnuvAda para AdhArita hai| isa anuvAda meM zAsana dvArA prakAzita pAribhASika zabdAvali kA upayoga kiyA gayA hai / saMskRta ke prUpha dekhane kA zreya DA. e. ena. upAdhye ko hai| isa kArya meM prayukta katipaya graMthoM kI pUrti pUjya zrI 105 kSu0 manoharalAla jI varNI "sahajAnanda" ne kI, jisake liye maiM unakA cira kRtajJa hU~ / ___ mahAkauzala mahAvidyAlaya (rAbarTasana kAlija ), jabalapura ke bhUtapUrva prAcArya svargIya zrI umAdAsa mukharjI kA maiM AbhArI hU~, jinhoMne mujhe apanI sahaja dayA kA pAtra banAkara prastuta anuvAda ke kArya ko bhalI bhA~ti sampanna karane hetu saMrakSaNa pradAna kiyA / isI mahAvidyAlaya ke gaNita vibhAga ke bhUtapUrva adhyakSa prophesara zrI sI. esa. rAghavana dvArA pradatta suvidhAoM ke liye bhI maiM unakA AbhArI huuN| maiM zrI vI. esa. paMDita, eDavokeTa, jabalapura, tathA zrI prabodhacaMdra jaina, eDavokeTa, chiMdavAr3A kA AbhArI hU~ jinakI apratyakSa sahAyatA ke binA yaha kArya na ho sakA hotaa| aprakaTa rUpa se sahAyaka vidyArthI varga bhI dhanyavAda kA pAtra hai| aMta meM, maiM una graMthakAroM ke prati kRtajJa hU~, jinake graMthoM kI sahAyatA lekara yaha kArya niSpanna huA hai| 3. janavarI, 1963 gavarnameMTa sAiMsa kAlija, jblpur| lakSmIcaMdra jaina

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mahAvIrAcAryapraNItaH gaNita sArasaMgrahaH 1. saMjJAdhikAraH maGgalAcaraNam alaGghayaM trijagatsAraM yasyAnantacatuSTayam / namastasmai jinendrAya mahAvIrAya tAyine // 1 // saMkhyAjJAnapradIpena jainendreNa mahotviSA / prakAzitaM jagatsarvaM yena taM praNamAmyaham // 2 // prINita: prANisasyaugho nirItirniravagrahaH / zrImatAmoghavarSeNa yena sveSTahitaiSiNA || 3 || pAparUpAH parA yasya cittavRttihavirbhuji / bhasmasAdbhavamIyuste'vandhyakopo'bhavattataH // 4 // vazIkurvan jagatsarvaM svayaM nAnuvazaH paraiH / nAbhibhUtaH prabhustasmAdapUrva makaradhvajaH // 5 // yo vikramakramAkrAntacaM kricakrakRtakriyaH / cakrikAbhaJjano nAmnA cakrikAbhaJjano'JjasA // 6 // 1 MB mahadeg / 2 M praNItaH / 3 M sargoM / 4 MK sadbhAM / 5 KPB bhavet / 6 B yo'yaM / 7M kI / 8 MB zadeg | 1. saMjJA ( pAribhASika zabda ) adhikAra maGgalAcaraNa jinhoMne tInoM lokoM meM sArabhUta evaM mithyA dRSTiyoM dvArA alaMghya ananta darzana, ananta jJAna, ananta vIrya aura ananta sukha nAmaka ananta catuSTaya ko prApta kiyA, aise rakSaka jinendra bhagavAn mahAvIra ko maiM namaskAra karatA hU~ // 1 // maiM mahAn vibhUti ko prApta jinendra ko namana karatA hU~ jinhoMne saMkhyAjJAna ke pradIpa se samasta vizva ko prakAzavAna kiyA hai // 2 // dhanya haiM ve amoghavarSa ( arthAt ve jo vAstava meM upayogI vRSTi kI varSA karate haiM, ) jo hamezA apane priyapAtroM ke hitacintana meM rahate haiM aura jinake dvArA prANI tathA vanaspati, mahAmArI aura durbhikSa Adi se mukta hokara sukhI hue haiM // 3 // jina ( amoghavarSa ) ke citta kI kriyAyeM agnipuMja sadRza hokara samasta pAparUpI vairiyoM ko bhasma meM pariNata karane meM saphala haiM, aura jinakA krodha vyartha nahIM jAtA // 4 // jinhoMne samasta saMsAra ko apane vaza meM kara liyA hai aura jo kisI ke vaza meM na rahakara zatruoM dvArA parAjita nahIM ho sake haiM, apUrva makaradhvaja kI taraha zobhAyamAna haiM // 5 // jinakA kArya, apane parAkrama dvArA parAbhUta rAjAoM ke cakra ( samUha ) dvArA hotA hai, aura jo na kevala nAma se cakrikA bhaMjana haiM varan vAstava meM bhI cakrikA aMjana ( arthAt janma aura maraNa ke cakra ke nAzaka' ) haiM // 6 // jo aneka jJAna saritAoM ke adhiSThAtA 1 bhaviSya kI apekSA se /

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gaNitasArasaMgrahaH [1.7yo vidyAnadyadhiSThAno maryAdAvajravedikaH / ratnagarbho yathAkhyAtacAritrajaladhirmahAn // 7 // vidhvastaikAntapakSasya syAdvAdanyAyavAdinaH / devasya nRpatuGgasya vardhatAM tasya zAsanam // 8 // gaNitazAstraprazaMsA laukike vaidike vApi tathA sAmAyike'pi yaH / vyApArastatra sarvatra saMkhyAnamupayujyate / / 9 // kAmatantre'rthazAstre ca gAndharve nATake'pi vA / sUpazAstre tI vaidye vAstuvidyAdivastuSu // 10 // chando'laGkArakAvyeSu tarkavyAkaraNAdiSu / kalAguNeSu sarveSu prastutaM gaNitaM param // 11 // sUryAdigrahacAreSu grahaNe grahasaMyutau / triprazne candravRttau ca sarvatrAGgIkRtaM hi tat // 12 // dvIpasAgarazailAnAM saMkhyAvyAsaparikSipaH / bhavanavyantarajyotirlokakalpAdhivAsinAm / / 13 / / 1P vedinaH / 2 M syAt ; B cApi / 3 B ca / 4 KM mahA / 5 MB dnnddaa| 6 MB purA / 7 MMdeg shipaaH| hokara saccaritratA kI vajramayI maryAdA vAle haiM aura jo jaina-dharma rUpI ratna ko hRdaya meM rakhate haiM, isaliye ve yathAkhyAta cAritra ke mahAn sAgara ke samAna suprasiddha hue haiM // 7 // ekAnta pakSa ko naSTa kara jo syAdvAdarUpI nyAyazAstra ke vAdI hue haiM aise mahArAja nRpatuMga kA zAsana phale-phUle // 8 // gaNitazAstraprazaMsA sAMsArika, vaidika tathA dhArmika Adi saba kAryoM meM gaNita upayogI hai // 9 // kAmazAstra meM, arthazAstra meM, saMgIta va nATyazAstra meM, pAkazAstra (sUpazAstra) meM aura isI taraha auSadhi-zAstra meM tathA vAstu-vidyA (nirmANa-kalA) meM, chanda, alaMkAra, kAvya, tarka, vyAkaraNa Adi ina sabhI kalAoM meM gaNanA kA vijJAna zreSTha mAnA jAtA hai // 10-11 // sUrya tathA anya graha-nakSatroM kI gati ke saMbaMdha meM grahaNa aura graha-saMyuti (saMyoga) ke sambandha meM, triprazna ke viSaya meM aura candramA kI gati ke viSaya meM-sarvatra ise upayoga meM lAte haiM // 12 // dvIpoM, samudroM aura parvatoM kI saMkhyA, vyAsa aura parimiti; bhavanavAsI, vyantara, jyotilokavAsI, kalpavAsI devoM ke tathA nArakI jIvoM ke zreNibaddha aura iMdraka (8) 'syAt' zabda nipAta hai jo ekAnta kA nirAkaraNa karake anekAnta kA pratipAdana karatA hai| yaha zabda 'kathaMcit' kA paryAyavAcI hai aura eka nizcit apekSA ko nirUpita karatA hai| isa prakAra, vaijJAnika evaM yuktiyukta syAdvAda jo jaina-darzana evaM tattvajJAna kI nIMva hai, vastu ke yathArtha svarUpa ko prakaTa karane ke hetu usake ananta dhamoM meM se eka samaya meM eka dharma kA pratipAdana karatA hai| pratyeka dharma kA varNana usake pratipakSI virodhI dharma kI apekSA se saptabhaMgI meM kiyA jAtA hai| udAharaNArthaastitva eka dharma hai, aura nAstitva usakA pratipakSI dharma hai| apane pratipakSI sApekSa astitva dharma kI apekSA se saptabhaMgI isa prakAra banegI-(1) ghaTa kathaMcit hai, (2) ghaTa kathaMcit nahIM hai, (3) ghaTa kathaMcit hai aura nahIM hai, (4) ghaTa kathaMcit avaktavya hai, (5) ghaTa kathaMcit hai aura avaktavya hai, (6) ghaTa kathaMcit nahIM hai aura avaktavya hai, (7) ghaTa kathaMcit hai, nahIM hai, aura avaktavya hai| (12) triprazna saMskRta ke jyotirloka vijJAna viSayaka granthoM meM varNita eka adhyAya kA nAma hai jo tIna praznoM ke viSaya meM pratipAdana karane ke kAraNa isa nAma se prasiddha hai| hAdi jyotiSa bimboM ke sambandha meM dik (dizA), dazA (sthiti) evaM kAla (samaya) viSayaka hote haiN|

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-1. 24] 1.saMjJAdhikAraH nArakANAM ca sarveSAM zreNIbandhendrakotkarAH / prakIrNakapramANAdyA budhyante gaNitena te // 14 // prANinAM tatra saMsthAnamAyuraSTaguNAdayaH / yAtrAdyAH saMhitAdyAzca sarve te gaNitAzrayAH / / 15 / / bahubhirvipralApaiH kiM trailokye sacarAcare / yatkiMcidvastu tatsarvaM gaNitena vinA na hi / / 16 / / tIrthakRyaH kRtArthebhyaH pUjyebhyo jagadIzvaraiH / teSAM ziSyapraziSyebhyaH prasiddhAdguruparvataH // 17 // jaladheriva ratnAni pASANAdiva kAJcanam / zuktemuktAphalAnIva saMkhyAjJAnamahodadheH / / 18 / / kiMciduddhRtya tatsAraM vakSye'haM matizaktitaH / alpaM granthamanalpArthaM gaNitaM sArasaMgraham / / 19 / / saMjJAmbhobhiraMtho pUrNa parikarmoruvedike / kalAsavarNasaMrUDhaluThatpAThInasaMkule // 20 // prakIrNakamahAgrAhe trairAzikataraGgiNi / mizrakavyavahArodyatsUktiratnAMzupiJjare // 21 // kSetravistIrNapAtAle khAtAkhyaMsikatAkule / karaNaskandhasaMbandhacchAyAvelAvirAjite // 22 // guNakairguNasaMpUrNaistadarthamaNayo'malAH / gRhyante karaNopAyaiH sArasaMgrahavAridhau / / 23 / / atha saMjJA na zakyate'rtho boDhuM yatsarvasmin saMjJayA vinaa|aadaavto'sy zAstrasya paribhASAbhidhAsyate // 24 // 1 KMB baddhe / 2 M vasu / 3 KP jJAna ke sthAna meM nava / 4 MB alpa / 5 K saMjJAtoyasamA / 6 M ddha ( sambhavataH ttha ko likhane meM bhUla huI hai|) 7 MB saMkaTe / 8 P cha / (zreNirahita ) nivAsa sthAnoM ke mApa aura anya saba prakAra ke vibhinna mApa-sabhI gaNita ke dvArA jAne jAte haiM // 13-14 // una sthAnoM meM rahane vAle jIvoM ke saMsthAna, Ayu, unake ATha guNa Adi, unakI gati (yAtrA) Adi, unakA sAtha rahanA Adi, ina sabakA AdhAra gaNita hai // 15 // aura vyartha ke pralApoM se kyA lAbha hai ? jo kucha ina tInoM lokoM meM carAcara (gatizIla aura sthira) vastue~ haiM unakA astitva gaNita se vilaga nahIM // 16 // maiM, tIrtha ko utpanna karane vAle, kRtArtha aura jagadIzvaroM se pUjita (tIrthaGkaroM) kI ziSya praziSyAtmaka prasiddha guru paramparA se Aye hue saMkhyAjJAna mahAsAgara se usakA kucha sAra ekatrita kara, usI taraha, jaise ki samudra se ratna, pASANamaya caTTAna se svarNa aura zukta (oyster shell) se muktAphala prApta karate haiM, alpa hote hue bhI analpa artha ko dhAraNa karane vAle sArasaMgraha nAmaka gaNita graMtha ko apanI buddhi kI zakti ke anusAra prakAzita karatA hU~ // 17-18-19 // tadanusAra, isa sArasaMgraha ke sAgara se, jo pAribhASika zabdAvali rUpI jala se paripUrNa hai aura jisakI ATha gaNita kI kriyAyeM kinAre rUpa haiM; punaH jo bhinna kI kriyAoM rUpI nirbhaya gatizIla machaliyoM se yukta hai aura vividha praznoM ke adhyAyarUpI mahAgrAha (magara) se vyApta hai| punaH jo trairAzika kI adhyAyarUpI laharoM se AMdolita hai aura mizra praznoM ke adhyAya-sambandhI utkRSTa bhASArUpI motiyoM kI AbhA se raMjita hai, aura punaH jo kSetraphala-sambandhI praznoM ke adhyAya dvArA pAtAla taka vistRta hai tathA ghanaphala ke adhyAya rUpI reta se pUrNa hai; aura jo jyotilokIya vyAvahArika gaNanA se sambandhita chAyA-sambandhI adhyAya rUpI bar3hate hue jvAra se camakatA hai-(aise jJAnasAgara se ) sampUrNa gaNa sampanna gaNitajJa gaNita kI sahAyatA se apanI icchAnusAra nirmala motI prApta kara sakeMge // 20-23 // isa vijJAna ke Arambha meM Avazyaka pAribhASika zabdAvali dI jAtI hai kyoMki binA zuddha paribhASAoM ke viSaya taka pahu~ca sambhava nahIM hai // 24 //

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gaNitasArasaMgrahaH [1. 25 tatra tAvat kSetraparibhASA jalAnalAdibhirnAzaM yo na yAti sa pudbalaH / paramANuranantaistairaNuH so'trAdirucyate // 25 / / trasareNuratastasmAdrathareNuH ziroruhaH / paremadhyajaghanyAkhyA bhogabhUkarmabhUbhuvAm // 26 // lIkSA tilassa eveha sarSapo'rthe yavo'Ggalam / krameNASTaguNAnyetadvayavahArAmulaM matam // 27 // tatpazcakazataM proktaM pramANaM mAnavedibhiH / vartamAnanarANAmaGgulamAtmAGgulaM bhavet // 28 // vyavahArapramANe dve"rAddhAnte laukike vidaH / AtmAGgalamiti tredhA tiryakpAdaH SaDaGgalaiH / / 29 / / pAdadvayaM vitastiH syAttato hasto dvisaGguNaH / daNDo hastacatuSkeNa krozastadvisahasrakam / / 30 / / yojanaM caturaH krozAnprAhuH kSetravicakSaNAH / vakSyate'taH paraM kAlaparibhASA yathAkramam / / 3 / / atha kAlaparibhASA aNuraNvantaraM kAle vyatikrAmati yAvati / sa kAla: samayo'saMkhyaiH samayairAvalirbhavet // 32 // 1 KP Nu / 2 MB vadeg / 3 PB khya / 4 / dhi / 5 M 'nye / kSetra paribhASA [ kSetramApa sambandhI pAribhASika zabdAvali ] pudgala kA anantavA~ sUkSma vaha bhAga jo na to pAnI dvArA, na agni dvArA aura na anya kinhIM aisI vastuoM dvArA nAzako prApta hai, paramANu kahalAtA hai| aise ananta paramANuoM dvArA utpanna eka-eka aNu kSetramApa meM prathama mApa hai| isase utpanna kramazaH ATha-ATha guNe trasareNu, rathareNu, bAlamApa, jUM mApa, tila yA sarasoM mApa, yava mApa tathA aMgula mApa haiN| aMgula mApa Adi unake liye haiM jo bhogabhUmi aura karmabhUmi meM utpanna hote haiN| ye utkRSTa, madhyama, jaghanya prakAra ke hote haiM / yaha aMgula vyavahArAMgula bhI kahalAtA hai // 25-27 // jo mApa kI vidhiyoM se paricita haiM, kathana karate haiM ki isa vyavahAra-aMgula kA 500 guNA pramANAMgula hotA hai| vartamAna kAla ke manuSyoM kI aMgalI kA mApa AtmAMgula kahA jAtA hai // 28 // ve kahate haiM ki saMsAra ke sthApita vyavahAroM meM aMgala tIna prakAra kA hotA hai, prathama vyavahArAMgula, dvitIya pramANAMgula aura tRtIya unakA AtmAMgula / chaH aMgula milakara pAda-mApa banatA hai jo ArapAra rUpa se nApA jAtA hai // 29 // do aise pAda milakara vitasti banAte haiM aura do vitasti mila kara eka hasta banatA hai| cAra hasta se eka daNDa banatA hai aura do hajAra daMDa milakara eka kroza banatA hai // 30 // jo kSetraphala ke mApajJAna meM siddhahasta haiM, kahate haiM ki cAra kroza milakara eka yojana hotA hai // 31 // isake pazcAt, maiM samaya ke mApa ke sambandha meM kramavAra pAribhASika zabdAvali kA ullekha karatA huuN| kAla-paribhASA [ kAla-sambandhI pAribhASika zabdAvali ] vaha kAla jisameM eka (gatizIla ) aNu' kisI pradezabindu se dUsare nikaTatama pradezabindu taka jAtA hai samaya kahalAtA hai| asaMkhya samaya milakara eka Avali banatI hai // 32 // (25-27) kSetramApa-sambandhI pAribhASika zabdAvali ko spaSTa rUpa se samajhane ke liye pariziSTa 3 dekhiye| ___ aNu se ATha gunA trasareNu, trasareNu se AThagunA rathareNu, rathareNu se AThagunA bAlamApa ityAdi jo mApa varNita kiye gaye haiN| ve kramavAra aise haiM ki pratyeka pUrvAnugAmI mApa se AThagunA hai; tathA pratyeka utkRSTa, madhyama aura jaghanya prakAra kA hai| 1 yahA~ aNu kA Azaya paramANu se hai|

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-1. 4.] 1. saMjJAdhikAra saMkhyA tAvalirucyAsaH stokastUcchAsasaptakaH / stokAH sapta lavasteSAM sArdhASTAtriMzatA ghaTI // 33 / / ghaTIdvayaM muhUrto'tra muhUrtestriMzatA dinam / paJcanaitridinaiH pakSaH pakSau dvau mAsa iSyate // 34 // RturmAsadvayena syAtribhistairayanaM matam / tavayaM vatsaro vakSye dhAnyamAnamataH param // 35 // atha dhAnyaparibhASA viddhi SoDazikAstatra catasraH kuDeho bhavet / kuDahA~zcaturaH prasthazcatuH prasthAnathADhakam // 36 // caturbhirADhoNo mAnI droNaizcaturguNaiH / khArI mAnI catuSkeNa khAryaH paJca pravartikAH // 37 // seyaM caturguNA vAhaH kumbhaH paJca pravartikAH / itaH paraM suvarNasya paribhASA vibhASyate // 38 / / atha suvarNaparibhASA caturbhirgaNDakairguJjA guJjAH paJca paNo'STa te / dharaNaM dharaNe karSaH palaM karSacatuSTayam / / 39 / / ___ atha rajataparibhASA dhAnyadvayena guJjakA guJjAyugmena mASakaH / mASaSoDazakenAtra dharaNaM paribhASyate // 4 // 1 KB vo| 2 K vAM / 3 sampUrNa dhAnya paribhASA ke lie, P aura B meM nimnalikhita rUpa meM vizeSa ullekha hai| M kA pAThAntara, koSThakoM meM aMkita kiyA gayA hai| Adya SoDazikA tatra kaDa (i) baH prastha ADhakaH / droNo mAnI tataH khArI krameNa ( mazaH) cturaahtaaH|| (sahastraizca tribhiSpaDabhizzataizca vrIhibhirasamam / yarasampUrNo'bhavatsoyaM kuDubaH paribhASyate // ) pravartikAtra tAH paJca vAhastasyAcaturguNaH / kumbhassapAdavAhassyAt (paJca pravartakAH kumbhaH) svarNasaMjJAtha varNyate / / saMkhyAta AvaliyoM se ucchAsa banatA hai, sAta ucchAsakA eka stoka aura sAta stoka kA eka lava hotA hai tathA sAr3he ar3atIsa lava milakara eka ghaTI banatI hai // 33 // do ghaTI kA eka muhUrta, tIsa mahata kA eka dina, paMdraha dina kA eka pakSa aura do pakSa kA eka mAsa hotA hai||34|| do mAsa milakara eka Rtu, tIna RtuyeM milakara eka ayana aura do ayana milakara eka varSa banatA hai| isake pazcAt maiM dhAnya ke mApa ke viSaya meM ullekha karatA hU~ // 35 // dhAnya-paribhASA [ dhAnyamApa sambandhI pAribhASika zabdAvali ] cAra SoDazikA milakara eka kuDahA banatA hai, cAra kuDahA milakara eka prastha banatA hai aura cAra prastha kA eka ADhaka hotA hai // 36 // cAra ADhaka kA droNa, cAra droNa kI eka mAnI, cAra mAnI kI. eka khArI aura pA~ca khArI kI pravartikA hotI hai // 37 // cAra pravartikA kA eka vAha aura pA~ca pravartikA kA eka kumbha hotA hai / isake pazcAt svarNamApa-sambandhI pAribhASika zabdAvali dI jAtI hai // 38 // suvarNa-paribhASA [ svarNamApa sambandhI pAribhASika zabdAvali ] cAra gaMDaka milakara eka guMjA banatI hai; pA~ca guMjA milakara eka paNa banatA hai aura isakA AThaguNA eka dharaNa hotA hai| do dharaNa milakara eka karSa banatA hai aura cAra karSa milakara eka pala banatA hai // 39 // rajata-paribhASA [ rajatamApa sambandhI pAribhASika zabdAvali ] do dhAnya milakara eka guMjA banatI hai, do guMjA milakara eka mAzA aura solaha mAzA milakara eka dharaNa banatA hai // 40 // DhAI dharaNa kA eka karSa evaM cAra purANa ( yA karSa ) kA eka dala hotA hai|

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gaNitasArasaMgrahaH tadvayaM sArdhakaM karSaH purANAMzcaturaH palam / rUpye mAgadhamAnena prAhuH saMkhyAnakovidAH // 41! atha lohaparibhASA kalA nAma catuSpAdAH sapAdAH SaTkalA yavaH / yavaizcaturbhiraMzaH syAdbhAgoM'zAnAM catuSTayam // 42 // drakSuNo bhAgaSaTkena dInAro'smAdvisaGguNaH / dvau dInArau sateraM syaatpraahulohe'tr sUrayaH / / 4 / / palaiAdazabhiH sArdheH prasthaH phalazatadvayam / tulAdazatulAbhAraH saMkhyAdakSAH pracakSate // 44 // vastrAbharaNavetrANAM yugalAnyatra viMzatiH / koTikAnantaraM bhASye parikarmaNi nAmataH / / 45 / / ___ atha parikamanAmAni AdimaM guNakAro'tra pratyutpanno'pi tadbhavet / dvitIyaM bhAgahArAkhyaM tRtIyaM kRtirucyate / / 4 / / caturtha vargamUlaM hi bhASyate paJcamaM ghanaH / ghanamUlaM tataH SaSThaM saptamaM ca citiH smRtam // 47 // tatsaMkalitamapyuktaM vyutklitmto'ssttmm| tacca zeSamiti proktaM bhinnAnyaSTAvamUnyapi / / 4 / / atha dhanarNazUnyaviSayakasAmAnyaniyamAH tADitaH khena rAziH khaM so'vikArI hRto yutH| hIno'pi khavadhAdiH khaM yoge khaM yojyarUpakam 49 / 1 . saterAkhyam / 2 M raM / 3 M Di / 4 M vidyAtkalA savarNasya / yahA~ cauthI saMyukti aura kartRvAcya hai| gaNanA meM kuzala vyakti kahate haiM ki magadha mApa ke anusAra uparyukta rajata-mApa haiM // 41 // __loha-paribhASA [ loha dhAtumApa-sambandhI pAribhASika zabdAvali ] eka kalA meM cAra pAda hote haiM; savA chaH kalA kA eka yava hotA hai; cAra yava kA eka aMza tathA cAra aMza kA eka bhAga hotA hai // 42 // chaH bhAga kA eka draSaNa, do draSaNa kA eka dInAra aura do dInAra kA eka satera hotA hai| loha dhAtu ke mApa ke sambandha meM vidvAn aisA kahate haiM // 43 // sAr3he bAraha pala milakara eka prastha hotA hai; do sau pala milakara eka tulA aura dasa tulA milakara eka bhAra hotA hai / aisA gaNanA meM dakSa vidvAn kahate haiM // 44 // isa mApa meM, beta athavA AbharaNa athavA vastroM ke bIsa yugmoM (jor3iyoM) kI eka koTikA hotI hai / isake pazcAt maiM gaNita kI mukhya kriyAoM ke nAma detA hU~ // 45 // ___ parikarma nAmAvali [ gaNita kI mukhya kriyAoM ke nAma ] ina kriyAoM meM prathama guNakAra ( guNA ) hai, aura vaha pratyutpanna bhI kahalAtA hai| dUsarI bhAgahAra ( bhAga yA bhAjana) kahalAtI hai; aura kRti ( varga karanA) tIsarI kriyA kA nAma hai // 4 // cauthI, sAmAnyataH vargamUla hai aura pA~cavI ghana kahalAtI hai; chaThavIM ghanamUla aura sAtavIM citi (yoga) kahalAtI hai // 47 // ise saMkalita bhI kahate haiN| AThavIM vyutkalita (pUrI zreDhi meM se Arambha se lI gaI usI zreDhi kA kucha bhAga ghaTA denA ) hai jo zeSa bhI kahalAtI hai // 48 // ye saba ATha kriyAyeM bhinna meM bhI prayukta hotI haiN| zUnya tathA dhanAtmaka evaM RNAtmaka rAziyoM sambandhI sAmAnya niyama koI bhI saMkhyA zUnya se gaNita hone para zUnya ho jAtI hai aura vaha cAhe zUnya ke dvArA vibhAjita athavA zUnya dvArA ghaTAI jAve yA zUnya meM jor3I jAve, badalatI nahIM hai| guNA tathA anya kriyAeM zUnya ke sambandha meM zUnya kI utpatti karatI hai aura yoga kI kriyA meM zanya vahI saMkhyA ho jAtA hai jisameM vaha jor3A jAtA hai||49|| (49) yaha saralatApUrvaka dekhA jA sakatA hai ki koI saMkhyA jaba zUnya dvArA bhAjita kI jAtI hai,

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-1. 60 ] 1. saMjJAdhikAraH RNayordhanayorghAte bhajane ca phalaM dhanam / RNaM dhanarNayostu syAtsvarNayorvivaraM yutau // 50 // RNayordhanayoryogo yathAsaMkhyamRNaM dhanam / zodhyaM dhanamRNaM rAzeH RNaM zodhyaM dhanaM bhavet // 51 // dhanaM dhanarNayorvargo mUle svarNe tayoH kramAt / RNaM svarUpato'vargo yatastasmAnna tatpadam // 52 // atha saMkhyAsaMjJA zaMzI somazca candrenda prAleyAMzU rjniikrH| zvetaM himagu rUpaM ca mRgAGkazca kalAdharaH // 53 // dvi dve dvAvubhau yugalayugmaM ca locanaM dvayam / dRSTirnebAmbakaM dvandvamakSicakSurnayaM dRzau // 54 // haranetraM puraM lokaM trai (tri) ratnaM bhuvanatrayam / guNo vahniH zikhI jvalanaH pAvakazca hutAzanaH / / 55 / / ambudhirviSadhirvAdhiH payodhiH sAgaro gatiH / jaladhirbandhazcaturvedaH kaSAyaH salilAkaraH // 56 / / iSurbANaM zaraM zastraM bhUtamindriyasAyakam / paJca vratAni viSayaH karaNIyaskantusAyakaH // 57 / / RtujIvo raso lekhyA dravyaM ca SaTukaM kharam / kumAravadanaM varNaM zilImukhapadAni ca / / 58 // zailamadriyaM bhUdhro nagAcalamunirgiriH / azvAzvipannagA dvIpaM dhAturvyasanamAtRkA / / 59 / / aSTau tanurgajaH karma vasuvAraNapuSkaram / dviradaM dantI digduritaM nAgAnIkaM karI yathA // 60 / / 1 kevala M meM 53 se 68 taka gAthAe~ prApta huI haiM / ye mUla meM yatra tatra azuddha haiM / do RNAtmaka yA do dhanAtmaka rAziyA~ eka dUsare se guNita karane para yA bhAjita hone para ] dhanAtmaka rAzi utpanna karatI haiM / parantu, do rAziyA~ jinameM eka dhanAtmaka tathA dUsarI RNAtmaka eka dUsare se guNita athavA bhAjita hote para RNAtmaka rAzi utpanna karatI haiN| dhanAtmaka aura RNAtmaka rAzi jor3ane para prApta phala unakA antara hotA hai // 50 // do RNAtmaka rAziyoM yA do dhanAtmaka rAziyoM kA yoga kramazaH RNAtmaka aura dhanAtmaka rAzi hotA hai| kisI dI huI saMkhyA meM se dhanAtmaka rAzi ghaTAne ke liye use RNAtmaka kara dete haiM aura RNAtmaka rAzi ghaTAne ke liye use dhanAtmaka kara dete haiM (tAki donoM kriyAoM meM kevala yoga se iSTa phala kI prApti ho jAve / ) // 5 // dhanAtmaka tathA RNAtmaka rAzi kA varga dhanAtmaka hotA hai; aura usa varga rAzi ke vargamala kramazaH dhanAtmaka aura RNAtmaka hote haiN| cUMki vastuoM ke svabhAva (prakRti ) meM RNAtmaka rAzi, vargarAzi nahIM hotI isaliye usakA koI vargamUla nahIM hotA // 52 // agale dasa sUtroM meM kucha vastuoM ke nAma diye gaye haiM jo vAraMvAra aMkoM aura saMkhyAoM ko pradarzita karane ke liye aMkagaNita saMketanA meM prayukta kiye taba vaha vAstava meM aparivartita nahIM rahatI hai| bhAskara ne aise zUnya bhAgoM ko khahara kahA hai aura usakA mAna ayathArtha ananta diyA hai| mahAvIrAcArya spaSTataH socate haiM ki zUnya dvArA bhAjana, bhAjana hI nahIM / DAkTara hIrAlAla jaina ne isa para yaha sujhAva diyA hai ki sambhavataH graMthakAra kA aise bhAjana se nimnalikhita abhiprAya ho mAnalo 20 vastue~ 5 vyaktiyoM meM baoNTanA hai, taba pratyeka vyakti ko 4 vastue~ upalabdha hoNgii| yadi ina 20 vastuoM kA vibhAjana 0 ( zUnya ) vyaktiyoM meM karanA ho taba koI vyakti hI na rahane seM vaha saMkhyA aparivartita rhegii| (52) yaha sUtra mahAvIrAcArya kI sUkSma aMtardRSTi kA prarUpaka hai| isake viSaya meM hama prastAvanA meM hI saMketa kara cuke haiN| sAdhAraNataH kisI dhanAtmaka rAzi kA vargamUla nikAlane para (dhanAtmaka evaM RNAtmaka) do rAziyA~ utpanna hotI haiM, unameM se iSTa phala prApti ke liye dhanAtmaka yA RNAtmaka vargamUla grahaNa karanA upayukta hotA hai| isa prakAra graMthakAra dvArA nirdiSTa yaha niyama bhI unakI pratibhA kA nirUpaka hai|

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* ] gaNitasArasaMgrahaH [ 1.61 nava nandaM ca randhaM ca padArthaM labdhakezavau / nidhiratnaM grahANaM ca durgAnAma ca saMkhyayA // 61 // AkAzaM gaganaM zUnyamambaraM khaM nabho viyat / anantamantarikSaM ca viSNupAdaM divi smaret // 62 // atha sthAnanAmAni ekaM tu prathamasthAnaM dvitIyaM dazasaMjJikam / tRtIyaM zatamityAhuH caturthaM tu sahasrakam ||63 || paJcamaM dazasAhasraM SaSThaM syAllakSameva ca / saptamaM dazalakSaM tu aSTamaM koTirucyate || 64 || navamaM dazakoTyastu dazamaM zatakoTayaH / arbudaM rudrasaMyuktaM nyarbudaM dvAdazaM bhavet || 65 // khavaM trayodazasthAnaM mahAkhavaM caturdazam / padmaM paJcadazaM caiva mahApadmaM tu SoDazam ||66 || kSoNI saptadazaM caiva mahAkSoNI dazASTakam / zaGkhaM navadazaM sthAnaM mahAzaGkhaM tu viMzakam || 67 || kSityaikaviMzatisthAnaM mahAkSityA dviviMzakam / triviMzakamatha kSobhaM mahAkSobhaM caturnayam // 68 // atha gaNakaguNanirUpaNam laghukaraNohApohAnAlasyagrahaNadhAraNopAyaiH / vyaktikarAGkaviziSTairgaNako'STAbhirguNairjJeyaH // 69 // iti saMjJA samAsena bhASitA munipuGgavaiH / vistareNAgamAdvedyaM vaktavyaM yaditaH param // 70 // iti sArasaMgrahe gaNitazAstre mahAvIrAcAryasya kRtau saMjJAdhikAra samAptaH // ye haiM / ve yahA~ anuvAdita nahIM kiye gaye haiM // 53-62 // sthAna-nAmAvali [ saMketanAtmaka sthAnoM ke nAma ] prathama sthAna vaha hai jo eka ( ikAI ) kahalAtA hai, dUsarA sthAna daza ( dahAI ), tIsarA sthAna zata ( saikaDA ) aura cauthA sahasra (hajAra ) kahalAtA hai // 63 // pA~cavA dasa sahasra ( dasa hajAra ), chaTavA~ lakSa ( lAkha ), sAtavA~ dazalakSa ( dasa lAkha ) aura AThavA~ koTi ( karor3a ) kahalAtA hai // 64 // nauvA~ dazakoTi (dasa karor3a) aura dasavA~ zatakoTi ( sau karor3a ) kahalAtA hai| gyArahavA~ sthAna ( araba ) aura bArahavA~ nyarbuda ( dasa araba ) kahalAtA hai // 65 // terahavA~ sthAna kharva (kha) caudahavA~ mahAkharva ( dasa kharaba ) kahalAtA hai / isI taraha, paMdrahavA~ padma aura solahava kahalAtA hai // 66 // punaH satrahavA~ kSoNI, aThArahavA~ mahAkSoNI kahalAtA hai / unnIsavA~ sthAna bIsavA~ mahAzaGkha kahalAtA hai // 67 // ikkIsavA~ sthAna kSityA bAIsavA~ mahAkSityA kahalAtA hai / teIsavA~ kSobha aura caubIsavA~ mahAkSobha kahalAtA hai // 68 // aura gaNakaguNanirUpaNa nimnalikhita ATha guNoM se gaNitajJa kI pahicAna hotI hai (1) laghukaraNa -- hala karane meM zIghra gati, (2) Uha -- agravikalpa, ki icchita phala prApta ho sakegA, (3) apoha - agravikalpa, ki icchita phala prApta nahIM hogA, (4) anAlasya - pramAda na honA, (5) grahaNa - samajhane kI zakti, (6) dhAraNa - smaraNa rakhane kI zakti, (7) upAya - sAdhana karane kI naI rItiyA~ khojanA, evaM (8) vyaktikarAGka - una saMkhyAoM taka pahu~cane kA sAmarthya rakhanA jo ajJAta rAziyoM ko jJAta banA sakeM // 69 // isa prakAra, muni puGgavoM ne saMkSepa meM paribhASAoM kA kathana kiyA hai| jo kucha isake viSaya meM Age vistAra rUpa se kahA jAnA cAhie use Agama' ke adhyayana se jJAta karanA cAhiye / isa prakAra, mahAvIrAcArya kI kRti sArasaMgraha nAmaka gaNita-zAstra meM, saMjJA adhikAra samApta huA // 70 // 1 yahA~ Agama kA Azaya, sambhavataH jinAgama praNIta alaukika gaNita se ho jisake viSaya meM graMthakAra dvArA mAtra yahIM saMketa kiyA gayA pratIta hotA hai /

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-2. 1 ] parikarmavyavahAraH 2. parikarmavyavahAraH itaH paraM parikarmAbhidhAnaM prathamavyavahAramudAhariSyAmaH / pratyutpannaH tatre prathame pratyutpannaparikarmaNi karaNasUtraM yathAguNaguNena guNyaM kavATa saMdhikrameNai saMsthApya / rAzyarghakhaNDatatsthairanuloma viloma mArgAbhyAm ||1|| 1 K tatra ca / 2 K aura B vinyasyobhau rAzI / 3 K aura B saguNayet / 2. parikarma vyavahAra [ aGkagaNita sambandhI kriyAe~ ] isake pazcAt, hama parikarma nAmaka prathama vyavahAra prakaTa karate haiN| pratyutpanna (guNana ) parikarma kriyAoM meM prathama guNana ke kriyA-sambandhI niyama nimnalikhita haiM jisa taraha daravAje kI koreM rahatI haiM, usI prakAra guNya aura guNaka ko eka-dUsare ke nIce rakhakara, guNya ko guNaka se do rItiyoM ( anuloma athavA viloma krama se hala karane kI vidhiyoM ) meM se kisI eka dvArA guNita karanA cAhiye / prathama vidhi meM guNya ke khaMDa dvArA guNya ko vibhA jita aura guNaka ko guNita karate haiM / dvitIya vidhi meM, guNaka ke khaMDa dvArA guNaka ko vibhAjita tathA guNya ko guNita karate / tRtIya vidhi meM unheM usI rUpa meM lekara guNana karate haiM // 1 // ( 1 ) pratIka rUpa se yaha niyama isa prakAra hai'aba' ko 'sada' se guNA karane para guNanaphala ( i ) aba a x (a x sada); yA (ii) (aba x sa) X sava yA (ii) aba X sada hotA hai / yaha spaSTa hai ki prathama do vidhiyoM ko uparyukta guNanakhaNDoM ke cunAva dvArA kriyA ko sarala karane ke upayoga meM lAte haiM / anuloma, athavA hala karane kI sAmAnya vidhi vaha hai jo vyApaka rUpase upayoga meM lAI jAtI hai / viloma vidhi nimnalikhita hai 1998 27 1998 meM 27 kA guNA karane ke liye pratyeka staMbha kA yoga karane para uttara 53946 prApta hotA hai ga0 sA0 saM0-2 241 249 2x9 248 71 79 79 0X6 2 * 1 8 1 6) me you [3 3 9 5 4

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10] gaNitasArasaMgrahaH [2.2 atroddezakaH dattAnyekaikasmai jinabhavanIyAmbujAni tAnyaSTau / vasatInAM caturuttaracatvAriMzacchatAye kati // 2 // nava padmarAgamaNayaH samarcitA ekajinagRhe dRssttaaH| sASTAzItidvizatImitavasatiSu te kiyantaH syuH // 3 // catvAriMzaccaikonazatAdhikapuSyarAgamaNayo'AH / ekasmin jinabhavane sanavazate brUhi kati maNayaH / / 4 / / padmAni saptaviMzatirekasmin jinagRhe pradattAni / sASTAnavatisahasraM sanavazate tAni kati kathaya / / 5 // ekaikasyAM vasatAvaSTottarazatasuvarNapadmAni / ekASTacatuH saptakanavaSaTpazcASTakAnAM kim // 6 // zazivasukharajalanidhinavapadArthabhayanayasamUhamAsthApya / himakaraviSanidhigatibhirguNite kiM "rAziparimANam // 7 // himagupayonidhigatizazivahnivratanicayamatra saMsthApya / saikAzItyA tvaM me guNayitvAcakSva tatsaMkhyAm // 8 // agnivasukharabhayendriyazazalAJchanarAzimatra saMsthApya / randhairguNayitvA me kathaya sakhe rAziparimANam / / 9 // 1 B sya hi / 2 B nsyaa| 3 B zatasya kati bhavanAnAm / 4 MB catvAriMzadvayakA zatAdhikA / 5 M'cchaaH| 6 M te kiyntssyuH| 7 M ekaikajinAlayAya dattAni / 8M prayuktanavazatagRhANAM kim / 9 ( yaha zloka kevala M aura B meM prApya hai)| 10 M aura B kintasya / 11 M pyam / 12 M aho / 13 M me zIghram / 14 B vinyasya / udAharaNArtha prazna pratyeka jinamandira meM ATha-ATha kamala puSpa car3hAye gye| batalAo ki 144 maMdiroM ko kitane diye gaye ? // 2 // nau padmarAga maNi kevala eka jinamandira meM pUjana meM arpita kiye hue dekhe jAte haiM / 288 maMdiroM meM (usI dara se) kitane arpita kiye gaye // 3 // eka jinamaMdira meM 139 puSyarAgamaNi pUjana meM bheMTa kiye jAte haiM / batalAo, 109 maMdiroM meM kitane maNi bheMTa kiye gaye? [ mUla gAthA meM 139 ko 100+40-1 rUpa meM likhA huA hai] // 4 // 27 kamala ke phUla eka jinamaMdira meM bheMTa kiye gaye / batalAo ki isa dara se 1998 maMdiroM meM kitane kamala bheMTa kiye gaye ? [ mUla gAthA meM 1998 ko 1098+900 likhA hai ] // 5 // pratyeka maMdira ko 108 svarNa kamala bheMTa kI dara se, 85697481 maMdiroM meM kitane diye jAyeMge ? // 6 // 1, 8, 6, 4, 9, 9, 7 aura 2 aMkoM ko ikAI ke sthAna se lekara Upara ke sthAnoM taka rakhane se banAI gaI saMkhyA ko 441 se guNita karane para kyA phala prApta hogA ? // 7 // isa prazna meM, 1, 4, 4, 1, 3 aura 5 aMkoM ko ikAI ke sthAna se lekara Upara ke sthAnoM taka rakhakara, prApta kI huI saMkhyA ko 81.se guNita karo aura batalAo ki kauna sI saMkhyA prApta hogI ? // 8 // isa prazna meM 157683 saMkhyA likhakara use 9 se guNita karo aura taba, he mitra ! mujhe batalAo ki guNanaphala rAzi kyA hogI? // 9 // isa prazna meM 12345679 saMkhyA ko 9 se guNita karate haiN| yaha guNanaphala rAzi AcArya mahAvIra ke kathanAnusAra, narapAla ke kaNTha AbharaNa

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[11 -2. 17 ] parikarmavyavahAraH nandAyatuzaracatutidvandvakaM sthApyamatra navaguNitam / AcAryamahAvIraiH kathitaM narapAlakaNThikAbharaNam // 10 // SatrikaM paJcaSaTakaM ca sapta cAdau pratiSThitam / trayastriMzatsaMguNitaM kaNThAbharaNamAdizait // 11 // hutavahagatizazimunibhirvasunayagaticandramatra saMsthApya / zailena tu guNayitvA kathayedaM ratnakaNThikAbharaNam // 12 // analAbdhihimagumunizaraduritAkSipayodhisomamAsthApya / zailena tu guNayitvA kathaya tvaM rAjakaNThikAbharaNam // 13 / / giriguNadivigiriguNadivigiriguNanikaraM tathaiva guNaguNitam / punarevaM guNaguNitam ekAdinavottaraM viddhi // 14 // sapta zUnyaM de'yaM dvandvaM paJcaikaM ca pratiSThitam / trayaH saptatisaMguNyaM" kaNThAbharaNamAdizet // 15 // jalanidhipayodhizazadharanayanadravyAkSinikaramAsthApya / guNite tu catuHSaSTayA kA saMkhyA gaNitavidvahi // 16 // zazAGkendukhaikenduzUnyaikarUpaM nidhAya krameNAtra rAzipramANam / himAMzvagrarandhaiH prasaMtADite'smin bhavetkaNThikA rAjaputrasya yogyA // 17 // iti parikarmavidhau prathamaH pratyutpannaH samAptaH / 1zloka 10 se 15 taka kevala M aura B meM prApya haiM / 2 sabhI hastalipiyoM meM 'sthApya tatra pATha hai| 3 B she| 4 B nayaM 1. sabhI hastalipiyoM meM chaMda rUpeNa azuddha pATha "kaNThAbharaNaM vinirdizetU, hai| kI racanA karatI hai // 10 // 3 ko chaH bAra, 6 ko pA~ca bAra, aura 7 ko eka bAra avarohI krama se (ikAI ke sthAna kI ora) likhakara, isa saMkhyA kA 33 se guNana karane para eka prakAra ke hAra kI saMkhyA prApta hotI hai // 11 // isa prazna meM, 3, 4, 1, 7, 8, 2, 4 aura 1 aMkoM ko ikAI ke sthAna se Upara kI ora ke krama meM likhane para saMkhyA kA 7 se guNana karo; aura taba kaho ki vaha ratna kaMThikA nAmaka AbharaNa hai // 12 // 142857143 saMkhyA ko likhakara use 7 se guNita karo; aura taba kaho ki vaha rAjakaNThikA AbharaNa hai / / 13 // isI taraha, 37037037 ko 3 se guNita karo / isa gaNanaphala ko phira guNita karo tAki guNaka kramazaH eka se lekara 9 taka hoN||14|| 7, 0,2, 2, 5 aura 1 aMkoM ko (ikAI ke sthAna se Upara kI ora ke krama meM ) rakhate haiM / aura isa saMkhyA ko 73 se guNita karate haiN| prApta saMkhyA ko kaNTha AbharaNa kahate haiM // 15 // ikAI ke sthAna se Upara kI ora aMka 4, 4, 1,2,6 aura 2 kramAnusAra likhakara, prarUpita saMkhyA ko 64 se guNita karane para he gaNita vidra hi, batalAo ki kauna sI saMkhyA prApta hogI ? // 16 // isa prazna meM, ikAI ke sthAna se Upara kI ora 1,1,0,1,1,0,1 aura 1 aMkoM ko kramAnusAra rakhane se eka vizeSa saMkhyA kA mAna hotA hai; aura taba isa saMkhyA meM 91 kA guNA karane para rAjaputra ke yogya kaNThahAra prApta hotA hai // 17 // isa prakAra, parikarma vyavahAra meM, pratyutpanna nAmaka pariccheda samApta huaa| (10) isameM tathA anya gAthAoM meM kucha saMkhyAe~ vibhinna prakAra ke hAroM kI racanA karatI haI mAnI gaI haiN| kyoMki unameM eka se aMkoM kA zIghra hI dRSTigocara honevAlA sammitIya vinyAsa rahatA hai| (11) yahA~ guNya 333333666667 hai / (14) yaha prazna, svataH, isa rUpameM avatarita ho jAtA hai : 37037037 4 3 ko 1, 2, 3, 4, 5, 6,7,8 aura 9 dvArA kramAnusAra guNita kro|

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gaNitasArasaMgrahaH [2. 18 bhAgahAraH dvitIye bhAgahArakarmaNi karaNasUtraM yathA'vinyasya bhAjyamAnaM tasyAdhaHsthena bhAgahAreNa / sadRzApavartavidhinA bhAgaM kRtvA phalaM pravadet / / 18 / / athavApratilomapathena bhajedbhAjyamadhaHsthena bhaaghaarenn| sadRzApavartanavidhiryadyasti vidhAya tamapi tyoH|19|| atroddezakaH dInArASTasahasraM dvAnavatiyutaM zatena saMyuktam / caturuttaraSaSTinarairbhaktaM ko'zo nurekasya // 20 // rUpAgrasaptaviMzatizatAni kanakAni yatra bhAjyante / saptatriMzatpuruSairekasyAMza mamAcakSva // 21 // dInAradazasahasraM trizatayutaM saptavargasaMmizram / navasaptatyA puruSairbhaktaM kiM labdhamekasya // 22 // ayutaM catvAriMzaJcatussahastraikazatayutaM hemnAm / navasaptativasatInAM dattaM vittaM kimeksyaaH||23|| saptadazatrizatayutAnyekatriMzatsahasrajambUni / bhaktAni navatriMzannarairvadaikasya bhAgaM tvam / / 24 / / 1 yaha zloka P meM prApya nahIM hai / 2 . sa / 3 M ko'zo nurekasya / 4 yaha zloka P meM prApya nahIM hai / 5 B aura K hemam / 6 isa zloka meM diye gaye prazna kA pATha M meM nimna prakAra hai trizatayutaikatriMzatsahasrayuktA dazAdhikAH sapta / bhaktAzcatvAriMzatpuruSairekonaistatra dInAram // bhAgahAra [ bhAga] parikarma kriyAoM meM dvitIya. bhAgahAra kriyA kA niyama nimnalikhita hai bhAjya ko likhakara use ubhayaniSTha (sAdhAraNa) guNanakhaMDoM ko alaga karane ke rIti ke anusAra bhAjaka dvArA bhAjita kro| bhAjaka ko bhAjya ke nIce rakho aura taba, pariNAmI bhajanaphala ko prApta karo // 18 // athavA-yadi sambhava ho, to ubhayaniSTha guNanakhaMDa ko nirasita karane kI vidhi se, bhAjya ke nIce bhAjaka ko rakhakara.bhAjya ko pratiloma vidhi se arthAt bAyeM se dAyeM bhAjita karanA cAhiye // 19 // udAharaNArtha prazna 64 vyaktiyoM meM 8192 dInAra bA~Te gaye haiN| pratyeka vyakti ke hisse meM kitane Aye haiM ? // 20 // mujhe eka vyakti kA hissA batalAo jaba ki 2701 svarNa ke Tukar3e 37 vyaktiyoM meM bA~Te jAte haiM / // 21 // 10349 dInAra 79 vyaktiyoM meM bA~Te jAte haiN| batalAo eka vyakti ko kyA prApta hogA? // 22 // 14141 svarNa ke Tukar3e 79 maMdiroM meM diye jAte haiN| batalAo pratyeka maMdira meM kitanA dhana diyA jAtA hai ? // 23 // 31317 jambU phala (gulAbI seva ) 39 vyaktiyoM meM bA~Te gaye haiN| pratyeka kA aMza ( hissA) batalAo ? // 24 // 31313 jambU phala 181 vyaktiyoM meM bA~Te gaye haiN| pratyeka kA aMza (20) mUla gAthA meM 8192 ko 8000 + 92+ 100 dvArA likhita kiyA gayA hai| (22) mUla gAthA meM 10349 ko 10000+300 + (7) dvArA nidarzita kiyA gayA hai| (23) yahA~ 14141 ko 10000 + (40 + 4000+1+100) dvArA kathita kiyA gayA hai| (24) yahA~ 31317 ko 17 + 300 +31000 dvArA darzAyA gayA hai|

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-2. 29 ] parikarmavyavahAraH [ 13 yadhikadazatrizatayutAnye katriMzatsahasrajambUni / saikAzItizatena prahRtAti narevaidaikAMzam ||25|| tridazasahasrI saikASaSTidvizatI sahasraSaTkayutA / ratnAnAM navapuMsAM dattaikanaro'tra kiM labhate ||26|| asara krameNa hInAni hATakAni sakhe / vidhujaladhibandhasaMkhyairnarairhRtAnyekabhAgaH kH||27|| yazItimizrANi catuHzatAni catussahasraghnanagAnvitAni / ratnAni dattAni jinAlayAnAM trayodazAnAM kathayaikabhAgam ||28|| iti parikarmavidhau dvitIyo bhAgahAraH samAptaH // vargaH tRtIye vargaparikarmaNikaraNasUtraM yathA dvisamavadho ghAto vA sveSTonayutadvayasya seSTakRtiH / ekAdvicayecchAgacchayutirvA bhavedvargaH ||29|| 1 yaha zloka kevala M meM prApya hai / RM ekadvitricatuHpaJcaSaT kaihIMnAH krameNa saMbhaktAH / saikacatuHzatasaMyutacatvAriMzajinAlayAnAM kim || batalAo ? ||25|| 36261 maNi 9 vyaktiyoM ko barAbara-barAbara diye jAte haiN| eka vyakti kitane maNi prApta karatA hai ? ||26|| he mitra, eka se Arambha kara 6 taka ke aMkoM ko ikAI ke sthAna se Upara kI ora ke krama meM rakhakara aura phira kramAnusAra hAsita aMkoM dvArA saMracita saMkhyA kI suvarNa mudrAe~ 441 vyaktiyoM meM vitarita kI jAtI haiN| pratyeka ko kitanI milatI haiM ? ||27|| 28483 maNi 13 jina maMdiroM meM bheMTa svarUpa diye jAte haiM / pratyeka maMdira ko kitanA aMza prApta hotA hai ? ||28|| isa prakAra, parikarma vyavahAra meM, bhAgahAra [ bhAga ] nAmaka pariccheda samApta huaa| varga parikarma kriyAoM meM tRtIya [ varga karane kI kriyA ] ke niyama nimnalikhita haiM do sama rAziyoM kA guNanaphala; athavA do sama rAziyoM meM se kisI eka cunI saMkhyA ko prathama rAzi meM se ghaTAkara prApta phala tathA dUsarI rAzi meM usa cunI huI saMkhyA ko jor3ane se prApta phala, ina donoM phaloM ke guNanaphala meM usa cunI huI saMkhyA kA vargaphala jor3ane para prAptaphala, athavA, guNottara Dhi ( jisameM prathamapada 1 hai aura pracaya 2 hai ) kA a padoM taka kA yogaphala, usa icchita rAzi kA varga hotA hai ||29|| do yA tIna yA isase adhika saMkhyAoM kA varga, una saba saMkhyAoM ke varga ke yoga (25) yahA~ 31313 ko 13+300 + 31000 dvArA darzAyA gayA hai / (26) yahA~ 36261 ko 30000+1+ (60 + 200 + 6000) dvArA darzAyA gayA hai / (27) yahA~ diyA gayA bhAjya, spaSTa rUpa se, 12345654321 hai / (28) yahA~ 28483 ko 83 + 400 + (4000 X 7) dvArA nirUpita kiyA gayA hai / (29) bIjagaNita dvArA batalAye jAne para yaha niyama isa taraha kA rUpa letA hai (i) a x a = a ' (iii) (a + ka) (a ka ) + kara = a (iii) 1+3+5+7+... a padoM taka = are

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gaNitasArasaMgrahaH [2.30 dvisthAnaprabhRtInAM rAzInAM sarvavargasaMyogaH / teSAM kramaghAtena dviguNena vimizrito vargaH // 30 // kRtvAntyakRtiM hanyAccheSapadairdviguNamantyamutsArya / zeSAnutsAyaivaM karaNIyo vidhirayaM varge // 31 // atroddezakaH ekAdinavAntAnAM paJcadazAnAM dvisaMguNASTAnAm / vratayugayozca rasAgnyoH zaranagayorvargamAcakSva // 32 / / sASTAviMzatrizatI catuHsahasbaikaSaSTiSaTchatikA / dvizatI SaTpaJcAzanmizrA vargIkRtA kiM syAt / / 3 / / lekhyAguNeSubANadravyANAM shrgtitrisuuryaannaam| guNaratnAgnipurANAM varga bhaNa gaNaka yadi vetsi // 34 / / tathA una saMkhyAoM ko eka bAra meM do lekara unake dugune guNanaphala ke yoga ko milAne ke barAbara hotA hai||30|| dAhinI ora se bAI ora ko aGka ginane ke krama meM saMkhyA ke antima aGka kA varga prApta karo, aura taba isa aGka ko dviguNita kara tathA eka saMketanA ke sthAna taka dAhinI ora haTA dene ke pazcAt , isa antima aGka ko zeSa sthAnoM ke aGkoM dvArA guNita kro| isa taraha saMkhyA ke zeSa aGkoM meM pratyeka ko eka-eka sthAna taka isI vidhi se haTAte jAo / yaha varga karane kI vidhi hai||31|| udAharaNArtha prazna se lekara 9 taka tathA 15, 16, 25, 36 aura 75-ina saMkhyAoM ke varga kA mAna nikAlo // 32 // 338,4661 aura 256 kA varga karane para kyA-kyA prApta hogA ? // 33 // he gaNitajJa ! yadi tuma jAnate ho to batalAo ki 65536, 12345 aura 3333 ke varga kyA hoMge? // 34 // (30) yahA~ sthAna zabda kA spaSTa artha saMketanA sthAna hotA hai| yahA~ eka TIkA ke nirvacana ke anusAra vaha yoga ke vighaTakoM kA bhI dyotaka hai, kyoMki yoga meM pratyeka aise bhAga kA sthAna hotA hai| ina donoM nivarcanoM ke anusAra niyama ThIka utaratA hai| jaise : (1234)2 = (10002 + 2002+302+42) + 2410004 200 + 24 1000 430 +241000 44 + 24 2004 30 + 24 20044 + 243044 isI taraha, (1+2+3+4)2 = (12+2+32 + 42) + 2(142+143 + 144 +243+244+344) (31) nimnalikhita sAdhita udAharaNoM dvArA dAhine ora haTAne kA ullikhita niyama spaSTa ho jaavegaa| yaha mahAvIra kI maulika vidhi hai| ina gaNanAoM meM stambhoM kA yoga isa prakAra kiyA jAve ki kisI bhI stambha ke dahAI ke aMka bAMI ora ke stambha meM jor3e jAveM / 131 kA varga nikAlanA 132 kA varga karanA 555 kA varga krnaa| 12= 52= 24143 = 24143= 24545= 241x1= 2x2x2% 24545% // 24341 // 24342% 24545%3 22 = 17 161 17424 / 3080 25 (33) mUla gAthA meM 4661 ko 4000+6+600 dvArA nirUpita kiyA gayA hai|

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-2.36] parikarmavyavahAraH saptAzItitrizatasahitaM SaTsahasraM punazca paJcatriMzacchatasamadhikaM saptanighnaM sahasram / dvAviMzatyA yutadazazataM vargitaM tatrayANAM brUhi tvaM me gaNakaguNavansaMguNayya pramANam / / 35 / / . iti parikarmavidhau tRtIyo vargaH samAptaH / vargamUlam caturthe vargamUlaparikarmaNi karaNasUtraM yathAantyaujAdapahRtakRtimUlena dviguNitena yugmahatau / labdhakRtistyAjyauje dviguNadalaM vargamUlaphalam // 36 / / 1P, K aura B rAziretatkRtInAm / 6387 aura taba 7135 aura taba 1022, inameM se pratyeka saMkhyA kA varga kiyA jAtA hai / he kuzala gaNitajJa ! acchI taraha gaNanA karane ke pazcAt mujhe batalAo ki ina tInoM ke varga kyA hoMge? // 35 // isa taraha, parikarma vyavahAra meM, varga nAmaka pariccheda samApta huaa| vargamUla parikarma kriyAoM meM vargamUla nAmaka caturtha kriyA ke sambandha meM nimnalikhita niyama haiM aMkoM dvArA pradarzita saMkhyA kI ikAI ke sthAna se bAI ora ke antima ayugma (viSama ) aMka meM se bar3I se bar3I varga saMkhyA ( aMka) ghaTAI jAtI hai| taba isa varga kI huI saMkhyA ko dviguNita kara prApta phala dvArA, zeSa saMkhyA ke sAtha dAhine yugmasthAna kI saMkhyA utAra kara rakhane ke pazcAt prApta huI saMkhyA meM bhAga dete haiN| aura taba, isa taraha prApta bhajanaphala kA varga, zeSa saMkhyA ke sAtha dAhine ayugma sthAna kI saMkhyA utAra kara rakhane ke pazcAt prApta huI saMkhyA meM se ghaTA dete haiN| taba, prathama vargasaMkhyA kA vargamUla aura dvitIya vargasaMkhyA kA vargamUla, (eka ke bAda dUsarI) dAhinI ora rakhane se prApta saMkhyA ko dviguNita kara zeSa saMkhyA ke nIce utArI huI saMkhyA rakhakara prApta saMkhyA meM bhAga dete haiM; aura phira zeSa saMkhyA ke sAtha utArI huI saMkhyA rakhakara prApta saMkhyA meM se sabase bar3I vargasaMkhyA ghaTAte haiN| isa prakAra, yaha kriyA aMta taka kI jAtI hai aura aMtima dviguNita bhAjaka saMkhyA kI arddha saMkhyA, pariNAmI vargamUla hotA hai // 36 // (35) yahA~ 7135 ko 135 + (100.47) dvArA darzAyA gayA hai| (36) isa niyama ko spaSTa karane hetu nimnalikhita udAharaNa nIce sAdhita kiyA jAtA hai| 65536 kA vargamUla nikaalnaa-655|36 22=4 242%4) 25 (5 52-25 2542=501303/6 .:. vargamUla = "32 = 256 / 36 25642=51200 /

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16] gaNitasArasaMgrahaH [2.37atroddezakaH ekAdinavAntAnAM vargagatAnAM vadAzu me mUlam / RtuviSayalocanAnAM dravyamahIdhendriyANAM ca // 37 // ekAgraSaSTisamadhikapazcazatopetaSasahasrANAm / SaDvargapaJcapaJcakaSaNNAmapi mUlamAkalaya // 38 / / dravyapadArthanayAcalalekhyAlabdhyabdhinidhinayAbdhInAm / zazinendriyayuganayajIvAnAM cApi kiM mUlam // 39 // candrAbdhigatikaSAyadravyartuhutAzanarturAzInAm / vidhulekhyendriyahimakaramunigirizazinAM ca mUlaM kim // 40 // dvAdazazatasya mUlaM SaNNavatiyutasya kathaya saMcintya / zataSaTakasyApi sakhepazcakavargaNa yuktasya // 41 / / aGkebhakarmAmbarazaMkarANAM somAkSivaizvAnarabhAskarANAma / candratuMbANAbdhigatidvipAnAmAcakSva mUlaM gaNakAgraNIstvam / / 42 // ___iti parikarmavidhau caturtha vargamUlaM samAptam // ghanaH paJcame ghanaparikarmaNi karaNasUtraM yathAtrisamAhatirghanaH syAdiSTonayutAnyarAzighAto vaa| alpaguNiteSTakRtyA kalito vRndena ceSTasya // 4 // iSTAdidviguNeSTapracayeSTapadAnvayo'tha veSTakRtiH / vyekeSTahataikAdidvicayeSTapadaikyayuktA vA // 44 // 1P aura M vargagatAnAM zIghraM rUpAdinavAvasAnarAzinAm / mUlaM kathaya sakhe tvaM / 2 1 nava / udAharaNArtha prazna he mitra! mujhe zIghra batalAo ki 1 se lekara 9 taka kI vargasaMkhyAoM, tathA 256 aura 576 ke vargamUla kyA haiM ? // 37 // 6561 aura 65536 ke vargamUla nikAlo // 38 // 4294967296 aura 622521 ke vargamUla kyA haiM ? // 39 // 63664441 aura 1771561 ke vargamUla kyA haiM ! // 40 // he mitra ! bhalIbhA~ti socakara mujhe batalAo ki 1296 aura 625 ke vargamUla kyA haiM ? // 41 // he gaNitajJoM meM agraNI ! 110889, 12321 aura 844561 ke vargamUla batAo? // 42 // isa prakAra, parikarma vyavahAra meM, vargamUla nAmaka pariccheda samApta huaa| ghana parikarma kriyAoM meM, paJcama ghana nAmaka kriyA kA niyama nimnalikhita hai koI tIna barAbara rAziyoM kA guNanaphala usa datta rAzi kA dhana hotA hai / athavA, koI dI huI rAzi kA, kisI cunI huI rAzi ko datta rAzi meM jor3ane se prApta phala kA tathA cunI huI rAzi ko datta rAzi meM se ghaTAne se prApta phala kA guNanaphala prApta karate haiN| isameM, cunI huI rAzi ke varga ko datta rAzi meM se cunI huI rAzi ko ghaTAne se prApta phala se guNita karane para prApta guNanaphala aura cunI huI rAzi kA dhana jor3ane para bhI datta rAzi kA dhana prApta hotA hai // 43 // athavA, jisakA prathama pada dI gaI rAzi hai tathA pracaya dI gaI rAzikA dugunA hai aura jisake padoM kI saMkhyA dI huI rAzi ke barAbara hai, aisI samAntara zreDhi kA yoga dI huI rAzi ke dhana ko utpanna karatA hai / athavA, jisa rAzi kA dhana prApta karanA hai usake varga meM, dI gaI rAzi meM se eka ghaTAkara prApta rAzi tathA dI gaI rAzi ke barAbara jisake padoM kI saMkhyA hai (aura jisakA prathama pada eka hai aura pracaya do hai) aisI samAntara zreDhi ke yoga kA guNanaphala milAkara usa dI huI rAzi kA dhana prApta karate haiM // 4 // (43) pratIka rUpa se yaha niyama (nirUpita karane para ) isa taraha sAdhita hotA hai: (i) aXaxxx = a (ii) a (a+ba) (a-ba)+ba (a-ba)+ba' =a (44) bIjagaNita se niyama kA artha : (i) a' a+3 +5 +a+..'a padoM tk| (ii) a = a + (a-1)(1+3+5+7+ 'a padoM taka)

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-2. 47 ] parikarmavyavahAraH [17 ekAdicayeSTapade pUrva rAziM pareNa saMguNayet / guNitasamAsatriguNazcarameNa yuto ghano bhavati // 45 // antyAnyasthAnakRtiH parasparasthAnasaMguNA trihtaa| punarevaM tadyogaH sarvapadaghanAnvito vRndam // 46 / / antyasya ghanaH kRtirapi sA trihatotsArya zeSagaNitA vaa| zeSakRtistryantyahatA sthApyotsAyaivamatra vidhiH // 47 // 1P meM yaha zloka prApya nahIM hai| 2 Mdegrpi| 3 Mdeggo vA / 4 yaha zloka M meM chUTa gayA hai| PK B meM nimnalikhita zloka pAThAntara rUpa meM prApya hai| uparyukta do vidhiyoM kA ullekha isameM bhI hai| trisamaguNo'ntyasya dhanastadvargastriguNito hataH zeSaiH / utsArya zeSakRtiratha niSThA triguNA ghanastathAgre vA / / samAntara rUpa se bar3hatI huI zreDhi meM (jisakA prathama pada eka hai tathA pracaya bhI eka hai aura padoM kI saMkhyA koI dI gaI rAzi ke barAbara hai), pratyeka pichale pada ko agale pada se guNA kara prApta guNanaphaloM kA yoga prApta kara prApta yogaphala ko tIna se guNita karate haiN| isa prakAra prApta guNanaphala meM zreDhi kA aMtima pada jor3ane para, dI huI rAzi kA dhana prApta hotA hai // 45 / / (jina do athavA adhika rAziyoM ke yoga kA ghana nikAlanA hai, unheM alaga-alaga sthAnoM meM sthApita karate haiN| ) prathama tathA anya sthAnoM ke varga nikAlakara unameM pratyeka ko anya sthAnoM kI rAziyoM se guNita kara tiguNA karate haiM aura jor3a dete haiM / isa prakAra prApta yogaphala meM saba sthAnoM kI rAziyoM meM se pratyeka ke dhana ko milAte haiM to datta rAziyoM ke yoga kA ghanaphala prApta hotA hai| (isa sUtra dvArA graMthakAra kA abhiprAya 236 jaisI saMkhyA kA ghanaphala, use (200+30+6) rUpa meM parivartita kara ina tIna rAziyoM ke yoga kA ghanaphala nikAlakara prApta karanA hai|)||46|| athavA; dI gaI saMkhyA meM dAhinI ora se bAI ora kI ginatI meM antima aMka kA ghana; aura antima aMka ke varga kI tigunI rAzi ko kevala eka saMketanA sthAna dvArA dAhinI ora haTAyA jAtA hai aura zeSa sthAnoM meM pAye jAne vAle aMkoM dvArA guNita kiyA jAtA hai ; taba Upara kI bhA~ti zeSa sthAnoM meM pAye jAne vAle aMkoM kA varga kevala eka saMketanA dAhinI ora haTAyA jAtA hai aura Upara kathita antima aMka kI tiganI rAzi dvArA use guNita kara eka sthAna haTA kara rakhA jAtA hai| ye rAziyA~ isI sthiti meM jor3a dI jAtI haiN| yaha niyama yahA~ prayojya hotA hai // 7 // (45) 3 [142+243 + 344 + 445 + ..' + a-14 a} + a = a] (46) 3 aba+3 aba+a+ba' (a+ba) / isa niyama ko do se adhika sthAna vAlI saMkhyAoM ke liye prayojya banAne ke hetu yahA~ spaSTataH artha nikalatA hai ki 3 a (ba+sa)+ 3 a (ba+sa)2+a + (ba+sa) -(a+ba+sa): aura yaha spaSTa hai ki koI bhI saMkhyA do anya upayukta rUpa se cunI huI saMkhyAoM ke yoga dvArA prarUpita kI jA sakatI hai| (47) granyakAradvArA diye gaye sUtra kA abhiprAya pradarzita vidhi se spaSTa ho jAvegAmAna lo 15 ghana kA prApta karanA hai| ise do sthAnoM se sthApita karake, nirUpita rIti se ghanaphala 124345= nikAlate haiN| sUtra meM granthakAra ne antima aMka 5 ke 524341= ghana ke yoga kA kathana nahIM kiyA hai| - - ga0 sA0 saM0-3

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gaNitasArasaMgrahaH [ 2. 44 atroddezakaH ekAdinavAntAnAM paJcadazAnAM zarekSaNasyApi / rasavahnayorgirinagayoH kathaya ghanaM dravyalabdhyozca // 48 // himakaragaganendUnAM nayagirizazinAM kharendubANAnAm / yada municandrayatInAM vRndaM caturudadhiguNazazinAm // 49 // rAzirghanIkRto'yaM zatadvayaM mizritaM tryodshbhiH| tadviguNo'smAstriguNazcaturguNaH paJcaguNitazca // 50 // zatamaSTaSaSTiyuktaM dRSTamabhISTe ghane viziSTatamaiH / ekAdibhiraSTAntyairguNitaM vada taddhanaM zIghram // 51 // bandhAmbarartugaganendriyakezavAnAM saMkhyA: krameNa vinidhAya ghanaM gRhItvA / AcakSva labdhamadhunA karaNAnuyogagambhIrasAratarasAgarapAradRzvan // 52 // iti parikarmavidhau paJcamo ghanaH samAptaH // ghanamUlam SaSThe ghanamUlaparikarmaNi karaNasUtraM yathAantyaghanAdapahRtaghanamUlakRtitrihatibhAjite bhAjye / prAvitrahatAptasya kRtiH zodhyA zodhye ghane'tha dhanam // 53 // 1. 48 aura 49 veM zlokoM ke sthAna meM, M meM nimna pATha hai ekAdinavAntAnAM rudrANAM himakarendUnAm / vada municandrayatInAM vRndaM caturudadhiguNazazinAm / / -------------- udAharaNArtha prazna eka se lekara 9 taka saMkhyAoM aura 15, 25, 36, 77 aura 96 ke ghana kyA hoMge? // 48 // 101, 172, 516, 717 aura 1344 ke ghana kyA hoMge ? // 49 // saMkhyA 213 kA ghana kiyA jAtA hai| isa saMkhyA kI dugunI, tigunI, caugunI aura pAMcagunI rAziyoM ke bhI ghana karane para prApta hone vAlI rAziyA~ prApta karo // 50 // yaha dekhA jAtA hai ki 168 meM eka se lekara ATha taka kI samasta saMkhyAoM kA guNana karane para prApta rAziyA~ dhana rAziyoM se sambandhita haiN| una dhana rAziyoM ko zIghra batalAo // 5 // he karaNAnuyoga gaNita kI kriyAoM ke abhyAsarUpI gahare tathA utkRSTa samudra ke pAradRSTA! dAhinI ora se bAI ora 4, 0, 6, 0, 5 aura 9 kramAnusAra likha kara prApta saMkhyA kA ghanaphala zIghra batalAo // 52 // isa prakAra, parikama vyavahAra meM, ghana nAmaka pariccheda samApta huaa| ghanamUla parikarma-kriyAoM meM SaSThama ghanamUla kriyA sambandhI nimnalikhita niyama hai antima ghana sthAna taka ke aMkoM dvArA nirUpita saMkhyA meM se sabase adhika sambhava ghana saMkhyA ghttaao| taba, (agrima) bhAjya sthAna dvArA nirUpita aMka ko sthiti meM rakhane ke pazcAt use usa dhana ke ghanamUla ke varga kI tigunI rAzi dvArA bhAjita kro| taba (agrima) zodhya sthAna dvArA nirUpita aMka ko sthiti meM rakhane ke pazcAt usameM se uparyukta bhajanaphala ke varga kI triguNita rAzi ko uparyukta ( sabase adhika sambhava ghana ke) mUla dvArA guNita karane se prApta rAzi ko ghttaao| aura taba (agrima) dhana sthAna dvArA nirUpita aMka ko sthiti meM rakhane ke pazcAt usameM se Upara prApta hue bhajanaphaka ke ghana ko ghttaao||53||

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-2. 56] parikarmavyavahAraH [ 19 ghenamekaM dve apane ghanapadakRtyA bhjetrigunnyaaghntH| pUrvatriguNAptakRtistyAjyAptaghanazca pUrvavallabdhapadaiH // 54 // atroddezakaH ekAdinavAntAnAM ghanAtmanAM ratnazazinavAbdhInAm / nagarasavasukha gajakSapAkarANAM ca mUlaM kim / / 55 / / gatinayamadazikhizazinAM muniguNakhatvekSinavakharAgrInAm / vasukhayugakhAdrigatikaricandratUMnAM gRhANa padam / / 56 / / 1 yaha zloka 1 meM prApya nahIM hai / 2 M giri / 3 // rasA / 4 / vidhupurakharasvarartujvalanadharANAM / tIna aMkoM ke vibhinna samUha meM se eka aMka ghana ( cubic) aura do aghana ( non-cubic) hote haiN| aghana aMka meM ghanamUla ke varga kI tigunI rAzi kA bhAga do| agrima aghana aMka meM se. Upara prApta hae bhajanaphala ko vargita karane se prApta huI rAzi tathA pichale ghana aMka meM se (ghaTAI gaI adhika se adhika ghanasaMkhyA ke) ghanamUla kI tigunI rAzi kA guNanaphala ghttaao| aura taba agrima ghana aMka ko sthiti meM lAkara, usameM se Upara prApta hue bhajanaphala kA ghana ghttaao| isa taraha sthiti meM lAkara prApta hue ghanamUla aMkoM kI sahAyatA se pUrva vidhi upayoga meM lAo // 54 // udAharaNArtha prazna 1 se lekara 9 taka kI dhana saMkhyAoM ke ghanamUla kyA hoMge? 4913 aura 1860867 ke ghanamUla batalAo ? // 55 // 13824, 36926037 aura 618470208 ke ghanamUla nikAlo // 56 // (53-54) jisakA ghanamUla nikAlanA hotA hai aisI dI gaI saMkhyA meM aMka niyamAnusAra samUhoM meM vibhakta kara diye jAte haiN| pratyeka samUha meM adhika se adhika 3 aMka hote haiN| unake nAma kramazaH dAhinI ora se bA~I ora : ghana ( athavA vaha jo dhanAtmaka hotA hai arthAt jisameM se ghana rAzi ghaTAnA hotI hai), zodhya (athavA vaha jo ghaTAyA jAtA hai) aura bhAjya haiN| bA~I ora kA aMtima samUha hamezA tIna aMkamaya nahIM hotaa| usameM eka, do, yA tIna aMka taka rahate haiN| nimnalikhita sAdhita udAharaNa se niyama spaSTa ho jaavegaa| 77308776 kA ghanamUla nikAlanA zo. gha. bhA. zo. gha. bhA. zo. gha. 6 4 gha.........43 = bhA......4243 yaha niyama ullekha nahIM karatA ki kauna se aMka ghanamUla kI saMracanA karate haiM / para yaha artha kiyA jAtA hai ki kriyA meM ghana kiye gaye aMkoM ko krama se bA~I ora se dAhinI ora rakhane saMkhyA (ghanamUla) prApta hotI hai| 370 zo...224344... = 48 3228 gha......22....... bhA......422 4 3.. =5292) 32207 (6 31752 zo...6243442...... ...... =4536 216 216 gha....63........ .....= ::.ghanamUla = 426 /

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20 ] gaNita sArasaMgrahaH catuH payodhyagnizarAkSidRSTihaye bhakhavyomabhayekSaNasya / dASTakarmAbdhikhaghAtibhAvadvivahniratnartunagasya mUlam // 57 // dravyAzvazailaduritakhavahnayadribhayasya vadata ghanamUlam / navacandra hima gumunizazilabdhyambarakharayugasyApi // 58 // gatigajaviSayeSuvidhusvarAdrikaragatiyugasya bhaNa mUlam / lekhyAzvanaganavAcalapurakharanayajIvacandramasAm // 59 // gatikharaduritebhAmbhodhitArkSyadhvajAkSadvikRti navapadArthadravyavahnInducandrajaladharapatharandhreSTakAnAM ghanAnAM gaNaka gaNitadakSAcakSva mUlaM parIkSya || 60|| iti parikarmavidhau SaSThaM ghanamUlaM samAptam / saMkalitam [ 2.57 saptame saMkalita parikarmaNi karaNasUtraM yathA- rUpeNono gaccho dalIkRtaH pracayatADito mizraH / prabhaveNa padAbhyastaH saMkalitaM bhavati sarveSAm // 61 // prakArAntareNa dhanAnayanasUtram ekavihIno gacchaH pracayaguNo dviguNitAdisaMyuktaH / gacchAbhyasto dvihRtaH prabhavetsarvatra saMkalitam // 62 / 1 yaha zloka M meM aprApya hai / 270087225344 aura 7632940488 ke ghanamUla prApta karo / / 57 / / 77308776 aura 260917119 ke bhI ghanamUla nikAlo / / 58 / / 2427715584 aura 1626379776 ke ghanamUla nikAlo || 59 // he gaNaka ! yadi tuma gaNita meM kuzala ho to 859011369945948864 ghanarAzi kA ghanamUla parIkSA se nikAlakara batalAo // 60 // isa prakAra, parikarma vyavahAra meM ghanamUla nAmaka pariccheda samApta huA / saMkalita [ zreDhiyoM kA saMkalana ] parikarma kriyAoM meM saptama saMkalita kriyA sambandhI niyama nimnalikhita hai pahile zredi ke padoM kI saMkhyA ko eka dvArA ghaTAyA jAtA hai aura taba prApta phala ko AdhA kara pracaya dvArA guNita kiyA jAtA hai / ise, jaba zreDhi ke prathama pada ke sAtha milAkara padoM kI saMkhyA se guNita karate haiM to samAntara zreDhi ke samasta padoM kA yoga prApta hotA hai || 61 // dUsarI taraha se zreDhi kA yoga prApta karane kA niyama zreDhi ke padoM kI saMkhyA ko eka dvArA hAsita kara pracaya dvArA guNita karate haiM / prApta phala meM ke prathama pada kI dugunI rAzi milAte haiM; aura jaba isa yoga ko zreDhi ke padoM kI saMkhyA se guNita kara do se bhAjita karate haiM, to sarvatra zreDhi kA yoga utpanna hotA hai // 62 // na - 1 (61) yaha niyama bIjIyarUpa se nimnalikhita rUpa meM pradarzita kiyA jA sakatA hai'ba + a na = ya, jahA~ a prathama pada hai; ba pracaya hai, na padoM kI saMkhyA hai aura ya samasta zredi kA yoga hai / - ( 62 ) isI taraha, { { (na - 1)ba + 2 a } na=ya hotA hai / 2

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-2. 64] parikarmavyavahAraH [ 21 AdyuttarasarvadhanAnayanasUtram-- padahatamukhamAdidhanaM vyekapadArthamnacayaguNo gacchaH / uttaradhanaM tayoryogo dhanamUnottaraM mukhe'ntyadhane / / 63 // anyadhanamadhyadhanasarvadhanAnayanasUtramcaiyaguNitaikonapadaM sAdyantyadhanaM tadAdiyogArdham / madhyadhanaM tatpadavadhamuddiSTaM sarvasaMkalitam // 64 / / ? M tadUnA saika (va ? ) padAptA yutiH prabhAvaH / 2 yaha zloka M meM chUTa gayA hai| Adidhana, uttaradhana aura sarvadhana nikAlane kA niyama --- prathama pada meM zreDhi ke padoM kI saMkhyA kA guNana karane se prApta rAzi Adidhana kahalAtI hai| pracaya dvArA gaNita zreDhi ke padoM kI saMkhyA tathA eka kama padoM kI saMkhyA kI AdhI rAzi kA guNanaphala uttara dhana kahalAtA hai| ina donoM kA yoga sarvadhana arthAt samasta zreDhi ke padoM kA yoga hotA hai / vahI aisI zredi ke yoga ke tulya bhI hotA hai jo zreDhi ke padoM kA krama ulaTa diyA jAne se prApta hotI hai, jahAM aMtima pada prathama pada ho jAtA hai tathA pracaya RNAtmaka ho jAtA hai // 63 // antyadhana, madhyadhana tathA sarvadhana nikAlane kI vidhi zreDhi ke padoM kI saMkhyA eka dvArA hAsita kI jAtI hai aura prApta saMkhyA pracaya dvArA guNita kI jAtI hai / taba ise prathama pada meM jor3ane para antyadhana prApta hotA hai| antyadhana aura prathama pada ke yoga kI AdhI rAzi madhyadhana kahalAtI hai| isa madhyadhana aura zreDhi ke padoM kI saMkhyA kA guNanaphala, zreDhi ke samasta padoM kA yoga hotA hai // 6 // (63-64) ina niyamoM meM samAntara zreDhi kA pratyeka pada, prathama pada meM pracaya kA guNaka jor3ane para prApta huA mAnA jAtA hai| isa guNaka kA mAna zredi meM pada vizeSa kI sthiti para nirbhara rahatA hai| isa avadhAraNA ke anusAra hameM zredi ke pratyeka pada meM prathama pada ke sAtha-sAtha pracaya kA guNaka bhI nikAlanA par3atA hai| isa taraha prApta prathama padoM ke yoga ko Adidhana kahate haiN| pracaya ke aise guNakoM ke yoga ko uttaradhana kahate haiN| sarvadhana jo ki ina donoM kA yoga hotA hai, zreDhi kA bhI yoga hotA hai / antyadhana, samAntara zreDhi kA aMtima pada hotA hai| madhyadhana kA artha madhyapada hotA hai jo isa zreDhi ke prathama pada aura aMtima pada kA samAntara-madhyaka (arithmetical mean ) hotA hai| isa taraha, jaba zreDhi meM (2 na+1) pada hote haiM taba (na+ 1) vA~ pada madhyadhana kahalAtA hai| paraMtu, jaba 2na pada hote haiM, to (na) veM aura (na+ 1) 3 pada ke samAntara-madhyaka ke tulya madhyadhana hotA hai| isa taraha, (1) Adidhana =na X a; (2) uttaradhana =1 x na 4 ba; (3) antyadhana = (na - 1) 4 ba + a; ++(5) sarvadhana = (1) + (2) = (na+a) + (24na ba). athavA, sarvadhana = (4)xna =na x {(na - 1) va+a}+ a Age yaha bilakula spaSTa hai ki RNAtmaka pracaya vAlI samAntara zreDhi dhanAtmaka pracaya vAlI samAntara zredi meM badala jAtI hai jaba ki padoM kA krama pUrI taraha ulTAyA jAtA hai jisase prathama pada aMtima pada ho jAtA hai| na - 1 (4) madhyadhana = (na- 1)va + a) + a (4) madhyadhana % 2 2 - hotA hai|

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22 ] gaNitasArasaMgrahaH atroddezakaH ekAdidazAntAdyAstAvatpracayAssamarcayanti dhanam / vaNijo daza daza gacchAsteSAM saMkalitamAkalaya ||65|| dvimukhatricayairmaNibhiH prAnarca zrAvakottamaH kazcit / paJcavasatIramISAM kA saMkhyA brUhi gaNitajJa ||66|| Adistrayazcayo'STau dvAdaza gacchastrayo'pi rUpeNa / A saptakAtpravRddhAH sarveSAM gaNaka bhaNa gaNitam // 67 // dvikRtimukhaM cayo'STau nagarasahasre samarcitaM gaNitam / gaNitAbdhisamuttaraNe bAhubalin' tvaM samAcakSva ||68|| gacchAnayanasUtram - [ 2.65 aSTottaraguNarAzerdviguNAdyuttaravizeSakRtisahitAt / mUlaM cayayutamardhitamAdyUnaM cayahRtaM gacchaH // 69 // prakArAntareNa gacchAnayanasUtram - aSTottaraguNarAzerdviguNAdyuttara vizeSakRti sahitAt / mUlaM kSepapadonaM dalitaM cayabhAjitaM gacchaH // 70 // / 1 M balI / udAharaNArtha prazna da vyApAriyoM meM se pratyeka samAntara zreDhi meM saMkalita dhana dAna karatA hai| dasa zreDhiyoM ke prathama pada eka se lekara dasa taka haiM, aura pratyeka zreDhi meM pracaya utanA hI hai jitanI ki unakI prathama pada rAzi / pratyeka zreDhi ke padoM kI saMkhyA dasa hai / una zreDhiyoM ke yogoM kI gaNanA karo || 65 || eka zreSTha zrAvaka eka-eka kara pA~ca mandiroM meM 2 maNiyoM se Arambha kara uttarottara 3 maNi bar3hAtA huA bheMTa car3hAtA hai / he gaNitajJa ! kaho ki unakI kula saMkhyA kyA hai ? || 66 || prathama pada 3 hai; pracaya 8 haiM; aura padoM kI saMkhyA 12 : / ye tInoM rAziyA~ krama se eka dvArA bar3hAI jAtI haiM jaba taka ki 7 zreDhiyA~ prApta nahIM hotIM / he gaNitajJa ! ina saba zreDhiyoM ke yogoM ko prApta karo || 67 || he gaNitarUpI samudra ko bhujAoM dvArA tarane meM samartha ! batalAo ki 1000 nagaroM meM kI jAne vAlI samasta bheToM kA mAna kyA hogA, jaba ki bheMTa 4 se Arambha kI jAtI hai aura uttarottara 8 se vRddhi ko prApta hotI hai // 68 // samAntara zreDhi ke padoM kI saMkhyA ( gaccha ) nikAlane kA niyama ( prathama pada kI dugunI ) rAzi aura pracaya ke antara ke varga meM zreDhi ke yoga dvArA guNita pracaya kI AThagunI rAzi jor3ate haiM / prApta yogaphala ke vargamUla meM pracaya jor3ate haiM aura pariNAmI rAzi AdhI karate haiM / ise prathama pada dvArA hAsita kara pracaya dvArA vibhAjita karate haiM to zreDhi ke par3oM kI saMkhyA prApta hotI hai // 69 // 1 dUsarI rIti dvArA padoM kI saMkhyA nikAlane kA niyama ( prathama pada kI dugunI ) rAzi aura pracaya ke antara ke varga meM, zredi ke yoga dvArA guNita pracaya kI aThagunI rAzi jor3akara prApta yogaphala ke vargamUla meM se kSepapada ko ghaTAte haiM / pariNAmI rAzi ko AdhA karate haiM / ise pracaya dvArA vibhAjita karane para zredi ke padoM kI saMkhyA prApta hotI haiM // 70 // (66) zrAvaka jainadharma ke gRhastha dharma ke gRhastha dharma kA pAlana karane vAlA hotA hai, jo kevala zravaNa karatA arthAt dharma yA kartavya ke viSaya meM sunatA aura sIkhatA hai / sAmAnyataH pAkSika zrAvaka ko mithyAtva, anyAya evaM abhakSya kA tyAga hotA hai / (69) bIjagaNita se yaha niyama isa bhA~ti prarUpita hogA- V (raa - ba ) + 8 ba ya + ba - a 2 = na ba 2a - ba (70) (prathama pada kI dugunI rAzi aura pracaya ke aMtara kI AdhI rAzi kSepapada kahalAtI hai / arthAt, 'yaha spaSTa hai ki isa sUtra meM kSepapada kA ullekha hone se pichale sUtra se mAtra ullekha meM bhinnatA hai / 2

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-2. 75] parikarmavyavahAraH [23 atroddezakaH Adiau pracayo'STau dvaurUpeNA trayAtkramAdvaddhau / khAko rasAdrinetraM khenduharA vittamatra ko gacchaH / / 71 / / AdiH paJca cayo'STau guNaratnAgnidhanamatra ko gacchaH / SaT prabhavazva cayo'STau khadvicatuH svaM padaM kiM syAt / / 72 / / uttarAdyAnayanasUtramAdidhanonaM gaNitaM padonapadakRtidalena saMbhajitam |prcystddhnhiinN gaNitaM padabhAjitaM prabhavaH // 73 // AdyuttarAnayanasUtramprabhavo gacchAptadhanaM vigtaikpdaardhgunnitcyhiinm| padahRtadhanamAyunaM nirekapadadalahataM prcyH||74|| prakArAntareNottarAdyAnayanasUtramdvihataM saMkalitadhanaM gacchahRtaM dviguNitAdinArahitam / vigataikapadavibhaktaM pracayaH syAditi vijAnIhi / / 75 / / udAharaNArtha prazna prathama pada 2 hai, pracaya 8 hai| ina donoM ko uttarottara eka dvArA bar3hAte jAte haiM jisase 3 zreDhiyA~ bana jAtI haiN| ina tIna zreDhiyoM ke yoga kramazaH 90, 276 aura 1110 haiN| pratyeka zreDhi ke padoM kI saMkhyA kyA hai ? // 71 // prathama pada 5 hai| pracaya 8 hai; zreDhi kA yoga 333 hai / padoM kI saMkhyA kyA hai ? anya zreDhi kA prathamapada 6 hai, pracaya 8 hai aura yoga 420 hai| padoM kI saMkhyA kyA hai ? // 72 // pracaya aura prathama pada ko nikAlane kA niyama-- zreDhi kA yoga Adidhana dvArA hAsita kiyA jAtA hai, aura ise. padoM kI saMkhyA dvArA hAsita padoM kI saMkhyA ke varga dvArA nirUpita rAzi kI AdhI rAzi dvArA vibhAjita karane para pracaya prApta hotA hai| zreDhi ke yoga ko uttaradhana dvArA hAsita karane para prApta phala ko padoM kI saMkhyA dvArA vibhAjita karane para zreDhi kA prathama pada prApta hotA hai // 73 // prathama pada aura pracaya prApta karane kA niyama zreDhi meM padoM kI saMkhyA dvArA bhAjita zreDhi kA yoga, jaba pracaya aura eka kama padoM kI saMkhyA kI AdhI rAzi ke guNana phala dvArA hAsita kara diyA jAtA hai to zreDhi kA prathama pada prApta hotA hai| yoga ko, padoM kI saMkhyA se bhAjita kara prathama pada dvArA hAsita karate haiN| prAptaphala ko eka kama padoM kI saMkhyA kI AdhI rAzi dvArA vibhAjita karane para pracaya prApta hotA hai // 74 // pracaya aura prathama rAzi ko anya vidhi dvArA nikAlane ke do niyamaH zrehi ke yoga ko 2 se guNita kara aura padoM kI saMkhyA se vibhAjita kara prathama pada kI dugunI rAzi se hAsita karate haiN| prAptaphala ko eka kama padoM kI saMkhyA kI AdhI rAzi dvArA vibhAjita karane para pracaya prApta hotA hai // 75 // zreDhi ke yoga kI dugunI rAzi ko padoM kI saMkhyA se vibhAjita kara (73) Adi-dhana aura uttaradhana ke liye isa adhyAya ke 63 aura 64 veM sUtra kI pAda TippaNI dekhiye / isa sUtra ko pratIka rUpase pradarzita karane para vaha nimnarUpa meM sAdhita hotA hai __ ya-na a ba aura (na (na ya- na (na-1). a% ......... 2 -na)/2 ... ya_na- 1.aura ( 74 ) bIjIya rUpa se : a =-- (2 ya/na)-2 a (75) pratIka rUpa se : ba= (1 na-1 aura ba= ( ya/na )-a na ba (yana ) (na-1)/2

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24 ] gaNita sArasaMgrahaH [ 2. 76 dviguNita saMkalitadhanaM gacchahRtaM rUparahitagacchena / tADitacayena rahitaM dvayena saMbhAjitaM prabhavaH // 76 // atroddezakaH navavadanaM tattvapadaM bhAvAdhikazatadhanaM kiyAnpracayaH / paJca cayo'STa padaM SaTpaJcAzacchatadhanaM mukhaM kathaya // 77 // sveSTAdyuttaragacchAnayanasUtram - saMkalite sveSTahRte hAro gaccho'tra labdha iSTone / UnitamAdiH zeSe vyekapadArthoddhRte pracayaH // 78 // atroddezakaH catvAriMzatsahitA paJcazatI gaNitamatra saMdRSTam / gacchapracayaprabhavAn' gaNitajJaziromaNe kathaya // 79 // Adyuttaragaccha sarvamizradhanavizleSaNe sUtratrayam -- uttaradhanena rahitaM gacchenaikena saMyutena hRtam / mizradhanaM prabhavaH syAditi gaNakaziromaNe viddhi ||80|| 1 M vigaNayya sakhe mamAcakSva / eka kama padoM kI saMkhyA kI AdhI rAzi dvArA hAsita karate haiM / prAptaphala ko pracaya dvArA guNita kara, jaba do ke dvArA vibhAjita karate haiM to zreDhi kA prathama pada prApta hotA hai // 76 // udAharaNArtha prazna prathama pada 9 hai; padoM kI saMkhyA 7 hai; aura zreDhi kA yoga 105 hai / pracaya kA mAna kyA hai ? anya zreDhi kA pracaya 5 hai, par3hoM kI saMkhyA 8 'aura yoga 156 hai / batalAo prathama pada kyA hai ? // 77 // jaba yoga diyA gayA ho to icchAnusAra prathama pada, pracaya aura padoM kI saMkhyA nikAlane kA niyama jaba yoga ko kisI cunI huI saMkhyA dvArA vibhAjita karate haiM to bhAjaka zreTi ke padoM kI saMkhyA bana jAtA hai / jaba isa bhajanaphala ko kisI phira se cunI huI saMkhyA dvArA hAsita karate haiM to yaha ghaTAI gaI saMkhyA kA prathama pada bana jAtI hai / ghaTAne ke bAda prApta zeSa jaba eka kama par3hoM kI saMkhyA kI AdhI rAzi dvArA vibhAjita kiyA jAtA hai to pracaya utpanna hotA hai // 78 // udAharaNArtha prazna isa prazna meM yoga 540 hai / he gaNitajJoM ke ziromaNi ! batalAo ki padoM kI saMkhyA, pracaya aura prathama pada kyA hoMge ? // 79 // prathama pada se saMyukta athavA pracaya athavA padoM kI saMkhyA se athavA ina sabhI se saMyukta samAntara zreDhi ke yoga ko vizleSita karane ke liye tIna niyama-he gaNaka ziromaNi ! mizradhana ko dvArA vibhAjita kiyA jAtA hai to prathama uttara dhana se hAsita kara, eka adhika padoM kI saMkhyA pada prApta hotA hai - aisA samajho // 80 // mizradhana ko ( 2ya / na ) - ( na - 1 ) ba 2 (76) bIjIya rUpa se : a = ( 78 ) pratIka rUpa se, isa prazna meM, jaba ya diyA gayA hotA hai aura a tathA na ko kisI bhI isaliye, diye gaye ya ke liye, bake taraha cunanA hotA hai, taba ba kA mAna nikAlanA par3atA hai / kitane hI mAna ho sakate haiM jo a aura na ke cune jAne para jAte haiM to ko nikAlane ke liye yahA~ diyA gayA niyama sUtra nirbhara hoM / jaba a aura na cuna liye 74 se milatA hai /

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-2. 83] parikarmavyavahAraH [25 AdidhanonaM mizraM ruuponpdaardhgunnitgcchen|saiken hRtaM pracayo gacchavidhAnAtpadaM mukhe saike||8|| mizrAdapanIteSTau mukhagacchau prcymishrvidhilbdhH| yo rAziH sa cayaH syAtkaraNamidaM srvsNyoge||2|| atroddezakaH dvitrikapaJcadazAmA catvArizanmukhAdi mizradhanam / tatra prabhavaM pracayaM gacchaM sarvaM ca me brUhi // 83 / / 1 M padonapadakRtidalena saikena / bhaktaM pracayo'tra padaM gacchavidhAnAnmukhe saike / / Adidhana se hAsita kara aura taba padoM kI saMkhyA tathA eka kama padoM kI saMkhyA kI AdhI rAzi ke guNanaphala meM eka jor3akara prApta huI rAzi dvArA vibhAjita karate haiM to pracaya prApta hotA hai| mizradhana meM se padoM kI saMkhyA vipATita ( bhaGga) karane meM padoM kI saMkhyA ko prApta karane kA niyama hI prayukta * karate haiM, jaba ki saba padoM ko saMvAdarUpa se (correspondingly ) bar3hAne ke liye prathama pada ko eka dvArA bar3hA huA mAna liyA jAya / / 8 / / mizradhana ko vizleSita karane kI vidhi isa prakAra haimizradhana ko mana se cune hue prathama pada aura padoM kI saMkhyA dvArA hAsita karate haiM aura taba uttaramizradhana ko bhaGga karane vAle niyama ko isa aMtara meM prayukta karane para pracaya prApta hotA hai / / 8 / / udAharaNArtha prazna 40 meM kramazaH 2, 3, 5 aura 50 jor3akara Adi mizradhana aura anya mizradhana banAte haiN| mujhe batalAo ki ina dazAoM meM prathama pada,pracaya, padoM kI saMkhyA aura kula tInoM, kramazaH kyA-kyA hoMge? // 8 // ( dRSTa ) jJAta yoga se dI huI samAntara zreDhi kA prathama pada aura pracaya, dvitIya zreDhi ke prathama pada aura pracaya; jahA~ mana se cunA huA yoga dI huI zreDhi ke jJAta yoga kA dugunA, tigunA, AdhA, tihAI athavA isI taraha kA guNaka athavA bhinnIya rUpa hai, nimnalikhita niyama se prApta karate haiM (80-82) mizradhana kA artha milA huA yoga hotA hai / jaba prathama pada athavA pracaya athavA padoM kI saMkhyA athavA ina saba tInoM ko samAntara zredi ke yoga meM jor3ate haiM taba mizradhana prApta hotA hai / isa taraha, yahA~ cAra prakAra ke mizradhana kA kathana kiyA hai aura ve kramazaH Adi mizradhana, uttara mizradhana, gaccha mizradhana aura sarva mizradhana haiN| Adidhana aura uttaradhana ke liye sUtra 63 aura 64 kI pAda TippaNI na+ ---jahA~ 'ya', dekhiye / bIjIya rUpa se sUtra 80 isa taraha sAdhita hotA hai- a= ...... 2 jahA~ 'ya" __ya" - na a Adi mizradhana hai, arthAt ya + a hai / sUtra 81 meM ba= 7 hai jahA~ ya" uttara na (na-1)/2}+1 mizradhana hai arthAt ya + ba hai| Age, jaba gaccha mizradhana ya" arthAt ya + na hotA hai to na kA mAna nikAlA jA sakatA hai; kyoMki ya = a+ (a+ba) + (a+2 ba)+......na padoM taka; aura ya" = (a+1)+ (a+3+ba)+ (a+1+2 ba)+......na padoM taka; hotA hai| cUMki sUtra 82 meM, a aura na kA mAna kisI bhI taraha cuna sakate haiM; a, na aura ba kA mAna athavA sarva mizradhana ya" (jo ya+a+na+ba ke tulya hotA hai ) nikAlane kA prazna ya" ke kisI diye gaye mAna se ba kA mAna nikAlane ke samAna ho jAtA hai / ] (83) pratIka rUpa se prazna yaha hai : (1) a kA mAna nikAlo jaba ya = 42, ba= 3, na=5 ho / (2) ba kA mAna nikAlo jaba ki ya" = 43; a =2 aura na 5 ho| (3)na kA mAna batalAo jaba ki ya+na= 45 a-2 aura ba=3 ho| (4) a, ba aura na kA mAna nikAlo jaba ki ya+a+ba+na =50 ho| ga0 sA0 saM0-4

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26] gaNitasArasaMgrahaH [2.84 __ dRSTadhanAdyuttarato dviguNatriguNadvibhAgatribhAgAdISTadhanAdyuttarAnayanasUtramdRSTavibhakteSTadhanaM dviSThaM tatpracayatADitaM pracayaH / tatprabhavaguNaM prabhavo guNabhAgasyeSTavittasya / / 8 / / atroddezakaH samagacchazcatvAraH SaSTirmukhamuttaraM tato dviguNam / tadvathAdi hatavibhaktasveSTasyAdyuttare brUhi / / 85 // iSTagacchayovyastAdyuttarasamadhanadviguNatriguNadvibhAgatribhAgAdidhanAnayanasUtramvyekAtmahato gacchaH sveSTano dviguNitAnyapadahInaH / mukhamAtmonAnyakRtirdvikeSTapaghAtavarjitA pracayaH // 86 // 1 M guNabhAgAdyuttarecchAyAH / 2 M guNa / saralatA ke liye, cune hue yoga ko jJAta yoga dvArA vibhAjita kara do sthAnoM meM rakhate haiM / isa bhajanaphala ko jaba jJAta pracaya dvArA guNita karate haiM to iSTa pracaya prApta hotA hai / vahI bhajanaphala jaba jJAta prathama pada se guNita kiyA jAtA hai to cAhA huA prathama pada usa zreDhi kA prApta hotA hai jisakA ki yoga jJAta zreDhi ke yoga kA yA to apavartya athavA bhinnAtmaka aMza (bhAga ) hotA hai // 84 // udAharaNArtha prazna 60, jJAta prathama pada hai, jJAta pracaya usase dugunA hai, aura padoM kI saMkhyA ( jJAta dI huI zreDhi meM tathA iSTa samasta zreDhiyoM meM) 4 hai| jJAta yoga ko 2 se Arambha hone vAlI saMkhyaoM dvArA guNita athavA bhAjita karane para prApta hue yogoM vAlI zreDhiyoM ke prathama pada aura pracaya nikAlo // 85 / / jinake padoM kI saMkhyA mana se cunI jAtI hai aisI do zreDhiyoM ke pArasparika vinimita prathama pada aura pracaya tathA una zreDhiyoM ke yogoM (jo barAbara hoM, athavA jinameM se eka dUsare kA dugunA, tigunA, AdhA, tihAI athavA aisA hI koI apavartya yA bhAga rUpa ho,) ko nikAlane kA niyama kisI eka zreDhi ke padoM kI saMkhyA svataH se guNita hokara tathA eka dvArA hAsita hokara aura phira cune hue (do zreDhiyoM ke yoga ke ) anupAta dvArA guNita hokara, aura taba dUsarI zreDhi ke padoM kI saMkhyA kI dugunI rAzi dvArA hAsita hokara koI eka zreDhi ke ( paraspara badalane yogya ) prathama pada ko prApta hotI hai| dUsarI zreDhi ke padoM kI saMkhyA kI vargarAzi padoM kI saMkhyA dvArA hI svataH hvAsita hokara aura taba cunI huI niSpatti dvArA tathA prathama zreDhi ke padoM kI saMkhyA ke guNanaphala kI dugunI rAzi dvArA hAsita hokara, usa zreDhi ke paraspara badalane yogya pracaya ko utpanna karatI hai // 86 // (84) pratIka rUpa se, a, =ya, a, ba, =ya ba; jahA~ ya,, a, ba, aisI zredi ke kramazaH yoga,prathama pada aura pracaya haiM jisakA yoga cuna liyA jAtA hai| yadi do zreDhiyoM kA yoga diyA gayA ho, to do prathama padoM kI niSpatti (ratio) aura do pracayoM kA anupAta meM hI sarvadA nahIM rahatA / yahA~ jo hala diye gaye haiM ve kucha viziSTa dazAoM meM prayukta hote haiN| (86) bIjIya rUpa se, ana (na-1)xpa-2na, aura ba= (na)2-na,-2pana; jahA~, a, ba aura na kramazaH prathamapada, pracaya aura zreTi ke padoM kI saMkhyA haiM; na, dvitIya zreDhi ke padoM kI saMkhyA hai, aura pado yogoM kI niSpatti hai| a aura ba isa taraha nikAlane ke bAda dUsarI zredi ke prathamapada aura pracaya kramazaH ba aura a hoNge|

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[27 -2. 90] parikarmavyavahAraH atroddezakaH pazcASTagacchapuMsoya'staprabhavottare samAnadhanam / dvitriguNAdidhanaM vA brUhi tvaM gaNaka vigaNayya // 87 // dvAdazaSoDazapadayoya'staprabhavottare samAnadhanam / dvyAdiguNabhAgadhanamapi kathaya tvaM gaNitazAstrajJa / / 88 / / asamAnottarasamagacchasamadhanasyAdyuttarAnayanasUtramaadhikacayasyaikAdizcAdhikacayazeSacayavizeSo guNitaH / vigataikapadArdhena sarUpazca mukhAni mitra zeSacayAnAm // 89 / / atroddezakaH ekAdiSaDantacayAnAmekatritayapaJcasaptacayAnAm / navanavagacchAnAM samavittAnAM cAzu vada mukhAni sakhe // 90 / / 1 M gaNakamukhatilaka / ___ udAharaNArtha prazna do manuSyoM ke dhana kramazaH do samAntara zreDhiyoM ke yoga se jJAta hote haiN| zreDhiyoM-sambandhI padoM kI saMkhyA 5 aura 8 hai / donoM zreDhiyoM ke prathama pada aura pracaya paraspara badalane yogya haiM / zreDhiyoM ke yoga barAbara haiM athavA unameM se eka kA yoga dUsare kA dugunA, tigunA, AdhA athavA aisA hI koI apavartya hai / he gaNitavettA, zuddha gaNanA ke pazcAt batalAo ki ina yogoM ke tathA paraspara badalane yogya prathamapada aura pracaya ke mAna kyA haiM? // 87 // do samAntara zreDhiyoM ke sambandha meM, jinake padoM kI saMkhyA 12 aura 16 hai, prathamapada aura pracaya paraspara badalane yogya haiN| zreDhiyoM ke yoga barAbara haiM athavA unameM se eka kA yoga dugunA athavA koI aisA hI apavartya athavA bhAga hai| he gaNitazAstrajJa batalAo ki ina yogoM ke tathA paraspara badalane yogya prathamapada aura pracaya ke mAna kyA hoMge ? // 8 // asamAna pracayoM, samagaccha aura samayoga dhanavAlI samAntara zreDhiyoM ke prathama pada prApta karane kA niyama jisakA pracaya sabase bar3A hai aisI zreDhi kA prathamapada eka le liyA jAtA hai| isa sabase bar3e pracaya aura zeSa pracaya ke antara ko eka se hAsita gaccha kI AdhI rAzi dvArA guNita karate haiM / jaba isa guNanaphala meM eka milAte haiM to he mitra hameM zeSa pracaya vAlI zreDhiyoM ke prathamapada prApta hote haiM // 89 // udAharaNArtha prazna he sakhe ! barAbara yoga vAlI do zreDhiyoM ke prathamapadoM ko batalAo jaba ki unameM se pratyeka meM 9 gaccha hai tathA pracaya kramazaH 1 se Arambha hokara 6 taka eka dazA meM aura 1, 3, 5 aura 7 dUsarI dazA meM ho // 9 // (89) yahA~ diyA gayA hala sAdhAraNa niyama kI vizeSa dazA hai / a, =na-(ba, - ba) + a, jahA~ a aura a, do zreDhiyoM prathamapada haiM: ba aura ba, unake saMvAdI pracaya haiM / isa sUtra ( formula) meM, jahA~ ba, ba, aura na diye gaye haiM: a, kA mAna a ke kisI mAna ko cuna lene para nikAlA jA sakatA hai| isa niyama meM a kA mAna 1 liyA gayA hai|

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28] gaNitasArasaMgrahaH [ 2. 91 visadRzAdisadRzagacchasamadhanAnAmuttarAnayanasUtramadhikamukhasyaikacayazcAdhikamukhazeSamukhavizeSo bhaktaH / vigataikapadArdhana sarUpazca cayA bhavanti zeSamukhAnAm // 9 // atroddezakaH ekatripaJcasaptanavaikAdazavadanapaJcapaJcapadAnAm / samavittAnAM kathayottarANi gaNitAbdhipAradRzvana gaNaka ||92 / / ___ atha guNadhanaguNasaMkalitadhanayoH sUtrampadamitaguNahatiguNitaprabhavaH syAdgaNadhanaM tadAbUnam / ekonaguNavibhaktaM guNasaMkalitaM vijAnIyAt / / 93 / / aisI samAntara zreDhiyoM ke pracayoM ko nikAlane kA niyama jinameM prathama pada visadRza, padoM kI saMkhyA sadRza aura yoga barAbara hoM-- jisakA prathamapada sabase bar3A ho usa zreDhi kA pracaya eka lete haiN| isa sabase bar3e prathamapada aura zeSa zreDhiyoM meM se pratyeka ke prathamapada ke antara ko eka kama padoM kI saMkhyA kI AdhI rAzi dvArA vibhAjita karate haiM aura isa prakAra pratyeka dazA meM prApta bhajanaphala meM eka milAte haiN| isa taraha, bhinna-bhinna zeSa zreDhiyoM ke pracayoM ko prApta karate haiM // 11 // udAharaNArtha prazna he gaNitarUpI samudra ke dUsare kinAre kA darzana karane vAle gaNaka ! una saba barAbara yogavAlI zreDhiyoM ke pracayoM ko nikAlo jinake prathamapada 1,3,5,7,9 aura 11 hoM tathA padoM kI saMkhyA ( pratyeka meM ) 5 ho.||92|| guNadhana aura guNottara zreDhi kA yoga nikAlane kI vidhi guNottara zreDhi ke prathamapada ko jaba aisI vAraMvAra svataH se guNita sAdhAraNa niSpatti dvArA guNita karate haiM, jahA~ isa guNanaphala meM zreDhi ke padoM kI saMkhyA dvArA sAdhAraNa niSpatti kI vAraMvAratA ( frequency ) ko mApA jAtA hai; taba guNadhana prApta hotA hai| yaha guNadhana jaba prathamapada dvArA hAsita kiyA jAtA hai tathA eka kama sAdhAraNa niSpatti dvArA vibhAjita kiyA jAtA hai taba guNottara zreDhi kA yoga prApta hotA hai // 93 / / (91) isa dazA meM sAdhAraNa sUtra (formula) yaha hai : ba, = +ba, jahA~ ki ba kA (na -1)2 mAna isa niyama meM 1 liyA gayA hai| (93) na padoM kI guNottara zreDhi kA guNadhana (na+1) veM pada ke tulya hotA hai, jaba ki zreDhi saMtata rahatI hai / bIjIya rUpa se, isa guNadhana kI arhA ( ra 4ra4 ra......na guNana khaMDoM taka a) arthAt (ana) hotI hai, jahA~ ki "ra" sAdhAraNa niSpatti hai / isakI tulanA uttaradhana se kara sakate haiM / yoga nikAlane kA niyama bIjIya rUpa se yaha hai / ara -a -, jahA~ a prathama pada hai, ra sAdhAraNa niSpatti hai aura na padoM kI saMkhyA hai /

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-2. 94 ] guNasaMkalite anyadapi sUtramsamadalaviSamakharUpo guNaguNito vargatADito gacchaH / rUponaH prabhavano vyekottarabhAjitaH sAram ||14|| parikarmavyavahAraH guNottara leDi kA yoga nikAlane kA anya niyama eka alaga stambha meM zredi ke padoM kI saMkhyA ko zUnya aura eka dvArA kramazaH darzAyA jAtA hai| jaba saMkhyA kA mAna yugma ( even ) ho to use AdhA kiyA jAtA hai aura mAna ayugma ( odd ) ho to usameM se eka ghaTA kara prApta phala ko AdhA kiyA jAtA hai--yaha taba taka kiyA jAtA hai jaba taka ki zUnya prApta nahIM hotA taba yaha nirUpita zredi jo zUnya aura eka dvArA banI huI hotI hai, kama se aMtima 'eka' se prayoga meM lAyI jAtI hai| vahA~ jahA~ eka prarUpaka hotA hai sAdhAraNa niSpatti dvArA guNita vaha eka punaH sAdhAraNa niSpatti dvArA guNita kiyA jAtA hai; aura jahA~ zUnya prarUpaka hotA jaba yaha phala eka dvArA hAsita hokara, prathamasAdhAraNa niSpatti dvArA vibhAjita kiyA jAtA hai / hai vahA~ bhI guNita kiyA jAtA hai tAki varga prApta ho pada dvArA punaH guNita kiyA jAtA hai aura eka kama taba vaha zredi ke yoga ko utpanna karatA hai // 94 // mAna lo ina meM na kA mAna 12 hai (94) yaha niyama pichale niyama se kevala isaliye bhinna hai ki isameM varga aura sarala guNana kI vidhiyoM ko upayoga meM lAkara ( rana) ko naI rIti se nikAlA gayA hai| nimnalikhita udAharaNa dvArA rIti spaSTa ho jAvegI ( na = 12 ) ,,, 35 33 33 0 "" 55 1 12 yugma rAzi hai, isaliye ise 2 ke dvArA vibhAjita karate haiM aura 0 dvArA pradarzita karate haiM / 3 = 6 bhI yugma rAzi hai, " 2 ke " I 3 ayugma rAzi hai, isaliye isameM se 1 paTAte haiM aura = 3-12 yugma rAzi hai, isaliye ise 2 dvArA vibhAjita karate 31 ayugma rAzi hai, isaliye isameM se eka ghaTAte haiM haiM aura 1 "" 0 "" aura 1 "" 33 " " "" [ 29 39 "" 93 39 "" | " | " | 1 - 1 = 0, jo kriyA ke isa bhAga ko samApta karatI hai / aba, nirUpaka stambha meM ( jisameM aGka uparyukta vidhi dvArA nikAlate haiM ) aMtima eka ko ra dvArA guNita karate haiM, jisase ra prApta hotA hai; kyoMki isa meM usake Upara hai, ra ko Upara kI taraha prApta kara vargita karate haiM jisase ra 0 hai; kyoMki isa * ke Upara 1 hai, 1 ra detA hai; cU~ki isa 1 ke Upara ra jo prApta hotA hai aba ra ke dvArA guNita karane para hai, isa ra ko vargita karate haiM jo ra 6 detA hai; aura 2' ko vargita karate haiM jora 0 cU~ki phira se isa ke Upara dUsarA zUnya hai, isa detA hai| isa taraha ra kA mAna sarala varga karane aura guNana karane kI kriyAoM dvArA prApta hotA hai / isa vidhi kA upayoga kebala rana ke mAna ko saralatA se prApta karane hetu hotA hai / aura, yaha saralatApUrvaka dekhA jAtA hai ki yaha rIti na kI samasta dhanAtmaka aura abhinnAtmaka ( integral ) arhAoM ( values ) ke liye prayukta kI jA sakatI hai / aMtima eka prApta hotA

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gaNitasArasaMgrahaH guNasaMkalitAntyadhanAnayane tatsaMkalitadhanAnayane ca sUtram guNasaMkalitAntyadhanaM vigataikapadasya guNadhanaM bhavati / taguNaguNaM mukhonaM vyekottarabhAjitaM sAram // 95 // guNadhanasyodAharaNam svarNadvayaM gRhItvA triguNadhanaM pratipuraM saMmArjayati / yaH puruSo'STanagaryAM tasya kiyadvittamAcakSva / 96 / guNadhanasyAdyuttarAnayanasUtram - guNadhanamAdivibhaktaM yatpadamitavadhasamaM sa eva cayaH / gacchapramaguNaghAtaprahRtaM guNitaM bhavetprabhavaH // 97 // 30 ] guNadhanasya gacchAnayana sUtram - bhakte guNavatte yathA nirayaM tathA guNena hRte / yAvatyo'tra zalAkAstAvAn gaccho guNadhanasya // 98|| 1 I samarcayati / [ 2.95 guNottara zreDhi ke aMtima pada tathA yoga ko nikAlane kA niyama guNottara zreDhi kA aMtima pada athavA antyadhana, ( jisameM padoM kI saMkhyA eka kama hotI hai aisI ) dUsarI Dhi, kA guNadhana hotA hai / yaha antyadhana, sAdhAraNa niSpatti dvArA guNita kiyA jAne para tathA eka kama sAdhAraNa niSpatti dvArA vibhAjita kiyA jAtA hai prathamapada dvArA hAsita kiyA jAtA hai, to DhikA yoga prApta hotA hai // 95 // udAharaNArtha prazna kisI nagara meM 2 svarNa mudrAe~ prApta kara eka manuSya eka nagara se dUsare nagara ko jAtA hai; aura pratyeka sthAna meM pichale sthAnoM se prApta mudrAoM se tigunI mudrAe~ prApta karatA hai / batalAo ki AThaveM nagara meM use kitanI mudrAe~ mileMgI ? || 96 // kisI diye gaye guNadhana sambandhI prathamapada aura sAdhAraNa niSpatti nikAlane kA niyama guNadhana jaba prathamapada dvArA vibhAjita hotA hai taba vaha aisI svaguNita rAzi ke guNanaphala ke tulya ho jAtA hai jisa guNana meM ki vaha rAzi, padoM kI saMkhyA kI rAzi bAra ( vAraMvAra ) prakaTa hotI hai; aura yaha rAzi cAhI huI sAdhAraNa niSpatti hai / guNadhana jaba sAdhAraNa niSpatti ke vAraMvAra guNana se prApta guNanaphala dvArA vibhAjita kiyA jAtA hai - ( sAdhAraNa niSpatti ke vAraMvAra svaguNana se prApta aisA guNanaphala jisameM isa sAdhAraNa niSpatti kA vAraMvAra prakaTapanA, padoM kI saMkhyA dvArA mApA jAtA hai ) taba prathamapada prApta hotA hai || 97 // kisI guNottara zreDhi meM diye gaye guNadhana sambandhI padoM kI saMkhyA nikAlane kA niyama Dhi ke guNadhana ko prathamapada dvArA vibhAjita kro| taba isa bhajanaphala ko sAdhAraNa niSpatti dvArA vAraMvAra taba taka vibhAjita karo jaba taka ki bhAjanayogya kucha na baca rahe / aise vAraMvAra diye gaye bhAga kI saMkhyA kA nirUpaNa karanevAlI zalAkAoM kI saMkhyA jo bhI ho vahI diye hue guNadhana ke sambandha meM padoM kI saMkhyA kA mAna hotA hai ||18|| na - 1 ara (95) bIjIya rUpa se, ya = Xra - a ra - 1 na - 1 antyadhana, guNottara zreTi ke aMtima pada ke mAna ke tulya hotA hai; guNadhana ke artha aura mAna ke liye sUtra 93 dekhiye / na padoM vAlI guNottara zreDhi kA antyadhana ara ke tulya hotA hai, jaba ki isI zreDhi kA guNadhana ara" hotA hai / isI taraha na - 1 padoM vAlI guNottara zreTi kA antya dhana ara ke tulya hotA hai, hotA hai / yahA~ spaSTa hai ki na padoM kI zreDhi kA antyadhana utanA hI vAlI zreTi kA guNadhana | na - 2 na - 1 jaba ki guNadhana ara hogA jitanA kI na 1 padoM na ( 97, 98 ) spaSTa hai ki ara" meM a kA bhAga dene para ra" prApta hotA hai, aura yaha ra dvArA *

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-2. 10.] parikarmavyavahAraH ___ guNasaMkalitodAharaNamdInArapaJcakAdidviguNaM dhanamarjayannaraH kazcit / prAvikSadaSTanagarIH kati jAtAstasya dInArAH // 99 // saptamukhatriguNacayatrivargagacchasya kiM dhanaM vaNijaH / trikpshckpnycdshprbhvgunnottrpdsyaapi||10|| guNasaMkalitottarAdyAnayanasUtramasakRdvayekaM mukhahRtavittaM yenoddhRtaM bhavetsa cyH| vyekaguNaguNitagaNitaM nirekapadamAtraguNavadhAptaM prabhavaH / / 101 / / udAharaNArtha prazna eka manuSya nagara se nagara bhramaNa karate hue guNottara zreDhi meM dhana kamAtA hai jisakA prathamapada 5dInAra aura sAdhAraNa niSpatti 2 hai| isa taraha usane ATha nagaroM meM praveza kiyaa| batalAo usake pAsa kitane dInAra haiM ? // 99 / / gaNottara zreDhi ke yoga dvArA dhana kA mApa kiyA jAtA hai| eka manuSya ke pAsa guNottara zreDhi vAlA kitanA dhana hogA jaba ki zreDhi kA prathamapada 7 hai, sAdhAraNa niSpatti 3 hai aura padoM kI saMkhyA 9 hai| punaH, jisake prathamapada, sAdhAraNa niSpatti aura padoM kI saMkhyA kramazaH 3, 5, 15 haiM aisI guNottara zreDhi vAlA dhana batalAo // 10 // guNottara zreDhi ke diye gaye yoga sambandhI prathamapada aura sAdhAraNa niSpatti nikAlane kA niyama vaha rAzi jisake dvArA, zreDhi ke yoga ko prathama pada dvArA vibhAjita karane se prApta huI rAzi ko 1 dvArA hAsita kara utpanna huI rAzi meM kathita bhAjana sambhava ho (jaba ki samaya samaya para saba uttarottara bhajanaphaloM meM se eka ghaTAne ke pazcAt bhAga dene kI yaha vidhi kI jAtI ho) to vaha rAzi sAdhAraNa niSpatti hai| vaha yoga, jo eka kama sAdhAraNa niSpatti dvArA guNita hokara, aura taba svataH meM vAraMvAra guNita sAdhAraNa niSpatti ke (svaguNita sAdhAraNa niSpatti kA aisA guNanaphala jisameM sAdhAraNa niSpatti utane bAra prakaTa hotI hai jitanI ki padoM kI saMkhyA rahatI hai ) guNanaphala dvArA vibhAjita hokara aura taba isa svataH meM vAraMvAra guNita sAdhAraNa niSpatti ke guNanaphala ko eka dvArA hAsita karane se prApta rAzi dvArA vibhAjita hokara prathamapada utpanna karatA hai // 101 // na bAra bhAga dene yogya hai aura 'na' hI zreDhi ke padoM kI saMkhyA hai| isI taraha ra 4 ra 4ra4......na padoM taka, ra" hotA hai; aura guNadhana arthAt ara', isa ra" dvArA vibhAjita hokara a detA hai jo ki zredi kA cAhA huA prathamapada hai / (101) nimnalikhita udAharaNa se niyama kA prathamabhAga spaSTa ho jAvegA--- zreDhi kA yoga 4095 hai, prathamapada 3 hai, padoM kI saMkhyA 6 hai| yahA~ 4095 ko 3 dvArA bhAjita karane para hameM 1365 prApta hotA hai / aba, 1365-1 = 1364 hai| taba anvIkSA dvArA 4 cunakara, 1364=341, 341-1 = 340, 340 = 85; 85 - 1 = 84; 4 = 21, 21-1 = 20; 1 hai / isaliye 4 yahA~ sAdhAraNa niSpatti hai| nimnalikhita se isa vidhikA AdhArabhUta siddhAnta spaSTa ho jAvegA a (ra"- 1)... ra"- 1 ; aura ra" - 1 - 1 = ra-ra ra-1 +a = ra-2 aura ra- ra-1 jo ki spaSTataH ra ke jo ki spaSTataH ra ke dvArA bhAjya hai / dUsarA bhAga bIjIya rUpa se isa taraha hai - 5. ra- 1 bha = a ( ra" - 1), ra-1 1

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32] gaNitasArasaMgrahaH [2. 102atroddezakaH trimukha gacchabANAGkAmbarajalanidhidhane kiyAnpracayaH / paguNacayapaJcapadAmbarazazi himagutrivittamatra mukhaM kim / / 102 / / guNasaMkalitagacchAnayanasUtramaekonaguNAbhyastaM prabhavahRtaM rUpasaMyutaM vittam / yAvatkRtvo bhaktaM guNena tadvArasaMmitirgacchaH / / 103 / / atroddezakaH triprabhavaM SaTkaguNaM sAraM saptatyupetasaptazatI / saptAmA brUhi sakhe kiyatpadaM gaNaka guNanipuNa // 104 // pazcAdidviguNottare zaragiridvathekapramANe dhane saptAdi' triguNe nagebhaduritastambaramatuprame / tryAsye pazcaguNAdhike hutavahopendrAkSavahnidvipazvetAMzudviradebhakarmakaradRGmAne'pi gacchaH kiyAn / 105 / " iti parikarmavidhau saptamaM saMkalitaM samAptam / / vyutkalitam aSTame vyutkalitaparikarmaNi karaNasUtraM yathA-. sapadeSTaM sveSTamapi vyekaM dalitaM cayAhataM samukham / zeSeSTagacchaguNitaM vyutkalitaM sveSTavittaM ca / / 106 // 1 M dy| sAdhAraNa niSpatti tara zredi meM prathama pada udAharaNArtha prazna yadi guNottara zreDhi meM prathama pada 3 hai, padoM kI saMkhyA 6 hai, aura yoga 4095 hai to usakI sAdhAraNa niSpatti batalAo / yadi sAdhAraNa niSpatti 6 ho, padoM kI saMkhyA 5 ho, aura yoga 3110 ho to aisI guNottara zreDhi kA prathamapada kyA hai ? // 12 // guNottara zreDhi ke padoM kI saMkhyA nikAlane kA niyama guNottara zreDhi ke yoga ko eka kama sAdhAraNa niSpatti dvArA guNita karo; taba isa guNanaphala ko prathamapada dvArA bhAjita karo aura taba isa bhajanaphala meM eka jodd'o| yaha pariNAmI rAzi sAdhAraNa niSpatti dvArA jitanI bAra uttarottara bhAjita hogI, vaha saMkhyA zreDhi ke padoM kI saMkhyA hogI / / 103 / / udAharaNArtha prazna he guNanipuNa gaNaka mitra ! mujhe batalAo ki jisa zreDhi meM prathamapada 3 hai; sAdhAraNa niSpatti 6 hai, aura yoga 777 hai, usake padoM kI saMkhyA kitanI hogI? // 10 // jisa zreDhi meM 5prathamapada haiM, 2 sAdhAraNa niSpatti hai, 1275 yoga hai; aura usa zreDhi meM jisakA prathamapada 7 hai; yoga 68887 hai aura sAdhAraNa niSpatti3 hai tathA usa zreDhi meM jisakA prathamapada 3 hai, sAdhAraNa niSpatti 5 hai aura yoga 22888183593 hai-padoM kI saMkhyA alaga-alaga nikAlo // 105 // isa prakAra parikarma vyavahAra meM, saMkalita nAmaka pariccheda samApta huaa| vyutkalita parikarma kriyAoM meM AThavIM kriyA vyutkalita' sambandhI niyama zreDhi ke kula padoM kI saMkhyA ko cune hue padoM kI saMkhyA se milA lo, aura apanI cunI huI padoM kI saMkhyA alaga se lo; ina rAziyoM meM se pratyeka ko eka dvArA hAsita kara AdhI karo aura taba pracaya dvArA guNita karo; aura taba ina pratyeka pariNAmI guNanaphaloM meM prathamapada ko jor3a do| prApta pariNAmI rAziyoM ko jaba kramazaH zeSa padoM kI saMkhyA tathA cune hue padoM kI saMkhyA dvArA guNita karate haiM to kramazaH zeSa zreDhi kA yoga aura zreDhi ke cune hue bhAga kA yoga prApta hotA hai // 106 // 1kisI dI huI zredi meM Arambha se cunA huA koI bhAga iSTa bhAga kahalAtA hai aura zeSa zredi meM zeSa pada rahane ke kAraNa vaha zeSa zredi kahalAtI hai / ina zeSa padoM kA yoga hI vyutkalita kahalAtA hai| (106) bIjIya rUpa se vyutkalita = ya = 5 na+da-13+a } (na - da ), aura cune hue bhAga ( iSTa ) kA yoga = ya, (18 ba+a) da; jahA~ da zreTi kA cune hue bhAga ke padoM kI saMkhyA hai|

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-2. 109] parikarmavyavahAraH [33 prakArAntareNa vyutkalitadhanasveSTadhanAnayanasUtramgacchasahiteSTamiSTaM caikonaM cayahataM dvihAdiyutam / zeSeSTapadArdhaguNaM vyutkalitaM sveSTavittamapi // 107 / / cayaguNabhavavyutkalitadhanAnayane vyutkalitadhanasya zeSeSTagacchAnayane ca sUtram - iSTadhanonaM gaNitaM vyavakalitaM cayabhavaM guNotthaM ca / sarveSTagacchazeSe zeSapadaM jAyate tasya // 108 / / zeSagacchasyAdyAnayanasUtrampracayaguNiteSTagacchaH sAdiH prabhavaH padasya zeSasya / prAktana eva cayaH syAdgacchasyeSTasya tAveva / / 109 / / 1M gaNitaM / dUsarI rIti dvArA zeSa zreDhi ( vyutkalita ) tathA dI gaI zreDhi ke cune hue iSTa bhAga ke yogaphaloM ko prApta karane kA niyama zreDhi ke kula padoM kI saMkhyA ko cune hue padoM kI saMkhyA meM milA lo aura apanI cunI huI padoM kI saMkhyA alaga se lo; ina rAziyoM meM se pratyeka ko eka dvArA hAsita karo aura taba pracaya dvArA guNita karo / ina pariNAmI guNanaphaloM meM prathamapada kI dugunI rAzi jodd'o| prApta pariNAmI rAziyoM ko jaba kramazaH zeSa padoM kI saMkhyA kI AdhI rAzi dvArA aura cunI huI padoM kI saMkhyA kI AdhI rAzi dvArA guNita karate haiM taba zeSa zreDi kA yoga aura zreDhi ke cune hue bhAga kA yoga prApta hotA hai // 107 // samAntara aura guNottara zreDhi ke zeSa zreDhi kI yoga tathA usake zeSa padoM kI saMkhyA nikAlane kA niyama-.. dI huI zreDhi kA yoga, zreDhi ke cune hue bhAga dvArA hAsita hokara samAntara tathA guNottara zreDhi ke zeSa bhAga ke yoga ko utpanna karatA hai| zreDhi ke kula padoM kI saMkhyA aura cunI huI zreDhi ke padoM kI saMkhyA kA antara zeSa zreDhi ke padoM kI saMkhyA hotA hai // 10 // zeSa zredi ke padoM sambandhI prathamapada nikAlane kA niyama cunI huI padoM kI saMkhyA ko pracaya dvArA guNita karane aura zreDhi ke prathamapada meM milAne para zeSa zreDhi ke ( zeSa ) padoM kA prathamapada utpanna hotA hai| uparyukta pracaya, zeSa padoM kA bhI pracaya hotA hai / cune hue bhAga ke padoM kI saMkhyA sambandhI prathamapada aura pracaya, dI huI zreDhi ke prathamapada aura pracaya ke tulya hote haiM // 109 // (107) phira se, vyutkalita = yava = { ( na + da - 1 ) ba+ 2 a } na-da aura iSTa kA yoga = yaha = { ( da - 1) ba+ 2 a} (109) zeSa zredi kA prathamapada =daxba+ a hai yaha zreDhi spaSTataH samAntara zreDhi hai| ga0 sA0 saM0-5

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3.] gaNitasArasaMgrahaH [2.11guNavyutkalita zeSagacchasyAdyAnayanasUtramguNaguNite'pi cayAdI tathaiva bhedo'yamatrazeSapade / iSTapadamitiguNAhatiguNitaprabhavo bhavedvaktram // 110 // atroddezakaH dvimukhanicayo gacchazcaturdaza svepsitaM padaM sapta / aSTanavaSaTkapaJca ca kiM vyutkalitaM samAkalaya // 111 / / SaDAdiraSTau pracayo'tra SaTkRtiH padaM daza dvAdaza SoDazepsitam / mukhAdiranyasya tu paJcapaJcakaM zatadvayaM brUhi zataM vyayaH kiyAn / / 112 / / SaDghanamAno gacchaH pracayo'STau dviguNasaptakaM vktrm| saptatriMzatsveSTaM padaM samAcakSva phalamubhayam / / 113 / / aSTakRtirAdiruttaramUnaM catvAri SoDazAtra padam / iSTAni tattvakezavarudrArkapadAni kiM zeSam / / 114 // guNottara zreDhi kI zeSa zreDhi ke (zeSa) padoM kI saMkhyA sambandhI prathamapada nikAlane kA niyama guNottara zreDhi ke viSaya meM bhI dI gaI zreDhi meM tathA iSTa bhAga meM sAdhAraNa niSpatti tathA prathama pada samAna hote haiN| parantu, zeSa zreDhi ke padoM kA prathamapada bhinna hotA hai| dI huI zreDhi kA prathamapada aise guNanaphala dvArA guNita hokara, jo sAdhAraNa niSpatti ke svataH utanI bAra guNita hone se utpanna hotA hai jitanI bAra ki cune hue padoM kI saMkhyA hotI hai, zeSa zreDhi ke prathamapada ko utpanna karatA hai // 11 // udAharaNArtha prazna samAntara zreDhi kI zeSa zreDhi ke yoga kI gaNanA karo jaba ki prathama pada 2 ho, pracaya 3 ho aura padoM kI saMkhyA 14 ho tathA cunI haI padoM kI saMkhyA kramazaH 7, 8, 9, 6 aura 5 ho // 111 // samAntara zreDhi ke sambandha meM yahA~ prathamapada 6 hai, pracaya 8 hai, padoM kI saMkhyA 36 hai aura cunI huI padoM kI saMkhyA kramazaH 10, 12 aura 16 hai| isI taraha kI dUsarI zreDhi ke prathamapada aura pracaya Adi kramazaH 5, 5, 200 aura 100 hai| batalAo ki saMvAdI zeSa zreDhiyoM ke yoga kyA-kyA haiM ? // 112 // samAntara zreDhi ke padoM kI saMkhyA 216 hai; pracaya 8 hai; prathamapada 14 hai; iSTa bhAga ke padoM kI saMkhyA 37 hai| zeSa zreDhi aura iSTa zreDhi (cune hue bhAga) ke yoga kyA-kyA hoMge? // 113 // samAntara zreDhi kA prathamapada 64 hai, pracaya-4 (RNa cAra ) hai tathA padoM kI saMkhyA 16 hai| batalAo ki zeSa zreDhi ke yoga kyA-kyA hoMge jaba ki iSTa bhAga ke padoM kI saMkhyA kramazaH 7, 9, 11 aura 12 ho // 11 // (110) zeSa guNottara zreDhi kA prathamapada arada hai|

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[35 -2. 115] parikarmavyavahAraH guNavyutkalitasyodAharaNamcaturAdidviguNAtmakottarayuto gacchazcaturNAM kRtir daza vAJchApadamaGkasindhuragiridravyendriyAmbhodhayaH / kathaya vyutkalitaM phalaM sakalasadbhajAgrimaM vyAptavAn karaNaskandhavanAntaraM gaNitavinmattebhavikrIDitam // 115 / / iti parikarmavidhAvaSTamaM vyutkalitaM samAptam / / iti sArasaMgrahe gaNitazAstre mahAvIrAcAryasya kRtau parikarmanAmA prathamo vyavahAraH samAptaH / / 1. praa.| guNottara zreDhi sambandhI vyutkalita para prazna kramabaddha gucchevAle vRkSoM ke phaloM kI saMkalana kriyA meM 4 prathamapada hai, 2 pracaya hai, padoM kI saMkhyA 16 hai jaba ki iSTa bhAga meM padoM kI saMkhyA kramazaH 10, 9,8, 7, 6, 5 aura 4 hai / he jaMgalI hastiyoM dvArA krIr3ita vana ke aMtasthala rUpI vyAvahArika gaNita kI kriyAoM ke vedhaka ! batalAo ki kathita vibhinna uttama vRkSoM ke zeSa phaloM kI kula saMkhyA kyA hai ? // 115 // isa prakAra, parikarma vyavahAra meM nyutkalita nAmaka pariccheda samApta huaa| isa prakAra, mahAvIrAcArya kI kRti sArasaMgraha nAmaka gaNita zAstra meM parikarma nAmaka prathama vyavahAra samApta huaa| (115) isa prazna meM bhinna-bhinna 7 phaloM ke vRkSa haiM jinameM se pratyeka meM phaloM ke 16 gucche haiM / pratyeka vRkSa meM sabase choTA gucchA 4 phaloM vAlA hai; bar3e-bar3e gucchoM meM guNottara zreDhi meM bar3hate hue phaloM kI saMkhyAe~ haiM, jisakI sAdhAraNa niSpatti 2 hai / 7 vRkSoM meM se haTAye hue gucchoM kI saMkhyA nIce se kramazaH 10, 9,8,7,6, 5 aura 4 hai| yahA~ vibhinna uttama vRkSoM para zeSa phaloM kI kula saMkhyA nikAlanA hai| 'mattebhavi krIDitaM' jo isa sUtra meM AyA hai, usI sUtra kA chanda ( metre) hai jisameM ki vaha saMracita kiyA gayA hai| isakA artha vanyahastiyoM kI krIr3A bhI hotA hai /

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3. kalAsavarNavyavahAraH 'trilokarAjendrakirITakoTiprabhAbhirAlIDhapadAravindam / nirmUlamunmUlitakarmavRkSaM jinendracandraM praNamAmi bhaktyA // 1 // - itaH paraM kalAsavaNaM dvitIyavyavahAramudAhariSyAmaH / bhinnapratyutpannaH tatra bhinnapratyutpanne karaNasUtraM yathAguNayedaMzAnazairhArAn hArairghaTeta yadi teSAm / vajrApavartanavidhividhAya taM bhinnaguNakAre // 2 // atroddezakaH zuNThyAH palena labhate caturnavAMzaM paNasya yaH puruSaH / kimasau brUhi sakhe tvaM triguNena palASTabhAgena / / 3 / / maricasya palasyAghaH paNasya saptASTamAMzako yatra / tatra bhavetika mUlyaM palaSaTpaJcAMzakasya vada // 4 // 1 yaha zloka P meM chUTa gayA hai / 2 M mau. / 3. kalAsavarNa vyavahAra ( bhinna ) jinhoMne karmarUpI vRkSa ko pUrNataH nirmUla kara diyA hai aura jinake caraNa kamala tInoM lokoM ke rAjendroM ke jhuke hue mastaka para lage hue mukuToM dvArA utpanna prabhAmaMDala dvArA veSTita haiM, aise jinendra candranAtha bhagavAn ko maiM bhaktipUrvaka praNAma karatA hU~ // 1 // isake pazcAt hama kalAsavarNa ( bhinna ) nAmaka dvitIya vyavahAra ko prakaTa kreNge| bhinna pratyutpanna ( bhinnoM kA guNana ) bhinnoM ke guNana ke sambandha meM nimnalikhita niyama hai bhinnoM ke guNana meM aMzoM ko aMzoM se guNita kiyA jAtA hai aura haroM ko haroM se guNita kiyA jAtA hai jaba ki unake sambandha meM ( sambhava ) tiryak prahAsana (vajra apavartana) kI kriyA kI jA cukI ho // 2 // udAharaNArtha prazna / he mitra, mujhe batalAo yadi adarakha ( ginger ) kA eka pala paNa meM milatA ho to kisI vyakti ko hai pala ke liye kyA milegA? // 3 // paNa meM 1 pala mirca milatI ho to batalAo ki pala mirca kI kyA kImata hogI? // 4 // eka vyakti ko lambI mirca eka paNa meM pala milatI 1 kalAsavarNa kA zAbdika artha bhAga hotA hai, kyoMki kalA kA artha solahavA~ bhAga hotA hai| isaliye, kalAsavarNa kA upayoga bhinna ko sAdhAraNa rUpa se darzAne ke liye kiyA gayA hai| (2) jaba 343 prahlAsita kiye jAte haiM to tiryak prahrAsana dvArA 34 prApta hotA hai /

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-3..] kalAsavarNavyavahAraH [37 kazcitpaNena labhate tripaJcabhAgaM palasya pipplyaaH| navabhiH paNairdvibhaktaiH kiM gaNakAcakSva guNayitvA // 5 // krINAti paNena vaNigajIrakapalanavadazAMzakaM yatra / tatra paNaiH pazcAdhaiH kathaya tvaM kiM samagramate // 6 // dhyAdayo dvitayavRddhayoM'zakAstryAdayo dvayacayA harAH punaH / te dvaye dazapadAH kiyatphalaM brUhi tatra guNane dvayordvayoH / / 7 // iti bhinngunnaakaarH| bhinnabhAgahAraH bhinnabhAgahAre karaNasUtraM yathAaMzIkRtyacchedaM pramANarAzestataH kriyA gunnvt| pramitaphale'nyaharaghne vicchidi vA sakalavacca bhAgahRtau // 8 // atroddezakaH hiGgoH palArdhamaulyaM paNatripAdAMzako bhavedyatra / tatrArdhe vikrINan palamekaM kiM naro labhate // 9 // agaroH palASTamena triguNena paNasya viMzatitryaMzAn / upalabhate yatra pumAnekena palena kiM tatra // 10 // paNapaJcamaizcaturbhirnakhasya palasaptamo vyazItiguNaH / saMprApyo yatra syAdekena paNena kiM tatra // 11 // ho to he gaNitajJa ! guNana ke pazcAt kaho ki use 3 paNa meM kitanI mirca milegI ? // 5 // eka vaNika eka paNa meM pala jIrA (cumin seeds) kharIdatA hai / he samagramate ! batalAo ki vaha 5 paNa meM kitanA kharIdegA? // 6 // diye gaye bhinnoM meM aMza 2 se Arambha hokara 2 se bar3hate cale jAte haiN| unake hara 3 se Arambha hokara 2 se bar3hate cale jAte haiM; ve aMza aura hara donoM dazAoM meM saMkhyA meM dasa rahate haiM / batalAo ki do bhinnoM ko eka bAra meM lene para unake guNanaphala alaga-alaga kyA hoMge? // 7 // isa prakAra, kalAsavarNa vyavahAra meM bhinna guNakAra nAmaka pariccheda samApta huaa| bhinna bhAgahAra ( bhinnoM kA bhAga ) bhinnoM ke bhAga ke sambandha meM nimnakhita niyama hai bhAjaka ke hara ko aMza tathA aMza ko hara banAne ke pazcAt kevala guNana kI kriyA karanA par3atI hai| athavA, bhAjaka aura bhAjya ko eka dUsare ke haroM dvArA guNita kara prApta hara rahita guNanaphaloM kA bhAga kevala pUrNa saMkhyAoM ke bhAga kI bhA~ti kiyA jAtA hai // 8 // udAharaNArtha prazna jaba 3 paNa meM pala hIMga milatI hai to eka vyakti ko eka pala hIMga usI bhAva se becane para kyA milegA? // 9 // hai pala ( lAla caMdana kI lakar3I) kA mUlya 2. paNa hai to eka pala agaru kA kyA mUlya hogA ? // 10 // nakha itra ke pala kA mUlya 6 paNa hai to eka paNa meM ( usI argha se) kitane pala ina milegA? // 11 // diye gaye bhinnoM ke aMza 3 se Arambha hokara kramazaH 1 dvArA (7) yahA~ kathita bhinna , , , ityAdi haiM / (8 ) ---adabasa .... to

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30] gaNitasArasaMgrahaH [3. 12tryAdirUpaparivRddhiyujoM'zA yAvadaSTapadamekavihInAH / hArakAstata iha dvitayAdyaiH kiM phalaM vada pareSu hRteSu // 12 // iti bhinnbhaaghaarH| bhinnavargavargamUlaghanaghanamUlAni 'bhinnavargavargamUlaghanaghanamUleSu karaNasUtraM yathAkRtvAcchedAMzakayoH kRtikRtimUle ghanaM ca ghanamUlam / tacchedairaMzahatau vargAdiphalaM bhavedbhinne // 13 / / atroddezakaH paJcakasaptanavAnAM dalitAnAM kathaya gaNaka varga tvam / SoDazaviMzatizatakadvizatAnAM ca tribhaktAnAm // 14 // trikAdirUpadvayavRddhayoM'zA dvikAdirUpottarakA harAzca / padaM mataM dvAdazavargameSAM vadAzu me tvaM gaNakAgragaNya // 15 // pAdanavAMzakaSoDazabhAgAnAM paJcaviMzatitamasya / SaTtriMzadbhAgasya ca kRtimUlaM gaNaka bhaNa zIghram / / 16 / / bhinne varge rAzayo vargitA ye teSAM mUlaM saptazatyAzca kiM syAt / tryaSTonAyAH paJcavarNoddhRtAyA brUhi tvaM me vargamUlaM pravINa // 17 // 1M bhinnavargabhinnavargamUlabhinnaghanatanmUleSu / bar3hate cale jAte haiM jaba taka ki unakI saMkhyA 8 nahIM ho jaatii| hara bhI do se Arambha hokara saMvAdI aMzoM se kramazaH eka kama haiN| mujhe batalAo ki yadi pratyeka agrima bhinna ko pUrvavartI bhinna ke dvArA vibhAjita kiyA jAya to kyA phala hogA ? // 12 // isa prakAra, kalAsavarNa vyavahAra meM, bhinna bhAgahAra nAmaka pariccheda samApta huaa| bhinna sambandhI varga, vargamUla, ghana, ghanamUla bhinnoM ke sambandha meM varga karane vargamUla nikAlane, ghana karane, aura ghanamUla nikAlane ke liye niyama jaba hala kiye gaye bhinna ke aMza aura hara kA alaga-alaga varga, vargamUla, ghana athavA ghanamUla nikAla liyA jAtA hai taba isa taraha prApta naye aMza ko naye hara dvArA bhAjita kiyA jAtA hai| isa prakAra bhinna ke sambandha meM varga athavA vargamUla, ghana athavA ghanamUla prApta hotA hai // 13 // udAharaNArtha prazna he aMkagaNitajJa ! mujhe batalAo ki 1, 2, 3, 4, aura 24 ke varga kyA. hoNge?||14|| diye gaye bhinnoM ke aMza 3se Arambha hote haiM aura uttarottara kramazaH 2 dvArA bar3hate cale jAte haiM; hara 2 se Arambha hote haiM aura uttarottara 1 dvArA bar3hate cale jAte haiN| ina bhinnoM kI saMkhyA 12 hai| he aMkagaNitajJoM meM agraNI! mujhe unake varga zIghra batalAo ? // 15 // he aMkagaNitajJa! mujhe zIghra batAo ki 1.1. 1 aura ke vargamUla kyA hoMge ? // 16 // he kuzala vyakti ! mujhe bhinnoM ke vargoM se sambandhita praznoM meM prApta vargita rAziyoM ke vargamUla tathA 66 kA vargamUla batalAo // 17 // * 700-348 ke rUpa meM darzAyA gayA hai| (17) yahA~ 26 ko mUla gAthA meM 12

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3. 23-] kalAsavarNavyavahAraH [39 ardhatribhAgapAdAH paJcAMzakaSaSThasaptamASTAMzAH / dRSTA navamazceSAM pRthak pRthagbehi gaNaka ghanam // 18 // tritayAdi catuzcayakoM'zagaNo dvimukhadvicayo'tra harapracayaH / dazakaM padamAzu tadIyaghanaM kathaya priya sUkSmamate gaNite // 19 // zatakasya paJcaviMzasyASTavibhaktasya kathaya ghanamUlam / navayutasaptazatAnAM viMzAnAmaSTabhaktAnAm // 20 // bhinnaghane paridRSTaghanAnAM mUlamudagramate vada mitra / byUnazatadvayayugdvisaharuyA zvApi navaprahatatrihRtAyAH // 21 // iti bhinnavargavargamUlaghanaghanamUlAni / bhinnasaMkalitam bhinnasaMkalite karaNasUtraM yathApadamiSTaM pracayahataM dviguNaprabhavAnvitaM cayenonam / gacchArdhanAbhyastaM bhavati phalaM bhinnasaMkalite // 22 // 1M saptazatasyApi sakhe vyekonatriMzakASTakAptasya / 1.16 , aura rAziyA~ dI gaI haiN| inake ghana alaga-alaga batalAo // 18 / / diye gaye bhinnoM ke aMza 3 se Arambha hokara 4 dvArA uttarottara bar3hate haiN| hara 2 se Arambha hokara uttarottara 2 dvArA bar3hate haiN| aise bhinnAtmaka padoM kI saMkhyA 10 hai| he tIvra buddhidhArI gaNaka mitra ! batalAo ki unake ghana kyA hoMge? // 19 // 15 aura 19 ke ghanamUla nikAlo // 20 // he agramate mitra ! bhinnoM ke ghana nikAlane ke praznoM meM prApta dhana rAziyoM ke ghanamUla aura 2197 kA ghanamUla nikAlakara btlaao| isa prakAra kalAsavarNa vyavahAra meM bhinna sambandhI varga, vargamUla, dhana, ghanamUla nAmaka pariccheda samApta huaa| bhinna saMkalita ( bhinnAtmaka zreDhiyoM kA yogakaraNa ) bhinnAtmaka zreDhiyoM kA saMkalana sambandhI niyama samAntara zreDhi meM bhinnAtmaka zreDhi ko banAne vAle padoM kI cunI huI saMkhyA ko pracaya dvArA guNita karate haiM aura prathamapada kI dviguNita rAzi meM milAte haiN| prApta phala ko pracaya se hAsita karate haiN| jaba yaha pariNAmI rAzi padoM kI saMkhyA kI AdhI rAzi se guNita kI jAtI hai, taba vaha samAntara zredi kI bhinnAtmaka zreDhi ke yoga ko utpanna karatI hai // 22 // hai| isake liye dvitIya adhyAya kI 62vIM (22) bIjIyarUpa se, ya = (naba+2a-ba) gAthA dekhiye /

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40] gaNitasArasaMgrahaH [3.24atroddezakaH dvitryaMzaH SaDbhAgastricaraNabhAgo mukhaM cayo gcchH| dvau paJcamI tripAdo dvitryaMzo'nyasya kathaya kiM vittam / / 23 / / AdiH pracayo gacchatripaJcamaH paJcamastripAdAMzaH / sarvAMzaharau vRddhau dvitribhirA saptakAJca kA citiH // 24 // ___ iSTagacchasyAdyuttaravargarUpaghanarUpadhanAnayanasUtrampadamiSTamekamAdivya'keSTadaloddhRtaM mukhonapadam / pracayo vittaM teSAM vargo gacchAhataM vRndam // 25 // udAharaNArtha prazna jisa zreDhi meM prathama pada, pracaya aura padoM kI saMkhyA kramazaH 3, aura hoM tathA aisI hI eka aura zreDhi meM ye kramazaH 3, 3 aura hoM to ina zreDhiyoM ke yoga batalAo // 23 // samAnAntara zreDhi meM dI gaI eka zreDhi ke prathama pada, pracaya aura padoM kI saMkhyA kramazaH 6, 6 aura hai hai| ina saba bhinnAtmaka rAziyoM ke aMza aura hara uttarottara 2 aura 3 dvArA kramazaH bar3hAye jAte haiM jaba taka ki 7 zreDhiyA~ isa prakAra taiyAra nahIM ho jaatiiN| batalAo ki inameM se pratyeka zreDhi kA yoga kyA hai ? // 24 // jaba yoga, dI huI zreDhi ke padoM kI saMkhyA kA vargarUpa yA dhanarUpa ho to cune hue padoM vAlI zreDhi ke sambandha meM prathama pada, pracaya aura yoga nikAlane kA niyama jo bhI padoM kI saMkhyA cunI gaI ho use lo aura prathama pada ko eka mAna lo| padoM kI saMkhyA ko prathama pada dvArA hAsita kara aura taba eka kama padoM kI saMkhyA kI AdhI rAzi dvArA bhAjita karane se pracaya prApta hotA hai| inake sambandha meM zreDhi kA yoga padoM kI saMkhyA kI rAzi kA varga hotA hai| yaha jaba padoM kI saMkhyA dvArA guNita kiyA jAtA hai to yoga kA dhana prApta hotA hai / / 25 / / na-1 (23) jaba zredi meM padoM kI saMkhyA bhinna ke rUpa meM dI gaI ho to spaSTa hai ki aisI zreDhi sAdhAraNataH banAI nahIM jA sktii| parantu, abhiprAya yaha pratIta hotA hai ki diyA gayA niyama ina dazAoM meM ThIka utaratA hai| ( 25 ) spaSTa hai ki, sUtra meM ya= na (a+na-1 ba), aura jaba a = 1aura ba = 2(na-a) ho to ya kA mAna na' ke tulya ho jAtA hai| isa yoga meM na kA guNana karane meM, a aura ba kA na dvArA guNana bhI aMtarbhUta hai tAki jaba a = na aura ba =na-12na ho, taba ya = na ho| kucha aura vicAra na-1 karane para jJAta hogA ki a kA mAna cAhe pUrNAMka athavA bhinnIya ho phira bhI ba kA nAma) na-1 rUpavAlA mAna ya kI arhA ko na ke rUpa meM lA sakatA hai| ' cihna kA artha antara hotA hai|

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kalAsavarNavyavahAraH atroddezakaH 'padamiSTaM dvitryaMzo rUpeNAMzo harazca saMvRddhaH / yAvaddazapadameSAM vada mukhacayavargavRndAni // 26 // iSTaghanadhanAdyuttaragacchAnayanasUtram iSTacaturthaH prabhavaH prabhavAtpracyo bhavedvisaMguNita: / pracayazcaturabhyasto gacchasteSAM yutirvRndam ||27|| -3.28 ] atroddezakaH dvimukhaikacayA aMzA striprabhavaikottarA harA ubhaye / pacapadA vada teSAM ghanadhanamukhacayapadAni sakhe ||28|| 1 yaha zloka M meM aprApya hai / udAharaNArtha dI huI zredi meM padoM kI cunI huI saMkhyA 3 hai; isa bhinna ke aMza aura hara uttarottara eka dvArA bar3hAye jAte haiM jaba taka ki 10 vibhinna bhinnAtmaka pada prApta nahIM hote| ina bhinnoM ko saMvAdI samAntara zreDhiyoM ke padoM kI saMkhyA mAnakara unake sambandha meM prathama pada, pracaya aura yoga ke varga tathA ghana nikAlo ||26|| samAntara zreDhi ke diye hue yoga ( jo ki kisI iSTa rAzi kA ghana ho ) ke sambandha meM prathama pada, pracaya aura padoM kI saMkhyA nikAlane kA niyama iSTa rAzi kA caturthAMza prathama pada hai / isa prathama pada meM do kA guNana karane para pracaya utpanna hotA hai / pracaya meM cAra kA guNA karane para ( eka ) iSTa zreDhi ke padoM kI saMkhyA prApta hotI hai| inase sambandhita yoga iSTa rAzi kA ghana hotA hai // 27 // udAharaNArtha prazna aMza 2 se Arambha hote haiM aura uttarottara 1 dvArA bar3hate haiM; hara ko 1 dvArA bar3hAte haiM jo ki Arambha meM 3 hai / ye donoM prakAra ke pada ( aMza aura hara ) meM se pratyeka saMkhyA meM pA~ca hai / ina cunI huI bhinnAtmaka rAziyoM ke sambandha meM, he mitra, ghanAtmaka yoga aura saMvAdI prathamapada, pracaya aura padoM kI saMkhyA nikAlo ||28|| ( 27 ) yaha niyama kevala vizeSa dazA meM prayukta kiyA gayA hai / yaha sAdhAraNa rUpa se bhI prayoga meM lAyA jA sakatA hai / niyama isa taraha hai : kyoMki prathama pada [ 41 ka ka 3ka 5 ka + + + * 2 ka padoM taka = 4 4 4 2 isa kriyA kI sAdhAraNa prayojyatA, samIkaraNa ka X ( paka) = ka se zIghra spaSTa ho sakatI para hai / ina saba dazAoM meM zreDhike padoM kI saMkhyA prathama pada ko pa se guNita karane para prApta ho sakatI hai ka para ga0 sA0 saM0-6 - ( 2 4 2 3 = ka ka ) hai / pratyeka dazA meM pracaya prathamapada se dviguNita liyA jAtA hai /

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gaNitasArasaMgrahaH dRSTadhanAdyuttarato dviguNatriguNadvibhAgatribhAgAdISTadhanAdyuttarAnayanasUtramdRSTavibhakteSTadhanaM dviSThaM tatpracayatADitaM pracayaH / tatprabhavaguNaM prabhavo [NabhAgasyeSTavittasya / / 29 / / / atroddezakaH prabhavasya| rUpaM pracayaH pazcASTamaH samAnapadam / icchAdhanamapi tAvatkathaya sakhe ko mukhapracayau // 30 // pracayAdAdirdviguNastrayodazASTAdazaM padaM sveSTam / vittaM tu saptaSaSTiH SaDghanabhaktA vadAdicayau // 31 // muMkhamekaM dvitryaMzaH pracayo gacchaH smshcturnvmH| dhanamiSTaM dvAviMzatirekAzItyA vadAdicayau // 32 // 1 . guNabhAgAdyattarAnayanasUtram / 24 pracayena / 3 M gunnbhaagaadyuttrecchaayaaH| 4 yaha zloka M meM 31 ve zloka ke sthAna meM hai tathA B meM chUTA huA hai / dI huI samAntara zreDhi ke jJAta yoga, prathama pada aura pracaya se kisI zredi ke prathamapada aura pracaya nikAlanA jabaki iSTa yoga dI gaI zreDhi ke jJAta yoga se dugunA, tigunA, AdhA, eka tihAI, athavA usakA apavartya yA aMza ho hala karane kI suvidhA ke lie iSTa yoga ko jJAta yoga dvArA vibhAjita kara do sthAnoM meM rakho / yaha bhajanaphala, jaba jJAta pracaya dvArA guNita kiyA jAtA hai taba cAhA huA pracaya prApta hotA hai / aura vahI bhajanaphala, jaba jJAta prathamapada dvArA guNita hotA hai taba cAhe hue prathama pada ko utpanna karatA hai // 29 // udAharaNArtha prazna kisI zreDhi kA prathama pada 3 hai, pracaya / hai aura padoM kI saMkhyA ( jo dI huI tathA iSTa, donoM zreDhiyoM, ke liye ubhayaniSTha hai ) 5 hai| iSTa zreDhi tathA dI gaI zreDhi kA yoga alaga-alaga hai hai| he mitra ! iSTa zreDhi kA prathamapada tathA pracaya nikAlo // 30 // (pracaya 1 hai ) aura prathamapada pracaya kA dugunA hai; padoM kI saMkhyA 3 hai; iSTa zreDhi kA yoga 214 hai| prathamapada aura pracaya nikAlo // 31 // prathama pada 1 hai, pracaya 3 aura padoM kI saMkhyA donoM (dI gaI zreDhi aura iSTa zreDhi ) ke liye ubhayasAdhAraNa hai hai / iSTa zreDhi kA yoga 13 hai / iSTa zreDhi ke prathamapada aura pracaya nikAlo // 32 // (29) 84 vIM gAthA kA noTa adhyAya 2 meM dekhiye / 2 vaya + (1-2)+2 (33) pratIka rUpa se, na% --- adhyAya 2 kI gAthA 69 vIM kA noTa bhI dekhiye /

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kalAsavarNavyavahAraH gacchAnayanasUtramdviguNacayaguNitavittAduttaradalamukhavizeSakRtisahitAt / mUlaM pracayAdhaMyutaM prabhavonaM cayahRtaM gacchaH / / 33 / / prakArAntareNa tadevAhadviguNacayaguNitavittAduttaradalamukhavizeSakRtisahitAt / mUlaM kSepapadonaM pracayena hRtaM ca gaccha: syAt // 34 // atroddezakaH dvipaJcAMzo vaktraM triguNacaraNaHsyAdiha cayaH SaDaMzaH saptannastrikRtivihRto vittamuditam / cayaH paMcASTAMzaH punarapi mukhaM dhyaSTamamiti tricatvAriMzA:svaM priya vada padaM shiighrmnyoH||35|| ___AdhuttarAnayanasUtram-. gecchAptagaNitamAdivigataikapadArdhaguNitacayahInam / padahRtadhanamAyUnaM nirekapadadalahRtaM pracayaH // 36 / / 1 nIce likhe hue do zlokoM meM sthAna meM M meM isa prakAra kA pATha hai aSTottaraguNarAzItyAdinA iSTa-dhanagaccha AnetavyaH / isake sAthahI, parikarma vyavahAra kI 70 vIM gAthA kI punarAvRtti hai| 2 K aura B prabhavo gacchAptadhanam / / samAntara zreDhi meM padoM kI saMkhyA nikAlane ke liye niyama prathama pada aura pracaya kI AdhI rAzi ke antara ke varga meM, pracaya kI dugunI rAzi ko zreDhi ke yoga dvArA guNita karane se prApta rAzi jor3I jAtI hai| isa prApta rAzi ke vargamUla meM pracaya kI AdhI rAzi jor3I jAtI hai| isa yogaphala ko prathama pada dvArA hAsita kara aura taba pracaya dvArA bhAjita karane para zreDhi ke padoM kI saMkhyA prApta hotI hai // 33 // padoM kI saMkhyA nikAlane kI dUsarI vidhi prathamapada aura pracaya kI AdhI rAzi ke antara ke varga meM, pracaya kI dugunI rAzi ko zreDhi ke yoga dvArA guNita karane se prApta phala milAte haiN| yogaphala ke vargamUla meM se kSepapada ghaTAte haiN| jaba ise pracaya dvArA bhAjita karate haiM taba zreTi ke padoM kI saMkhyA prApta hotI hai // 34 // udAharaNArtha prazna __dI huI zreDhi ke sambandha meM, prathama pada 3 hai, pracaya hai hai aura yoga 54 hai| punaH, dUsarI zreDhi ke sambandha meM, pracaya hai, prathamapada hai hai aura yoga hai| he mitra ! ina do zreDhiyoM ke viSaya meM, padoM kI saMkhyA zIghra nikAlo // 35 // prathama pada aura pracaya nikAlane ke liye niyama zredi ke yoga ko padoM kI saMkhyA dvArA bhAjita karane se prApta rAzi jaba eka kama padoM kI saMkhyA kI AdhI rAzi aura pracaya ke guNanaphala dvArA hvAsita kI jAtI hai, taba zreDhi kA prathama pada utpanna hotA hai| jaba yoga ko padoM kI saMkhyAse bhAjita kara aura prathamapada dvArA hAsita kara eka kama padoM kI saMkhyA kI AdhI rAzi dvArA bhAjita karate haiM taba pracaya prApta hotA hai| (34) kSepa pada ke liye adhyAya 2 kI 70 vI gAthA dekhiye / (36) dvitIya adhyAya kI 74 vIM gAthA kA noTa dekhiye|

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44] gaNitasArasaMgrahaH atroddezakaH tricaturthacatuHpaJcama cayagacche khessushshihtaiktriNshd-| vitte vyaMzacatuHpaJcamamukhagacche ca vada mukhaM pracayaM ca // 37 // - iSTagacchayorvyastAdyuttarasamadhanadvigutriguNadvibhAgatribhAgadhanAnayanasUtramvyekAtmahato gacchaH sveSTanA dviguNitAnyapadahInaH / mukhamAtmonAnyakRtiDhikeSTapaghAtavarjitA pracayaH // 38 // atroddezakaH ekAdiguNavibhAgaH svaM vyastAdyattare hi vada mitra / dvidhyaMzaunaikAdazapaJcAMzakamizranavapadayoH // 39 / / guNadhanaguNasaMkalitadhanayoH sUtrampadamitaguNahatiguNitaprabhavaH syAhuNadhanaM tadAbUnam / ekonaguNavibhaktaM guNasaMkalitaM vijAnIyAt // 40 // udAharaNArtha prazna do zreDhiyoM ke prathama pada aura pracaya nikAlo jaba ki eka dazA meM yoga 44 hai, hai pracaya hai aura 6 padoM kI saMkhyA hai, tathA anya dazA meM yoga ka hai, prathama pada hai aura 3 padoM kI saMkhyA hai // 37 // jaba padoM kI saMkhyA koI bhI cunI huI rAzi ho, taba do zreDhiyoM ke sambandha meM paraspara badale hue prathama pada, pracaya, tathA unake yoga (jinameM eka-dUsare ke barAbara athavA eka dUsare se dugunA, tigunA, AdhA yA tihAI ho) nikAlane ke liye niyama eka zreDhi ke padoM kI saMkhyA svataH ke dvArA guNita kara eka dvArA hAsita karate haiN| ise donoM zreDhiyoM ke yoga kI iSTa niSpatti dvArA guNita kara, aura taba, dUsarI zreDhi ke padoM kI saMkhyA kI dugunI rAzi dvArA hAsita kara paraspara badalane yogya prathama pada prApta karate haiM // 38 // dUsarI zreDhi ke padoM kI saMkhyA kA varga, padoM kI saMkhyA dvArA hI hAsita karate haiN| ise iSTa niSpatti aura prathama zreDhi ke padoM kI saMkhyA ke guNanaphala kI dugunI rAzi dvArA hAsita karane para, paraspara badalane yogya usa zreDhi kA pracaya utpanna hotA hai| udAharaNArtha prazna do zreDhiyoM ke sambandha meM, jinameM 103 aura 96 padoM kI saMkhyA hai, prathama pada aura pracaya paraspara badalane yogya haiN| eka zreDhi kA yoga dUsarI zreDhi ke yoga kA apavartya athavA aMza hai jo eka se Arambha honevAlI prAkRta saMkhyAoM dvArA guNana athavA bhAga dvArA prApta huA hai / he mitra ! ina yogoM ko, prathama padoM aura pracayoM ko nikAlo // 39 // guNottara zreDhi meM guNadhana evaM zreDhi kA yoga nikAlane ke liye niyama guNottara zreDhi meM prathamapada ko, jitanI padoM kI saMkhyA hotI hai utanI bAra sAdhAraNa niSpatti dvArA guNita karane para guNadhana prApta hotA hai| yaha guNadhana prathamapada dvArA hAsita hokara tathA eka kama sAdhAraNa niSpatti dvArA bhAjita hokara guNottara zreDhi ke yoga ke barAbara ho jAtA hai // 40 // (38) dvitIya adhyAya kI 86 vIM gAthA kA noTa dekhiye / (40) dvitIya adhyAya kA 93 vIM gAthA kA noTa dekhiye|

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-3. 53 ] kalAsavarNavyavahAraH guNasaMkalitAntyadhanAnayane tatsaMkalitAnayane ca sUtramguNasaMkalitAntyadhanaM vigataikapadasya guNadhanaM bhavati / tahuNaguNaM mukhonaM vye kottarabhAjitaM sAram // 41 // atroddezaka: prabhavo'STamazcaturthaH pracayaH paJca padamatra guNaguNitam / guNasaMkalitaM tasyAntyadhanaM cAcakSva me zIghram // 42 // guNadhanasaMkalitadhanayorAdyuttarapadAnyapi pUrvoktasUtrairAnayet / ___samAneSTottaragacchasaMkalitaguNasaMkalitasamadhanasyAdyAnayanasUtrammukhamekaM cayagacchAviSTau mukhvittrhitgunncityaa| hRtacayadhanamAdiguNaM mukhaM bhavedvicitidhanasAmye // 43 // 1 kevaLa B meM prApya / guNottara zreDhi kA antimapada tathA yoga nikAlane ke liye niyama guNottara zreDhi kA aMtyadhana athavA aMtima pada, dUsarI aisI hI zreDhi kA guNadhana hotA hai jisameM padoM kI saMkhyA eka nyUna hotI hai| yaha aMtyadhana sAdhAraNa niSpatti dvArA guNita hokara aura prathama pada dvArA hAsita hokara tathA eka kama sAdhAraNa niSpatti dvArA bhAjita hokara zreDhi ke yoga ko utpanna karatA hai // 41 // udAharaNArtha prazna guNottara zreDhi ke sambandha meM prathamapada hai hai, sAdhAraNa niSpatti 1 hai aura padoM kI saMkhyA 5 hai / mujhe zIghra batalAo ki zreDhi kA yoga tathA aMtima pada kyA kyA haiM ? // 42 // samAna yoga vAlI do samAntara evaM guNottara zreDhi ke ubhaya sAdhAraNa prathama pada ko nikAlane ke liye niyama, jaba ki unakI cunI huI padoM kI saMkhyA barAbara ho aura isI taraha se varaNa kiye gaye pracaya aura sAdhAraNa niSpatti barAbara hoM prathama pada ko eka lete haiM, padoM kI saMkhyA aura sAdhAraNa niSpatti tathA pracaya mana se kucha bhI cuna kiye jAte haiM / yahAM uttara dhana ko guNottara zreDhi ke yoga meM se Adi dhana ko ghaTAne se prApta huI rAzi dvArA bhAjita karate haiM / ise cune hue prathama pada se guNita karane para, ina donoM zreDhiyoM ke sambandha meM cAhA huA ubhayasAdhAraNa prathamapada utpanna hotA hai // 43 // (41) dvitIya adhyAya kI 95 vIM gAthA kA noTa dekhiye| [ pichale adhyAya meM kathita niyamoM dvArA guNadhana aura zredi ke yoga ke sambandha meM guNottara zredi ke prathamapada, sAdhAraNa niSpatti aura padoM kI saMkhyA nikAlI jA sakatI haiN| ina niyamoM ke liye adhyAya 2 kI 87, 97, 101 aura 103 vIM gAthAyeM dekhiye| ] (43) Adi dhana aura uttaradhana ke liye 63 aura 64 vIM gAthAyeM (adhyAya 2 dekhiye / yaha niyama pratIka rUpa se isa taraha sAdhita hotA hai-a = 1 na(na- 1)xba} {(rana-11-nax1 } jahA~ ba = ra hai| sarala sAdhana ke hetu prathamapada ko 1 cuna liyA jAtA hai, paraMtu spaSTa hai ki koI rAzi pahile isa taraha mAnI jA sakatI hai| Adi dhana aura uttaradhana ke dvArA niyama ke kathana ko sarala banAne ke liye yahA~ prathamapada ko mAna liyA gayA hai| yahAM prApta sUtra guNottara zredi ke yogasUtra aura samAntara zreDhi ke sUtra ko samIkAra rUpa meM likhane se milA hai| yahAM dhyAna dene yogya zabda caya hai jisakA upayoga guNottara aura samAntara zreDhi, donoM ke kramazaH sAdhAraNa niSpatti aura pracaya ke liye kiyA gayA hai|

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gaNita sArasaMgrahaH atroddezakaH bhAvavArdhibhuvanAni padAnyambhodhipaJca munayastrihRtAste / uttarANi vadanAni kati syuryugma saMkalita vittasameSu ||44 || iti bhinnasaMkalitaM samAptam / bhinnanyutkalitam 46 ] [ 3. 44- bhinnavyutkalite karaNasUtraM yathA gacchAdhikeSTamiSTaM cayahatamUnottaraM dvihAdiyutam / zeSeSTapadArdhaguNaM vyutkalitaM svaSTavittaM ca ||45 || zeSa gaccha syAdyA nayanasUtram - precayArghonaH prabhavo yutazcayadhneSTapadacayArthAbhyAm / zeSasya padasyAdizcayastu pUrvokta eva bhavet // 46 // guNaguNatespi cayAdI tathaiva bhedo'yamatra zeSapade / iSTapadamitaguNAitiguNitaprabhavo bhavedvakvam ||47|| 1 M pracayaguNiteSTagacchassAdiH prabhavaH padasya zeSasya / pUrvoktaH pracayassyAdiSTasya prAktanAdeva // udAharaNArtha prazna padoM kI saMkhyA kramazaH 5, 4 aura 3 hai / sAdhAraNa niSpatti tathA barAbara pracaya kramazaH 3, aura haiM / ina samAna yoga vAlI guNottara tathA samAntara zreDhiyoM ke saMvAdI prathama padoM kI arhAoM ( values ) ko nikAlo // 44 // isa prakAra, kalAsavarNaM vyavahAra meM, saMkalita nAmaka pariccheda samApta huA / bhinna vyutkalita [ zreDhirUpa bhinnoM kA vyutkalana ] bhinna vyutkalita kriyA ko karane kA niyama nimnalikhita hai zreDhi meM kula padoM kI saMkhyA ko cune hue padoM kI saMkhyA meM sammilita karo aura svayaM cunI huI padoM kI saMkhyA ko alaga se lo / ina rAziyoM meM se pratyeka ko pracaya dvArA guNita karo aura guNanaphaloM ko pracaya dvArA hAsita karo tathA do dvArA guNita kro| ina pariNAmI rAziyoM ko jaba kramazaH zeSapadoM kI saMkhyA kI AdhI rAzi aura padoM kI cunI huI saMkhyA kI AdhI rAzi dvArA guNita karate haiM taba krama se zeSa zreDhi kA yoga tathA zreDhi ke cune hue bhAga kA yoga prApta hotA hai // 45 // zeSa gaccha sambandhI prathama pada ko nikAlane ke liye niyama -- Dhi kA prathamapada, pracaya kI AdhI rAzi dvArA hAsita hokara aura pracaya dvArA guNita cunI huI padoM kI saMkhyA dvArA milAyA jAkara tathA pracaya kI AdhI rAzi dvArA bhI milAyA jAkara zeSa zreDhi ke zeSa padoM kI saMkhyA ke prathama pada ko utpanna karatA hai| pracaya zeSa zreDhi kA hotA hai // 46 // guNottara zreDhi ke ThIka vaise hI hote haiM jaise ki dI huI zreDhi aura usake pada meM sAdhAraNa niSpatti ko utane bAra guNita karate haiM hai| prApta guNanaphala zeSa zreDhi kA prathamapada hotA hai| prathamapada meM yahI aMtara hotA hai ||47|| jaisA pracaya dI huI zreDhi meM hotA hai vaisA hI viSaya meM bhI, sAdhAraNa niSpatti aura prathamapada cune hue bhAga meM hote haiN| dI huI zreDhi ke prathama jitanI ki cunI huI padoM kI saMkhyA hotI zeSa zreDhi ke prathamapada aura dI huI zreDhi ke (45) dvitIya adhyAya kI 106 vIM gAthA kA noTa dekhiye / (46) dvitIya adhyAya kI 109 vIM gAthA kA noTa dekhiye / (47) dvitIya adhyAya kI 110 vIM gAthA kA noTa dekhiye /

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kalAsavarNavyavahAraH [47 atroddezakaH pAdottaraM dalAsyaM padaM tripAdAMzakaHsamuddiSTaH / sveSTaM caturthabhAgaH kiM vyutkalitaM samAkalaya // 48 // prabhavo'dhaM paJcAMzaH pracayo dvitryaMzako bhavedgacchaH / paJcASTAMzaHsveSTaM padamRNamAcakSva gaNitajJa // 49 // AdizcaturthabhAgaH pracayaH pnycaaNshktripshcaashH| gaccho vAlchAgaccho dazamo vyavakalitamAnaM kim // 50 // tribhAgau dvau vakraM paJcamAMzazcayaHsyAt padaM trighnaH pAdaH paJcamaHsveSTagacchaH / SaDaMza:saptAMzo vA vyayaH ko vada tvaM kalAvAsa prajJAcandrikAbhAsvadindo // 5 // dvAdazapadaM caturtharNottarama?napazcakaM vadanam / tricatuHpaJcASTeSTapadAni vyutkalitamAkalaya // 52 // guNasaMkalitavyutkalitodAharaNam / dvitribhAgarahitASTamukhaM dvitryaMzako guNacayo'STa padaM bhoH| mitra ratnagati pazcapadAnISTAni zeSamukhavittapadaM kim // 53 // iti bhinnavyutkalitaM samAptam / 1M ca cturbhaagH| 2 M kiM vyutkalitaM samAkalaya / 3K aura M meM isake pazcAt "iti sArasaGghahe mahAvIrAcAryasya kRtau dvitIyavyavahArassamApta" jor3A gayA hai / yaha vAstava meM bhUla pratIta hotI hai| udAharaNArtha prazna dI huI zreDhi meM pracaya hai, prathamapada 3 hai, padoM kI saMkhyA hai hai aura cunI huI padoM kI ( haTAI jAne vAlI ) saMkhyA 1 hai| aisI zreDhi kI zeSa zreDhi kA yoga nikAlo // 48 // samAntara zreDhi ke sambandha meM prathamapada hai. pracaya hai aura padoM kI saMkhyA 3 hai| yadi haTAye jAne vAle padoM kI saMkhyA hai to he gaNitajJa, zeSa zreDhi kA yogaphala batAo // 49 // dI huI zreDhi meM prathamapada 1 hai, pracaya 6 hai aura padoM kI saMkhyA 6 hai / yadi cunI huI padoM kI saMkhyA ho to zeSa zreDhi kA yogaphala batalAo // 50 // prathamapada 3 hai, pracaya 6 hai, padoM kI saMkhyA hai aura cunI gaI padoM kI saMkhyA 6, athavA hai / he caMdramA ke prakAza rUpI buddhi se camakate hue caMdramA ki bhAMti kalA ke vAsa ! mujhe batalAo ki zeSa padoM kI saMkhyA kA yoga kyA hogA ? // 51 // dI huI zreDhi ke padoM kI saMkhyA 12 hai, pracaya-2 (RNa) hai aura prathamapada 43 hai tathA cunI gaI padoM kI saMkhyAeM kramazaH 3, 4, 5 athavA 8 haiM / zeSa padoM kI saMkhyA kA yogaphala alaga-alaga nikAlo // 52 // guNottara zreDhi meM vyutkalit kA udAharaNArtha prazna prathamapada 71 hai, sAdhAraNa niSpatti hai aura padoM kI saMkhyA 8 hai| cunI huI padoM kI saMkhyAeM kramazaH 3,4,5 haiN| batalAo ki zeSa zreDhiyoM ke sambandha meM prathamapada, yoga aura padoM kI saMkhyA kyA-kyA hai ? // 53 // isa prakAra, kalAsavarNa vyavahAra meM, bhinna vyutkalit nAmaka pariccheda samApta huaa| (51) kalA ke yahA~ do artha haiM-prathama to jJAna aura anya "caMdramA ke aNk"|

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* 48 ] gaNita sArasaMgrahaH kalA savarNaSaDjAtiH itaH paraM kalAsavarNe SaDjAtimudAhariSyAmaHbhAgaprabhAgAvatha bhAgabhAgo bhAgAnubandhaH parikIrtito'taH / bhAgApavAhaH saha bhAgamAtrA SaDjAtayo 'mutra kalA savarNe || 54 || bhAgajAtiH tatra bhAgajAta karaNasUtraM yathAsahazahRtacchedahatau mithoM'zahArau samacchidAvaMzau / karau yojya tyAjyau vA bhAgajAtividhau // 55 // kalAsavarNa SaDjAti ( chaH prakAra ke bhinna ) aba hama chaH prakAra ke bhinnoM kA pratipAdana kareMge - bhAga ( sAdhAraNa bhinna ), prabhAga ( bhinnoM ke bhinna), bhAgabhAga ( jaTila yA saMkara bhinna complex fractions ), bhAgAnubaMdha ( saMyava bhinna fractions in association ), bhAgApavAha (viyavana bhinna fractions in dissociation ) aura bhAga mAtra ( bhinna jinameM Upara kathita bhinnoM meM se do yA adhika bhinna sammilita hoM ); ye bhinnoM ke chaH bheda kahalAte haiM ||54 || bhAgajAti [ sAdhAraNa bhinnoM kA jor3a aura ghaTAnA ] aga baka + kakhaga kakhaga sAdhAraNa bhinnoM kA kriyA (karaNa) sambandhI niyama diye gaye do sAdhAraNa bhinnoM sambandhI kriyAoM meM pratyeka ke aMza aura hara ko, ubhaya sAdhAraNa guNanakhaMDa dvArA haroM ko vibhAjita karane se prApta bhajanaphaloM dvArA ekAntara se guNita karate haiM / ve bhinna isa taraha prahAsita hokara samAna hara vAle ho jAte haiM / taba inameM se koI eka hara alaga kara, aMzoM ko jor3ate athavA ghaTAte haiM [ tAki dUsare samAna hara ke sambandha meM pariNAmI rAzi aMza ho ] || 55 || (55) bhinnoM ko sAdhAraNa haroM meM prahAsita karane kA niyama kevala bhinna yugma ke liye prayojya hai / nimnalikhita udAharaNa se yaha niyama spaSTa ho jAvegA - a ba kakha kha ga + ko hala karane ke liye yahA~, "a" aura "kakha" ko "ga" se guNita karate haiM joki dUsare bhinna ke hara "khaga" ko haroM ke sAdhAraNa guNanakhaNDa kha dvArA vibhAjita karane para bhajanaphala "ga" ke rUpa meM prApta hotA hai / isI prakAra dUsare bhinna meM "ba" aura "khaga" ko "ka" se guNita karate haiM jo prathama bhinna ke hara " kakha" ko haroM ke sAdhAraNa guNanakhaNDa "kha" dvArA vibhAjita karane para "ka" ke rUpa meM prApta hotA hai / isa taraha hameM kramaza: aura prApta hote haiM / isa taraha [ 3.54 aga + baka kakhaga aga kakhaga baka kakhaga

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-3. 60] kalAsavarNavyavahAraH [49 prakArAntareNa samAnacchedamudbhAvayitumuttarasUtramchedApavartakAnAM labdhAnAM cAhatau niruddhaH syAt / harahRtaniruddhaguNite hArAMzaguNe smohaarH||56|| atroddezakaH jembUjambIranAraGgacocamocAmradADimam / akraSIddalaSaDbhAgadvAdazAMzakaviMzakaiH // 57 // henastriMzacaturviMzenASTamena yathA kramam / zrAvako jina pUjAyai tadyoge kiM phalaM vada // 58 / / aSTapaJcadazaM vizaM saptaSatriMzadazakam / ekAdazatriSaSTathaMzamekaviMzaM ca saGkSipa // 51 // ekdviktrikaayekottrnvdshkssoddshaantyhraaH| nijanijamukhapramAMzAH svaparAbhyastAzca kiM phalaM teSAm / / 60 / / 1 yaha aura anugAmI zloka M meM aprApya haiM / 2 P meM 57 aura 58 zloka chUTa gaye haiN| 3 yaha zloka kevala 5 aura B meM prApya hai| sAdhAraNa ( common ) hara ko dUsarI vidhi dvArA nikAlane kA niyama haroM ke sabhI saMbhava guNanakhaMDoM aura unake sabhI antima ( ultimate) bhajana phaloM ke santata guNana se niruddha (laghuttama samApavartya ) prApta hotA hai / niruddha ko haroM dvArA bhAjita karane se prApta bhajana phaloM meM haroM aura aMzoM kA guNana karate haiM / isa prakAra se prApta haroM aura aMzoM sambandhI apavayoM ke hara samAna hote haiM / / 56 / / udAharaNArtha prazna eka zrAvaka ne jina pUjA ke lie jambUphala, nIbU , nAraMgI, nAriyala, kele, Ama aura anAra kramazaH3, 3 , 21 aura hai svarNa mudrAoM ke kharIde; mujhe batalAo ki jaba ina bhinnoM kA yoga kiyA jAya to kyA pariNAma hogA? // 57-58 // 1,20, OM aura 21 ko jor3o // 55 // bhinnoM ke 3 samUha haiM, jahA~ hara 1, 2, aura 3 se kramazaH Arambha hote haiM aura uktarottara eka dvArA bar3hate cale jAte haiM jaba taka ki aise haroM meM aMtima 9,10 aura 16 (kramazaH vibhinna samUha meM) nahIM ho jAte / ina bhinnoM ke samUha meM aMza, haroM ke samUha kI prathama saMkhyA ke tulya haiM, aura ina upara kathita pratyeka samUha vAloM kA pratyeka hara uttaravartoM dvArA guNita kiyA jAtA hai| aMtima hara, pratyeka dazA meM aparivartita rahatA hai kyoMki usake uttaravartI hara kA abhAva rahatA hai)| batalAo ki aMtameM ina pariNAmI bhinnoM ke pratyeka samUha kA yoga kyA hogA ? // 60 // bhinnoM ke cAra kulaka (sets) haiM / hara 1,2,3 aura 4 se kramazaH Arambha hote haiM aura uttarottara eka dvArA bar3hate cale jAte haiM jaba taka ki aMtima hara bhinna 2 kulakoM meM kramavAra 20, 42, 25 aura 36 nahIM ho jAte / ina bhinnA ke kulakoM ke aMza ina haroM ke kulakoM kI prathama saMkhyA ke barAbara haiN| haroM ke kulaka kA pratyeka bhinna uttaravatI dvArA guNita kiyA jAtA hai (aMtima hara pratyeka dazA meM aparivartita rahatA hai|) aMta meM, pariNAmI bhinnA meM (60 ) pariNAmI prazna ye haiM:-mAna batalAo (i) 14* 2xs+sxe+.....+ 1, ga. sA0 saM0-7

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50] gaNitasArasaMgrahaH [3.61 ekadvikatrikAdyAzcaturAdyAzcaikavRddhikA hArAH / nijanijamukhapramAMzAH svAsannaparAhatAH kramazaH / / 6 / / viMzatyantAH SaDguNasaptAntA: pnycvgepshcimkaaH| SaTtriMzatpAzcAtyAH saGkSepe kiM phalaM teSAM // 62 / / candanaghanasArAgarukuGkamamakreSTa jinamahAya naraH / caraNadalaviMzapaJcamabhAgaiH kanakasya kiM zeSama / / 63 / / pAdaM paJcAMzamadhaM trigaNitadazamaM saptaviMzAMzakaM ca svarNadvandaM pradAya smitasitakamalaM styAnadadhyAjyadugdham / zrIkhaNDaM tvaM gRhItvAnaya jinasadanaprArcanAyAbravInmAmityadya zrAvakAryo bhaNa gaNaka kiyaccheSamaMzAnvizodhya / / 64 / / aSTapaJcamukhau hArAvubhaye'pyekavRddhikAH / triMzadantAH parAbhyastAzcaturguNitapazcimAH // 65 / / svasvavaktapramANAMzA rUpAtsaMzodhya tavayam / zeSaM sakhe samAcakSva prottIrNagaNitArNava // 66 / / ekonaviMzatiratha kramAt trayoviMzatidviSaSTizca / rUpavihInA triMzattatastrayoviMzatizataM syAt / / 67 / / pazcatriMzattasmAdaSTAzItikazataM vinirdiSTam / saptatriMzadamuSmAdaSTAnavatitrikonapaJcAzat // 68 / / catvAriMzacchatikA saikA ca punaH zataM saSoDazakam / ekatriMzadataH syAdvAnavatiH saptapazcAzat // 69 163 aura 64 zloka K aura B meM prApya haiN| 2 M muru 3 yaha zloka M meM chUTa gayA hai| 4 B viMzatya / 5 yaha zloka M meM aprApya hai| 6K aura B bhaagjaatybdhipaarg| . kulakoM ko jor3ane para kyA yoga prApta hogA? // 61-62 // eka manuSya ne jina utsava para saMdala (caMdana) lakar3I, kapUra, agaru aura sauMpha (kuMkumamakreSTa ) kramazaH .. aura6 svarNa mudrA ke, 1 svarNa mudrA meM se, khriide| batalAo kyA zeSa hai ? // 63 // eka yogya zrAvaka ne mujhe do svarNa mudrAeM dete hue kahA ki jina maMdira meM pUjA ke liye...:. aura svarNa mudrA ke kramazaH vikasita zveta kamala, gAr3hA dahI, ghRta, dugdha aura caMdana lakar3I laao| he mitra ! mujhe batalAo ki itane kharca ke pazcAt mere pAsa svarNa mudrA kA kitanA bhAga bcaa?||6|| bhinnoM ke do kulaka haiN| hara kramazaH 8 aura 5 se Arambha hote haiM aura donoM dazAo meM uttarottara eka dvArA bar3hate jAte haiM jaba taka ki donoM dazAoM meM aMtima hara 30 nahIM ho jAtA / ina kulakoM ke aMza donoM kalakoM ke hara ke prathama pada ke tulya haiN| pratyeka kulaka ke haroM meM se pratyeka apane uttaravartI dvArA guNita hotA hai / aMtima hara donoM dazAoM meM 4 dvArA guNita kiyA jAtA hai / bhinnoM ke donoM pariNAmI kulakoM ko jor3ane se prApta donoM yogo meM pratyeka meM se eka ghaTAne ke pazcAt, he sAdhAraNa bhinna mahAsAgara ke pAra utarane vAle mitra, mujhe batalAo ki kyA zepa rahegA ? // 65-66 // kucha diye hue bhinnoM ke hara kramazaH 19, 23, 62, 29, 123, 35, 188, 37, 98, 47, 140, 41, 116, 31, 92, 57, 73, 55, 110, 49, 74, 219 haiM; aura, (ii) 22+2+ 28 + ....+ 2 2..., (ii) 3+2++ ...+ 15216+he.

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3. 73 ] kalAsavarNavyavahAraH tryadhikA saptatirasmAtsapaJcapaJcAzadapi ca sA dviguNA / saptakRtiH sacatuSkA saptatirekonaviMzatidvizatam // 70 // hA nirUpitA aMzA ekAdyekottarA amUnan / prakSipya phalamAcakSva bhogajAtyabdhipAraMga // 71 // atrAMzotpattau sUtram - ekaM parikalpyAMzaM tairiSTaiH samaharAMzakAn hanyAt / yahuNitAMzasamAsaH phalasadRzoM'zAsta eveSTA // 72 // aikAMzavRddhInAM rAzInAM yutAvaMzAddhArasyAdhikye satyaMzotpAdaka sUtram - samahAraikAMzakayutihRtayutthaMzoM'za eka vRddhInAm / zeSamitarAMzayutihRtamanyAMzo'styevamA caramAt // 73 // 1 B prottIrNagaNitArNava / 2 B sadRzavRddhayaMzarAzInAM aMzotpAdaka sUtram / [ 51 aMza 1 se Arambha hokara uttarottara kramavAra 1 dvArA bar3hate cale jAte haiM / isa saba bhinnoM ko jor3akara, he bhinna rUpI mahAsAgara ke usapAra pahu~canevAle, yogaphala ko batalAo // 67-71 // jaba bhinnoM ke hara tathA yoga diye gaye hoM to aMza nikAlane ke liye niyama saba diye gaye haroM ke sambandha meM aMza ko 'eka' banAo; taba kisI bhI taraha cunI huI saMkhyAoM dvArA sAdhAraNa haroM meM lAye gaye aMzoM ko guNita kro| yahAM ve saMkhyAyeM cAhe hue aMzoM meM badala jAtI haiM, jinakA yoga saMbaMdhita bhinnoM ke yoga ke barAbara hotA hai // 72 // jaba bhinnoM ke yoga kA hara aMza se bar3A ho aura aMza uttarottara eka dvArA bar3hate cale jAte hoM, to aise bhinnoM ke sambandha meM aMzoM ke nikAlane ke liye niyama sambandhita bhinnoM ke diye gaye yoga ko tathA jinake aMza 'eka' hote haiM aise bhinnoM ko sAdhAraNa haroM meM prAsita kara liyA jAtA hai / bhinnoM ke diye gaye yoga ko aise bhinnoM ke yoga dvArA bhAjita karane se prApta bhajanaphala una aMzoM meM se prathama cAhA huA aMza bana jAtA hai / isake pazcAt ke iSTa aMza uttarottara eka dvArA bar3hate cale jAte haiM aura jinheM nikAlA jA sakatA hai| isa bhAga meM prApta zeSaphala ko samAna hara vAle anya aMzoM dvArA vibhAjita karane para, pariNAmI bhajanaphala dUsarA cAhA huA aMza bana jAtA hai jaba ki vaha prathama meM jo ki pahile hI prApta ho cukA hai, jor3a diyA jAya / isa taraha aMta taka prazna kA sAdhana karanA par3atA hai // 73 // ke sambandha meM aMza eka mAna liyA jAtA hai; isa taraha hameM prahAsita kiye jAne para karate haiM to isa taraha prApta guNanaphaloM kA isaliye, 2, 3, aura 4 cAhe hue aMza haiN| jitanA ki bhinnoM kA sAdhAraNa hara hai / (72) sUtra 74 ke prazna ko hala karane se yaha niyama spaSTa ho jAvegA / yahA~ pratyeka diye gaye hara prApta hote haiM jo eka se haroM meM ho jAte haiM / jaba aMzoM ko kramavAra 2, 3 aura 4 se guNita yoga diye gaye yoga kA aMza ( 877 ) ho jAtA hai / AlokanIya hai, ki isa diye gaye yoga kA hara utanA hai ( 73 ) isa niyama ke anusAra 74 vIM gAthA kA prazna isa prakAra sAdhita hotA hai

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52] gaNitasArasaMgrahaH [3.74atroddezakaH navakadazaikAdazahRtarAzInAM navatinavazatobhaktA / tryUnAzItyaSTazatI saMyogaH keM'zakAH kathaya // 74 / / chedotpattau sUtramrUpAMzakarAzInAM rUpAdyAstriguNitA harAH kramazaH / dvidvitryaMzAbhyastAvAdimacaramau phale rUpe // 75 / udAharaNArtha prazna 9, 10 aura 11 dvArA kramazaH vibhAjita kI gaI kucha saMkhyAoM kA yoga 877 bhAjita 990 hai| batalAo ki bhinnoM ko jor3ane kI isa kriyA meM aMza kyA kyA haiM ? // 7 // cAhe hue haroM ko nikAlane ke liye niyama 'eka' aMza vAlI vibhinna bhinnIya rAziyoM kA yoga jaba 'eka' ho, taba cAhe hue hara eka se Arambha hokara kramavAra, uttarottara 3 se guNita kiye jAte haiM, isa taraha prApta prathama aura aMtima hara phira se kramazaH 2 aura 3 dvArA guNita kiye jAte haiM // 75 / / pratyeka diye gaye haroM ke sambandha meM aMza ko eka mAnakara tathA bhinnoM ko samAna haroM meM pravAsita karane para 150, 111 aura 291. prApta hote haiM / diye gaye yoga 664 ko ina bhinnoM ke yoga 330 dvArA vibhAjita karane para hameM bhajanaphala 2 prApta hotA hai jo prathama hara sambandhI aMza hai| isa bhAga meM prApta zeSa, 279, ko zeSa mAne hue aMzoM ke yoga 189 dvArA vibhAjita karate haiM jisase bhajanaphala 1 prApta hotA hai| isa bhajanaphala 1 ko prathama bhinna ke aMza 2 meM jor3ane para dvitIya hara sambandhI aMza prApta ho jAtA hai / isa dUsare bhAga ke zeSa 90 ko aMtima bhinna ke mAne hue aMza 90 ke dvArA vibhAjita karate haiM, aura prApta bhajanaphala 1 ko jaba pichale bhinna ke aMza 3 meM jor3ate haiM taba aMtima hara kA aMza prApta hotA hai / isaliye, ve bhinna, jinakA yoga 634 hai, ye haiM:-, . aura . yahA~ isa taraha uttarottara nikAle gaye aMza kramabaddha diye gaye haroM ke sambandha meM cAhe hue aMza bana jAte haiN| bIjIya rUpa se bhI, tIna bhinnoM kA yogabasaka+(ka+1) asa + ( ka +2) aba hai aura hara a, ba aura sa haiN| inake aMza isa abasa vidhi se ka, ka + 1 aura ka+ 2 saralatA se nikAle jA sakate haiN| (75) uparyukta pradarzita rIti dvArA prazna ko hala karane se yaha jJAta hogA ki jaba na bhinna hoM, to prathama aura antima bhinna ko chor3akara (na-2) pada guNottara zredi meM hote haiM jisakA prathamapada aura sAdhAraNa niSpatti (common ratio) hotI hai| (na-2) padoM kA yoga 11-(3) }/(1-5) hotA hai jo prahAsita karane para 3-3 inara athavA, ke tulya hotA hai| isase spaSTa hai ki jaba prathama bhinna ho to antima bhinna 25 ko isa antima phala meM jor3ane para yoga 1 ho jAtA hai| isa sambandha meM, na padoM vAlI

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-3. 77 ] paJcAnAM rAzInAM rUpAMzAnAM yutirbhavedrUpam / SaNNAM saptAnAM vA ke hArAH kathaya gaNitajJa // 76 // viSamasthAnAM chedotpattau sUtram ekAMzakarAzInAM vyAdyA rUpottarA bhavanti harAH / svAsannaparAbhyastAH sarve dalitAH phale rUpe // 77 // ekAMzAnAmanekAMzAnAM caikAMze phale chedotpattau sUtram - udAharaNArtha prazna jinameM pratyeka kA aMza eka hai aisI pAMca yA chaH athavA sAta vibhinna bhinnIya rAziyoM kA yoga pratyeka dazA meM 1 hai / he gaNitajJa ! cAhe hue haroM ko nikAlo // 76 // bhinnoM kI ayugma saMkhyA lene para haroM ko nikAlane ke liye niyama jinake pratyeka aMza 1 hoM aisI vibhinna bhinnIya rAziyoM kA yoga 1 ho, to cAhe hue hara 2 Arambha hokara, uttarottara mAna meM 1 dvArA bar3hate cale jAte haiM / pratyeka aisA hara usa saMkhyA se guNita kiyA jAtA hai jo mAna meM tatkAla uttaravartI ke barAbara hotA hai aura taba use AdhA kiyA jAtA hai // 77 // kucha iSTa bhinnoM ke viSaya meM cAhe hue haroM ko nikAlane ke lie niyama jabaki unake aMzoM meM pratyeka 1 athavA 1 se anya ho aura jaba unake bhinnIya yoga kA aMza bhI 1 ho 1 1 guNottara meM jisakA prathama pada : hai aura sAdhAraNa niSpatti hai a kI sabhI pUrNAka dhanAtmaka a a 1 1 se (a a - 1 hai / isaliye, yadi hama guNottara zredi ke yoga meM 1 arghAoM (mAnoM ) ke liye yoga (a - kalAsavarNavyavahAraH atroddezakaH 1 x (na - 1) vAM pada } jor3ate haiM 1 1 = ? [ -x + x x x 2 1 2xix + 2x3x 33x4 x re 1 x x x + _ 243 3x4 445 - to 3 a - 2 ke liye usameM jor3anA par3atA hai / isa ko niyama meM prathama bhinna kahA gayA hai aura a- 2 a - 1 a - 1 isakA mAna 3 cunA gayA hai kyoMki sabhI bhinnoM kA aMza 1 honA cAhie / 1 ( 77 ) yahA~ ) + + hameM (3-8) 1)/a' isa gAthA ke niyama ke anusAra antima bhinna X zreDhi kA ( na + 1 ) vAM pada } nyUna hotA + 1 anra + [ 53 prApta hogA / isa se yoga 1 prApta karane 1 a- 1 1 4x5X3 + 1 = ( -- -- -- -- ) + ] =2 2 [ ( 3 ... + =2x3=1 .....+. + 1 na X re 1 (-1)=+] na 1) na na + 1 ( na - 1) na X re

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54] gaNitasArasaMgrahaH [3.74 labdhaharaH prathamasyacchedaH sasvAMzako'yamaparasya / prAk svapareNa hato'ntyaH svAMzenaikAMzake yoge|78| _atroddezakaH saptakanavakatritayatrayodazAMzaprayuktarAzInAm / rUpaM pAdaH SaSThaH saMyogAH ke harAH kathaya / / 79 / / ekAMzakAnAmekAMze'nekAMze ca phale chedotpattau sUtramseSTo hAro bhaktaH svAMzena niragramAdimAMzaharaH / tadyutihArAptaSTaH zeSo'smAditthamitareSAm // 8 // ___ jaba kucha iSTa bhinnoM ke yoga kA aMza 1 ho, taba unake cAhe hue haroM ko nikAlane ke liye yoga ke hara ko prathama rAzi kA hara mAna lo aura isa hara ko apane aMza se saMyukta kara use uttaravatI rAzi kA hara mAna lo, aura aise pratyeka hara ko kramavAra tatkAla uttaravartI ke dvArA guNita karate cale jAo / antima hara ko usI ke aMza dvArA guNita karo // 78 // udAharaNArtha prazna jinake aMza kramazaH 7, 9, 3 aura 13 haiM aise bhinnoM ke yoga 1, 1, haiN| batalAo ki una bhinnIya rAziyoM ke hara kyA haiM / / 79 // jinakA aMza 1 hai aise kucha icchita bhinnoM ke hara nikAlane ke liye niyama jaba ki una bhinnoM ke yoga kA aMza 1 athavA aura koI dUsarI rAzi ho diye gaye yoga ke hara ko jaba koI cunI huI rAzi meM milAte haiM aura tAki kucha bhI zeSa na bace isa taraha use usa yoga ke aMza dvArA vibhAjita karate haiM to vaha bhinnoM kI cAhI huI zreDhi ke prathama aMza ke sambandha meM hara bana jAtA hai| Upara cunI huI rAzi jaba prathama bhi ke hara dvArA vibhAjita kI jAtI hai aura diye gaye yoga ke hara dvArA bhI vibhAjita kI jAtI hai taba vaha iSTa zreDhi ke zeSa bhinnoM ke yoga ko utpanna karatI hai| iSTa zreDhi ke zeSa bhinnoM ke isa jJAta yoga se isI taraha anya haroM ko nikAlate haiM // 8 // (78 ) bIjIya rUpa se yadi yoga - ho, aura a, ba, sa tathA da diye gaye aMza hoM to bhinnoM ko nimna rIti se jor3ate haiM a yoga = na (na + a) + (na + a) (na +a+ba) + (na + a + ba) (na + a + ba+sa) 'da (na+a+ba+sa) a (na+a+ba)+bana sa+na+a+ba na (na+ a) (na+a+ba) '(na+a+ ba)(na+a+ ba+sa) (na+a) (a+ba) a+ba+na na (na+a) (na+a+ba) 'na+a+ba na (na+a+ba) ( 80 ) bIjIya rUpa se, yadi meM yoga hai to prathama bhinna kA hotA hai; aura niyama

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kalAsavarNavyavahAraH atroddezakaH trayANAM rUpakAMzAnAM rAzInAM ke harA vada / phalaM caturthabhAgaH syAccaturNAM ca trisaptamam / / 81 / / aikAMzAnAmanekAMzAnAM cAnekAMze phale chedotpattau sUtramiSTahatA dRSTAMzAH phalAMzasadRzo yathA hi tdyogH| nijaguNahRtaphalahArastaddhAro bhavati nirdissttH||82|| atroddezakaH ekakAMzena rAzInAM trayANAM ke harA vada / dvAdazAptA trayoviMzatyazaMkA ca yutirbhavet / / 83 // trisaptakanavAMzAnAM trayANAM ke harA vada / dvayanapazcAzadAptA trisaptatyaMzA yutibhavet / / 84 // ekAMzakayo rAzyorekAMze phale chedotpattau sUtram1 83 aura 84 zloka B meM chUTa gaye haiN| udAharaNArtha prazna tIna vibhinna bhinnIya rAziyoM kA yoga hai hai, tathA unameM se pratyeka kA aMza 1 hai| aiso cAra anya rAziyoM kA yoga hai| batalAo ki hara kyA haiM ? // 81 // jinakA aMza eka athavA koI aura saMkhyA ho aise kucha icchita bhinnoM ke hara nikAlane ke liye niyama jaba ki una bhinnoM ke yoga kA aMza 1 kI apekSA anya saMkhyA ho jJAta aMza kucha cunI huI rAziyoM dvArA guNita kiye jAte haiM, tAki ina guNanaphaloM kA yoga iSTa bhinnoM ke diye gaye yoga ke aMza ke barAbara ho jAve / yadi iSTa bhinnoM ke diye gaye yoga ke hara ko usI guNaka se vibhAjita kiyA jAya ( jisase ki diyA gayA aMza guNita kiyA gayA hai) to vaha aMza sambandhI cAhe hue hara ko utpanna karatA hai||42|| udAharaNArtha prazna tIna bhinnIya rAziyoM meM, pratyeka kA aMza hai| unake haroM kA mAna nikAlo jaba ki una rAziyoM kA yoga23 ho // 43 // kramazaH 3, 7 aura 9 aMzavAlI tIna bhinnIya rAziyoM ke haroM kA mAna batalAo jaba ki una rAziyoM kA yoga ho // 44 // aMzavAlI do bhinnIya rAziyoM ke haroM kA mAna nikAlane ke liye niyama jaba ki una bhinnIya rAziyoM ke yoga kA aMza ho diye gaye yoga ke hara ko cunI huI saMkhyA dvArA guNita karane para kisI eka iSTa bhinnIya rAzi kA hara prApta hotA hai| yaha hara, eka kama (pichalI) cunI huI saMkhyA dvArA vibhAjita kiyA jAne para meM zeSa bhinnoM kA yoga kathita hai, jahAM 'pa' cunI huI rAzi hai / yaha spaSTa rUpa na+pa. a -nA a se ko hala karane se prApta hotI hai| yahAM pa ko isa taraha cunanA cAhiye ki (na+pa) na na+pa a meM a kA pUrA pUrA bhAga jA ske|

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gaNitasArasaMgrahaH [3. 85 vAchAhatayutihArazchedaH sa vyakavAJchayApto'nyaH / phalahArahAralabdhe svayogaguNite harau vA staH // 85 / / atroddezaka: rAzyorekAMzayozchedI kau bhavetAM tayoryutiH / SaDaMzo dazabhAgo vA brUhi tvaM gaNitArthavit // 86 / / ekAMzakayoranekAMzayozca ekAMze'nekAMze'pi phale chedotpattau prathamasUtramiSTaguNAMzo'nyAMzaprayutaH zuddhaM hRtaH phalAMzena / iSTAptayutiharaghno haraH parasya tu tadiSTahatiH / / 8 / / 1 P aura B meM yaha pAThAntara jur3A hai: zuddhaM phalAMzabhaktaH svAnyAMzayuto nijessttgunnitaaNshH| dUsare iSTa aMza ko utpanna karatA hai| athavA, diye gaye yoga ke hara ke sambandha meM kisI cune hue bhAjaka aura prApta bhajanaphala meM se pratyeka ko unake yoga dvArA guNita karane para do iSTa haroM kI utpatti hotI hai // 45 // udAharaNArtha prazna he aMkagaNita ke siddhAntoM ke jJAtA ! do iSTa bhinnIya rAziyoM ke hara nikAlo jaba ki unakA yoga yA to athavA ho // 86 // jinakA aMza 1 athavA koI aura saMkhyA hai aise do iSTa bhinnoM ke haroM ko nikAlane ke liye niyama jaba ki una bhinnoM ke yoga kA aMza 1 athavA koI aura saMkhyA ho koI bhI eka (either) aMza cunI huI saMkhyA dvArA guNita hokara, taba abhya aMza dvArA milAyA jAkara, taba iSTa bhinnoM ke diye gaye yoga ke aMza dvArA vibhAjita hokara ( tAki kucha bhI zeSa na rahe,) aura taba Upara kI cunI huI saMkhyA dvArA vibhAjita hokara tathA iSTa bhinnoM ke yoga ke hara dvArA guNita hokara, cAhe hue hara ko utpanna karatA hai / anya bhinna kA hara isa hara ko Upara kI cunI huI rAzi dvArA guNita kara prApta kara sakate haiM / / 8 / / ( 85 ) bIjIya rUpa se, jaba do iSTa bhinnoM kA yoga hai, to isa niyama ke anusAra bhinna kramazaH tathA (pana-1) hote haiM, jahAM pa koI bhI cunI huI rAzi hai| yaha zIghra dekhane meM AvegA ki ina donoM bhinnoM kA a (a+ba) athavA, jaba , taba bhinnoM ko -liyA jA sakatA hai| taba bhinnA kA +ba) ( 87 ) bIjIya rUpa se, yadi a aura ba aMza vAle do iSTa bhinnoM kA yoga meM hai to ve bhinna a aura _____ hoMge, jahA~ 'pa' koI bhI saMkhyA isa taraha cunI gaI hai ki apa+bana ma pa pa apa + ba ko ma dvArA vibhAjita kiyA jA sake / ina bhinnoM kA yoga prApta hogaa| a- aura apa+banapa

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-3. 93] kahAsavarNavyavahAraH atroddezakA rUpAMzakayo rAzyoH kau syAtAM hArakau yutiH paadH| paJcAMzo vA dvihataH saptakanavakAzayozca vada // 8 // dvitIyasUtramphalahAratADitAMzaH parAMzasahitaH phalAMzakena hRtaH / syAdekasya cchedaH phalaharaguNito'yamanyasya // 89 // atroddezakaH rAzidvayasya ko hArAvekAMzasyAsya saMyutiH / dvisaptAMzo bhavebrUhi SaDaSTAMzasya ca priya // 90 // ardhatryaMzadazAMzakapaJcadazAMzakayutirbhavedrUpam / tyakte paJcadazAMze rUpAMzAvatra kau yojyau // 11 // dalapAdapazcamAMzakaviMzAnAM bhavati saMyutI rUpam / saptaikAdazakAMzau ko yojyAviha vinA viNshm||92 / yugmAnyAzriya cchedotpattau sUtramyugmapramitAn bhAgAnekaikAMzAn prakalpya phlraasheH| tebhyaH phalAtmakebhyo dvirAzividhinA harAH sAdhyAH / / 93 // udAharaNArtha prazna do iSTa minnIya rAziyoM meM pratyeka kA aMza 1 hai| inake haroM ko nikAlo jaba ki una rAziyoM kA yoga yA to athavA 3 ho| sAtha hI, una do anya bhinIya rAziyoM ke hara nikAko jinake aMza kramazaH aura 9 haiM // 8 // dUsarA niyama nimnalikhita hai: iSTa bhinnoM meM kisI eka ke aMza ko iSTa bhinnoM ke yoga ke hara dvArA guNita kara dUsare aMza meM milAte haiN| prApta phala ko iSTa bhinnoM ke yoga ke aMza dvArA vibhAjita karate haiM to iSTa bhinnoM meM se eka bhinna kA hara utpanna hotA hai| isa hara ko jaba iSTa bhinnoM ke yoga ke hara dvArA guNita karate haiM taba vaha dUsare bhinna kA hara ho jAtA hai / / 89 // udAharaNArtha prazna he mitra ! mujhe batalAo ki do bhinnIya rAziyoM ke (jinameM pratyeka ke aMza 1, haiM ) hara kyA hoMge jaba ki una iSTa bhinnoM kA yoga hai| do anya iSTa bhinnoM ke bhI hara kyA hoMge jinake aMza kramazaH 6 aura 8 hoM // 90 // 3, 3, aura 15 kA yoga / hai / yadi 15 chor3a diyA jAve to do aise 1 aMza vAle bhinna batalAo jinako zeSa bhinnoM meM jor3ane para yoga punaH kula ke tulya ho jAve // 11 // 16 aura kA yoga 1 hai| yadi chor3a diyA jAya to kramazaH 7 aura 11 hara vAle aise do bhinna kauna se hoMge jinako zeSa meM jor3ane para unakA yoga kula yoga ke tulya ho jAve / / 12 / / kucha iSTa bhinnoM ko yugmoM (pairs) meM lekara unake haroM ko nikAlane ke liye niyama saba iSTa bhinnoM ke yoga ko diye gaye aMzoM ke yugmoM kI saMkhyA ke tulya bhAgoM meM vipATita karane ke bAda, ( isa taraha ki pratyeka ke aMza 1, . hoM), ina bhAgoM ko yugmoM ke yoga meM alaga-alaga (89) gAthA 87 meM diye gaye niyama kI yaha vizeSa sthiti hai kyoMki iSTa mitroM ke hara kA Adezana (substitution) isa niyama meM, pichale niyama meM cunI gaI rAzi ke sthAna meM karate haiN| ga0 sA0 se0-8

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5.] gaNitasArasaMgraha [3. 94atroddezakA trikapaJcakatrayodazasaptanavaikAdazAMzarAzInAm / ke hArAH phalamekaM paJcAMzo vA caturguNitaH // 14 // __ekasUtrotpannarUpAMzahAraiH sUtrAntarotpannarUpAMzahAraizca phale rUpe chedotpattau naSTabhAgAnayaneca sUtramvAnchitasUtrajahArA harA bhavantyanyasUtrajaharaghnAH / dRSTAMzaikyonaM phalamabhISTanaSTAMzamAnaM syAt // 15 // atroddezaka parahatidalanavidhAnAttrayodaza svaparasaMguNavidhAnAt / bhAgAzcatvAro'taH kati bhAgAH syuH phale rUpe // 9 // prAkakhaparahatavidhAnAtsaptasvAsannaparaguNAdhavidhAnAt / bhAgAsthitayazcAtaH kati bhAgAH syuH phale rUpe // 97 // rUpAMzakA dviSaTkadvAdazaviMzatiharA vinaSTo'tra / pazcamarAzI rUpaM sarvasamAsaH sa rAziH kaH // 9 // iti bhaagjaatiH| lete haiN| unameM se cAhe hue haroM ko, do ghaTaka bhitrIya rAziyoM ke sambandha meM batalAye gaye niyama dvArA nikAlate haiM / / 13 / / udAharaNArtha prazna ___ una iSTa miloM ke hara kyA hoMge jinake aMza kramazaH 3, 5, 13, ., 9 aura 11 haiM, jabaki una bhinnIya rAziyoM kA yoga : athavA hai ? // 9 // jinakA saMvAdI aMza 1 hai aura jo uparyukta niyamoM dvArA prApta kiye gaye haiM aise haroM kI sahAyatA se kucha haroM ko nikAlane ke liye (niyama); tathA jinakA saMvAdI zahai aura jinake iSTa bhinnoM kA yoga eka hai tathA jo uparyukta anya niyamoM dvArA prApta kiye gaye haiM aise bhinnoM kI sahAyatA se haroM ko nikAlane ke liye (niyama) aura naSTa bhAga kA mAna nikAlane ke liye niyama kisI bhI cune hae niyama ke anusAra prApta haroM ko dUsare niyama se prApta haroM dvArA guNita karane para cAhe hue hara prApta hote haiN| ina bhinnoM kA yoga, viziSTa bhAga ke yoga dvArA hAsita kiye jAne para chor3e hue naSTa bhAga kA mAna hotA hai // 15 // udAharaNArtha prazna niyama 77 dvArA prApta bhinnoM kI saMkhyA 13 hai aura niyama krama 78 dvArA prApta bhinnoM kI saMkhyA 4 hai| ina niyamoM kI sahAyatA se prApta bhinnoM kA yoga hai, to batalAo ki vighaTaka bhinna kitane haiM // 9 // gAthA 78 ke niyama dvArA prApta bhinnoM kI saMkhyA 7 hai aura niyama 77 gAthAnusAra prApta saMkhyA 3 hai| yadi ina niyamoM dvArA prApta bhinnoM kA yoga ho to batalAo vighaTaka bhinna kitane haiM // 97 // jinake aMza 1.1 haiM aise kucha bhinnoM ke hara kramazaH 2, 6, 12 aura 20 haiN| yahAM pAMcavIM bhinnIya rAzi chor3a dI gaI hai| ina pA~coM bhinnoM kA yoga 1 hai, batalAo ki vaha chor3I gaI bhinnIya rAzi kyA hai ? // 9 // isa prakAra, kalAsavarNa SaDjAti meM bhAga jAti nAmaka pariccheda samApta huaa| (93) do bhinnIya rAziyoM ke sambandha meM gAthA 85, 87 aura 89 meM niyama de diye gaye hai|

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-1...] kalAsavarNavyavahAraH [59 prabhAgabhAgabhAgajAtyoH sUtramaMzAnAM saMguNanaM hArANAM ca prabhAgajAtau syAt / guNakAroM'zakarAzerhAraharo bhAgabhAgajAtividhau // 19 // prabhAgajAtAvuddezakaH rUpAdhaM tryaMzAdhaM vyaMzArdhAdhaM dalArdhapazcAMzam / paJcAMzArdhatryaMzaM tRtIyabhAgAdhasaptAMzam // 10 // daladaladalasaptAMzaM vyaMzavyaMzakadalArdhadalabhAgam / ardhavyaMzavyaMzakapaJcAMza paJcamAMzadalam // 101 // krItaM paNasya dattvA kokanadaM kundaketakIkumudam / jinacaraNaM prArcayituM prakSipyaitAn phalaM brUhi // 102 rUpAdhaM vyaMzakArdhAdhaM pAdasaptanavAMzakam / dvitribhAgadvisaptAMzaM dvisaptAMzanavAMzakam // 10 // dattvA paNadvadhaM kazcidAnaiSInUtanaM ghRtam / jinAlayasya dIpAthaM zeSaM kiM kathaya priya // 104 // tryaMzAdvipaJcamAMzastRtIyabhAgAt tryodshssddNshH| pazcASTAdazabhAgAt trayodazAMzo'STamAnavamaH // 105 // navamAcatutrayodazabhAgaH paJcAMzakAt tripAdArdham / saMkSipyAcakSvaitAn prabhAgajAtau zramo'sti yadi // 106 // prabhAga aura bhAgabhAga jAti ( saMyuta aura jaTila bhinna ) saMyuta (compound) aura jaTila (complex) bhinoM ko sarala karane ke liye niyama saMyuta bhinnoM ko saraka karane meM, aMzoM kA unameM hI guNana tathA haroM kA unameM hI guNana hogaa| saMkara ( complex) bhivoM sambandhI saralIkaraNa kriyA meM bhinna ke hara kA hara, diye gaye bhinna ke aMza kA guNaka ho jAtA hai // 99 / / prabhAga jAti (saMyuta bhinnoM) para udAharaNArtha prazna jina prabhu ke caraNoM meM pUjana ke arpaNa ke nimitta nimnalikhita paNa mUlya para kokanada ( kamala ) kunda (jasamins), ketakI aura kumuda (lily) kharIde gaye : 1 kA 3, 3 kA 3, 6 kA 3 kA 33 kAkAkA kAkA kAkA kAkA kAkA kA kA33 kA kAkA aura kA, eka paNa ke ina diye hae bhAgoM ko jor3akara phala nikAlo // 100 se 102 / / eka manuSya kisI vikretA ko paNa ke kramazaH 1 kA... kAkA kA hai, kA aura kA 3 bhAga do paNa meM se dekara jina maMdira meM dIpaka jalAne ke liye nUtana ghI kharIda kara laayaa| he mitra ! batalAo ki zeSa kitane paNa rakama usake pAsa bacI? // 103-104 // yadi tumane saMyuta bhinnoM ke sambandha meM parizrama kiyA hai to batalAo ki nimnalikhita bhinnoM kA yoga karane para pariNAmI yogaphala kyA hogA? kA3,kA3, kAkA kA aura kAkA 3 // 105-106 // (99) yahAM sekara bhinna meM aMza pUrNAka hai aura hara bhinnIya hai|

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60 gaNitasArasaMgrahaH [3.107 akAvyaktAnayanasUtramrUpaM nyasyAvyakte prAvidhinA yatphalaM bhavettena / bhaktaM paridRSTaphalaM prabhAgajAtau tadajJAtam // 107 // atroddezakaH rAzeH kutazcidaSTAMzastryaMzapAdo'rdhapazcamaH / SaSThatripAdapaJcAMzaH kimavyaktaM phalaM dalam // 108 // anekAvyaktAnayanasUtramkRtvAjJAtaniSThAna phalasadRzI tadyutiryathA bhavati / vibhajeta pRthagvyakteraviditarAzipramANAni // 109 // ___ atroddezakaH rAzeH kutazcix kutazcidaSTAMzakatripaJcAzaH / kasmAvinyaMzAdhaM phalamadhaM ke syurajJAtAH // 110 // ____ bhAgabhAgajAtAbuddezakaH SaTsaptabhAgabhAgastryaSTAMzAMzazcaturnavAMzAMzaH / tricaturthabhAgabhAgaH kiM phalametadyato brUhi // 111 // __jinakA yoga diyA gayA hai aise saMyuta bhinnoM ke pratyeka samUha kA eka sAdhAraNa ajJAta (tatva) nikAlane ke liye niyama diyA gayA yoga jaba saMyuta bhinnoM ke ajJAta tatva ke sthAna meM eka rakhane ke uparyukta niyamAnusAra prApta yoga dvArA vibhAjita kiyA jAtA hai taba saMyuta bhinnoM kI yoga kriyA meM cAhe hue ajJAta tatva ko utpanna karatA hai / / 107 // udAharaNArtha prazna kisI rAzi kA ?, 3 kA , 3 kA aura kAkA kA yoga 3 hai; batalAo ki yaha ajJAta rAzi kyA hai ? // 10 // diye gaye yoga vAle saMyuta bhinnoM ke pratyeka samUha meM rahane vAle eka se adhika ajJAta tatvoM ko nikAlane ke liye niyama AMzika rUpa se jJAta vibhinna saMyuta bhinnoM ke ajJAta mAnoM ko una cunI huI rAziyoM ke samAna banAo jo diye hue saMyuta bhinnoM kI saMkhyA ke barAbara hoM aura jinakA yoga diye gaye AMzika saMyuta bhinnoM ke datta yoga ke tulya ho| taba ina cunI huI ajJAta saMyata bhinnIya rAziyoM ke mAnoM ko unake jJAta tatvoM dvArA kramazaH vibhAjita karo / / 109 // udAharaNArtha prazna (nimnalikhita AMzika rUpa se jJAta saMyuktabhinna, nAmnA,) koI rAzi kA kisI anya rAzi kAkA aura anya rAzi kAkA; ina sabakA yoga hai| inake sambandha meM ajJAta tatva kyA kyA haiM ? // 11 // ___saMkara bhinnoM para prazna vo aura kA, diye gaye haiM; batAo ki inakA yogaphala kyA hogA ? (109) 110vI gAthA ke prazna ke nimnalikhita sAdhana dvArA niyama spaSTa ho jaavegaa| iSTa bhinnoM ke yoga 3 ko, gAthA 78 ke niyamAnusAra 3 bhinnoM meM vipATita karane para hameM hai, para aura ke prApta hote haiM / ina AMzika rUpa se jJAta saMyuta bhinnoM ko hama kramavArakA aura 3 kA dvArA vibhAjita karate haiM jisase 1,..aura rAziyAM prApta hotI hai|

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-3. 110] kalAsavarNavyavahAraH dvitryaMzAptaM rUpaM tripAdabhaktaM dvikaM dvayaM cApi / dvivyaMzoddhRtamekaM navakAtsaMzodhya vada zeSam // 112 // iti prbhaagbhaagbhaagjaatii| bhAgAnubandhajAtau sUtramharahatarUpedhvaMzAn saMkSipa bhaagaanubndhjaatividhau| guNayAgrAMzacchedAvaMzayutacchedahArAbhyAm // 113 / / __ rUpabhAgAnubandha uddezakaH 'dvitriSaTakASTaniSkANi dvAdazASTaSaDaMzakaiH / paJcASTamaiH sametAni viMzataH zodhaya priya // 114 // sArdhanaikena paGkajaM sASTAMzairdazabhihimama / sArdhAbhyAM kuchamaM dvAbhyAM krItaM yoge kiyadbhaveta // 15 // 'sASTamASTau SaDaMzAn SaDdvAdazAMzayutaM dvayam / trayaM paJcASTamopetaM viMzateH zodhaya priya // 116 // saptASTau navadazamASakAn sapAdAna dattvA nA jinanilaye cakAra pUjAm / unmIlatkurabakakundajAtimallImAlAbhirgaNaka vadAzu tAn samasya // 117 / / 1 B meM guNayeyAMzaharau sahitAMzaccheda', pATha hai| 3 M dvadet 2 yaha zloka P meM aprApya hai| 4 yaha zloka kevala P meM prApya hai| ne para kyA zeSa rahegA? // 112 // isa prakAra, kalAsavarNa SaDjAti meM, prabhAgajAti nAmaka pariccheda samApta huaa| bhAgAnubaMdha jAti [ saMyava bhinna ] bhAgAnubaMdha bhinnoM ke saralIkaraNa ke sambandha meM niyama bhAgAnabaMdha bhinna ko sarala karane ke liye aMza ko saMyavita pUrNasaMkhyA (associated whole number ) aura hara ke guNanaphala meM jor3a dete haiN| yadi sambandhita saMkhyA pUrNAka na hokara bhinIya ho to prathama bhinna ke aMza aura hara ko dUsare bhinna ke kramazaH aMzasahita hara tathA hara se guNita karo // 11 // rUpabhAgAnubaMdha (saMyavita pUrNAka vAle bhAgAnubaMdha bhinna) para udAharaNArtha prazna : niSka kramazaH 2, 3, 6 aura 8 haiM aura ve aura 1 se saMyavita haiN| he mitra inake yoga ko 20 meM se ghaTAo // 114 // 13 niSka ke kamala, 101 niSka kA kapUra aura 23 niSka kI sauMpha kharIdI gii| yoga karanepara unakA kula mAna batalAo? // 115 // he mitra 20 meM se nimnalikhita ko ghaTAo-1,61.21aura 35 // 116 // eka vyakti jina maMdira meM pUjana hetu 71.81. 91 aura 101 mASoM ke khile hue kuravaka, kunda, jAti aura mallikA ( jUhI) phUloM ke hAra bheMTa karatA, hai| he gaNitajJa ! mujhe zIghra batAo ki una mASoM ko jor3ane ke bAda kyA prApta hogaa?|| 117 // (113) bhAgAnubaMdha kA zAbdika artha saMyavita bhinna hai| yaha niyama do prakAra ke saMyavita bhinnoM meM prayojya hotA hai| prathama mizra saMkhyA hai arthAt pUrNAka se saMyavita bhinna hai, aura dUsarA prakAra vaha hai jisameM bhinna se saMyavita bhinna rahate haiN| jaise 3 se saMyavita; sva ke 3 se saMyavita | aura isa saMyavita rAzi ke 1 se saMyavita 3 / " se saMyavita 3" kA artha hotA hai 3+3kA; dUsare udAharaNa kA artha hai:3+3 kA +2 kA (3+3 kA 3) isa prakAra ke saMyavana ko "yojita anugamana" (additive consecution) kahate haiN|

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gaNitasArasaMgrahaH bhAgAnubandha uddezakaH svatryaMzapAdasaMyuktaM dalaM paJcAMzako'pi ca / tryaMzaH svakIyaSaSThArdhasahitastadyutau kiyat // 11 // tryaMzAcaMzakasaptamAMzacaramaiH svairanvitAdardhataH puSpANyardhaturIyapazcanavamaiH svIyairyutAtsaptamAt / gandhaM paJcamabhAgato'rdhacaraNavyaMzAMzakaimizritAd dhUpaM cArcayituM naro jinavarAnAneSTa kiM tadyutau // svadalasahitaM pAdaM svatryaMzakena samanvitadviguNanavamaM svASTAMzatryaMzakAvimizritam / navamamapi ca svASTAMzAdyardhapazcimasaMyutaM nijadalayutaM vyaMzaM saMzodhaya tritayAtpriya // 120 / / svadalasahitapAdaM sasvapAdaM dazAMzaM nijadalayutaSaSThaM sasvakatryaMzamadham / caraNamapi sametasvatribhAgaM samasya priya kathaya samagraprajJa bhAgAnubandhe // 121 // atrAgrAvyaktAnayanasUtramlabdhAtkalpitabhAgA ruupaaniitaanubndhphlbhktaaH| kramazaH khaNDasamAnAste'jJAtAMzapramANAni // 122 1 B. svacaraNAdyardhAntimaiH / bhAga bhAgAnubaMdha [ saMyavita bhinnoM vAle ] bhinna para udAharaNArtha prazna yahA~ / sva ke bhAga aura isa rAzi (3) ke bhAga se saMyavita hai| : bhI isI taraha saMyavita hai svake bhAga aura isa saMyavita rAzi (1) ke 3 bhAga se saMyavita hai| batalAo ki ina sabakA yoga prApta karane para kyA mAna prApta hogA ? // 118 // zrI jinavara ke pUjana ke liye koI vyakti, se bhArambha hokara 3 meM aMta honevAle bhinnoM se saMyavita niSka ke phUla, aura se saMyavita niSka ke intra (gaMdha); aura 3,1aura se isI taraha saMyavita niSka kI dhUpa kharIdatA hai| ina niSkoM kA yogaphala kyA hogA? // 119 // he mitra! 3 meM se nimnalikhita ko ghaTAo: sva ke se tathA isa rAzi ke bhAga se saMyavita; sva ke hai, aura 3 bhAgoM se saMyavita 3 (yaugika anugama meM); se Arambha hokara meM aMta hone vAle bhinnoM se saMyavita hai, aura svaH ke bhAga se saMyavita // 120 // he bhAgAnubaMdha meM samagra prajJa mitra ! kyA yogaphala hogA jaba ki nimnalikhita bhinna jor3e jAveMge? sva ke 3 se saMyavita 1; sva ke bhAga se saMyavita; svake : bhAga se saMyavita , sva ke bhAga se saMyavita aura svake 3 se saMyavita // 121 // aba agra avyakta (jinakA yoga diyA gayA hai aise saMyavita bhinnoM meM pratyeka ke Arambha meM Ane vAlA eka ajJAta ) nikAlane ke liye niyama yaha hai-- jo iSTa vighaTaka tatvoM kI saMkhyA ke barAbara hai tathA jinakA yoga diyA gayA hai aise kalpita bhAgoM ko, jaba krama se, ina vighaTaka tatvoM sambandhI saMyavita rAzi ko mAnakara prApta kI huI pariNAmI rAziyoM dvArA vibhAjita kiyA jAtA hai taba iSTa ajJAta sambandhI rAziyoM kA mAna utpanna hotA hai // 12 // (122) gAthA 123 ke prazna ko sAdhita karane para yaha niyama spaSTa ho jAvegA kisI bhinna ke tIna kulaka ( sets ) diye gaye haiM; yoga 1 ko, niyama 75 ke anusAra tIna bhinnoM meM vipATita karane para hameM 3, aura prApta hote haiN| ina bhinnoM ko tIna diye gaye, ajJAta rAzi 1 vAle, bhitroM ke kulakoM ko sarala karane se prApta huI rAziyoM dvArA bhAjita karane para hameM, aura pI iSTa rAziyA~ prApta hotI haiN|

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kalAsavarNavyavahAraH atroddezakaH kazcitsvakairardha tRtIyapAdairaMzo'paraH paJcacaturnavAMzaiH / anyastripaJcAMza navAMzakA dhairyuto yutI rUpamihAMzakAH ke || 123|| ko'pyaMzaH svArdhapaJcAMzatripAdanavamairyutaH / ardhaM prajAyate zIghraM vadAvyaktaprama priya // 124 // zeSeSTaMsthAnAvyaktabhAgAnayanasUtram - labdhAtkalpitabhAgAH savarNitairvyaktarA zibhirbhaktAH / 'kramazo rUpavihInAH sveSTapadeSvaviditAMzAH syuH // 125 // iti bhAgAnubandhajAtiH / atha bhAgApavAhajAtau sUtram - harahatarUpeSvaMzAnapanaya bhAgApavAhajAtividhau / guNayA prAMzacchedAvaMzonaccheda hArAbhyAm // 126 // -3. 126 ] 1 B guNayedagrAMzaharau rahitAMzacchedahArAbhyAm / [" udAharaNArtha prazna ( yaugika anugama meM ) svake 2, 3 aura 8 bhAgoM se saMyavita eka bhinna diyA gayA hai| anya bhinna, sva ke phe, aura I bhAgoM se saMyavita haiM / punaH anya bhinna svake hai, hai aura 2 bhAgoM se saMyavita haiM / isa taraha saMyavita bhinnoM kA yoga 1 ho to batalAo ki ye bhinna kyA-kyA haiM ? // 123 // eka bhinna svake 2, pe, aura bhAgoM se saMyavita hokara u ho jAtA hai| he mitra ! mujhe zIghra hI usa ajJAta bhinna kA mAna batalAo // 124 // Arambha kA sthAna chor3akara anya iSTa sthAnoM ke kisI ajJAta bhinna ko nikAlane ke liye niyamadiye gaye yoga ke, mana se vipATita bhAgoM ko jaba kramazaH iSTa bhAgAnubaMdha bhinnoM kI sarala kI gaI jJAta rAziyoM dvArA vibhAjita karate haiM aura taba 1 dvArA dvAsita karate haiM, taba iSTa sthAnoM kI ajJAta bhanIya rAziyA~ prApta hotI haiM // 125 // isa prakAra, kalAsavarNa SaDjAti meM bhAgAnubaMdha jAti nAmaka pariccheda samApta huA / bhAgApavAha jAti [ viyavita bhinna ] viyavita ( Dissociated ) bhinnoM ko sarala karane ke liye niyamabhAgApavAha bhinnoM ko sarala karane ke liye hara dvArA ghaTAo / jaba vidyuta rAzi pUrNAMka na hokara bhinnIya ho taba aMza dvArA dvAsita hara aura dUsare bhinna ke hara dvArA guNita karo // 126 // guNita viyuta pUrNa saMkhyA meM se aMza ko kramazaH aMza aura prathama bhinna ke hara ko (125) isa niyama meM dI gaI vidhi gAthA 122 ke samAna hai : isameM prApta phaloM ko eka dvArA hAsita kiyA jAtA hai / (126) bhAgApavAha kA zAbdika artha bhinnIya viyavana hai / jisa taraha bhAgAnubaMdha meM bhinna ke do prakAra haiM, usI taraha yahA~ bhI 2 prakAra haiN| jaba eka pUrNAMka aura eka bhinna bhAgApavAha sambandha meM rahate haiM taba pUrNAMka meM se bhinna ghaTAyA jAtA hai| do yA do se adhika bhinna bhI isa sambandha meM ho sakate haiM, jaise, svake hai bhAga dvArA vidyuta ke athavA sva ke hai, Tere bhAgoM dvArA viyuta hai; yahA~ artha yaha hai ki pe kA hai, meM meM se ( prathama udAharaNa meM ) ghaTAyA jAyagA dUsare prazna meM : De - De kA hai (Da - kA hai) kA Te - 5 - De kA hai - (3 - De kA hai) kA Te} kA de prApta hotA hai /

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gaNitasArasaMgraha [3.127 rUpabhAgApavAha uddezakA tryaSTacaturdazakarSAH paadaardhdvaadshaaNshsssstthonaaH| savanAya narairdattAstIrthakRtAM tadyutau kiM syAt // 12 // triguNapAdadalatrihatASTamaivirahitA nava sapta nava kramAt / priya vizodhya caturguNaSaTkataH kathaya zeSadhanapramitiM drutam // 128 // bhAgabhAgApavAha uddezaka: dviguNitapaJcamanavamatryaMzASTAMzadvisaptamAn krmshH| -- svaSaDaMzapAdacaraNajyazASTamavarjitAn samasya vada // 129 // SaTsaptAMzaH svaSaSThASTamanavamadazAMzaiviyuktaH paNasya syAtpazcadvAdazAMzaH svkcrnntRtiiyaaNshpshcaaNshkonH| svadvitryaMzadvipaJcAMzakadalaviyutaH paJcaSaDbhAgarAzirdvivyaMzo'nyaH svapazcASTamaparirahitastatsamAse phalaM kim // 130 / / adhaM vyaSTamabhAgapAdanavamaiH svIyairvihInaM punaH svairaSTAMzakasaptamAMzacaraNairUnaM tRtIyAMzakam / adhyardhatparizodhya saptamamapi svASTAMzaSaSThonitaM zeSa brUhi parizramo'sti yadi te bhAgApavAhe sakhe // 13 // . atrAgrAvyaktabhAgAnaya nsuutrmlbdhaatklpitbhaagaaruupaaniitaapvaahphlbhktaaH| kramazaH khaNDasamAnAste'jJAtAMzapramANAni / 132 // viyuta pUrNAkoM vAle bhAgApavAha bhinnoM para prazna 3, 8, 4 aura 10 karSa ko, 3,15 aura karSa dvArA hAsita kara zeSa karSa kucha manuSyoM dvArA tIrthaMkaroM ke pUjana ke liye bheMTa kiye gaye / inakA yoga karane para yogaphala kyA hogA? // 27 // he mitra ! mujhe zIghra batalAo ki aura dvArA hAsita kramavAra 9, . aura 9 rAziyoM ko 6x4 dvArA ghaTAyA jAne para kitanA zeSa rahegA ? // 12 // viyuta bhinnoM vAle bhAgApavAha bhinnoM para prazna kramazaH ... aura dvArA hAsita 3,1... aura 3 ko kramavAra jor3o aura taba yogaphala batalAo // 129 // diye gaye paNa meM, anugAmI sva kI , aura rAziyoM ko hAsita karo, punaH sva kI aura rAziyoM dvArA 13 ko hAsita karo, isI taraha sva kI 3,3 aura rAziyoM dvArA ko hAsita karo aura anya rAzi 3 ko sva kI saMkhyA dvArA hAsita kro| i sabhI pariNAmoM ko jor3akara phala batalAo // 130 // bhAgApavAha bhinna ke sambandha meM, he mitra, yadi tumane kaSTa kiyA hai to batalAo ki 11 meM se nimnalikhita rAziyA~ ghaTAne para kyA zeSa rahegA ? sva ke hai. aura bhAgoM dvArA hAsita: isI taraha sva ke aura bhAgoM dvArA hAsita; aura isI taraha sva ke hai aura bhAgoM dvArA hAsita // 13 // diye gaye yoga vAle pratyeka viyavita bhinna meM Arambha meM rahanevAle eka ajJAta tatva ko nikAlane ke liye niyama- joki saMkhyA meM iSTa vighaTaka tatvoM ke tulya haiM aise diye gaye yoga ke, mana se vipATita bhAgoM ko, jaba kramavAra ina vighaTaka tatvoM sambandhI viyuta rAzi ko mAnane se prApta pariNAmI rAziyoM dvArA vibhAjita kiyA jAtA hai to ichaviyuta ajJAta rAziyoM ke mAna prApta hote haiM // 132 // (132 ) isa gAthA kI rIti 122vIM gAthA ke samAna hai| ..

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-3. 136] kalAsavarNavyavahAraH atroddezaka kazcitsvakaizcaraNapazcamabhAgaSaSThaH ko'pyaMzako dlssddNshkpshcmaaNshaiH| hIno'paro dviguNapaJcamapAdaSaSThaiH tatsaMyutirdalamihAviditAMzakAH ke // 133 / / ko'pyaMzassvArdhaSaDbhAgapaJcamASTamasaptamaiH / vihIno jAyate SaSThaH sa ko'zo gaNitArthavit // 134 // zeSeSThasthAnAvyaktabhAgAnayanasUtramlabdhAtkalpitabhAgAH savarNitaiya'ktarAzibhibhaktAH / rUpAtpRthagapanItAH sveSTapadeSvaviditAMzAH syuH // 135 / / iti bhAgApavAhajAtiH / bhAgAnubandhabhAgApavAhajAtyoH sarvA vyaktabhAgAnayanasUtramtyaktvaikaM sveSTAMzAn prakalpayedaviditeSu sarveSu / aitaistaM punaraMzaM praaguktairaanyetsuutraiH||136|| 1 P, K aura B meM jAyate ke lie tadyatiH / udAharaNArtha prazna ___ koI bhinna nija kI aura rAziyoM dvArAanugamana meM ( in consecution) hAsita kiyA jAtA hai| dUsarA bhinna bhI isI taraha nija ke 3., aura 6 bhAgoM dvArA hAsita kiyA jAtA hai| tIsarA bhinna bhI isI taraha nija ke aura bhAgoM dvArA hAsita kiyA jAtA hai| ina tInoM dvAsita rAziyoM kA yoga hai| batalAo ki ve ajJAta bhinna kauna-kauna haiM ? // 133 // koI bhinna nija ke 3, 6 tathA hai aura bhAgoM dvArA anugamana meM hAsita kiyA jAtA hai aura isa taraha ho jAtA hai / he aMkagaNita siddhAnta vettA ! batalAo ki vaha ajJAta kyA hai ? // 13 // anya cAhe hue sthAnoM vAlA koI ajJAta bhinna nikAlane ke niyama diye gaye yoga se prApta mana se cune hue vipATita bhAga kramazaH iSTa bhAgApavAha bhinnoM vAlI saralIkRta jJAta rAziyoM dvArA vibhAjita hokara aura taba 9 meM se alaga alaga ghaTAye jAkara, cAhe hue sthAnoM kI bhinnIya rAziyA~ ho jAte haiM // 135 // isa prakAra kalAsavarNa SaDjAti meM bhAgApavAha jAti nAmaka pariccheda samApta huaa| bhAgAnubandha athavA bhAgApavAha prakAra ke bhinnoM ke sambandha meM aMtimamAna jJAta hone para ( sarva sthAna vAle) ajJAta bhinnoM ko nikAlane ke liye niyama mana se, icchAnusAra, kevala eka sthAna chor3akara saba ajJAta sthAnoM sambandhI bhinna cuno| taba Upara likhe hue niyamoM dvArA, usa ajJAta bhinna ko, ina mana se cunI huI bhinnIya rAziyoM kI sahAyatA se prApta karo // 136 // ( 135 ) gAthA 125 meM diye gaye niyama ke samAna yaha bhI hai / (136 ) 122, 125, 132 aura 135 gAthAoM meM diye gaye niyamAnusAra yaha bhI hai / ga0 sA0 saM0-9

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66] maNinasArasaMgrahaH avoddezaka kazcidaMzoM'zakaiH kaizcitpazcabhiH svairdheto dalam / viyukto vA bhavetpAdastAnaMzAn kathaya priya // 137 / / __ bhAgamAtRjAtau sUtrambhAgAdimajAtInAM svasvavidhirbhAgamAtRjAtau syAt / sA SaDviMzatibhedA rUpaM chedo'cchido rAzeH // 138 // udAharaNArtha prazna eka bhinna nija ke pA~ca anya bhinnoM se milAyA jAne para ho jAtA hai; aura, eka anya bhinna nija ke pA~ca anya bhinnoM dvArA hAsita hokara ho jAtA hai| he mitra ! una saba akSAta miloM kA mAna nikAlo // 137 // bhAgamAtR jAti [ do yA adhika prakAra ke bhinnoM se saMyukta bhinna ] Upara varNita sabhI prakAra ke bhinnoM kA jisameM samAveza hai aise bhAgamAtra prakAra ke bhinna sarala karane ke liye niyama bhAgamAtra bhinnoM meM, sarala bhinnoM ko Adi lekara vibhinna prakAra ke bhinnoM sambandhI niyama prayojya hote haiM / bhAgamAtra bhinna ke 26 prakAra hote haiN| jisa rAzi kA hara nahIM hotA usa rAzi kA hara eka le lete haiM // 13 // ( 137 ) isa prazna meM, prathama dazA ko hala karane meM, Arambha ke sthAnoM ko chor3akara anya sthAnoM meM hai aura bhinnoM ko cuno; aura taba gAthA 122 meM diye gaye niyama dvArA prathama bhinna ko nikAlo jo prApta hogA / athavA, 125vIM gAthA ke anusAra Adi bhinna ke sivAya chor3e hue anya sthAnoM ke bhinna ko nikAlane ke liye aura cuno; bhinna aavegaa| isI taraha viyuta bhinnoM vAlI dUsarI dazA ko 132vIM aura 135vIM gAthA ke niyama kI sahAyatA se sAdhita kiyA jA sakatA hai| (138 ) 26 prakAra ke bhinna taba prApta hote haiM jaba ki bhAga, prabhAga, bhAgabhAga, bhAgAnubaMdha aura bhAgApavAha ko eka bAra meM kramazaH do, tIna, cAra athavA pA~ca lekara saMcaya (combinations) saMkhyA nikAlate haiN| jaise, bhAga aura prabhAga mizrita hote haiM, bhAga aura bhAgabhAga mizrita rahate haiM, Adi / do kA mizraNa karane para 10 saMcaya prApta hote haiM, 3 kA mizraNa eka bAra meM lene se 10 saMcaya, cAra kA mizraNa eka bAra lene para 5 saMcaya aura sabako eka bAra lene para 1 saMcaya, isa taraha kula 26 prakAra prApta hote haiN| 13vI gAthA ke anta meM aise mAgamAtra prakAra kA prazna haiM jisameM pA~coM prakAra sammilita haiN|

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kalAsavarNavyavahAraH atroddezakaH zaH pAdo'rghAdhaM paJcamaSaSThakhipAdahatamekam / pazcArdhahRtaM rUpaM saSaSThamekaM sapanamaM rUpam // 139 // svIyatRtIyamugdalamato nijaSaSThayuto dvisaptamo hI navAMza kamapanItadazAMzakarUpamaSTamaH / svena navAMzakena rahitazcaraNaH svakapaJcamojjhito brUhi samasya tAn priya kalAsamakotpalamAlikAvidhau // 140 // iti bhAgamAtRjAtiH / iti sArasaGgrahe gaNitazAstre mahAvIrAcAryasya kRtau kalAsavarNo nAma dvitIyavyavahArassamAptaH // -3. 140 ] udAharaNArthaM prazna diyA gayA hai ki bhinna 3 nija ke, hai, hai, 3 kA 3, pe kA hai / [ 67 , " 5/2 13, 13 bhAgoM se saMyukta hai / punaH, nima ke he bhAga se saMyukta u; de dvArA hAsita ; pa dvArA hAsita 1; nija ke bhAga dvArA hAsita hai; nija ke pe bhAga dvArA hAsita hai; jo nIlakamala puSpoM kI mAlA ( utpalamAlikA) ke samAna guMthe hue haiM aise bhinna sambandhI niyamoM ke anusAra, he mitra, inheM jor3akara batAo ki yogaphala kyA hogA ? // 139 aura 140 // isa prakAra, kalAsavarNa SaDjAti meM bhAgamAtR jAMti nAmaka pariccheda samApta huA / isa prakAra, mahAvIrAcArya kI kRti sArasaMgraha nAmaka gaNitazAstra meM kalAsavarNa nAmaka dvitIya vyavahAra samAsa huA / ( 139 aura 140 ) isa gAthA meM utpalamAlikA zabda AyA hai jisakA artha nIlakamala puSpamAlA hotA hai | gAthA kI saMracanA kA chaMda bhI yahI hai /

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4. prakorNaka vyavahAraH praNutAnantaguNaughaM praNipatya jinezvara mahAvIram / praNatajagattrayavaradaM prakIrNakaM gnnitmbhidhaasye||1|| 'vidhvastadurnayadhvAntaH siddhaH syAdvAdazAsanaH / vidyAnando jino jIyAdvAdIndro munipuGgavaH / / 2 / / itaH paraM prakIrNakaM tRtIyavyavahAramudAhariSyAmaHbhAgaH zeSo mUlakaM zeSamUlaM syAtAM jAtI dve dviraprAMzamUle / bhAgAbhyAso'toM'zavargo'tha mUlamizraM tasmAdbhinnadRzyaM dazAmUH / / 3 // 1 B aura M meM yaha zloka chUTA huA hai| 4. prakIrNakavyavahAra [bhinnoM para vividha prazna ] stavanIya ananta guNoM se pUrNa aura namana karate hue tInoM lokoM ke jIvoM ko vara dene vAle jinezvara mahAvIra ko namaskAra kara maiM bhinnoM para vividha praznoM kA pratipAdana karU~gA // 1 // jinhoMne durnaya ke aMdhakAra kA vidhvaMsa kara syAdvAda zAsana ko siddha kiyA hai, jo vidyAnanda haiM, vAdiyoM meM advitIya haiM aura munipuMgava haiM aise jina sadA jayavaMta hoN| isake pazcAt , maiM tIsare viSaya ( bhinnoM para vividha prazna ) kA pratipAdana karU~gA // 2 // bhinnoM para vividha praznoM ke dasa prakAra haiM; bhAga, zeSa, mUla, zeSamUla, dviramazeSamUla, aMzamUla, bhAgAbhyAsa, aMzavarga, mUlamizra aura bhinnadRzya // 3 // (3) 'bhAga' prakAra meM ve prazna hote haiM jinameM nikAlI jAnevAlI kula rAzi ke kucha viziSTa bhinnIya bhAgoM ko haTAne ke pazcAt zeSa bhAga kA saMkhyAtmaka mAna diyA gayA hotA hai| haTAye gaye bhinnIya bhAga meM se pratyeka 'bhAga' kahalAtA hai aura jJAta zeSa kA saMkhyAtmaka mAna 'dRzya' kahalAtA hai| 'zeSa prakAra meM ve prazna hote haiM jinameM nikAlI jAnevAlI kula rAzi ke jJAta bhinnIya bhAga ko haTAne ke pazcAt athavA uttarottara zeSa ke kucha jJAta bhinnIya bhAga haTAne ke pazcAt zeSa bhAga kA saMkhyAtmaka mAna diyA gayA hotA hai| 'mUla' prakAra meM ve prazna hote haiM jinameM kula rAzi meM se kucha bhinnIya bhAga athavA usa kula rAzi ke vargamUla kA guNaka ghaTAne ke pazcAt zeSa bhAga kA saMkhyAtmaka mAna diyA gayA hotA hai| 'zeSamUla', 'mUla se kevala isa bAta meM bhinna hai ki yaha vargamUla pUrI rAzi ke sthAna meM usakA vargamUla hotA hai jo diye gaye bhinnIya bhAgoM ko ghaTAne ke pazcAt zeSa rUpa meM bacatA hai| dviragra zeSamUla' prakAra meM ve prazna hote haiM jinameM jJAta vastuoM kI saMkhyA pahile haTAI jAtI hai; taba uttarottara zeSa ke kucha bhinnIya bhAga aura taba agra zeSa ke vargamUla kA koI guNaka haTAyA jAtA hai; aura anta meM, zeSa bhAga kA saMkhyAtmaka mAna diyA gayA hotA hai| prathama haTAI gaI jJAta saMkhyA pUrvAgra kahalAtI hai| 'aMzamUla' prakAra meM kula saMkhyA ke bhinnIya bhAga ke vargamUla ke eka guNaka ko haTAyA jAtA hai aura taba zeSa bhAga kA saMkhyAtmaka mAna diyA gayA hotA hai|

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-4.5] prakIrNakavyavahAraH ___ tatra bhAgajAtizeSajAtyoH sUtrambhAgonarUpabhaktaM dRzyaM phalamatra bhAgajAtividhau / aMzonitarUpAhatihRtamagraM zeSajAtividhau // 4 // bhAgajAtAvuddezakaH dRSTo'STamaM pRthivyAM stambhasya vyaMzako mayA toye / pAdAMzaH zaivAle kaH stambhaH sapta hastAH khe // 5 // SaDbhAgaH pATalISu bhramaravaratatestatribhAgaH kadambe pAdazcUtadrumeSu pradalitakusume campake pazcamAMzaH / bhinnoM para vividha praznoM meM 'bhAga' aura 'zeSa' bhinnoM sambandhI niyama ... 'bhAga' prakAra (bhAga prakAra kI prakriyAoM) meM, jJAta bhinna se hAsita 1 ke dvArA dI gaI rAzi ko bhAjita kara cAhA huA phala prApta kiyA jAtA hai| 'zeSa' prakAra kI prakriyAoM meM, jJAta bhitroM ko eka meM se kramazaH ghaTAne se prApta rAziyoM ke guNanaphala dvArA dI gaI rAzi ko bhAjita kara iSTa phala prApta kiyA jAtA hai // 4 // ___ 'bhAga' jAti ke udAharaNArtha prazna mere dvArA eka stambha kA bhAga jamIna meM pAnI meM kAI meM aura 7 hasta havA meM dekhA gyaa| batalAo stambha kI lambAI kyA hai ? // 5 // zreSTha bhramaroM ke samUha meM se pATalI vRkSa meM, kadamba vRkSa meM, Amra vRkSa meM, 6 vikasita puSpoM vAle campaka vRkSa meM, 3 sUrya kiraNoM dvArA pUrNa vikasita kamala vRnda meM Ananda le rahe the aura eka matta bhRGga AkAza meM bhramaNa kara rahA thaa| (4) 'bhAga' prakAra ke sambandha meM niyama bIjIya rUpa se yaha hai : ka = . jahA~ ka ajJAta samuccaya rAzi hai, jise nikAlanA hai; a 'dRzya' athavA agra hai; aura, ba diyA gayA bhAga athavA diye 'bhAgAbhyAsa' athavA 'bhAga sambarga' prakAra meM, kula saMkhyA ke kucha bhinnIya bhAgoM ke guNanaphala athavA guNanaphaloM ko do, do ke saMcaya meM lekara unheM kula saMkhyA meM se ghaTAne se prApta zeSa bhAga kA saMkhyAtmaka mAna diyA gayA hotA hai| 'aMzavarga' prakAra meM ve prazna hote haiM jinameM kula meM se bhinnIya bhAga kA varga ( jahAM, yaha bhinnIya bhAga dI gaI saMkhyA dvArA bar3hAyA athavA ghaTAyA jAtA hai) haTAne ke pazcAt zeSa bhAga kA saMkhyAtmaka mAna diyA gayA hotA hai| 'mUlamizra' prakAra meM ve prazna hote haiM jinameM kucha dI gaI saMkhyAoM dvArA ghaTAI yA bar3hAI gaI kula saMkhyA ke vargamUla meM kula ke vargamUla ko jor3ane se prApta yoga kA saMkhyAtmaka mAna diyA gayA hotA hai / ... ___ 'bhinna dRzya prakAra meM kula kA bhinnIya bhAga, dUsare bhinnIya bhAga dvArA guNita hokara, usameM se haTA diyA jAtA hai aura zeSa bhAga kula ke bhinnIya bhAga ke rUpa meM nirupita kiyA jAtA hai| yaha vicAraNIya hai ki isa prakAra meM, anya prakAroM kI apekSA zeSa ko kula ke bhinnIya bhAga ke rUpa meM rakhA jAtA hai|

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..] gaNitasArasaMgrahaH protphullAmbhojaSaNDe ravikaradalite triMzadaMzo'bhireme tatraiko mattabhRGgo bhramati nabhasi kA tasya vRndasya saMkhyA // 6 // AdAyAmbhoruhANi stutizatamukharaH zrAvakastIrthakRdbhayaH / pUjAM cakre caturyo vRSabhajinavarAt vyaMzameSAmamuSya / vyaMzaM turya SaDaMzaM tadanu sumataye tannavadvAdazAMzI zeSebhyo dvidvipanaM pramuditamanasAdatta kiM tatpramANam // 7 // khavazIkRtendriyANAM dUrIkRtaviSakaSAyadoSANAm / zIlaguNAbharaNAnAM dayAGganAliGgitAGgAnAm // 8 // sAdhUnAM sadvandaM sandRSTaM dvAdazo'sya tarkajJaH / svayaMzavarjito'yaM saiddhAntazchAndasastayoH zeSaH // 9 // SaDno'yaM dharmakathI sa eva naimittikaH svapAdonaH / vAdI tayorvizeSaH SaGguNito'yaM tapasvI syAt // 10 // girizikharataTe mayopadRSTA yatipatayo navasaguNASTasaGkhyAH / ravikaraparitApitojjavalAGgAH kathaya munIndrasamUhamAzu me tvam // 11 // batalAo ki usa samUha meM bhramaroM kI saMkhyA kitanI thI? // 6 // eka vaka ne kamaloM ko ekatrita kara, jora se zata stutiyA~ karate hue, pUjana meM ina kamaloM ke bhAga aura isa bhAga ke 31 aura / bhAgoM ko kramazaH jinavara RSama se Adi lekara cAra tIrthaMkaroM ko; inhIM 3 bhAga kamaloM ke aura bhAgoM ko sumati nAtha ko; taba, zeSa 19 tIrthaMkaroM ko pramudita mana se 2,2 kamala meMTa kiye| batalAo ki una saba kamaloM kA saMkhyAtmaka mAna kyA hai ? // 7 // kucha sAdhuoM kA samUha dekhA gyaa| ve sAdhu indriyoM ko apane vazameM kara cuke the, viSarUpI kaSAya ke doSoM ko dUra kara cake the| unake zarIra saccaritratA se aura sadaguNoM rUpI AbharaNoM se zobhAyamAna the tathA dayA rUpI aMganA se AliMgita the / usa samUha kA 12 bhAga tarka zAstriyoM yukta thaa| nija ke bhAga dvArA hAsita yaha 13 vA bhAga sadunda, saMdRSTa sAdhuoM yukta thA / ina donoM kA antara [12 au kA] siddhAnta jJAtAoM kI saMkhyA thii| isa aMtima anupAtI rAzi meM 6 kA guNana karane se prApta rAzi dharma kathikoM kI saMkhyA thI / nija ke ? bhAga dvArA hAsita baha rAzi naimittika jJAniyoM kI saMkhyA thI / ina aMta meM kathita do rAziyoM ke antara kA rAziphala vAdiyoM kI saMkhyA thii| 6 dvArA guNita yaha rAzi kaThora tapasviyoM kI saMkhyA thii| aura, 948 yati mere dvArA giri ke zikhara ke pAsa dekhe gaye, jinakA zarIra sUrya ke kiraNoM dvArA paritapta hokara ujvala dikhAI detA thaa| mujhe zIghra, isa munIndra samuha kA mAna batalAo // 8-11 // pake hue phaloM (baliyoM) ke bhAra se jhuke hue sandara zAli kSetra meM kucha tote (zukra) utre| kisI manuSya dvArA bhayagrasta hokara ve saba sahasA Upara udd'e| unameM se Adhe pUrva dizA kI ora, dakSiNa pUrva (Agneya) dizA meM udd'e| jo pUrva aura Agneya dizA meM ur3e unake antara ko nija kI AdhI rAzi dvArA hAsitakara aura punaH isa pariNAmI rAzi kI gaye minnIya bhAgoM kA yoga hai| yaha spaSTa hai, ki yaha samIkaraNa ka-baka = a dvArA prApta kiyA jA sakatA hai| zeSa prakAra kA niyama, bIjIya rUpa se nidarzita karane para, hotA hai, jahA~ ba,, bara, ba Adi uttarottara zeSoM ke (1-ba)(1-bara) (1-ba)x...... a

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-4.22] prakIrNakamyavahAraH phalabhAranamrakane zAlikSetre zukAH samupaviSTAH / sahasotthitA manuSyaiH sarva saMtrAsitAH santaH / / 12 / / teSAmadhaM prAcImAgneyoM prati jagAma SaDbhAgaH / pUrvAgneyozeSaH svadalonaH svArdhavarjito yAmIm // 13 // yAmyAgneyIzeSaH sa naiRti svadvipazcabhAgonaH / yAmonaiRtyaMzakaparizeSo vAruNImAzAm // 14 // nairRtyaparavizeSo vAyavyAM sasvakatrisaptAMzaH / vAyavyaparavizeSo yutasvasaptASTamaH saumIm // 15 // vAyavyuttarayoyutiraizAnI svatribhAgayugahInA / dazaguNitASTAviMzatiravaziSTA vyoni kati kiiraaH||16|| kAcidvasantamAse prsuunphlgucchbhaarnmrodyaane| kusumAsavarasaraJjitazukakokilamadhupamadhuranisvananicite // 17 // himakaradhavale pRthule saudhatale sAndrarundramRdutalpe / phaNiphaNanitambabimbA kanadamalAbharaNazobhAGgI // 18 // pAThInajaTharanayanA ktthinstnhaarnmrtnumdhyaa| saha nijapatinA yuvatI rAtrau protyAnuramamANA // 19 // praNayakalahe samutthe muktAmayakaNThikA tdblaayaaH| chinnAvannau nipatitA tataJyaMzazceTikAM prApat // 20 // SaDbhAgaH zayyAyAmanantarAntarArdhamitibhAgAH / SaTsaMkhyAnAstasyAH sarve sarvatra sNptitaaH||21|| ekAgraSaSTizatayutasahastramuktAphalAni dRSTAni / tanmauktikapramANaM prakIrNakaM vetsi cet kathaya // 22 // arddha rAzi dvArA hAsita karane se prApta rAzi ke tote dakSiNa dizA kI ora udd'e| jo dakSiNa kI ora ur3e tathA Agneya dizA meM ur3e unake antara ko, nija ke 3 bhAga dvArA hAsita karane se prApta rAzi ke tote dakSiNa pazcima (naiRtya) dizA meM udd'e| jo naiRtya meM ur3e tathA pazcima meM ur3eM, unake antara meM usa nija ke bhAga ko jor3ane se prApta saMkhyA ke tote uttara-pazcima (vAyavya ) meM ur3e / jo vAyavya aura pazcima meM ur3e unake antara meM nija ke hai bhAga ko jor3ane se prApta saMkhyA ke tote uttara dizA meM udd'eN| jo vAyavya aura uttara meM ur3e unakA yogaphala nija ke 3 bhAga dvArA hAsita hone se prApta rAzi ke tote uttara pUrva (IzAna) dizA meM ur3e / tathA, 280 tote Upara AkAza meM zeSa rhe| batalAo kula kitane tote the? // 12-16 // vasanta Rtu ke mAsa meM eka rAtri ko, koI......yuvatI apane pati ke sAtha, phala aura puSpoM ke gucchoM se namrIbhUta hue vRkSoMvAle, aura phUloM se prApta rasa dvArA matta zuka, koyala tathA bhramaravRnda ke madhura svaroM se guMjita bagIce meM sthita .....mahala ke pharza para sukha se tiSThI thii| tabhI pati aura patnI meM praNayakalaha hone ke kAraNa, usa abalA ke gale kI muktAmayI kaThikA TUTa gaI aura pharza para gira pdd'ii| usa muktA ke hAra ke muktA dAsI ke pAsa pahuMce zayyA para gire, taba zeSa ke, aura punaH agrima zeSa ke aura phira agrima zeSa ke isI taraha kula 6 bAra meM prApta muktA rAzi sarvatra girii| zeSa binA bikhare hue 1161 motI pAye gye| yadi tuma prakIrNaka bhinnoM kA sAdhana karanA jAnate ho to usa hAra ke motiyoM kA saMkhyAtmaka mAna batalAo // 17-22 // sphurita indranIlamaNi samAna nIle raMga bhinnIya bhAga haiM / yaha sUtra nimnalikhita samIkaraNa se prApta kiyA jA sakatA hai / ka-ba, ka-ba. (ka-ba, ka)-ba haka-baka-ba, (ka-ba, ka)}-(ityAdi)...... a. (17) kucha zabdoM kA anuvAda chor3a diyA gayA hai, jinheM pAThaka mUla gAthA meM dekha sakate haiN|

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gaNitasArasaMgrahaH [4. 23-- sphuradindranIlavarNa SaTpadavRndaM prphullitodyaane| dRSTaM tasyASTAMzo'zoke kuTaje SaDaMzako lInaH // 23 // kuTajAzokavizeSaH SaDguNito vipulapATalISaNDe / pATalyazokazeSaH svanavAMzono vizAlasAlavane // 24 // pATalyazokazeSo yutaH svasaptAMzakena madhukavane / paJcAMzaH saMdRSTo bakule pUraphullamukuleSu // 25 // tilakeSu kurabakeSu ca saraleSvAneSu padmaSaNDeSu / vanakarikapolamUleSvapi santasthe sa evAMzaH // 26 // kiJjalkapuJjapiJjarakaJjavane madhukarAtrayastriMzat / dRSTA bhramarakulasya pramANamAcakSva gaNaka tvam // 27 // goyUthasya kSitibhRti dalaM taddalaM zailamUle SaT tasyAMzA vipulavipine puurvpuurvaardhmaanaaH| saMtiSThante nagaranikaTe dhenavo dRzyamAnA dvAtriMzat tvaM vada mama sakhe gokulasya pramANam // 28 // iti bhaagjaatyuddeshkH| zeSajAtAvuddezakaH SaDbhAgamAmrarAze rAjA zeSasya pazcama rAjJo / turyatryaMzadalAni trayo'grahISuH kumAravarAH // 29 // zeSANi trINi cUtAni kaniSTho dArako'grahIt / tasya pramANamAcakSva prakIrNakavizArada // 30 // carati girau saptAMzaH kariNAM sssstthaadimaaiipaashcaatyaaH| pratizeSAMzA vipine SaDdRSTAH sarasi kati te syuH // 31 // . 1 M meM 'sphuritendra0', pATha hai / vAle bhramaroM ke samUha (SaTpada vRnda ) ko praphullita udyAna meM dekhA gyaa| usa samUha kA bhAga azoka vRkSoM meM tathA bhAga kuTaja vRkSoM meM chipa gyaa| jo kramazaH kuTaja aura azoka vRkSoM meM chipa gaye una samUhoM ke aMtara ko 6 dvArA guNita karane se prApta bhramaroM kI rAzi vipula pATalI vRkSoM ke samUha meM chipa gaI / pATalI aura azoka vRkSoM ke bhramara samUhoM ke antara ko nija ke bhAga dvArA hAsita karane se prApta bhramara rAzi vizAla sAla vRkSoM ke vana meM chipa gii| usI aMtara ko nija ke bhAga meM milAne se prApta bhramara rAzi madhuka vRkSoM ke vana meM chipa gii| kula samUha kI bhramararAzi acchI taraha khilIhuI kaliyoM vAle bakula vRkSoM meM chipI dekhI gaI aura vahI bhramara rAzi tilaka, kurabaka, sarala aura Ama ke vRkSoM meM, kamaloM ke samUha meM aura vanahastiyoM vAle maMdiroM ke mUla meM chipa gaI / aura, zeSa 33 mara bar3IrAzi ke vibhinna raMgAM se vyApta kamala puMja meM dekhe gaye / he gaNitajJa ! bhramara samUha kA saMkhyAtmaka mAna do // 23-27 // gokula (pazuoM ke jhuNDa ) meM se 3 bhAga parvata para hai| usakA 3 bhAga parvata ke mUla meM hai| aise hI 6 aura bhAga (jinameM se pratyeka uttarottara pUrvavartI bhAga kA AdhA hai), kisI vipula vana meM hai| zeSa 32 gAyeM nagara ke nikaTa dekhI jAtI haiN| he mere mitra ! usa pazu jhuNDa kA saMkhyAtmaka mAna batalAo // 28 // isa prakAra, 'bhAga' jAti ke udAharaNArtha prazna samApta hue| 'zeSa' jAti ke udAharaNArtha prazna Amra phaloM ke samUha meM se rAjA ne bhAga liyA; rAnI ne zeSa kA bhAga liyA aura pramukha rAjakumAroM ne usI zeSa ke kramazaH 1, 3 aura 3 bhAga liye / sabase choTe ne zeSa 3 Ama liye| he prakIrNaka vizArada ! AmasamUha kA saMkhyAtmaka mAna batalAo // 29-30 // hAthiyoM ke jhuNDa kA bhAga parvata para vicaraNa kara rahA hai| krama se uttarottara zeSa ke bhAga ko Adi rekara taka jhuNDa bhAga vana meM Dola rahe haiN| zeSa 6 sarovara ke nikaTa haiN| batalAo ki ve kitane hAthI haiM ? // 31 //

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prakIrNakavyavahAraH koSThasya lebhe navamAMzamekaH pare'STabhAgAdidalAntimAzAn / zeSasya zeSasya punaH purANA dRSTA mayA dvAdaza tatpramA kA // 32 // iti zeSajAtyuddezakaH / atha mUlajAtau sUtrammUlArdhAgre chindyAdaMzonaikena yuktamUlakRteH / dRzyasya padaM sapadaM vargitamiha mUlajAtau svam // 33 // atroddezakaH dRSTo'TavyAmuSTrayUthasya pAdo mUle ca dve zailasAnau niviSTe / uSTrAstrinAH paJca nadyAstu tIre kiM tasya syAduSTrakasya pramANam // 34 // zrutvA varSAbhramAlApaTahapaTuravaM zailazRGgoruraGge nATyaM cakre pramodapramuditazikhinAM SoDazAMzo'STamazca / vyaMzaH zeSasya SaSTho varabakulavane paJca mUlAni tasthuH punnAge paJca dRSTA bhaNa gaNaka gaNaM barhiNAM saMguNayya // 35 // 1 B meM 'hasti' pATha hai| 2 B meM 'nAgA: pATha hai| 3 B meM 'kiM syAtteSAM kuJjarANAM pramANam' pATha hai / eka AdamI ko khajAne kA hai bhAga milaa| dUsaroM ko uttarottara zeSoM ke 2 se Arambha kara, krama se 3 taka bhAga mile| aMta meM zeSa 12 purANa mujhe dikhe| batalAo ki koSTha meM kitane purANa haiM? // 32 // isa taraha zeSa jAti ke udAharaNArtha prazna samApta hue| 'mUla' jAti sambandhI niyama___ ajJAta rAzi ke vargamUla kA AdhA guNAMka ( vAra dyotaka coefficient ) aura jJAta zeSa meM se pratyeka ko ajJAta rAzi ke bhincIya guNAMka se hAsita eka dvArA bhAjita karanA caahiye| isa taraha varte hue jJAta zeSa ko ajJAta rAzi ke vargamUla ke guNAMka ke varga meM jor3ate haiN| prApta rAzi ke vargamUla meM isI prakAra varte hue ajJAta rAzi ke vargamUla ke guNAMka ko jor3ate haiN| tatpazcAt pariNAmI rAzi kA pUrNa varga karane para, isa mUla prakAra meM iSTa ajJAta rAzi prApta hotI hai // 33 // udAharaNArtha prazna U~ToM ke jhuNDa kA bhAga vana meM dekhA gyaa| usa jhuNDa ke vargamUla kA dugunA bhAga parvata ke utAroM para dekhA gyaa| 5 U~ToM ke tigune, nadI ke tIra para dekhe gye| U~ToM kI kula saMkhyA kyA hai ? // 34 // varSA Rtu meM, ghanAvali dvArA utpanna huI spaSTa dhvani sunakara, mayUroM ke samUha ke para aura hai bhAga tathA zeSa kA bhAga aura tatpazcAt zeSa kA bhAga, AnandAtireka hokara parvata zikhararUpI vizAla nATyazAlA para nAcate rhe| usa samUha ke vargamUla ke pA~cagune bakula vRkSoM ke utkRSTa vana meM Thahare rhe| aura, zeSa 5 punnAga vRkSa para dekhe gaye / he gaNitajJa ! gaNanA karake kula mayUroM kI saMkhyA batalAo // 35 // kisI ajJAta saMkhyA vAle sArasa pakSiyoM ke jhuNDa kA bhAga kamala SaNDa (samUha) (33) bIjIya rUpa se, yaha niyama nimnalikhita rUpa meM AtA hai-yahA~ ajJAta rAzi 'ka' hai / ka = 13-4+N A +(sa/2)2}..yaha, samIkaraNa ka - ( baka + sa ka + a) 30 ke dvArA saralatA se prApta kiyA jA sakatA hai| ga0 sA0 saM0-10

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74 ] gaNitasArasaMgrahaH carati kamalaSaNDe sArasAnAM caturtho navamacaraNabhAgau sapta mUlAni cAdrau / vikacabakulamadhye saptanighnASTamAnAH kati kathaya sakhe tvaM pakSiNo dakSa sAkSAt // 36 // na bhAgaH kapivRndrasya trINi mUlAni parvate / catvAriMzadvane dRSTA vAnarAstadguNaH kiyAn // 37 // kalakaNThAnAmardhaM sahakArataroH praphullazAkhAyAm / tilake'STAdaza tasthurno mUlaM kathaya pikanikaram // 38 // haMsakulasya dalaM bakule'sthAt paJca padAni tamAlakujAye / atra na kiMcidapi pratidRSTaM tatpramitiM kathaya priya zIghram // 39 // itimUlajAtiH / atha zeSamUlajAtau sUtram -- padaddalavargayutAgrAnmUlaM saprAkpadArdhamasya kRtiH / dRzye mUlaM prApte phalamiha bhAgaM tu bhAgajAtividhiH // 40 // / para cala rahA hai; usake de aura bhAga tathA usake vargamUla kA 7 gunA bhAga parvata para vicara rahe haiM / kucha puSpayukta bakula vRkSoM ke madhya meM zeSa 56 haiM / he nipuNa mitra ! mujhe ThIka batalAo ki kula pakSI haiM // 36 // bandaroM ke samUha kA koI bhI bhinIya bhAga kahIM nahIM hai / usake vargamUla kA tigunA bhAga parvata para hai, aura zeSa 40 vana meM dekhe gaye haiM una bandaroM kI saMkhyA kyA hai ? // 37 // koyaloM kI AdhI saMkhyA Amra kI praphullita zAkhA para hai / 18 koyaleM eka tilaka vRkSa para dekhI gaI haiM / unakI saMkhyA ke vargamUla kA koI bhI guNaka kahIM nahIM dekhA gayA hai / una koyaloM kI saMkhyA kyA hai ? ||38|| haMsoM kI AdhI saMkhyA bakula vRkSoM ke madhya meM dekhI gaI; unake samUha ke vargamUla kI pA~ca gunI saMkhyA tamAla vRkSoM ke zikhara para dekhI gii| zeSa kahIM nahIM dikhAI dI / he mitra ! usa samUha kA saMkhyAtmaka mAna zIghra batalAo || 39 // isa prakAra 'mUla' jAti prakaraNa samApta huA / zeSamUla jAti sambandhI niyama [ 4. 36 ajJAta samuccaya rAzi ke zeSa bhAga ke vargamUla ke guNAMka kI AdhI rAzi ke varga ko lo| usameM zeSa jJAta saMkhyA milAo / yogaphala kA vargamUla nikaalo| ajJAta samuccaya rAzi ke zeSa bhAga ko vargamUla ke guNAMka kI AdhI rAzi meM isa vargamUla ko milAo / yadi ajJAta samuccaya rAzi ko mUla (original) samuccaya rAzi hI le liyA jAtA hai to isa aMtima yoga kA varga iSTa phala hogaa| parantu, yadi usa ajJAta samuccaya rAzi kA zeSa bhAga kevala eka bhAga kI taraha hI vartA jAtA hai, to "bhAga" prakAra sambandhI niyama upayoga meM lAnA par3egA // 40 // yaha samIkaraNa isa prakAra ke praznoM kA bIjIya nirUpaNa hai / yahA~ 'sa' ajJAta rAzi ka ke vargamUla kA guNAMka hai / sa 2 2 (40) bIjIya rUpa se, ka-baka = { (' + a } ' hai / isa mAna se adhyAya meM diye gaye niyama 4 ke anusAra ka kA mAna nikAlA jA sakatA hai| samIkaraNa ka - baka + +

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-4. 46] prakIrNakagyavahAraH [75 atroddezakaH gajayUthasya tryaMzaH zeSapadaM ca trisaMguNaM sAnau / sarasi trihastinIbhirnAgo dRSTaH katIha gjaaH||41 / / nirjantukapradeze nAnAdrumaSaNDamaNDitodyAne / AsInAnAM yaminAM mUlaM tarumUlayogayutam // 42 // zeSasya dazamabhAgo mUlaM navamo'tha mUlamaSTAMzaH / mUlaM saptamamUlaM SaSTho mUlaM ca paJcamo mUlaM // 43 // ete bhAgAH kAvyapravacanadharmapramANanayavidyAH / vAdacchandojyautiSamantrAlaGkArazabdajJAH // 44 // dvAdazatapaHprabhAvA dvaadshbhedaanggshaastrkushldhiyH|...... dvAdaza munayo dRSTAH kiyatI municandra yatisamitiH // 45 // mUlAni paJca caraNena yutAni sAnau zeSasya paJcanavamaH kariNAM nagAgre / mUlAni paJca sarasIjavane ramante nadyAstaTe SaDiha te dviradAH kiyantaH // 46 // iti shessmuuljaatiH| 1 B meM zeSasya padaM trisaMguNaM pATha hai / udAharaNArtha prazna hAthiyoM ke yUtha ( jhuMDa ) kA bhAga tathA zeSa bhAga kI vargamUla rAzi ke hAthI, parvatIya utAra para dekhe gye| zeSa eka hAthI 3.hastiniyoM ke sAtha eka sarovara ke kinAre dekhA gyaa| batalAo kitane hAthI the? // 45 // kaI prakAra ke vRkSoM ke samUha dvArA-maMDita udyAna ke nirjantuka pradeza meM kaI sAdhu AsIna the| unameM se kula ke vargamUla kI saMkhyA ke sAdhu tarUmUla meM baiThe hue yogAbhyAsa kara rahe the| zeSa ke , ( isako ghaTAkara ) zeSa kA vargamUla, ( isako ghaTAkara ) zeSa ke 2, ( isako ghaTAkara ) zeSa kA; (isako ghaTAkara ) zeSa kA; (isako ghaTAkara ) zeSa kA vargamUla; (isako ghaTAkara ) zeSa kA; (isako ghaTAkara) zeSa kA isako ghaTAkara zeSa ke vargamUla dvArA nirUpita saMkhyAoM vAle ve the jo ( kramazaH) kAnya pravacana, dharma, pramANa nayavicA, vAda, chanda, jyotiSa, maMtra, alaMkAra aura zabda zAstra (vyAkaraNa) jAnane vAle the, tathA ve bhI the jo bAraha prakAra ke tapa ke prabhAva se prApta honevAlI RddhiyoM ke dhArI the. tathA bAraha-prakAra ke aMga zAstra ko kuzalatA pUrvaka jAmane vAle the / inake atirikta aMta meM 12 muni dekhe gaye / he municaMdra ! batalAo ki yati samiti kA saMkhyAtmaka mAna kyA thA ? // 42-45 // hAthiyoM ke samUha ke vargamUla kA 51 gunA bhAga parvatIya utAra para krIr3A kara rahA hai| zeSa kA bhAga parvata ke zikhara para krIr3A kara rahA hai| (isako ghaTAkara) zeSa kA vargamUla pramANa hastIgaNa kamala ke vana meM ramaNa kara rahA hai| aura, zeSa 6 hastI nadI ke tIra para haiN| yahA~ saba hastI kitane haiM ? // 46 // ---- isa prakAra, 'zeSamUla' jAti prakaraNa samApta huaa| "dvirama zeSa mUla" jAti | zeSoM kI saMracanA karane vAlI do jJAta rAziyoM vAle 'zeSamUla' prakAra] sambandhI niyama ( samUha vAcaka ajJAta rAzi ke ) vargamUla kA guNAMka, aura ( zeSa rahane vAlI ) aMtima jJAta (sa/ ka - baka + a) = * dvArA uparyukta ka - baka kA mAna saralatApUrvaka prApta kiyA jA sakatA hai| yahA~ bhI 'ka' ajJAta rAzi hai|

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6] gaNitasArasaMgrahaH atha dviraprazeSamUlajAtau sUtram- mUlaM dRzyaM ca bhajedazakaparihANarUpaghAtena / parvAgramagrarAzau kSipedataH zeSamUlavidhiH / / 47 / / atroddezakaH madhukara ko dRSTaH khe padma zeSapazca macaturthau / zeSatryaMzo mUlaM dvovAne te kiyantaH syuH // 48 // siMhAzcatvAro'drau pratizeSa SaDaMzakAdimArdhAntAH / mUle catvAro'pi ca vipine dRSTAH kiyantaste / / 49 / 1 B meM 'dvau cAmre' pATha hai / lekara eka meM se hAsita karane se jJAta rAzi ko usa anya jJAta rAzi, ina donoM ko, pratyeka dazA meM bhinIya samAnupAtI rAziyoM ko prApta zeSoM ke guNanaphala dvArA vibhAjita karanA caahiye| taba prathama rAzi meM (jise Upara sAdhita kiyA hai ) jor3a denA cAhiye / tatpazcAt prakIrNaka bhinnoM ke 'zeSamUla' prakAra sambandhI kriyA kI jAtI hai // 47 // 15 udAharaNArtha prazna vargamUla pramANa kamaloM meM dikhAI madhumakkhiyoM ke jhuMDa meM se eka madhumakkhI AkAza meM dikhAI dI / zeSa kA pe bhAga; punaH, zeSa kA bhAga; punaH, zeSa kA u bhAga tathA jhuMDa ke saMkhyAtmaka mAna kA hiyA / aMta meM zeSa do madhumakkhiyA~ eka AmravRkSa para dikhAI diiN| batalAo ki usa jhuMDa meM kitanI madhumakkhiyA~ haiM ? // 48 // siMha dala meM se cAra parvata para dekhe gaye / dala ke kramika zeSoM ke veM bhAga se Arambha hokara veM bhAga taka ke bhinIya bhAga; dala ke saMkhyAtmaka mAna ke vargamUla kA dviguNita pramANa tathA anta meM zeSa rahane vAle 4 siMha vanameM dikhAI diye / batalAo ki usa dala meM kitane siMha hai ? // 49 // mRga dala meM se taruNa hariNiyoM ke do yugma vana meM dekhe gaye / jhuNDa ke kramika zeSoM aura (47) bIjIya rUpa se, isa niyama se [ 4.47 sa 1 - ba ) ( 1 - ba 2 ) X ... ityAdi a (1 - ba 1) (1 - ba2) X * * * ityAdi + a pada saMhatiyA~ prApta hotI haiM jinakA zeSamUla ke sUtra meM sa aura a ke sthAna para pratisthApana karanA par3atA hai / 'zeSamUla' kA sUtra yaha hai 2 ka - baka {i+()' + a } ' / isa sUtra kA prayoga karane meM ba kA mAna zUnya ho jAtA hai; 2 kyoMki dviragra zeSamUla meM garbhita rahane vAlA mUla athavA vargamUla kula rAzi kA hotA hai na ki rAzi ke bhinnIya bhAga kA / jaisA ki iSTa hai, Adezana karane se hameM ka = {2(1-ba,) (1-ba,) X...ityAdi + a + 2 (1 - ba ) (1 - ba 2 ) x ityAdi sa N(12 (1 -caa) (1 -ba3)X...ityAdi) prApta hotA hai| yaha phala samIkaraNa ka - a, - ba, (ka - a0 ) - ba2 { ka - a, tApUrvaka prApta ho sakatA hai; jahA~ ki ba1, ba2 aura a, tathA a, kramazaH prathama jJAta rAzi aura + a ba, ( ka - a ) }...... - ka - a = 0 se ityAdi uttarottara zeSoM ke vibhinna bhinnIya bhAga haiM aMtima jJAta rAzi haiN| punaH, yahA~ 'ka' ajJAta rAzi hai|

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-4. 52] prakIrNakavyavahAraH taruNahariNIyugmaM dRSTaM dvisaMguNitaM vane kudharanikaTe zeSAH pnycaaNshkaadilaantimaaH| vipulakalamakSetre tAsAM padaM tribhirAhataM kamalasarasItIre tasthurdazaiva gaNaH kriyAn // 50 // _____ iti dvirprshessmuuljaatiH|| athAMzamUlajAtau sUtrambhAgaguNe mUlAgre nyasya padaprAptadRzyakaraNena / yallabdhaM bhAgahRtaM dhanaM bhavedaMzamUlavidhau / / 51 // anyadapi sUtramdRzyAdaMzakabhaktAJca guppAnmUlakRtiyutAnmUlam / saMpadaM dalitaM vargitamaMzAbhyastaM bhavet saarm||52|| ke bhAga se lekara bhAga taka ke bhinnIya bhAga parvata ke pAsa dekhe gye| usa jhuNDa ke saMkhyAtmaka mAna ke vargamUla kI tigunI rAzi vistRta kalama (cAMvala ) kSetra meM dekhI gii| aMta meM, kamala sarovara ke kinAre zeSa kevala 10 dekhe gaye / jhuNDa kA pramANa kyA hai ? // 50 // isa prakAra 'dvirama zeSamUla' jAti prakaraNa samApta huaa| "aMzamUla" jAti sambandhI niyama ajJAta samUha vAcaka rAzi ke diye gaye bhitrIya bhAga ke vargamUla ke guNAMka ko tathA aMta meM zeSa rahanevAlI jJAta rAziko likho| ina donoM rAziyoM ko diye gaye samAnupAtI mina dvArA guNita kro| jo 'zeSamUla' prakAra meM ajJAta rAziko nikAlane kI kriyA dvArA prApta hotA hai, usa phala ko jaba diye gaye samAnupAtI bhinna dvArA bhAjita karate haiM taba aMzamUla prakAra kI iSTa rAzi prApta hotI hai| // 51 // 'aMzamUla' prakAra kA anya niyama aMtima zeSa ke rUpa meM dI gaI jJAta rAzi diye gaye samAnupAtI bhinna dvArA bhAjita kI jAtI hai aura 4 dvArA guNita kI jAtI hai / prApta phala meM ajJAta samUha vAcaka rAzi ke datta bhinna ke vargamUla ke guNAMka kA varga jor3A jAtA hai| isa yogaphala ke vargamUla ko Upara kathita ajJAta rAzi ke bhinnIya bhAga ke vargamala ke gaNAMka meM jor3ate haiM aura taba AdhA kara vargita karate haiN| prApta phala ko datta samAnupAtI bhinna dvArA guNita karane para iSTa phala prApta hotA hai| // 52 // . (50) isa gAthA meM AyA huA zabda 'hariNIM" kA artha na kevala mAdA hariNa hotA hai varan usa chanda kA bhI nAma hotA hai jisameM yaha gAthA saMracita huI hai| .. (51) bIjIya rUpa se kathana karane para, yaha niyama 'sa ba' aura 'a ba ke mAna nikAlane meM sahAyaka hotA hai, jinakA pratisthApana, zeSamUla prakAra meM kiye gaye anusAra. sUtra ka - baka = } + (sa) +a } meM kramazaH sa aura a ke sthAna para karanA par3atA hai / 47 vIM gAthA ke TippaNa ke samAna, ka- baka yahA~ bhI ka ho jAtA hai / iSTa pratisthApana ke pazcAt aura phala ko ba dvArA vibhAjita karane para hameM ka= {+ (saba) +aba +ba prApta hotA hai / - ka kA yaha mAna samIkaraNa ka - sa./baka - a = 0 se bhI saralatA se prApta ho sakatA hai| 4a (52) bIjIya rUpa se kathana karane para, ka=1 x ba hotA hai| yaha pichalI gAthA ke TippaNa meM diye gaye samIkAra se bhI spaSTa hai|

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74] gaNitasArasaMgrahaH [ 4.53atroddezakaH padmanAlatribhAgasya jale mUlASTakaM sthitam / SoDazAGgulamAkAze jalanAlodayaM vada / / 53 / / dvitribhAgasya yanmUlaM navaghnaM hastinAM punaH / zeSatripaJcamAMzasya mUlaM SaDbhiH samAhatam // 54 // vigaladdAnadhArArdragaNDamaNDaladantinaH / caturviMzatirAdRSTA mayATavyAM kati dvipAH // 55 // kroDaughArdhacatuHpadAni vipinaM zArdUlavikrIDitaM prApuH zeSadazAMzamUlayugalaM zaila catustADitam / zeSArdhasya padaM trivargaguNitaM varSa varAhA vane dRSTAH saptaguNASTakapramitayasteSAM pramANaM vada / / 56 / / ityNshmuuljaatiH| atha bhAgasaMvargajAtau sUtramsvozAptaharAdUnAccaturguNAgreNa taddhareNa hatAt / mUlaM yojyaM tyAjyaM tacchede taddalaM vittam // 57 / / 1 B meM 'vArA' pATha hai| 2 isa zloka ke pazcAt sabhI hastalipiyoM meM nimnalikhita zloka hai jo kevala 57 veM zloka kA vyAkhyAnuvAda haianyazca- . caturhatadRSTe nonAdbhAgAhatyazahRtahArAt / tacchedena hatAnmUlaM yojyaM tyAjyaM tacchede tadardhavittam // udAharaNArtha prazna kamala kI nAla ke vibhAga ke vargamUla kA AThagunA bhAga pAnI ke bhItara hai aura 16 aMgula pAnI ke Upara vAyu meM hai| batalAo ki talI se pAnI kI U~cAI kitanI hai tathA kamala nAla kI lambAI kyA hai?||53|| hAthiyoM ke jhuNDa meM se. unakI saMkhyA ke 2/3 bhAga ke vargamUla kA 9 gunA pramANa, aura zeSabhAga ke 6 bhAga ke vargamUla kA 6 gunA pramANa; aura, aMta meM zeSa 24 hAthI vana meM aise dekhe gaye jinake caur3e gaNDa maNDala se mada jhara rahA thaa| batalAo kula kitane hAthI haiM ? // 54-55 // varAhoM ke jhuNDa ke arddha aMza ke vargamUla kI caugunI rAzi jaMgala meM gaI jahA~ zera krIr3A kara rahe the| zeSa jhuMDa ke dasaveM bhAga ke vargamUla kI aThagunI rAzi parvata para gii| zeSa ke arddhabhAga ke vargamUla kI 9 gunI rAzi nadI ke kinAre gii| aura anta meM 56 varAha vana meM dekhe gye| batAo ki kula varAha kitane the?||56|| isa prakAra, 'aMzamUla' jAti prakaraNa samApta huaa| 'bhAga saMvarga' jAti sambandhI niyama (ajJAta samUha vAcaka rAzi ke viziSTa mizra bhinnIya bhAga ke saralIkRta) hara ko sva sambandhita ( saralIkRta) aMza dvArA vibhAjita karane se prApta phala meM se diye gaye jJAta bhAga kI caugunI rAzi ghaTAo / taba isa aMtara phala ko usI (Upara varte hue saralIkRta ) hara dvArA guNita kro| isa guNanaphala ke vargamUla ko varte hue usI hara meM jor3o aura phira usI meM se ghttaao| taba yogaphala athavA aMtara phala meM se kisI eka kI arddha rAzi, iSTa ( ajJAta samUha vAcaka) rAzi hotI hai| // 57 // (56) "zArdUla vikrIDita" kA artha zeroM kI krIr3A hotA hai| isake sivAya yaha nAma usa chanda kA bhI hai jisameM ki yaha zloka saMracita huA hai| ___ma (mapha-4a)mapa (57) bIjIya rUpa se kathana karane para, ka= - hotA hai / ka kI

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[.9 prakoNakavyavahAraH atroddezakaH aSTamaM SoDazAMzaghnaM zAlirAzeH kRSIvalaH / caturviMzativAhAMzca lebhe rAziH kriyAn vada // 58 // zikhinAM SoDazabhAgaH svaguNazte tamAlapaNDe'sthAt / zeSanavAMzaH svahatazcaturapradazApi kati te syuH // 59 // jale triMzadaMzAhato dvAdazAMzaH sthitaH zeSaviMzo hataH SoDazena / trinighnena pake karA viMzatiH khe sakhe stambhadaiya'sya mAnaM vada tvam // 60 / / iti bhaagsNvrgjaatiH| athonAdhikAzavargajAtau sUtramsvAMzakabhaktaharAdha nyUnayugadhikonitaM ca tdvrgaat| nyUnAdhikavargAgrAnmUlaM svarNa phalaM padeM'zahRtam // 61 // udAharaNArtha prazna koI kRSaka zAli ke DherI kI bhAga pramANa rAzi dvArA guNita usI Dhero kI bhAga pramANa rAzi ko prApta karatA hai / isake sivAya usake pAsa 24 vAha aura rahatI hai / batalAo DherI kA parimANa kyA hai ? // 54 // jhuMDa ke paraveM bhAga dvArA guNita mayUroM ke jhuMDa kA vA bhAga, Ama ke vRkSa para pAyA gyaa| sva [ arthAt zeSa ke veM bhAga] dvArA guNita zeSa kA vAM bhAga, tathA zeSa 14 mayUroM ko tamAla vRkSa ke jhuMDa meM dekhA gyaa| batalAo ve kula kitane haiM ? // 59|| kisI stambha ke 133 bhAga ko stambha ke bhAga dvArA guNita karane se prApta bhAga pAnI ke nIce pAyA gyaa| zeSa ke 20 veM bhAga ko usI zeSa ke 4veM bhAga dvArA gaNita karane se prApta bhAga kIcar3a meM gar3A huA pAyA gyaa| zeSa 20 hasta pAnI ke Upara havA meM pAyA gyaa| he mitra ! stambha kI lambAI btaao| // 60 // isa prakAra, "bhAga saMvarga" jAti prakaraNa samApta huaa| UnAdhika 'aMzavarga' jAti sambandhI niyama (ajJAta rAzi ke viziSTa bhinIya bhAga ke) hara kI arddha rAzi ke sva aMza dvArA vibhAjita karane se prApta rAziyoM ko ( samUha vAcaka ajJAta rAzi ke viziSTa bhinnIya bhAga meM se ghaTAI jAne vAlI) dI gaI jJAta rAzi dvArA mizrita athavA hAsita kro| isa pariNAmI rAzi ke varga ko (ghaTAI jAne vAlI athavA jor3I jAne vAlI) jJAta rAzi ke varga dvArA tathA rAzi ke jJAta zeSa dvArA hAsita kro| jo phala mile usakA vargamUla nikaalo| isa vargamUla dvArA uparyukta prathama varga rAzi kA vargamUla mizrita athavA hAsita kiyA jAtA hai| jaba prApta rAzi ko ajJAta rAzi ke viziSTa bhinnIya bhAga dvArA vibhAjita karate haiM taba ajJAta rAzi kI iSTa arhA ( value ) prApta hotI hai // 31 // isa arhA ko samIkAra ka - ma ka paka-a dvArA bhI prApta kara sakate haiM, jahA~ ma/na aura pa/pha niyama meM avekSita bhinna haiN| ....(61) bIjIya rUpa se, ka = { +(* da)'-da'-a+ (ma + da)} *ma: ka kI yaha arhA samIkAra, ka-(maka+da) - a = 0, dvArA bhI prApta ho sakatI hai, jahAM da dI gaI zAta rAzi hai, jo ajJAta rAzi ke isa ullikhita bhinnIya bhAga meM se ghaTAI jAtI hai athavA usameM jor3I jAtI hai| -----

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gaNita sArasaMgrahaH 'hInAlApa udAharaNam mahiSINAmaSTAMzo vyeko vargIkRto vane ramate / paJcadazAdrau dRSTAstRNaM carantyaH kiyantyastAH // 62 // anekapAnAM dazamo dvivarjitaH svasaMguNaH krIDati sallakIvane / co] caranti SaDurgamitA gajA girau kiyanta ete'tra bhavanti dantinaH // 63 // 'adhikAlApa udAharaNam jambUvRkSe paJcadazAMzo dvikayuktaH svenAbhyastaH kekikulasya dvikRtighnAH / pacApyanye mattamayUrAH sahakAre raMramyante mitra vadaiSAM parimANam // 64 // ityUnAdhikAMzavargajAtiH / / atha mUlamizrajAtau sUtrammizrakRtirUnayuktA vyadhikA ca dviguNamizrasaMbhaktA / vargIkRtA phalaM syAtkaraNamidaM mUlamizravidhau / / 65 / / 1 2 M meM yaha tathA anugAmI zloka chUTa gaye haiM / hInAlApa prakAra ke udAharaNa kula jhuMDa ke Te veM bhAga ke pUrNa varga se eka kama mahiSa (bhaiMsA) rAzi vana meM krIr3A kara rahI hai / zeSa 15, parvata para ghAsa carate hue dikhAI de rahe haiN| batalAo kula kitane bhaiMse haiM ? ||12|| kula jhuMDa ke bhAga se do kama pramANa, usI pramANa dvArA guNita hone se labdha hasti rAzi sallakI vana meM krIr3A kara rahI hai| zeSa hAthI jo saMkhyA meM 6 kI vargarAzi pramANa haiM, parvata para vicara rahe haiN| lAbha ve kula kitane haiM ? // 63 // [ 4.62 M meM 'hIna' chUTa gayA hai / adhikAlApa prakAra kA udAharaNa kula jhuMDa ke bhAga se 2 adhika rAzi ko sva dvArA guNita karane se prApta rAzi pramANa mayUra jambU vRkSa para khela rahe haiN| zeSa gavale 22 x 5 mayUra Ama ke vRkSa para khela rahe haiM / he mitra ! usa jhuMDa ke kula mayUroM kI saMkhyA batalAo ? // 64 // isa prakAra UnAdhika 'aMza varga' jAti prakaraNa samApta huA / 'mUlamizra' jAti sambandhI niyama ( viziSTa ajJAta rAziyoM ke vargamUloM ke ) mizrita (jJAta ) yoga ke varga meM ( dI gaI ) RNAtmaka rAzi jor3a dI jAtI hai, athavA dI gaI dhanAtmaka rAzi usameM se ghaTA dI jAtI hai / pariNAmI rAzi ko uparyukta mizrita yoga kI dugunI rAzi dvArA vibhAjita karate haiN| ise vargita karane para iSTa ajJAta samUha kI aha ( value) prApta hotI hai| yahI, 'mUlamizra' prakAra ke praznoM kA sAdhana karane kA niyama haiM // 65 // :: ( 64 ) isa gAthA meM 'mattamayUra' zabda kA artha 'garvIlA mayUra' hotA hai| yaha isa chanda kA bhI nAma hai jisameM yaha gAthA saMracita huI hai| ( 65 ) baujIya rUpa se, ka = { ma #da } hai yaha ka kI arjA samIkAra ka +ka=da = ma dvArA saralatA se prApta ho sakatI hai / yahA~ 'ma'; niyama meM ullikhita zAta mizrita yoga hai / 2 ma

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-4, 70 nAlApa uddezakaH mUlaM kapotavRndasya dvAdazonasya cApi yat / tayoryoge kapotAH SaD dRSTAstannikaraH kiyAn // 66 // pArAvatIyasaMghe caturghanone'pi tatra yanmUlam / tadddvayayogaH SoDaza tadvRnde kati vihaGgAH syuH // 67 // adhikAlApa uddezakaH rAjahaMsanikarasya yatpadaM sASTaSaSTisahitasya caitayoH / saMyutirdvikavihInaSaTkRtistadgaNe kati marAlakA vad // 68 // iti mUlamizrajAtiH / 1 prakIrNakavyavahAraH atha bhinnadRzyajAtau sUtram - dRzyAMzone rUpe bhAgAbhyAsena bhAjite tatra / yallabdhaM tatsAraM prajAyate bhinnadRzyavidhau / / 69 / / atroddezakaH sikatAyAmaSTAMzaH saMdRSTo'STAdazAMza saMguNitaH / stambhasyArdhaM dRSTaM stambhAyAmaH kiyAn kathaya ||70|| 2 B, M aura K meM 'gagane' pATha hai / nAlApa ke udAharaNArtha prazna kapotoM kI kula saMkhyA ke vargamUla meM 12 dvArA hAsita kapotoM kI kula saMkhyA ke vargamUla ko jor3ane para ( ThIka phala ) 6 kabUtara pramANa dekhane meM AtA hai / usa vRnda ke kapotoM kI kula saMkhyA kyA hai ? // 66 // kapotoM ke kula samUha kA vargamUla, tathA 4 ke ghana dvArA hAsita kapotoM kI kula saMkhyA kA vargamUla nikAlakara ina ( donoM rAziyoM ) kA yoga 16 prApta hotA hai / batalAo samUha meM kula kitane vihaMga haiM ? // 67 // B meM 'yogaH', pATha hai | [ 2 adhikAlApa kA udAharaNArtha prazna rAjahaMsoM ke samUha ke saMkhyAtmaka mAna kA vargamUla tathA 68 adhika usI samUha kI saMkhyA kA vargamUla nikAlane se prApta ) ina ( donoM rAziyoM) kA yoga 62 - 2 hotA hai / batalAo usa samUha meM kitane haMsa haiM ? // 68 // isa prakAra 'mUla mizra' jAti prakaraNa samApta huA / 'bhinna dRzya' jAti sambandhI niyama -- (69) bIjIya rUpa se, ka = ga0 sA0 saM0-11 jaba eka ko ( ajJAta rAziyoM se sambandhita dI gaI ) bhinnIya zeSa rAzi dvArA dvAsita kara ( sambandhita viziSTa ) bhinnIya bhAgoM ke guNana phala dvArA bhAjita karate haiM, taba prApta phala (bhinoM para praznoM ke ) 'bhinna dRzya' prakAra kA sAdhana karane meM, iSTa uttara hotA hai // 69 // udAharaNArtha prazna kisI stambha kA hai bhAga, uso stambha ke paTe bhAga dvArA guNita hotA hai / isase prApta bhAga pramANa reta meM gar3A huA pAyA gyaa| usa stambha kA 3 bhAga Upara dRSTigocara huA / batalAo ki stambha kI ( udadma vertical ) lambAI kyA hai ? // 70 // kula hAthiyoM ke jhuMDa ke 23 veM bhAga (1 - 7 ) + maya hai / yaha, samIkaraNa kanapha mana ka na

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gaNita sArasaMgrahaH dvibhaktanavamAMzakaprahatasaptaviMzAMzakaH pramodamavatiSThate karikulasya pRthvItale / vinIlajaladAkRtirviharati tribhAgo nage vada tvamadhunA sakhe karikulapramANaM mama // 71 // sAdhUtkRternivasati SoDazAMzakastribhAjitaH svakaguNito vanAntare / pAdo girau mama kathayAzu tanmitiM prottIrNavAn jaladhisamaM prakIrNakam // 72 // iti bhinnadRzyajAtiH // 82 ] 4. 71- ] iti sArasaMgrahe gaNitazAstre mahAvIrAcAryasya kRtau prakIrNako nAma tRtIyavyavahAraH samAptaH // ko usI jhuMDa ke bhAga se guNita karane tathA 2 dvArA vibhAjita karane se prApta phala pramANa ke hAthI maidAna meM prasanna dazA meM viSThe haiN| zeSa ( bacA huA ) 3 bhAga jhuMDa jo bAdaloM ke samAna atyanta kAle hAthiyoM kA hai, parvata para krIr3A kara rahA hai / he mitra ! saMkhyAtmaka mAna kyA hai ? // 71 // sAdhuoM ke samUha kA vAM bhAga 3 dvArA vibhAjita karane ke pazcAt sva dvArA guNita ( arthAt 3 dvArA guNita ) karane se prApta bhAga pramANa vana ke antaH bhAga meM raha rahA hai; usa samUha kA ( baccA rahane vAlA ) hai bhAga parvata para raha rahA hai / he prakIrNaka ke pratIrNavAn ! mujhe zIghrahI sAdhuoM ke samUha kA saMkhyAtmaka mAna batalAo / // 72 // batalAo ki hAthiyoM ke jhuMDa kA ma isa prakAra, 'bhinna dRzya' jAti prakaraNa samApta huA / isa prakAra, mahAvIrAcArya kI kRti sArasaMgraha nAmaka gaNita zAstra meM 'prakIrNaka' nAmaka tRtIya vyavahAra samApta huA / ka = 0 se spaSTa hai / (71) 'pRthvI' zabda jo isa gAthA meM AyA hai, usakA artha pRthvI hai tathA yaha usa chanda kA nAma bhI hai jisameM yaha gAthA saMracita huI hai /

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5. trairAzikavyavahAraH trilokabandhave tasmai kevalajJAnabhAnave / namaH zrIvardhamAnAya nirdhUtAkhilakarmaNe // 1 // itaH paraM trairAzikaM caturthavyavahAramudAhariSyAmaH / ___ tatra karaNasUtraM yathAtrairAzike'tra sAraM phalamicchAsaMguNaM prmaannaaptm| icchApramayoH sAmye viparIteyaM kriyA vyaste // 2 // ___ pUrvArdhoddezakaH divasainibhiH sapAdairyojanaSaTkaM caturthabhAgonam / gacchati yaH puruSo'sau dinayutavarSeNa kiM kathaya / / 3 / / vyardhASTAbhirahobhiH krozASTAMzaM svapaJcamaM yAti / paGguH sapaJcabhAgairvatribhiratra kiM hi // 4 // aGgulacaturthabhAgaM prayAti kITo dinASTabhAgena / merormUlAcchikharaM katibhirohobhiH samApnoti // 5 // 1 P, K aura M meM sva ke liye sa pATha hai / 5. trairAzikavyavahAra tInoM lokoM ke bandhu tathA sUrya ke samAna kevala jJAna ke dhArI zrI varddhamAna ko namaskAra hai jinhoMne samasta karma (mala ) ko nirdhUta kara diyA hai / // 1 // isake pazcAt, hama trairAzika nAmaka caturtha vyavahAra kA pratipAdana kreNge| trairAzika sambandhI niyama yahA~ trairAzika niyama meM, phala ko icchA dvArA guNita kara pramANa dvArA vibhAjita karane se iSTa uttara prApta hotA hai, jaba ki icchA aura pramANa samAna ( anukrama direct anupAta meM ) hote haiM / jaba yaha anupAta pratiloma ( inverse ) hotA hai taba yaha guNana tathA bhAga kI kriyA viparIta ho jAtI hai ( tAki bhAga kI jagaha guNana ho aura guNana ke sthAna meM bhAga ho)| // 2 // pUrvArdha, anukrama trairAzika para udAharaNArtha prazna vaha manuSya jo 31 dina meM 53 yojana jAtA hai, 1 varSa aura 1 dina meM kitanI dUra jAtA hai ? // 3 // eka laMgar3A manuSya 71 dina meM eka kroza kA hai tathA usakA bhAga calatA hai / batalAo vaha ha? // 4 // eka kIr3A dina meM 2 aMgula calatA hai / batalAo ki vaha meruparvata kI talI se usake zikhara para kaba pahu~cegA ? // 5 // vaha manuSya jo 33 dina meM 3 kArSA (2) pramANa aura phala ke dvArA argha ( rate) prApta hotI hai| phala, iSTa uttara ke samAna rAzi hotI hai aura pramANa, icchA ke samAna hotA hai / 'icchA' vaha rAzi hai jisake viSaya meM, kisI argha (dara) se, koI vastu nikAlanA hotI hai| jaise ki gAthA 3 ke prazna meM 3 dina pramANa hai, 51 yojana phala hai, aura 1 varSa 1 dina icchA hai| (5) meru parvata kI U~cAI 99,000 yojana athavA 76,032,000,000 aMgula mAnI jAtI hai| ..............

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gaNitasArasaMgrahaH [5. 6kArSApaNaM sapAdaM nirvizati tribhirahobhirardhayutaiH / yo nA purANazatakaM sapaNaM kAlena kenAsau // 6 // . kRSNAgarusatkhaNDaM dvAdazahastAyataM trivistAram / kSayametyaGgulamahnaH kSayakAlaH ko'sya vRttasya || svarNaidazabhiH sArdhedrauNADhakakuDabamizritaH krItaH / vararAjamASavAhaH kiM hemazatena sArdhena // 8 // sArthaitribhiH purANaiH kuGkamapalamaSTabhAgasaMyuktam / saMprApyaM yatra syAt purANazatakena kiM tatra // 9 // sArdhAdrakasaptapalaizcaturdazA!nitAH paNA labdhAH / dvAtriMzadAkapalaiH sapaJcamaiH kiM sakhe brUhi // 10 // kArSApaNaizcaturbhiH paJcAMzayutaiH palAni rajatasya / SoDaza sArdhAni naro labhate kiM krssniyuten||11|| kapUrasyASTapalaistryaMzonairnAtra paJca dInArAn / bhAgAMzakalAyuktAna labhate kiM palasahasreNa // 12 // sAdhaitribhiH paNairiha ghRtasya palapaJcakaM sapaJcAMzam / krINAti yo naro'yaM kiM saassttmkrssshtken||13|| sArdheH paJcapurANaiH SoDaza sadalAni vastrayugalAni / labdhAni saikaSaSTayA karSANAM kiM sakhe kathaya // 14 // vApI samacaturazrA salilaviyuktASTahastaghanamAnA / zailastasyAstIre samutthitaH zikharatastasya // 15 // vRttAGgulaviSkambhA jaladhArA sphaTikanirmalA patitA / - - vApyantarajalapUrNA nagocchitiH kA ca jalasaMkhyA // 16 // 1 B meM satkRSNAgarukhaNDaM pATha hai| 2 M aura B meM labhyAH pATha hai| 3 B meM samutthitA zi pATha hai| paNa upayoga meM lAtA hai yaha paNa sahita 100 purANa kitane dina meM kharca karegA / // 6 // 12 hAtha lambe ( Ayata ) tathA 3 hAtha vyAsa (vistAra) vAle kRSNAgaru kA satkhaMDa ( acchA Tukar3A ) eka dina meM eka ghana aMgula ke argha (rate) se kSaya hotA hai| batalAo kula belanAkAra Tukar3e ko kSaya hone meM kitanA samaya lagegA? // 7 // 103 svarNa meM zreSTha kAle cane kA vAha, droNa, 1 ADhaka aura 1 kuDaba kharIde jAte haiN| batalAo 10.1 svarNa meM kitanA kitanA pramANa kharIdA jA sakegA ? // 8 // yadi 33 purANoM ke dvArA pala kuma prApta ho sakatA ho to 100 purANoM meM kitanA prApta ho sakegA ? // 9 // 73 pala 'Ardraka' ke dvArA 133 paNa prApta kiye gaye / he mitra ! 326 pala Ardraka meM kyA prApta hogA ? // 10 // 46 kArSApaNa meM eka manuSya 163 pala rajata prApta karatA hai to use 100,000 karSa meM kitanI rajata prApta hogI? ||1 // 73 pala kapUra ke dvArA eka manuSya 5 dInAra tathA 1 bhAga, 1 aMza aura 1 kalA prApta karatA hai| batalAo ki use 1000 pala ke dvArA kyA prApta hogA? // 12 // vaha manuSya jo 33 paNa meM 56 paladhI prApta karatA ho to vaha 1001 karSa meM kitanA prApta karegA ? // 13 // 56 purANa ke dvArA eka manuSya 163 yugala vastra prApta karatA hai| he mitra ! 61 karSa meM use kitane prApta hoMge? jala rahita eka vargAkAra kUpa 5.2 dhana hasta hai| usake tIra para eka pahAr3I hai| usake zikhara se sphaTika kI bhAMti nirmala jala dhArA jisake vartula cheda ( circular section) kA vyAsa , aMgula hai, talI meM giratI hai aura kUpa pAnI se pUrI taraha bhara jAtA hai| pahAr3I kI U~cAI kyA hai tathA pAnI kA mApa ( saMkhyAtmaka mAna meM) kyA hai? // 15-16 // kisI rAjA ne saMkrAMti ke avasara para (7) yahA~ kriyA meM diye gaye vyAsa se raMbha (belana) ke anuprastha cheda (cross-section) kA kSetraphala jJAta mAna liyA jAtA hai / vRtta kA kSetraphala anumAnataH vyAsa ke varga ko 4 dvArA bhAjita kara aura 3 dvArA guNita karane se prApta rAzi mAna liyA jAtA hai| kRSNAgaru eka prakAra kI sugandhita lakar3I hai jise sugandha ke lie agni meM jalAte haiM / (15-16) isa prazna meM pAnI kI dhArA kI lambAI parvata kI U~cAI ke barAbara hai, jisase jyoMhI vaha parvata kI talI meM pahu~catI hai, tyoMhI vaha zikhara se bahanA baMda huI mAna lI jAtI hai| vAhoM meM

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. [85 trairAzikamyavahAraH mudgadroNayugaM navAjyakuDabAn SaT taNDuladroNakAnaSTau vastrayugAni vatsasahitA gASSaT suvarNatrayam / saMkrAntau dadatA narAdhipatinA SaDbhyo dvijebhyaH sakhe SaDviMzatrizatebhya Azu vada kiM taddattamudgAdikam // 17 // iti trairAzikaH / vyastatrairAzike turIyapAdasyoddezakaH kalyANakanakanavateH kiyanti navavarNakAni kanakAni / sASTAMzakadazavarNakasaguJjahemnAM zatasyApi // 18 // vyAsena dairyeNa ca SaTakarANAM cInAmbarANAM trizatAni tAni / tripazcahastAni kiyanti santi vyastAnupAtakramavidvada tvam // 19 // iti vyastatrairAzikaH / vyastapazcarAzika uddezakaH pazcanavahastavistRtadairdhyAyAM cInavastrasaptatyAm / dvitrikaravyAsAyati tacchrutavastrANi kati kathaya // 20 // 1 isa zloka ke sthAna meM B aura K meM nimna pATha hai dugdhadroNayugaM navAjyakuDabAn SaT zarkarAdroNakAnaSTau cocaphalAni sAndradadhikhAryaSaT purANatrayam / zrIkhaNDaM dadatA nRpeNa savanArtha SaDjinAgArake SaTtriMzatrizateSu mitra vada me taddattadugdhAdikam // ibrAhmaNoM ko 2 droNa mud (kidney-bean),6 kuDava ghI, 6 droNa cAMvala, 8 yugma ( pairs) kapar3e, 6 bachar3oM sahita gAyeM aura 3 suvarNa diye / he mitra ! zIghra batalAo ki usane 336 brAhmaNoM ko kitanI-kitanI mudrAdi anya vastue~ dii||10|| isa prakAra anukrama trairAzika prakaraNa samApta hubhaa| / cauthe pAda* ke anusAra vyasta trairAzika para udAharaNArtha prazna zuddha svarNa ke 90 ke liye 9 varNa kA svarNa kitanA hogA, tathA 101 varNa ke svarNa kI banI huI guMja sahita 100 svarNa (dharaNa) ke liye (9 varNa kA svarNa) kitanA hogA? // 18 // 6 hasta lambe aura 6 hasta caur3e cInI rezama ke TukaDe 300 Tukar3e haiN| he vyasta anupAta kI rIti jAnane vAle, batalAo ki usI rezama ke 5 hasta lambe, hasta caur3e kitane Tukar3e unameM se mila sakeMge // 19 // isa prakAra vyasta trairAzika prakaraNa samApta humaa| vyasta paMcarAzika para udAharaNArtha prazna 9 hasta lambe, 5 hasva caur3e .. cInI rezama ke Tukar3oM meM 2 hasta caur3e aura 3 hasta lambe mApa ke kitane Tukar3e prApta ho sakeMge raNA pAnI kI mAtrA nikAlane ke liye dhana-mApa tathA drava mApa meM sambandha diyA jAnA cAhiye thaa| P meM kI saMskRta aura B meM kI kannar3I TIkAoM ke anusAra 1 ghana aMgula pAnI, drava mApa meM 1karSa ke barAbara hotA hai| * (17) eka rAzi se dUsarI rAzi meM sUrya ke pahu~cane ke mArga ko saMkrAMti kahate haiN| (18) zuddha svarNa yahA~ 16 varNa kA liyA gayA hai| * yahA~ isa adhyAya kI dUsarI gAthA ke cauthe caturthAza kA nirdeza hai|

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gaNitasArasaMgrahaH [5.21 vyastasaptarAzika uddezakaH vyAsAyAmodayato bahumANikye caturnavASTakare / dviSaDekahastamitayaH pratimAH kati kathaya tIrthakRtAm // 21 // ___ vyastanavarAzika uddezakaH vistAradairyodayataH karasya SaTtriMzadaSTapramitA nvaarghaa| .. zilA tayA tu dviSaDekamAnAstAH paJcakArghAH kati caityayogyAH // 22 // iti vyastapaJcasaptanavarAzikAH / gatinivRttau sUtramnijanijakAloddhatayorgamananivRttyorvizeSaNAjAtAm / dinazuddhagatiM nyasya trairAzikavidhimataH kuryAt // 23 // atroddezakaH krozasya paJcabhAgaM nauryAti dinatrisaptabhAgena / vAdhau vAtAviddhA pratyeti krozanavamAMzam // 24 // kAlena kena gacchet tripaJcabhAgonayojanazataM saa|| saMkhyAbdhisamuttaraNe bAhubaliMstvaM samAcakSva // 25 // 1 B aura K meM tasminkAle vAdhoM, pATha hai| vyasta saptarAzika para udAharaNArtha prazna batalAo ki 4 hasta caur3e, 9 hasta lambe, 8 hasta UMce bar3e maNi meM se 2 hasta caur3I 6 hasta lambI tathA 1 hasta U~cI tIrthaMkaroM kI kitanI pratimAeM bana sakeMgI? // 21 // __vyasta nava rAzika para udAharaNArtha prazna / jisakI kImata 9 hai aisI 6 hasta caur3I 30 hasta lambI tathA 8 hasta uMcI eka zilA dI gaI hai| batalAo ki jina maMdira banavAne ke liye isa zilA meM se, jisakI kImata 5 hai aisI 2 hasta caur3I 6 hasta lambI tathA 1 hasta U~cI kitanI zilAyeM prApta ho sakeMgI? // 22 // isa prakAra vyasta paMcarAzika, saptarAzika aura navarAzika prakaraNa samApta huaa| gati nivRtti sambandhI niyama dina kI zuddha gati ko likho jo agra tathA pazca ( Age tathA pIche kI ora hone vAlI) gatiyoM ke diye gaye aghoM ( rates ) ke antara se prApta hotI hai. jabaki ina arSoM meM se pratyeka ko prathama unake viziSTa samayoM dvArA vibhAjita kara liyA jAtA hai| aura taba, isa zuddha dainika gati ke sambandha meM trairAzika niyama kI kriyA kro| udAharaNArtha prazna dina meM, eka jahAja samudra meM 6 kroza jAtI hai; usI samaya vaha pavana ke virodha se hai kroza pIche haTa jAtI hai| he saMkhyA samudra ko pAra karane ke artha bAhubala dhArI ! batalAo ki vaha jahAja 993 yojana kitane samaya meM jAvegI? // 24-25 // eka manuSya jo 36 dinoM meM 11 svarNa

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[87 -5. 3.] trairAzikavyavahAraH sapAdahema tridinaiH sapaJcamainaro'rjayan vyeti suvarNaturyakam / nijASTamaM paJcadinairdalonitaiH sa kena kAlena labheta saptatim // 26 // gandhebho madalubdhaSaTpadapadaprodbhinnagaNDasthalaH sAdhaM yojanapaJcamaM brajati yaH ssddbhirdlonairdinaiH| pratyAyAti dinaitribhizca sadalai: krozadvipaJcAMzakaM brUhi krozadalonayojanazataM kAlena kenApnuyAt // 27 // vApI payaHprapUrNA dazadaNDasamucchritAJjamiha jAtam / aGgulayugalaM sadalaM pravardhate sArdhadivasena / / 28 // nissarati yantrato'mbhaH sArdhenAhAGgule saviMze dve / zuSyati dinena salilaM sapaJcamAGgulakaminakiraNaiH // 29 // kUrmo nAlamadhastAt sapAdapaJcAGgulAni cAkRSati / sArdhastridinaiH padmaM toyasamaM kena kAlena // 30 // dvAtriMzaddhastadIrghaH pravizati vivare paJcabhiH saptamAdhaiH kRSNAhIndro dinasyAsuravapurajitaH sArdhasaptAGgulAni / pAdenAhro'Ggule dve tricaraNasahite vardhate tasya pucchaM randhaM kAlena kena pravizati gaNakottaMsa me behi so'yam // 31 / / iti gtinivRttiH| mudrA kamAtA hai, 43 dina meM 3 svarNa mudrA tathA usa (1) kI ? svarNamudrA kharca karatA hai; batalAo ki vaha 70 svarNa mudrAyeM kitane dinoM meM bacA sakegA ? // 26 // eka zreSTha hAthI, jisake gaNDa sthala para jharate hue mada kI sugandha se lubdha bhramara rAzi padoM dvArA AkramaNa kara rahI hai, 56 dina meM eka yojana kA bhAga tathA 3 bhAga calatA hai; aura, 33 dina meM 3 kroza poche haTa jAtA hai; batalAo ki vaha kroza kama 100 yojana kI kula dUrI kitane samaya meM taya karegA? // 27 // eka vApikA pAnI se pUrI bharI rahane para gaharAI meM daza daNDa rahatI hai| aMkurita hotA huA eka kamala talI se 13 dina meM 23 aMgula ke ardha ( rate) se UgatA hai| yantra dvArA 13 dina meM vApikA kA pAnI nikala jAne se pAnI kI gaharAI 23. aMgula kama ho jAtI hai| aura, sUrya kI kiraNoM dvArA 16 aMgula (gaharAI kA ) pAnI vASpa banakara ur3a jAtA hai; tathA, eka kachuA kamala kI nAla ko 33 dina meM 51 aMgula nIce kI ora khIMca letA hai| batalAo ki vaha kamala pAnI kI sataha taka kitane samaya meM Uga AvegA? // 28-30 // eka balayukta, ajita, zreSTha kRSNAhIndra (kAlA sarpa) jo 32 hasta lambA hai, kisI chidra meM 2 dina meM 73 aMgula praveza karatA hai aura dina meM usakI pU~cha 29 aMgula bar3ha jAtI hai| he aMkagaNitajJoM ke bhUSaNa ! mujhe batalAo ki yaha sarpa isa chidra meM kitane samaya meM pUrI taraha praveza kara sakegA ? // 31 // isa prakAra, gati nivRtti prakaraNa samApta huaa| paMcarAzika, saptarAzika aura navarAzika sambandhI niyama sva sthAna se 'phala' ko anya sthAna meM pakSAntarita karo (jahA~ vaisI hI mUrta rAzi AvegI); ( taba iSTa uttara ko prApta karane ke liye vibhinna rAziyoM kI) bar3I saMkhyAoM vAlI paMkti ko ( sabako (28-30) kue~ kI gaharAI mUla gAthA meM talI se nApI gaI 'U~cAI' kahI gaI hai|

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66 ] paJcasaptanavarAzikeSu karaNasUtram - lAbhaM nItvAnyonyaM vibhajet pRthupakimalpayA paMktyA / guNayitvA jIvAnAM krayavikrayayostu tAneva // 32 // gaNitasArasaMgrahaH atroddezakaH dvitricatuHzatayoge paJcAzatSaSTisaptatipurANAH / lAbhArthinA prayuktA dazamAseSvasya kA vRddhiH // 33 // hemnAM sArdhAzItermAsatryaMzena vRddhiradhyardhA / satricaturthaM navatyAH kiyatI pAdonaSaNmAsaiH // 34 // 1 P meM nimnalikhita pAThAntara hai / prakAntareNa sUtram saMkramya phalaM chindyAlaghupaMktyAne karA zikAM paMktim / svaguNAmazvAdInAM krayavikrayayostu tAneva / anyadapi sUtram - saMkramya phalaM chindyAt pRthupaMktyabhyAsamalpayA paMktyA / azvAdInAM krayavikrayayorazvAdikAM saMkramya // B kevala bAda kA zloka diyA gayA hai jisake dUsare cauthAI bhAga kA pAThAntara yaha haipRthupaMktyabhyAsamalpa paMktyA hatyA | sAtha guNita karane ke pazcAt ), sabako sAtha lekara guNita kI gaI vibhinna rAziyoM kI choTI saMkhyAoM parantu, jIvita pazuoM ko becane aura kharIdane ke praznoM meM sambandha meM hI pakSAntaraNa karate haiM // 32 // udAharaNArtha prazna vAlI paMkti dvArA vibhAjita karanA caahiye| kevala unheM prarUpaNa karanevAlI saMkhyAoM ke kisI vyakti dvArA 50, 60 aura 70 ( dara ) se lAbha ke liye byAja para diye gye| mAsa meM 803 svarNa mudrAoM para byAja 13 kitanA hogA ? // 34 // vaha jo 16 varNa ke ( 32 ) phala kA pakSAntaraNa tathA anya kathita kriyAyeM nimnalikhita sAdhita udAharaNa se spaSTa ho jAyeMgI / gAthA 36 ke prazna meM diyA gayA nyAsa (data) prathama nimna prakAra prarUpita kiyA jAtA hai| 9 mAnI 3 yojana yathA, [ 5.32 60 paNa jaba yahA~ phala, jo 60 paNa hai, ko anya paMkti meM pakSAntarita karate haiM taba 9 mAnI 3 yojana 1. purANa kramazaH 2, 3 aura 4 pratizata pratimAsa ke ardha dasa mAha meM use kitanA byAja prApta hogA ? // 33 // hotA hai / 5 mAha meM 903 svarNa mudrAoM para vaha 100 svarNa khaMDoM meM 20 rakha prApta karatA hai to 10 varNa * x10x60 943 1 vAha + 1 kumbha 10 yojana aba, jisameM vibhinna rAziyoM kI saMkhyA adhika hai aisI dAhine hAtha kI paMkti kI saba rAziyoM ko guNita kara use vAma paMkti (jisameM vibhinna rAziyoM kI saMkhyA kama hai) kI saba rAziyoM ko guNita karane se prApta guNanaphala dvArA bhAjita karanA caahiye| taba hameM paNoM kI saMkhyA prApta hogI jo ki iSTa uttara hogA / 9 vAha + 1 kumbha = 14 vAha 10 yojana 60 paNa

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-5.41 ] trairAzika vyavahAraH [ 89 SoDazavarNakakAJcanazatena yo ratnaviMzatiM labhate / dazavarNasuvarNAnAmaSTAzItidvizatyA kim // 35 // godhUmAnAM mAnIrnava nayatA yojanatrayaM labdhAH / SaSTiH paNAH savAhaM kumbhaM dazayojanAni kati ||36|| bhANDapratibhANDasyoddezakaH kastUrIkarSatrayamupalabhate dazabhiraSTabhiH kanakaiH karSadvayakarpUraM mRganAbhitrizatakarSakaiH kati nau ||37|| panasAni SaSTimaSTabhirupalabhate'zItimAtuluGgAni / dazabhirmASai navazatapanasaiH kati mAtuluGgAni ||38|| jIvakrayavikrayayoruddezakaH SoDazavarSAsturagA viMzatirarhanti niyutakanakAni / dazavarSasaptisaptatiriha kati gaNakAgraNIH kathaya / / 39 // svarNatrizatI mUlyaM dazavarSANAM navAGganAnAM syAt / SaTtriMzannArINAM SoDazasaMvatsarANAM kim ||40|| SaTkazatayuktanavaterdazamAsairvRddhiratra kA tasyAH / kaH kAlaH kiM vittaM viditAbhyAM bhaNa gaNakamukhamukura // 41 // 1 B meM anta meM nA jur3A haiM / 2 K, M aura B meM nA ke lie hemakarSAH pATha hai / vAle 288 svarNa khaMDoM meM kyA prApta karegA ? // 35 // eka manuSya jo 9 mAnI gehU~ 3 yojana taka le jAkara 60 paNa prApta karatA hai, vaha eka kumbha aura eka vAha gehU~ 10 yojana taka lejAkara kyA prApta karegA ? // 36 // bhAMDa pratibhAMDa ( vinimaya ) para udAharaNArtha prazna eka manuSya 10 svarNa mudrAoM meM 3 karSa kastUrI tathA 8 svarNa mudrAoM meM 2 karSa karpUra prApta karatA hai / batalAo ki use 300 karSa kastUrI ke badale meM kitane karSa karpUra prApta hogA ? // 37 // eka manuSya 8 mAzA cA~do ke badale meM 60 panasa prApta karatA hai aura 10 mAzA cA~dI ke badale meM 80 anAra prApta karatA hai / batalAo ki 900 panasa phaloM ke badale meM vaha kitane anAra prApta karegA ? // 38 // pazuoM ke kraya aura vikraya para udAharaNArtha prazna 100,000 svarNa mudrAe~ haiM / he gaNitamUlya isa ardha se kyA hogA ? // 39 // 300 svarNa mudrAe~ haiM / pratyeka 16 varSa pratyeka 16 varSa kI umra vAle bIsa ghor3oM kI kImata jJApraNI ! batalAo ki pratyeka 10 varSa vAle 70 ghor3oM kA pratyeka 10 varSa kI umra vAlI 9 navAGganAoM kA mUlya kI umra vAlI 36 navAGganAoM kA mUlya kyA hogA ? ||40|| 6 pratizata pratimAsa kI dara se 90 para 10 mAsa meM kyA byAja hogA ? he gaNaka mukha mukura ! do anya Avazyaka jJAta rAziyoM kI sahAyatA se batalAo ki usa byAja ke sambandha meM samaya kyA hogA aura usa byAja tathA samaya ke sambandha meM mUladhana kyA hogA ? // 41 // ga0 sA0 saM0-12

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9.] gaNitasArasaMgrahaH [5.42saptarAzika uddezakaH tricaturvyAsAyAmau zrIkhaNDAvahato'STahemAni / SaNNavavistRtirdhyA hastena caturdazAtra kati / / 42 // iti sptraashikH| navarAzika uddezakaH pazcASTatrivyAsadairyodayAmbho dhatte vApI zAlinI vAhaSaTkam / saptavyAsA hastataH SaSTidairdhyAH pAtsedhoH kiM navAcakSva vidvana // 43 / / iti sArasaMgrahe gaNitazAstre mahAvIrAcAryasya kRtau trairAziko nAma caturthavyavahAraH // 1 43 veM zloka ke sivAya K aura B meM nimnalikhita zloka prApya hai dvayaSTAzItivyAsadaionnatAmbho dhatte vApI zAlinI saardhvaahau| hastAdaSTAyAmakAH SoDazocchrAH SaTakavyAsAH kiM catasrA vada tvam / / saptarAzika para udAharaNArtha prazna jinameM pratyeka kA vyAsa 3 hasta aura lambAI ( AyAma ) 4 hasta hai, aise saMdala-lakar3I ke do Tukar3oM kA mUlya 8 svarNa mudrAeM haiN| isa argha se, jinameM pratyeka 6 hasta vyAsa meM aura 9 hasta lambAI meM hai aise saMdala-lakar3I ke 14 Tukar3oM kA kyA mUlya hogA ? // 42 // navarAzika para udAharaNArtha prazna jo caur3AI, lambAI aura (talI se ) uMcAI meM kramazaH 5, 8 aura 3 hasta hai aisI kisI ghara kI vApikA meM 6 vAha pAnI bharA hai| he vidvAn ! batalAo ki 7 hasta caur3I, 60 hasta lambI aura talI se 5 hasta U~co 9 vApikAoM meM kitanA pAno samAvegA? // 43 // isa prakAra saptarAzika aura navarAzika prakaraNa samApta huaa| isa prakAra mahAvIrAcArya kI kRti sArasaMgraha nAmaka gaNita zAstra meM trairAzika nAmaka caturtha vyavahAra samApta huaa| (43) isa gAthA meM 'zAlinI' zabda kA artha "ghara kI hotA hai| yaha usa chaMda kA bhI nAma hai jisameM yaha gAthA saMracita huI hai|

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6. mizrakavyavahAraH prAptAnantacatuSTayAn bhagavatastIrthasya kartana jinAn siddhAn zuddhaguNAMtrilokamahitAnAcAryavaryAnapi / siddhAntArNavapAragAna bhavabhRtAM netRnupAdhyAyakAn sAdhUna sarvaguNAkarAna hitakarAn vandAmahe zreyase // 1 // itaH paraM mizragaNitaM nAma paJcamavyavahAramudAhariSyAmaH / tadyathA saMkramaNasaMjJAyA viSamasaMkramaNasaMjJAyAzca sUtramyutiviyutidalanakaraNaM saMkramaNaM chedalabdhayo rAzyoH / saMkramaNaM viSamamidaM prAhurgaNitatArNavAntagatAH // 2 // 6. mizrakavyavahAra jinhoMne ananta catuSTaya prApta kara dharma tIrtha kI pravartanA kI hai aise arihaMta prabhuoM kI, jo aSTakSAyika guNa sampanna haiM tathA tInoM lokoM meM Adara ko prApta haiM aise siddha prabhuoM ko, zreSTha AcAryoM kI, jo jaina siddhAnta sAgara ke pAragAmI haiM tathA saMsArI jIvoM ko mokSamArga ke upadezaka haiM aise upAdhyAyoM kI aura jo sarva sadguNoM ke dhAraka haiM tathA dUsaroM ke hitakartA haiM aise sAdhuoM kI hama apane sarvopari hita ke liye vandanA karate haiM // 1 // isake pazcAt hama mizrita udAharaNa nAmaka pA~caveM vyavahAra kA pratipAdana kreNge| pAribhASika zabda 'saMkramaNa' aura 'viSama saMkramaNa' ke arthoM ko spaSTa karane ke liye sUtra gaNita samudra ke pAragAmI, kinhIM do rAziyoM ke yoga athavA antara ke AdhA karane ko saMkramaNa kahate haiM / aura, aisI do rAziyA~ jo kramazaH bhAjaka tathA bhajanaphala rahatI haiM, unake saMkramaNa ko viSama saMkramaNa kahate haiM // 2 // (1) karma aura janma maraNa ke duHkhoM se pUrNa saMsArIjIvanarUpI nadI ko pAra karane ke liye 'tIrtha' zabda kA prayoga 'eka aise sthAna ke liye huA hai jo uthalA hone ke kAraNa nadI ko pAra karane meM sahAyaka siddha hotA hai| saMsAra arthAt catuzcakramaNa ke duHkhoM rUpI sAgara ko pAra karAne ke liye bhagavAn AtmAoM ke liye naimittika sahAyaka mAne gaye haiN| isaliye ina jinoM ko tIrthakara kahA jAtA hai| ( 2 ) bIjIya rUpa se, do rAziyoM a aura ba kA saMkramaNa aba aura aba ke mAna nikA lanA hai / unakA viSama saMkramaNa, aura "ba ke mAna nikAlanA hai /

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92] gaNitasArasaMgrahaH atroddezakaH dvAdazasaMkhyArAzeAbhyAM saMkramaNamatra kiM bhavati / tasmAdrAzerbhaktaM viSamaM vA kiM tu saMkramaNam // 3 // paJcarAzikavidhiH paJcarAzikasvarUpavRddhathAnayanasUtramicchArAziH svasya hi kAlena guNaH pramANaphalaguNitaH / kAlapramANabhakto bhavati tadicchAphalaM gaNite / / 5 / / atroddezakaH trikapaJcakaSaTakazate pnycaashtssssttispttipuraannaaH| lAbhArthataH prayuktAH kA vRddhirmAsaSaTkasya / / 5 // vyardhASTakazatayuktAstrizatkArSApaNAH paNAzcASTau / mAsASTakena jAtA dalahInenaiva kA vRddhiH // 6 // SaSTayA vRddhidRSTA paJca purANAH paNatrayavimizrAH / mAsadvayena labdhA zatavRddhiH kA tu varSasya / / 7 / / sArdhazatakaprayoge sArdhakamAsena paJcadaza lAbhaH / mAsadazakena labdhA zatatrayasyAtra kA vRddhiH / / 8 / / sASTazatakASTayoge triSaSTikArSApaNA vizA dttaaH| saptAnAM mAsAnAM paJcamabhAgAnvitAnAM kim||9|| udAharaNArtha prazna jaba saMkhyA 12, do se Ayojita ho to saMkramaNa kyA hogA? aura, 2 ke sambandha meM usI saMkhyA 12 kA bhAgIya viSama saMkramaNa kyA hogA? paMcarAzika vidhi paMcarAzika prakAra ke byAja ko nikAlane kI vidhi ke liye niyama icchA kA prarUpaNa karanevAlI saMkhyA, arthAta jisa para byAja nikAlanA iSTa hotA hai aise dhana ko usase sambandhita samaya dvArA guNita kiyA jAtA hai aura taba diye hue mUladhana para byAja dara kA nirUpaNa karane vAlI saMkhyA dvArA guNita kiyA jAtA hai| guNanaphala ko samaya tathA mUladhana rAzi dvArA bhAjita kiyA jAtA hai| yaha bhajanaphala, gaNita meM. iSTa dhana kA byAja hotA hai // 4 // udAharaNArtha prazna 50, 60 aura 70 purANa kramazaH 3.5 aura 6 pratizata pratimAha kI dara ( rate) se byAja para diye gaye, unakA 6 mAha meM byAja kyA hogaa?||5|| 30 kArSApaNa aura 8 paNa, 73 pratizata pratimAha kI dara se byAja para diye gaye.71 mAha meM kitanA byAja hogA? // 60para 2 mAha meM 5 purANa aura 3 paNa vyAja hotA hai; 10. paNa / varSa kA byAja batalAo // 7 // 150 ko 13 mAha taka udhAra dene se 15 byAja prApta hotA hai| isI argha se 300 para 10 mAha kA byAja kyA hogA? // 8 // eka vyApArI ne 63 kArSApaNa, 108 para 8 pratimAha kI dara se udhAra diye, batalAo 76 mAha meM kitanA byAja hogA // 1 // (4) bIjIya rUpa se ba= AdhA sadha aXbA "jahA~ A, dhA aura bA pramANa athavA dara sambandhI kramazaH avadhi, mUladhana aura nyAja haiM aura a, dha tathA ba icchA kI kramazaH avadhi, mUladhana aura byAja haiN| pramANa aura icchA ke vizeSa spaSTIkaraNa ke liye adhyAya 5 kI gAthA 2 kI pAda TippaNI dekhiye / (5) byAja kI dara yadi ullikhita na ho to use pratimAsa samajhanA caahiye|

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-6.14] mizrakavyavahAraH [93 mUlAnayanasUtrammUlaM svakAlaguNitaM svaphalena vibhAjitaM tdicchaayaaH| kAlena bhajellabdhaM phalena guNitaM tadicchA syAt // 10 // atroddezakaH pazcArdhakazatayoge paJca purANAndalonamAsau dvau / vRddhiM labhate kazcit kiM mUlaM tasya me kathaya // 11 // saptatyAH sArdhamAsena phalaM paJcArdhameva ca / vyardhASTamAse mUlaM kiM phalayoH sArdhayordvayoH // 12 // trikapaJcakaSaTkazate yathA navASTAdazAtha pazcakRtiH / paJcAMzakena mizrA SaTsu hi mAseSu kAni mUlAni // 13 // kAlAnayanasUtram-- kAlaguNitapramANaM svaphalecchAbhyAM hRtaM tataH kRtvA / tadihecchAphalaguNitaM labdhaM kAlaM budhAH prAhuH // 14 / / udhAra diye gaye mUladhana ko nikAlane ke liye niyama mUladhana rAzi ko usI se sambandhita samaya dvArA guNita karate haiM aura sambandhita byAja dvArA vibhAjita karate haiN| taba isa bhajanaphala ko ( udhAra diye gaye ) maladhana se sambandhita avadhi dra vibhAjita karate haiM; yaha aMtima bhajanaphala jaba upArjita byAja dvArA guNita kiyA jAtA hai taba vaha mUladhana prApta hotA hai jisa para ki ukta byAja prApta huA hai // 10 // udAharaNArtha prazna byAja dara 23 pratizata pratimAha se "mAha taka rakama udhAra dekara eka vyakti 5 purANa vyAja prApta karatA hai| mujhe batalAo ki usa byAja ke sambandha meM mUladhana kyA hai ? // 11 // 7. para 13 mAha meM 23 vyAja hotA hai| yadi 73 mAha meM 23 byAja hotA ho to batalAo ki kitanA mUladhana byAja para diyA gayA hai? // 12 // kramazaH 3.5 aura 6 pratizata prati mAha kI dara se udhAra dene para 6 mAha meM prApta hone vAle vyAja kramazaH 9, 18 aura 256 haiM; kauna-kauna se mUladhana byAja para diye gaye haiM? // 13 // avadhi nikAlane ke liye niyama mUladhana ko sambandhita avadhi se guNita karo; taba isa guNanaphala ko uso se sambandhita byAja dara se bhAjita karo aura udhAra dI huI rakama se bhI bhAjita kro| prApta bhajanaphala ko udhAra dI huI rakama ke byAja dvArA guNita kro| buddhimAna manuSya kahate haiM ki pariNAmI guNanaphala (upArjita vyAja kI) avadhi hotA hai // 14 // (10) pratIka rUpa se, dhA-AbA =dha bAraa dhA A4ba (14) pratIka rUpa se, bAba

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4] gaNitasArasaMgrahaH atroddezakaH saptArdhazataka yoge vRddhistvaSTAgraviMzatirazItyA | kAlena kena labdhA kAlaM vigaNayya kathaya sakhe / / 15 / / viMzatiSaTzatakasya prayogataH saptaguNaSaSTiH / vRddhirapi caturazItiH kathaya sakhe kAlamAzu tvam // 16 // SaTakazatena hi yuktAH SaNNavatirvRddhiratra saMdRSTA / saptottarapaJcAzat tripaJcabhAgazca kaH kAlaH ||17|| bhANDapratibhANDasUtram - bhANDasvamUlyabhaktaM pratibhANDaM bhANDamUlyasaMguNitam / svecchAbhANDAbhyastaM bhANDapratibhANDamUlyaphalametat // 18 // atrodezakaH krItAnyaSTau zuNThyAH palAni pabhiH paNaiH sapAdAMzaiH / pippalyAH palapaJcakamatha pAdonaiH paNairnavabhiH // 19 // zuNThyAH palaizca kenacidazItibhiH kati palAni pippalyAH / krItAni vicintya tvaM gaNitavidAcakSva me zIghram // 20 // iti mizrakavyavahAre paJcarAzividhiH samAptaH / vRddhividhAnam itaH paraM mizrakavyavahAre vRddhividhAnaM vyAkhyAsyAmaH / 1 M aura B donoM meM azuddha pATha hai : kazcit tvazItibhiH sa ca palAni pippalyA H . [ 6.15 udAharaNArtha prazna he mitra ! avadhi kI gaNanA kara batalAo ki 33 pratizata pratimAha ke arghaM se 80 para 28 byAja kitane samaya meM prApta hogA ? // 15 // 20 prati 600 pratimAha ke ardha se udhAra diyA gayA dhana 420 / byAja bhI 84 hai / he mitra ! mujhe zIghra batalAo ki yaha byAja kitanI avadhi meM upArjita huA hai ? // 16 // 6 pratizata pratimAha ke ardha se 96 udhAra diye jAte haiM / una para 573 byAja hotA hai / yaha byAja kitanI avadhi meM prApta huA hogA ? // 17 // I pratibhAMDa ( vastuoM ke pArasparika vinimaya ) ke sambandha meM niyama badale meM lI gaI vastu ke parimANa ko usake svamUlya tathA badale meM dI gaI vastu ke parimANa dvArA vibhAjita karate haiM / taba use badale meM dI gaI vastu ke mUlya dvArA guNita karate haiM aura taba, badalI jAne vAlI ( jise badalanA iSTa hai ) vastu ke parimANa dvArA guNita karate haiM / yaha pariNAmI guNanaphala, badale meM lI gaI vastu tathA badale meM dI gaI vastu ke mUlyoM kI saMvAdI iSTa rAzi hotI hai // 18 // udAharaNArtha prazna 8 pala zuNThi ( sUkhI adarakha ) 64 paNa meM kharIdI gaI aura 5 pala lambI mirca 8 paNa meM kharIdI gaI / he gaNitajJa ! vicArakara mujhe zIghra batalAo ki Upara likhI huI dara se kharIdI jAne vAlI lambI mirca, 80 pala sUkhI adarakha ( soMTha ) ke badale meM kitane pala kharIdI jA sakegI ? // 19-20 // isa prakAra, mizraka vyavahAra meM paMcarAzika vidhi nAmaka prakaraNa samApta huA / isake pazcAt vRddhi vidhAna [ byAja ] mizraka vyavahAra meM hama vyAja para vyAkhyA kareMge /

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-6. 24 ] mizrakavyavahAra: mUlavRddhimizravibhAgAnayanasUtramrUpeNa kAlavRddhathA yutena mizrasya bhAgahAravidhim / kRtvA labdhaM mUlyaM vRddhidlonamizradhanam / / 21 / / atroddezakaH paJcakazataprayoge dvAdazamAsairdhanaM prayuGkte cet / sASTA catvAriMzanmizraM tanmUlavRddhI ke // 22 / / punarapi malavRdbhimizravibhAgasatramaicchAkAlaphalanaM svakAlamUlena bhAjitaM saikam / saMmizrasya vibhaktaM labdhaM mUlaM vijAnIyAt / / 23 / / atroddezakaH sArdhadvizatakayoge mAsacatuSkeNa kimapi dhanamekaH / dattvA mizraM labhate kiM mUlyaM syAt trayastriMzat / / 24 // kAlavRddhimizravibhAgAnayanasUtrammUlaM svakAlaguNitaM svaphalecchAbhyAM hRtaM tataH kRtvA / mizrita rakama meM se dhana aura byAja alaga karane ke liye niyama mUladhana aura byAja sambandhI diye gaye mizradhana ko jo dI gaI avadhi ke byAja meM jor3akara . prApta kiyA jAtA hai, aisI (byAja) rAzi dvArA hAsita kiyA jAya to iSTa mUladhana prApta hotA hai| aura iSTa nyAja ko mizrita dhana meM se (nikAle hue) iSTa mUladhana ko ghaTAkara prApta kara lete haiM // 21 // udAharaNArtha prazna yadi koI dhana 5 pratizata pratimAha ke argha se vyAja para diyA jAya to 12 mAha meM mizradhana 48 ho jAtA hai / batalAo ki mUladhana aura byAja kyA haiM ? // 22 // mizradhana meM se mUladhana aura vyAja alaga karane ke liye dUsarA niyama diye gaye samaya tathA byAja dara ke guNanaphala ko samayadara tathA mUladhanadara dvArA bhAjita karate haiN| prApta phala meM 1 jor3ane se prApta rAzi dvArA mizradhana ko bhAjita karate haiM jisase pariNAmI bhajanaphala iSTa mUladhana hotA hai // 23 // udAharaNArtha prazna 23 pratizata pratimAha ke argha se rakama ko byAjapara dene se kisI ko cAra mAha meM 33 mizradhana prApta hotA hai / batalAo mUladhana kyA hai ? // 24 // mizra yoga meM se avadhi tathA byAja ko alaga karane ke liye niyamamUladhanadara ko avadhi dara dvArA guNita karo aura byAja dara tathA diye gaye mUladhana dvArA ( 21 ) pratIka rUpa sedha --- ma jahA~ ma =+ba hai; isaliye ba-ma-dha 1+ 1XaXbA AdhA aXbA (23) pratIka rUpa se, STa hai ki yaha bahuta kucha gAthA 21 meM AraghA diye gaye sUtra ke samAna hai|

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gaNitasArasaMgrahaH saikaM tenAptasya ca mizrasya phalaM hi vRddhiH syAt / / 25 // atroddezaka: paJcakazataprayoge phalArthinA yojitaiva dhanaSaSTiH / kAlaH svavRddhisahito viMzatiratrApi kaH kAlaH / / 26 // ardhatrikasaptatyAH sArdhAyA yogayojitaM mUlam / zItiH svakAlavRddhathohi // 27 // vyardhacatuSkAzItyA yuktA mAsadvayena sArdhena / mUlaM catuHzataM SaTtriMzanmizraM hi kAlavRddhathohi // 28 // mUlakAlamizravibhAgAnayanasUtramsvaphaloddhRtapramANaM kAlacaturvRddhitADitaM zodhyam / mizrakRtestanmUlaM mizre kriyate tu saMkramaNam // 29 // - vibhAjita kro| pariNAmI rAziko meM milaao| prAptaphala dvArA mizrayoga ko vibhAjita karane para iSTa byAja prApta hotA hai // 25 // udAharaNArtha prazna 5 pratizata pratimAha ke argha se kisI sAhUkAra ne 60 udhAra diye| avadhi tathA samaya milAkara 20 hotA hai| batalAo ki avadhi kyA hai? // 26 // 11 prati 7.3 prati mAsa kI dara se byAja para diyA gayA mUladhana 705 hai / samaya aura byAja kA mizrayoga 80 hai| samaya tathA byAja ke mAnoM ko alaga-alaga nikAlo // 27 // 33 prati 80 kI dara se 23 mAhoM ke liye byAja para diyA gayA mUladhana 400 hai aura samaya tathA byAja kA mizrayoga 36 hai| samaya tathA byAja alaga-alaga batalAo // 28 // mUladhana aura byAja kI avadhi ko unake mizrayoga meM se alaga karane ke liye niyama avadhi aura mUladhana ke diye gaye mizrayoga ke varga meM se vaha rAzi ghaTAI jAtI hai jo mUladhanadara ko byAjadara se bhAjita karane aura avadhidara tathA diye gaye byAja kI caugunI rAzi dvArA guNita karane para prApta hotI hai / isa pariNAmI zeSa ke vargamUla ko diye gaye mizrayoga ke sambandha meM saMkramaNa kriyA karane ke upayoga meM lAte haiM // 29 // (25 ) pratIka rUpa se, ba = ma+ +1 } = ba, jahA~ ma = ba+ a dhAXA44baxma ! (29) pratIka rUpa se, 1 = dha athavA a, ( yathA sthiti) jahA~, madha+aB diye gaye niyama ke anusAra, mUla (karaNI) gata rAzi kA mAna (dha-a)ra hai; isake vargamUla tathA mizra ina donoM ke sambandha meM saMkramaNa kI kriyA kI jAtI hai| * saMkramaNa kriyA ko samajhane ke liye adhyAya 6 kA zloka 2 dekhiye|

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-6. 34] mizrakavyavahAraH atroddezakaH saptatyA vRddhiriyaM catuHpurANAH phalaM ca paJcakRtiH / mizra nava paJcaguNAH pAdena yutAstu kiM mUlam // 30 // trikaSaSTyA dattvaikaH kiM mUlaM kena kAlena / prApto'STAdazavRddhiM SaTSaSTiH kAlamUlamizraM hi // 31 // adhyardhamAsikaphalaM SaSTyAH paJcArdhameva saMdRSTam / vRddhistu caturviMzatiratha SaSTirmUlayuktakAlazca // 32 // pramANaphalecchAkAlamizravibhAgAnayanasUtrammUlaM svakAlavRddhidvikRtiguNaM chinnamitaramUlena / mizrakRtizeSamUlaM mizre kriyate tu saMkramaNam // 33 // atroddezakaH adhyardhamAsakasya ca zatasya phalakAlayozca mizradhanam / dvAdaza dalasaMmizraM mUlaM triMzatphalaM paJca / / 34 // udAharaNArtha prazna 4 purANa, 70 para pratimAha byAja hai| kula para prApta byAja 25 hai| mUladhana tathA byAja ko bhavadhi kA mizrayoga 453 hai| kitanA mUladhana udhAra diyA gayA hai| // 30 // 3 prati 60 pratimAsa ke ardha se koI manuSya kitanA mUladhana kitane samaya ke liye byAja para lagAye tAki use byAja 18 prApta ho jabaki usa avadhi tathA usa mUladhana kA mizrayoga 66 diyA gayA hai // 31 // 6. para 11 mAha meM byAja kevala 23 hai| yahA~ byAja 24 hai aura mUladhana tathA avadhi kA mizrayoga 60 hai| samaya tathA mUladhana kyA haiM ? // 32 // byAjadara tathAiSTa avadhi ko mizritayoga meM se alaga-alaga karane ke liye niyama mUladhanadara sva samayadara dvArA guNita kiyA jAtA hai, tathA diye gaye byAja se aura 4 se bhI guNita karane ke uparAnta anya diye gaye mUladhana dvArA vibhAjita kiyA jAtA hai| isa pariNAmI bhajanaphala ko diye gaye mizrayoga ke varga meM se ghaTAkara prApta zeSa ke vargamUla ko mizrayoga ke sambandha meM saMkramaNa kriyA karane ke upayoga meM lAte haiM // 33 // ___ udAharaNArtha prazna ardha adhika pratizata pratimAha kI iSTa dara se byAja dara aura avadhi kA mizrayoga 123 hotA hai / mUladhana 30 hai aura usa para byAja 5 hai / batalAo byAja dara aura bhavadhi kyA-kyA hai ? // 3 // (33) pratIka rUpa se, /2 dhA 4 A.xbaX4 ko 'ma' ke sAtha iSTa saMkramaNa kriyA karane ke upayoga meM lAte haiN| yahA~ ma-bA+a hai| ga0 sA0 saM0-13

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98] gaNitasArasaMgrahaH [-6.35 mUlakAlavRddhimizravibhAgAnayanasUtrammizrAdUnitarAziH kAlastasyaiva rUpalAbhena / saikena bhajenmUlaM svakAlamUlonitaM phalaM mizram // 35 // atroddezakaH paJcakazataprayoge na jJAtaH kAlamUlaphalarAziH / tanmibhaM dvAzItimUlaM kiM kAlavRddhI ke // 36 // bahumUlakAlavRddhimizravibhAgAnayanasUtramavibhajetsvakAlatADitamUlasamAsena phalasamAsahatam / kAlAbhyastaM mUlaM pRthak pRthak cAdized vRddhim / / 37 / / atroddezakaH catvAriMzattriMzaviMzatipaJcAzadatra mUlAni / mAsAH paJcacatuslikaSaTa phalapiNDazcatustriMzat // 38 // 1 hastalipi meM yaha azuddha rUpa prApya hai; zuddha rUpa 'dvayazIti' cheda kI AvazyakatA ko samAdhAnita nahIM karatA hai| mUladhana, byAja aura samaya ko unake mizrayoga meM se alaga-alaga prApta karane ke liye niyama diye gaye mizrayoga meM se koI mana se cunI huI saMkhyA ko ghaTAne para iSTa samaya prApta huA mAna liyA jAtA hai / usa avadhi ke liye para byAja nikAlakara usameM 1 jor3ate haiN| taba, diye gaye mizritayoga meM se mana se cunI gaI avadhi ghaTAkara zeSa rAzi ko uparyukta prApta rAzi dvArA vibhAjita karate haiM / pariNAmI bhajanaphala iSTa mUladhana hotA hai| mizrayoga ko nija ke saMvAdI samaya aura mUladhana dvArA hvAsita karane para iSTa byAja prApta hotA hai||35|| udAharaNArtha prazna 5 pratizata pratimAha ke argha se udhAra dI gaI rakama ke viSaya meM avadhi, mUladhana aura byAja kA nirUpaNa karane vAlI rAziyA~ jJAta nahIM haiN| unakA mizrayoga 82 hai| avadhi, mUladhana aura byAja nikAlo // 36 // vibhinna dhanoM para vibhinna avadhiyoM meM upArjita vibhinna byAjoM ko unhIM ke mizrayoga meM se alaga-alaga byAja prApta karane ke liye niyama pratyeka mUladhana saMvAdI samaya se guNita hokara tathA byAjoM kI kula datta rakama dvArA guNita hokara, alaga-alaga una guNanaphaloM ke yoga dvArA vibhAjita kiyA jAtA hai jo pratyeka mUladhana ko usake saMvAdI samaya dvArA guNita karane para prApta hote haiN| prApta phala usa mUladhana sambandhI byAja ghoSita kiyA jAtA hai // 37 // udAharaNArtha prazna isa prazna meM diye gaye mUladhana 40, 30, 20 aura 50 haiM: aura mAsa kramazaH 5, 4, 3 aura 6 haiM / byAja kI rAziyoM kA yoga 34 hai| pratyeka vyAja rAzi nikAlo // 38 // (35) yahA~ 3 ajJAta rAziyA~ dI gaI haiN| samaya kA mAna mana se cuna liyA jAtA hai aura anya do rAziyA~ adhyAya 6 kI 21vIM gAthA ke niyamAnusAra prApta ho jAtI haiN| __ dha, a, ma (37) pratIka rUpa se, dha,a, +dha,adhi .a.+... =ba, aura ___. a. ma --- = ba; jahA~ ma ba, +4 dha,a, +dha.a. +dha a + +...; dha, dhana, dha +... Adi vibhinna mUladhana haiM tathA a,, ara, a, Adi vibhinna avadhiyA~ haiN|

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-6. 42 ] bahumUlamizravibhAgAnayanasUtram - svaphalaiH svakAlabhaktaistadyutyA mUlamizradhanarAzim / chindyAdaMzaM guNayet samAgamo bhavati mUlAnAm // 39 // - atroddezakaH dazaSaTtripaJcadazakA vRddhaya iSavazcatustriSaNmAsAH / mUlasamAso dRSTazcatvAriMzacchatena saMmizrA / / 40 / / paJcArdhaSadazApi ca sArdhAH SoDaza phalAni ca triMzat / mAsAstu paJca SaT khalu saptASTa dazApyazItiratha piNDaH // 41 // bahukAlamizravibhAgAnayanasUtram - svaphalaiH svamUlabhaktaistadyutyA kAlamizradhanarAzim / chindyAdaMzaM guNayet samAgamo bhavati kAlAnAm // 42 // 1 hastalipi meM chindyAdaMzAn pATha hai jo zuddha pratIta nahIM hotA hai / vibhinna mUladhanoM ko unhIM ke mizrayoga se alaga-alaga karane ke niyama udhAra dI gaI vibhinna mUladhana kI rAziyoM ke mizrayoga kA nirUpaNa karanevAlI rAzi ko una bhajanaphakoM ke yoga dvArA vibhAjita karo jo vibhinna vyAjoM ko unakI saMvAdI avadhiyoM dvArA alagaalaga vibhAjita karane para prApta hote haiN| pariNAmI bhajanaphala ko kramazaH aise vibhinna bhajanaphaloM dvArA vibhAjita karo jo ki vibhinna vyAjoM ko unakI saMvAdI avadhiyoM dvArA vibhAjita karane para prApta hote haiM / isa prakAra vibhinna mUladhana kI rAziyoM ko alaga-alaga nikAlate haiM // 39 // udAharaNArtha prazna diye gaye vibhinna byAja 10, 6, 3 aura 15 haiM aura saMvAdI avadhiyA~ kramazaH 5, 4, 3 aura 6 mAsa haiM; vibhinna mUladhana kI rakamoM kA yoga 140 hai / ye mUladhana kI rakameM kauna-kauna sI haiM ? // 40 // vibhinna byAja rAziyA~ 5, 6, 102, 16 aura 30 haiM / unakI saMvAdI avadhiyA~ kramazaH 5, 6, 7, 8 aura 10 mAha haiN| vibhinna mUladhana kI rakamoM kA mizrayoga 80 hai / ina rakamoM ko alagaalaga batalAo // 41 // vibhinna avadhiyoM ko unake mizrayoga meM se alaga-alaga prApta karane ke liye niyama - aura, vibhinna avadhiyoM ke mizrayoga kA nirUpaNa karanevAlI rAzi ko una vibhinna bhajanaphaloM ke yoga dvArA vibhAjita karo jo ki vibhinna vyAjoM ko unake saMvAdI mUladhanoM dvArA vibhAjita karane para prApta hote haiM / aura taba, pariNAmI bhajanaphala ko alaga-alaga uparyukta bhajanaphaloM meM se pratyeka dvArA guNita kro| isa prakAra vibhinna avadhiyA~ nikAlI jAtI haiM // 42 // ma (39) pratIka rUpa se, ma mizraka vyavahAraH ba a ba 3 +... a ba + a. a (42) pratIka rUpa se, 2 + bra 2 + ma bara ra + + a s = gha 21 ma phing ba 2 ba 3 dha, ba uu a X jahA~ ma = dha, + + dhag + ... ityAdi ba uu [ 99 dha = gha; + + +... dha2 dha ...ityAdi; isI taraha a, a ityAdi ke mAna nikAlate haiN| = a, jahA~ ma = a + a + a +

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1001 gaNitasArasaMgrahaH [ 6. 43 atroddezakaH catvAriMzattriMzaviMzatipaJcAzadatra mUlAni / dazaSatripaJcadaza phalamaSTAdaza kAlamizradhanarAziH // 43 // pramANarAzau phalena tulyamicchArAzimUlaM ca tadicchArAzau vRddhiM ca saMpIDya tanmizrarAzau pramANarAzevRddhivibhAgAnayanasUtramkAlaguNitapramANaM parakAlahRtaM tadekaguNamizradhanAt / itarArdhakRtiyutAt padamitarA?naM pramANaphalama // 44 / atroddezakaH mAsacatuSkazatasya pranaSTavRddhiH prayogamUlaM tat / svaphalena yutaM dvAdaza paJcakRtistasya kAlo'pi / / 45 // mAsatritayAzItyAH pranaSTavRddhiH svamUlaphalarAzeH / paJcamabhAgenonAzcASTau varSeNa mUlavRddhI ke / / 46 / / ___ udAharaNArtha prazna isa prazna meM, diye gaye mUladhana 40,30, 20 aura 50 haiM tathA saMvAdI byAja rAziyA~ kramazaH 10, 6, 3 aura 15 haiN| vibhinna avadhiyoM kA mizrayoga 18 hai| batalAo ki avadhiyA~ kyAkyA haiM? // 43 // byAjadara ke barAbara diyA gayA mUladhana aura isa udhAra diye gaye mUladhana ke byAja, ina donoM ke mizrayoga ko nirUpita karanevAlI rAzi meM se mUladhanadara evaM vyAjadara alaga-alaga nikAlane ke liye niyama mUladhanadara ko avadhidara dvArA guNita kara use jisa samaya taka byAja lagAyA gayA hai usa samaya dvArA vibhAjita karate haiN| isa pariNAmI bhajanaphala ko diye gaye mizrayoga dvArA eka bAra guNita karate haiM, aura taba, usameM uparyukta bhajanaphala kI AdhI rAzi ke varga ko jor3ate haiN| isa taraha prApta rAzi kA vargamUla nikAlate haiN| prApta phala ko usI bhajanaphala kI arddharAzi dvArA hAsita karate haiM to mUladhana ke barAbara iSTa byAjadara prApta hotI hai // 44 // udAharaNArtha prazna byAjadara pratizata prati 4 mAha ajJAta hai| vahI ajJAta rAzi udhAra diyA gayA mUladhana bhI hai / yaha khuda ke byAja se jor3I jAne para 12 ho jAtI hai| 25 mAha avadhi hai jisameM ki vaha byAja upArjita huA hai / byAjadara ko nikAlo jo mUladhana ke tulya hai // 45 // byAjadara prati 80 prati 3 mAha ajJAta hai / eka sAla ke byAja tathA usa ajJAta rAzi ke tulya mUladhana kA mizrayoga 74 hai| batalAo ki mUladhana aura byAjadara kyA kyA hai ? // 46 // (44) pratIka rUpa se, VdhA A xma + (a) -ma = ghA A) 2_dhA A bA jo dha ke tulya hai|

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mizrakanyavahAraH [101 .. samAnamUlavRddhimizravibhAgasUtramanyonyakAlavinihatamizravizeSasya tasya bhaagaakhym| kAlavizeSeNa hRte teSAM mUlaM vijAnIyAt // 47 // atroddezakaH paJcAzadaSTapaJcAzanmizraM SaTSaSTireva ca / paJca saptaiva nava hi mAsAH kiM phalamAnaya / / 48 // triMzaJcaikatriMzadviyaMzAH syuH punastrayastriMzat / satryaMzA mizradhanaM pazcatriMzacca gaNakAdAt / / 4 / / kazcinnarazcaturNA tribhizcaturbhizca paJcabhiH SaDbhiH / mAsailabdhaM kiM syAnmUlaM zIghraM mamAcakSva // 50 // samAnamUlakAlamizravibhAgasUtramanyonyavRddhisaMguNamizravizeSasya tasya bhAgAkhyam / vRddhivizeSeNa hRte labdhaM mUlaM budhAH prAhuH / / 51 // atroddezakaH ekatripaJcamizritaviMzatiriha kAlamUlayormizram / SaD daza caturdaza syuAbhAH kiM mUlamatra sAmyaM syAt / / 52 // mUladhana jo saba dazAoM meM ekasA rahatA hai, aura ( vibhinna avadhiyoM ke ) byAjoM ko, unake mizrayoga meM se alaga-alaga karane ke liye niyama- koI bhI do diye gaye mizrayogoM ko kramazaH eka dUsare ke vyAja kI avadhiyoM dvArA guNita karane se prApta rAziyoM ke aMtara dvArA vibhAjita karane para jo bhajanaphala prApta hotA hai vaha una diye gaye mizrayogoM sambandhI iSTa mUladhana hai // 47 // . udAharaNArtha prazna mizrayoga 50, 58 aura 66 hai aura avadhiyA~ jinameM ki byAja upArjita hue haiM, kramazaH 5.. aura 4 mAha haiM / pratyeka dazA meM byAja batalAo // 48 // he gaNitajJa ! kisI manuSya ne 4 vyaktiyoM ko kramazaH 3, 4, 5 aura 6 mAsa ke anta meM uso mUladhana aura byAja ke mizrayoga 30. 312 33. aura 35 diye / mujhe zIghra batalAo ki yahA~ mUladhana kyA hai ? // 49.50 // mUladhana (jo pratyeka dazA meM vahI rahatA ho) aura avadhi (jitane samaya meM byAja upArjita kiyA gayA ho) ko unhIM ke mizrayoga meM se alaga-alaga karane ke liye niyama--. . koI bhI do mizrayogoM ko kramazaH eka dUsare ke byAja dvArA guNita kara, prApta rAziyoM ke antara ko do cune hue byAjoM ke antara dvArA vibhAjita karane para bhajanaphala ke rUpa meM iSTa mUladhana prApta hotA hai, aisA vidvAn kahate haiM // 51 // ----------- udAharaNArtha prazna mUladhana aura avadhiyoM ke mizrayoga 21, 23 aura 25 haiN| yahA~ byAja 6, 10 aura 14 hai| batalAo ki samAna aho vAlA mUladhana kyA hai ? // 52 // diye gaye mizrayoga 35, 37 aura 39 haiM; (47 ) pratIka rUpa se, ma, a3 ma. a.. a. ara (51) pratIka rUpa se, ma, bamaba, .. -dha, jahA~ ma,, mana, Adi, vibhinna mizrayoga hai|

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102] gaNitasArasaMgrahaH [ 6. 53pazcatriMzanmizraM saptatriMzacca navayutatriMzat / viMzatiraSTAviMzatiratha SaTtriMzaJca vRddhidhanam / / 53 / / ubhayaprayogamUlAnayanasUtramrUpasyecchAkAlAdubhayaphale ye tayorvizeSeNa / labdhaM vibhajenmUlaM svapUrvasaMkalpitaM bhavati // 54 // atroddezakaH uvRttyA SaTakazate prayojito'sau punazca nvkshte| .. mAsaistribhizca labhate saikAzIti krameNa mUlaM kim // 55 // -- - trivRddhayaiva zate mAse prayuktazcASTabhiHzate / lAbho'zItiH kiyanmUlaM bhavettanmAsayordvayoH / / 56 / / vRddhimUlavimocanakAlAnayanasUtrammUlaM svakAlaguNitaM phalaguNitaM tatpramANakAlAbhyAm / bhaktaM skandhasya phalaM mUlaM kAlaM phalAtprAgvat / / 57 // 1 isI niyama ko kucha azuddha rUpa meM parivartita pATha meM isa prakAra ullikhita kiyA gayA hai punarapyubhayaprayogamUlAnayanasUtramicchAkAlAdubhayaprayogavRddhiM samAnIya / tavRddhayantarabhaktaM labdhaM mUlaM vijAnIyAt / / byAja 20, 28 aura 36 haiM / samAna are vAlA mUladhana kyA hai ? // 53 // do bhinna byAjadAroM para lagAyA huA mUladhana prApta karane ke liye niyama do byAja rAziyoM ke aMtara ko una do rAziyoM ke aMtara dvArA vibhAjita karo jo dI huI avadhiyoM meM 1 para byAja hotI haiM / yaha bhajanaphala svapUrva saMkalpita mUladhana hotA hai // 54 // udAharaNArtha prazna 6 pratizata kI dara para udhAra lekara, aura taba 9 pratizata kI dara para udhAra dekara koI vyakti calana ( differential) lAbha ke dvArA ThIka 3 mAha ke pazcAt 81 prApta karatA hai / mUladhana kyA hai ? // 55 / / 3 pratizata pratimAsa ke argha se koI rakama udhAra lI jAkara 8 pratizata pratimAha ke argha se byAja paradI jAtI hai| calana lAbha, 2 mAha ke anta meM 80 hotA hai| batalAo vaha rakama kyA hai ? // 56 // jaba mUladhana aura byAja donoM (kiztoM dvArA) cukAye jAte hoM taya samaya nikAlane ke niyama udhAra diyA gayA mUladhana kizta ke samaya dvArA guNita kiyA jAtA hai aura phira byAja dara dvArA guNita kiyA jAtA hai| isa guNanaphala ko mUladhanadara dvArA aura avadhidara dvArA vibhAjita karane para usa kizta sambandhI byAja prApta hotA hai| isa byAja se, kizta kA mUladhana aura RNa ko cukAne kA samaya, donoM ko prApta kiyA jAtA hai // 57 // barAbara (54) pratIka rUpa se, 14a, bA, 14 a.x bAra gha A.xdhA, A24dhAra (57) pratIka rUpa se, dha bA -kita sambandhI vyAja. jahA~ pa pratyeka kizta kI avadhi hai| dhA A

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mizrakavyavahAraH atroddezakaH mAse hi paJcaiva ca saptatInAM mAsadvaye'STAdazakaM pradeyam / skandhaM caturbhiH sahitA tvazItiH mUlaM bhavetko nu vimuktikAlaH / / 58 / / SaSTyA mAsikavRddhiH paJcaiva hi mUlamapi ca SaTtriMzat / mAtrita skandhaM tripaJcakaM tasya kaH kAlaH / / 59 / / samAnavRddhimUlamizravibhAgasUtram - --6. 62 ] mUlaiH svakAlaguNitairvRddhivibhaktaiH samAsa kairvibhajet / mizraM svakAlanighnaM vRddhirmUlAni ca prAgvat // 60 // atroddezakaH dvikaSaTakacatuH zatake catuH sahasraM catuH zataM mizram / mAsadvayena vRddhayA samAni kAnyatra mUlAni / / 61 // trikazatapaJcakasaptatipAdonacatuSkaSaSTiyogeSu / navazatasahasrasaMkhyA mAsatritaye samA yuktA // 62 // udAharaNArtha prazna byAjadara 5 prati 70 pratimAsa hai; pratyeka 2 mAha meM cukAI jAne vAlI kizta 18 hai evaM udhAra diyA gayA mUladhana 84 / vimukti kAla ( karja cukAne kA samaya ) batalAo // 58 // 60 era pratimAsa vyAja 5 hotA hai / udhAra diyA gayA mUladhana 36 hai / 3 mAha meM cukAI jAne vAlI pratyeka kizta 15 hai / usa karja ke cukane kA samaya batalAo / / 59 / / jina para samAna byAja upArjita huA hai aise vibhinna mUladhanoM ko mizrayoga se alaga-alaga karane ke liye niyama - mizrayoga ko avadhi dvArA guNita kara, una rAziyoM ke yoga se vibhAjita karo jo ( rAziyA~ ) vibhinna mUladhanadaroM ko unakI saMvAdI avadhidaroM dvArA guNita karane tathA saMvAdI vyAjadaroM dvArA vibhAjita karane para prApta hotI haiN| isa prakAra byAja prApta hotA hai aura usase mUladhana prApta kiye jAte haiM // 60 // [ 103 udAharaNArtha prazna 2, 6 aura 4 pratizata pratimAsa kI dara se diye gaye mUladhanoM kA mizrayoga 4,400 hai / ina samasta mUladhanoM kI 2 mAha kI vyAja rAziyA~ barAbara hotI haiN| batalAo ki vaha byAjarAzi kyA hai aura vibhinna mUladhana kyA-kyA haiM ? // 61 // kula rakama 1,900; 3 pratizata, 5 prati 70 aura 33 prati 60 pratimAha kI dara se vibhinna mUladhanoM meM byAja para vitarita kara dI gii| pratyeka dazA meM 3 mAha meM byAja barAbara-barAbara upArjita huA / usa samAna byAjarAzi ko tathA vibhinna mUladhanoM ko alagaalaga prApta karo // 62 // ma X a dhA2 X A ( 60 ) pratIka rUpa se, dhA, XA, +' bA 2 bA ko adhyAya 6 kI 10 vIM gAthA ke niyama dvArA prApta kiyA jA sakatA hai / ...ityAdi +... = ba; isake dvArA mUladhanoM

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104 ] vimuktakAlasya mUlAnayanasUtram - skandhaM svakAlabhaktaM vimuktakAlena tADitaM vibhajet / nirmuktakAlavRddhayA rUpasya hi saikayA mUlam / / 63 / / atroddezakaH gaNitasArasaMgrahaH paJcakazataprayoge mAsau dvau skandhamaSTakaM dattvA / mAsaiH SaSTibhiriha vai nirmuktaH kiM bhavenmUlam // 64 // dvau tripaJcabhAgau skandhaM dvAdazadinairdadAtyekaH / trikazatayoge dazabhirmAsairmuktaM hi mUlaM kim || 65|| - vRddhiyuktahIna samAnamUlamizravibhAgasUtram - kAlasvaphalonAdhikarUpo dhRtarUpayogahRtamizre' / 1 "mizraH" pATha hastalipiyoM meM hai; yahA~ vyAkaraNa kI dRSTi se mizra zabda adhika saMtoSajanaka hai / jJAta avadhi meM cukAI jAne vAlI kiztoM sambandhI udhAra diye gaye mUladhana ko nikAlane kA niyama [ 5.63 kizta kI rakama ko usakI avadhi dvArA vibhAjita karate haiM aura karja cukAne ke samaya ( vimukti kAla ) dvArA guNita karate haiN| aba prApta rAzi ko usa rAzi dvArA vibhAjita karate haiM jo 1 meM 1 para karja nirmukti samaya ke liye lagAye hue byAja ko jor3ane para prApta hotI hai / isa prakAra mUladhana prApta hotA hai / / 63 / / udAharaNArtha prazna 5 pratizata pratimAsa kI dara se jaba pratyeka kizta kI avadhi 2 mAsa rahI, aura pratyeka bAra meM. 8 kizta rUpa meM cukAyA gayA taba eka manuSya 60 mAha meM RNamukta huA / batalAo usane kitanA dhana udhAra liyA thA ? / / 64 / / koI vyakti 12 dinoM meM eka bAra 23 kiztarUpa meM detA hai / yadi byAja dara 3 pratizata pratimAsa ho to 10 mAha meM cukane vAle RNa ke parimANa ko batalAo ? // 65 // (63) pratIka rUpa se, sa pa a 1 x aX bA A x dhA aise vibhinna mUladhanoM ko alaga-alaga nikAlane ke liye niyama jo unake mizrayoga meM jaba unhIM ke vyAjoM dvArA milAye jAne para athavA usameM se hAsita kiye jAne para eka dUsare ke tulya ho jAte haiM ( sabhI datta dazAoM meM mUladhanoM meM byAja rAziyA~ jor3I jAtI haiM athavA unameM se ghaTAyI jAtI haiM ) - kramazaH dI gaI byAja dara ke anusAra, pratyeka dazA meM, eka meM upArjita byAja yA to milAyA . jAtA hai athavA eka meM se hAsita kiyA jAtA hai| taba, pratyeka dazA meM, ina rAziyoM dvArA eka ko vibhAjita kiyA jAtA hai| isake pazcAt vibhinna udhAra diye gaye dhanoM ke mizrayoga ko ina pariNAmI bhajanaphaloM ke yoga dvArA vibhAjita kiyA jAtA hai| aura mizra yoga sambandhI isa taraha varte gaye una uparyukta bhajanaphaloM ke yoga ke saMvAdI samAnupAtI bhAga dvArA alaga-alaga pratyeka dazA meM use guNita " 1+ = dha; jahA~ sa = kizta ( skaMdha ) hai pa - kizta kA samaya hai aura a = RNa ke cukane kI avadhi hai /

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[105 -1.69] mizrakanyavahAra prakSepo guNakAraH svaphalonAdhikasamAnamUlAni // 66 // atroddezakaH trikapaJcakASTakazataiH prayogato'STAsahastrapaJcazatam / viMzatisahitaM vRddhibhiruddhRtya samAni paJcabhirmAsaiH // 67 // trikaSaTakASTakaSaSTyA mAsadvitaye catussahasrANi / paJcAzadvizatayutAnyato'STamAsakaphalAhate sadRzAni / / 68 // dvikapaJcakanavakazate mAsacatuSke trayodazasahasram / saptazatena ca mizrA catvAriMzatsavRddhisamamUlAni / / 69 / / kiyA jAtA hai| isase udhAra dI gaI rakameM utpanna hotI haiM jo unake byAjoM dvArA milAI jAne para athavA hAsita kiye jAne para samAna ho jAtI haiM // 66 // udAharaNArtha prazna 8,520 rupaye kramazaH 3, 5 aura 8 pratizata pratimAsa kI dara se ( bhAgoM meM ) byAja para diye jAte haiN| 5 mAha meM upArjita byAjoM dvArA hAsita karane para ve datta rakameM barAbara ho jAtI haiN| isa taraha byAja para lagAye hue dhanoM ko batalAo // 67 // 1,250 dvArA nirUpita kula dhana ko (bhAgoM meM) kramazaH 3, 6 ora 8prati 60 kI dara se 2 mAha ke liye byAja para lagAyA gayA hai / 8 mAha meM hone vAle byAjoM ko dhanoM meM se ghaTAne para jo dhana prApta hote haiM ve tulya dekhe jAte haiN| isa prakAra viniyojita vibhinna dhanoM ko btlaao|| 6 // 13,740 rupaye, (bhAgoM meM )2,5 aura 9 pratizata pratimAha ke argha se byAja para lagAye jAte haiN| 4 mAha ke liye udhAra diye gaye dhanoM meM vyAjoM ko jor3ane para ve barAbara ho jAte haiN| una dhanoM ko batalAo // 69 // 3,643 rupaye (bhAgoM meM ) kramazaH 13, 3 aura I prati 80 pratimAha kI dara se byAja para lagAye jAte haiN| 8 mAha meM (66) pratIka rUpa se, - 1 (kxxbA.) 1 (1XXX vA.) va 1. (1XXbA A.XdhA, - + ityAdi /1XaXbAra) A3 dhAra (14aXbAra A, dhA, isI prakAra, 1 /1XXbA, A. dhA / -- + ityAdi /14aXbA) AdhA 1+(1XxbAgha, isI taraha (A.xdhAra gha, dhara Adi ke liye| ma. sA. sa0-14 ga0 sA0 saM0-14

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106 ] gaNita sArasaMgrahaH [ 6.70 saikArdhakapaJcArdhakaSaDardhakAzItiyogayuktAstu / mAsaSTa SaDadhikA catvAriMzacca SaTkRtizatAni // 70 // saMkalitaskandhamUlasya mUlavRddhivimuktikAlanayanasUtram -- skandhAptamUlacitiguNitaskandhecchAgraghAtiyutamUlaM syAt / skandhe kAlena phalaM skandhoddhRtakAlamUlahatakAlaH // 71 // atroddezakaH kenApi saMprayuktA SaSTiH paJcakazataprayogeNa / mAsa tripaJcabhAgAt saptottaratazca saptAdiH // 72 // tatSaSTisaptamAMzakapadamitisaMkalitadhanameva / dattvA tatsaptAMzakavRddhiM prAdAcca citimUlam // kiM tadvRddhiH kA syAt kAlastadRNasya maukSiko bhavati / / 733 // utpanna hue vyAjoM ko mUladhanoM meM jor3ane para dekhA jAtA hai ki ve barAbara ho jAte haiM / una viniyojita rakamoM ko nikAlo // 70 // samAntara zreDhi baddha kistoM dvArA cukAI gaI RNa kI rakama ke sambandha meM dhana, byAja aura RNa mukti kA samaya nikAlane ke liye niyama iSTa RNa dhana vaha mUladhana hai jo mana se cunI huI ( mahattama prApya kista kI ) rakama aura zreDhi ke padoM kI saMkhyA ke bhinnIya bhAga ke guNanaphala ko ( 1 jisakA prathama pada hai, 1 pracaya hai aura uparyukta mahattama RNa kI rakama ko prathama kista dvArA vibhAjita karane se prApta pUrNAGka mAna vAlI saMkhyA ( bhajanaphala ) jisake padoM kI saMkhyA hai, aisI ) samAntara zreDhi dvArA guNita prathama kista se milAne para prApta hotA hai / byAja vaha hai jo kista kI avadhi meM utpanna hotA hai / kista kI avadhi ko prathama fara dvArA vibhAjita karane aura mana se cunI huI RNa kI mahattama rakama dvArA guNita karane para jo prApta hotA hai vaha RNa mukta hone kA samaya hai // 71 // udAharaNArtha prazna eka manuSya ne 5 pratizata pratimAha kI dara se byAja lagAye jAne vAle RNa kI mukti ke liye 60 ko mahattama rakama cunA tathA 7 prathama kista cunI jo uttarottara mAha meM honevAlI kistoM meM 7 dvArA bar3hatI calI gaI / isa prakAra, usane - padoM vAlI samAntara zreDhi ke yoga ko RNa rUpa meM cukAyA tathA una 7 ke apavaya ( multiples ) para lagane vAle byAja ko bhI cukAyA / zreDhi ke yoga kI saMvAdI RNa rakama ko nikAlo, cukAye gaye vyAja ko nikAlo aura batalAo ki usa RNa kI mukti kA samaya kyA hai ? // 72-733 // kisI manuSya ne 5 pratizata pratimAsa vyAja kI dara lagAye jAne 1 athavA 8 hotI hai jisameM se 8 ( 71 ) yaha niyama ( kaI zabda chUTa jAne ke kAraNa ) atyanta bhramotpAdaka hai tathA 72 - 733 vIM gAthA ke udAharaNa hala karane para spaSTa ho jAvegA / yahA~ mUla athavA kista kI mahattama prApya rakama 60 hai / yaha prathama kista kI rakama 7 dvArA vibhAjita hone para samAntara zreDhi ke padoM kI saMkhyA hai| aisI samAntara zreTi kA 1 prathama pada hai, 1 pracaya hai aura agra athavA Upara kA bhinnIya bhAga hai| uparyukta bheTi ke yoga 36 ko prathama kista 7 dvArA guNitakara u aura 60 ke guNanaphala meM jor3a dete haiM / yahA~ 60 mahattama prApya rakama hai / isa prakAra 36x7+ x 60 = 34 prApta hotA hai jo RNa kA iSTa mUladhana hai / mAha meM 5 pratizata pratimAha kI dara pUrNa para cukAyA gayA byAja hogA / RNa mukti kI avadhi ( 7 ) 60 = mAha hogI / para

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- 6. 783 ] mizrakavyavahAraH kenApi saMprayuktAzItiH paJcakazataprayogeNa / / 743 / / aSTAdyaSTottaratastadazItyaSTAMzagacchena / mUladhanaM dattvASTAdyaSTottarato dhanasya mAsArdhAt // 753 / / vRddhiM prAdAnmUlaM vRddhizca vimuktikAlazca / eSAM parimANaM kiM vigaNayya sakhe mamAcakSva // 763 / / ekIkaraNasUtram - vRddhisamAsaM vibhajenmAsaphalaikyena labdhamiSTaH kAlaH / kAlapramANaguNitastadiSTakAlena saMbhaktaH / / vRddhisamAsena hato mUlasamAsena bhAjito vRddhiH // 773 // atroddezakaH yuktA caturazatIha dvitrikapaJcakacatuSkazatena / mAsAH paJca caturdvitrayaH prayogakakAlaH kaH // 783 / / iti mizrakavyavahAre vRddhividhAnaM samAptam / vAle RNa kI mukti ke liye 80 ko mahattama rakama cunaa| isake sAtha, 8 prathama kista kI rakama thI jo prati mAha meM uttarottara 8 dvArA bar3hatI calI gii| isa prakAra usane samAntara zreDhi ke yoga ko RNa rUpa meM cukAyA / isa samAntara zreDhi meM padoM kI saMkhyA thI / una 8 ke apavayoM para byAja bhI cukAyA gayA / he mitra ! zreDhi ke yoga kI saMvAdI RNa kI rakama, cukAyA gayA byAja aura RNa mukti kA samaya acchI taraha gaNanA kara nikAlo / / 733-76 / / ausata sAdhAraNa byAja ko nikAlane ke liye niyama - ( vibhinna upArjita hone vAle ) byAjoM ke yoga ko ( vibhinna saMvAdI ) eka mAha ke dAtavya vyAjoM ke yoga dvArA vibhAjita karane para pariNAmI bhajanaphala, iSTa samaya hotA hai / ( kAlpanika ) samayadara aura mUladhanadara ke guNanaphala ko iSTa samaya dvArA vibhAjita karate haiM aura ( upArjita hone vAle vibhinna ) vyAjoM ke yoga dvArA guNita karate haiM / prAptaphala ko vibhinna diye gaye mUladhanoM ke yoga dvArA phira se vibhAjita karate haiM / isase iSTa byAja dara prApta hoto hai | // 77 - 773 // udAharaNArtha prazna isa prazna meM, cAra sau kI 4 rakameM alaga-alaga kramazaH 2, 3, 5 aura 4 pratizata pratimAsa kI dara se 5, 4, 2 aura 3 mAhoM ke liye byAja para lagAI giiN| ausata sAdhAraNa avadhi aura vyAjadara nikAlo // 78 // isa prakAra, mizraka vyavahAra meM vRddhi vidhAna nAmaka prakaraNa samApta huA / ( 77 aura 773 ) vibhinna utpanna hone vAle byAja ve hote haiM jo alaga-alaga rakamoM ke, vibhinna daroM para unakI kramavAra avadhiyoM ke liye byAja hote haiM / pratIka rUpa se, dha2 X a2 X bA 2 AX dhA dha2 x 1 x bA 2 A X dhA + * athavA ausata avadhi ; aura dhA X A a au dha X a, X bA AX dhA {44 X 2 X @19 A X dhA X + = a au XX bA A X dhA gha, + +....... 107 + + + *}+ **} dha2 X a2 X bA 2 A X dhA .. ) = ba o athavA ausata byAja | }+

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gaNita sArasaMgrahaH prakSepaka kuTTIkAraH itaH paraM mizrakavyavahAre prakSepakakuTTIkAragaNitaM vyAkhyAsyAmaH / prakSepakakaraNamidaM savargavicchedanAMzayutihRtamizraH / prakSepaka guNakAraH kuTTIkAro budhaiH samuddiSTam // 793 // 108 ] [ 6.793 atroddezakaH dvitricatuSSaDbhAgairvibhAjyate dviguNaSaSTiriha hemnAm / bhRtyebhyo hi caturyo gaNakAcakSvAzu me bhAgAn // 803 // prathamasyAMzatritayaM triguNottaratazca paJcabhirbhaktam / dInArANAM trizataM triSaSTisahitaM ka ekAMzaH // 813 / / AdAya cAmbujAni pravizya sacchrAvako'tha jinanilayam / pUjAM cakAra bhaktyA pUjArhebhyo jinendrebhyaH / / 823 / / vRSabhAya caturthAMzaM SaSThAMzaM ziSTapArzvAya / dvAdazamatha jinapataye tryaMzaM munisuvratAya dadau / / 833 / / naSTASTakarmaNe jagadiSTAyAriSTanemaye'STAMzam / SaSThaghnacaturbhAgaM bhaktyA jinazAntaye pradadau / 843 // kamalAnyazItimizrANyAyAtAnyatha zatAni catvAri / kusumAnAM bhAgAkhyaM kathaya prakSepakAkhyakaraNena / / 853 // prakSepaka kuTTIkAra ( samAnupAtI bhAga ) ) isake pazcAt hama isa mizraka vyavahAra meM samAnupAtI bhAga ke gaNita kA pratipAdana kareMgesamAnupAtI bhAga kI kriyA vaha hai jisameM dI gaI ( samUha vAcaka ) rAzi pahile ( vibhinna samAnupAtI bhAgoM kA nirUpaNa karane vAle samAna (sAdhAraNa) hara vAle bhinnoM ke aMzoM ke yoga dvArA vibhAjita kI jAtI hai| aise samAna hara vAle bhinnoM ke haroM ko ucchedita kara vicArate nahIM haiM / prApta phala ko pratyeka dazA meM kramazaH ina samAnupAtI aMzoM dvArA guNita karate haiN| ise budhajana (vidvajjana) 'kuTTIkAra' kahate haiM // 79 // udAharaNArtha prazna isa prazna meM 120 svarNa mudrAe~ 4 naukaroM meM kramazaH 2, 3 aura dve ke bhinnIya bhAgoM meM jAtI haiM / he aMkagaNitajJa ! mujhe zIghra batalAo ki unheM kyA milA ? / / 803 / / 363 dInAroM ko pA~ca vyaktiyoM meM bA~TA gyaa| unameM se prathama ko 3 bhAga mile aura zeSa bhAga ko uttarottara 3 kI sAdhAraNa niSpatti meM bA~TA gyaa| pratyeka kA hissA batalAo / / 813 / / eka sacce zrAvaka ne kisI saMkhyA ke kamala ke phUla liye aura jina maMdira meM jAkara pUjyanIya jinendroM kI bhaktibhAva se pUjA kii| usane vRSabha bhagavAn ko pUjya pArzva bhagavAn ko, bare jina pati ko muni suvrata bhagavAn ko bheMTa kiye; Te bhAga AThoM karmoM kA nAza karane vAle jagadiSTa ariSTanemi bhagavAn ko aura ThekA hai zAMti jina bhagavAn ko bheMTa kiye| yadi vaha 480 kamala ke phUla isa pUjA ke liye lAyA ho to isa prakSepa nAmaka kriyA dvArA phUloM kA samAnupAtI vitaraNa prApta karo / / 823-853 / / 480 kI ( 793 ) 803 vIM gAthA ke prazna ko isa niyamAnusAra hala karane meM hameM 2, 3, hai, se 12, 12, 12, 1re prApta hote haiN| haroM ko haTAne ke pazcAt, hameM 6, 4, 3, 2 prApta hote haiM / ye prakSepa athavA samAnupAtI aMza bhI kahalAte haiN| inakA yoga 15 hai, jisake dvArA bA~TI jAnevAlI rakama

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-6. 893 ] mizrakavyavahAraH [ 109 catvAri zatAni sakhe yutAnyazItyA narairvibhaktAni / pazcabhirAcakSva tvaM dvitricatuHpaJcaSaDguNitaiH // 863 // ____ iSTaguNaphalAnayanasUtrambhaktaM zeSairmUlaM guNaguNitaM tena yojitaM prakSepam / tadrvyaM mUlyaghnaM kSepavibhaktaM hi mUlyaM syAt / / 873 / / asminnarthe punarapi sUtramphalaguNakArairhatvA paNAn phalaireva bhAgamAdAya / prakSepake guNAH syurAzikaH phalaM vadenmatimAn // 883 // ___asminnarthe punarapi sUtram-, svaphalahRtAH svaguNaghnAH paNAstu tairbhavati pUrvavaccheSaH / iSTaphalaM nirdiSTaM trairAzikasAdhitaM samyak // 893 / / rakama 5 vyaktiyoM meM 2,3, 4, 5 aura 6 ke anupAta meM vibhAjita kI gii| he mitra ! pratyeka ke hisse meM kitanI rakama par3hI ? // 863 // iSTa guNaphala ko prApta karane ke liye niyama--- mUlyadara ko kharIdane yogya vastu (ko prarUpita karane vAlI saMkhyA) dvArA vibhAjita kiyA jAtA hai / taba ise ( dI gaI ) samAnupAtI saMkhyA dvArA guNita karate haiN| isake dvArA, hameM yoga karane kI vidhi se samAnupAtI bhAgoM kA yoga prApta ho jAtA hai| taba dI gaI rAzi kramAnusArI samAnupAtI bhAgoM dvArA guNita hokara tathA unake uparyukta yogadvArA vibhAjita hokara iSTa samAnupAta meM vibhinna vastuoM ke mAna ko utpanna karatI hai| isI ke liye dUsarA niyama mUlyadaroM (kA nirUpaNa karane vAlI saMkhyAoM) ko kramazaH kharIdI jAne vAlI vibhinna vastuoM ke (diye gaye) samAnupAtoM ko nirUpita karane vAlI saMkhyAoM dvArA guNita karate haiN| taba phala ko mUlyadara para kharIdane yogya vastuoM kI saMkhyAoM se kramavAra vibhAjita karate haiN| pariNAmI rAziyA~ prakSepa kI kriyA meM (cAhe hue) guNaka ( multipliers) hotI haiN| buddhimAna loga phira iSTa uttara ko trairAzika dvArA prApta kara sakate haiM // 4 // isI ke liye eka aura niyama vibhinna mUlyadaroM kA nirUpaNa karane vAlI saMkhyAe~ kramazaH unakI svasaMbandhita kharIdane yogya vastuoM kA nirUpaNa karanevAlI saMkhyAoM dvArA guNita kI jAtI haiN| aura taba, unakI saMbandhita samAnupAtI saMkhyAoM dvArA guNita kI jAtI haiN| inakI sahAyatA se, zeSa kriyA sAdhita kI jAtI hai| iSTaphala trairAzika nirdiSTa kriyA dvArA samyaka rUpa se prApta ho jAtA hai / / 493 // 120 vibhAjita kI jAtI hai aura pariNAmI bhajanaphala 8 ko alaga-alaga samAnupAtI aMzoM 6, 4, 3, 2 dvArA guNita karate haiN| isa prakAra prApta rakameM 648 arthAt 48, 448 athavA 32, 348 arthAt 24, 248 athavA 16 haiM / prakSepa kA artha samAnupAtI bhAga kI kriyA bhI hotA hai tathA samAnupAtI aMza bhI hotA hai| (873-891) ina niyamoM ke anusAra 903 vIM aura 911 vIM gAthAoM kA hala nikAlane ke liye 2,3 aura 5 ko kramazaH 3, 5 aura 7 se vibhAjita karate haiM tathA 6,3 aura 1 dvArA guNita

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11. ] gaNitasArasaMgrahaH [ 6. 903 atroddezakaH dvAbhyAM trINi tribhiH paJca paJcabhiH sapta mAnakaiH / dADimAmrakapitthAnAM phalAni gaNitArthavit // 903 / / kapitthAt triguNaM hyAnaM dADimaM SaDguNaM bhavet / krItvAnaya sakhe zIghraM tvaM SaTsaptatibhiH paNaiH / / 913 // dadhyAjyakSIraghaTairjinabimbasyAbhiSecanaM kRtavAn / jinapuruSo dvAsaptatipalaistrayaH pUritAH kalazAH // 923 / / dvAtriMzatprathamaghaTe punshcturviNshtiddhitiiyghtte| SoDaza tRtIyakalaze pRthak pRthak kathaya me kRtvA / / 933 / / teSAM dadhighRtapayasAM tatazcaturviMzatighRtasya palAni / SoDaza payaHpalAni dvAtriMzad dadhipalAnIha // 943 / / vRttistrayaH purANAH puMsazcArohakasya tatrApi / sarve'pi pazcaSaSTiH kecidbhagnA dhanaM teSAm / / 953 / / saMnihitAnAM dattaM labdhaM puMsA dazaiva caikasya / ke saMnihitA bhannAH ke mama saMcintya kathaya tvam // 963 / / udAharaNArtha prazna anAra, Ama aura kapittha kramazaH 2 paNa meM 3, 3 paNa meM 5 aura 5 paNa meM 7 kI dara se prApya haiM / he gaNanA ke siddhAMtoM ko jAnane vAle mitra ! 76 paNoM ke phala lekara zIghra Ao tAki AmoM kI saMkhyA kapitthoM kI saMkhyA kI tigunI ho aura anAroM kI saMkhyA 6 gunI ho // 90-913 // kisI jinAnugAmI ne jina pratimA kA dahI, ghI aura dugdha se pUrita kalazoM dvArA abhiSeka karAyA / inake 72 paloM dvArA 3 pAtra bhara gye| prathama ghaTa meM 32 pala, dUsare ghaTa meM 24 tathA tIsare meM 16 pala pAye gye| ina dadhi, ghI, dUdha mizrita pAtroM meM mizrita dravyoM ko alaga-alaga jJAta aura prApta karo jabaki kula milAkara 24 pala ghI, 16 pala dUdha aura 32 pala dahI hai // 92-943 // eka azvArohI sainika kA vetana 3 purANa thaa| isa dara para kula 65 vyakti niyukta the| unameM se kucha mAre gaye aura unake vetana kI rakama raNakSetra meM zeSa rahanevAle sainikoM ko de dI gaI / isa prakAra, pratyeka manuSya ko 10 purANa prApta hue| mujhe batalAo ki raNakSetra meM kitane sainika kheta rahe aura kitane jIvita bace ? // 95-963 // karate haiM / isa prakAra hameM 46, 343,741 se kramazaH 4, 6 aura " prApta hote haiM / ye samAnupAtI bhAga haiN| 883 aura 891 sUtroM meM ina samAnupAtI bhAgoM ke saMbaMdha meM prakSepa kI kriyA kA prayoga karanA par3atA hai| parantu, 871 karaNa niyama meM yaha kriyA pUrI taraha varNita hai|

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-6. 1013] mizrakavyavahAraH [111 iSTarUpAdhikahInaprakSepakakaraNasUtrampiNDo'dhikarUpono hInottararUpasaMyutaH zeSAt / prakSepakakaraNamataH kartavyaM tairyutA hInAH // 973 // atroddezakaH prathamasyaikAMzo'to dviguNadviguNottarAdbhajanti nraaH| catvAroM'zaH kaH syAdekasya hi saptaSaSTiriha // 983 // prathamAdadhyardhaguNAt triguNAdrapottarAdvibhAjyante / sASTA saptatirebhizzcaturbhirAptAMzakAn brUhi // 993 // prathamAdadhyardhaguNAH pazcArdhaguNottarANi rUpANi / paJcAnAM pazcAzatsaikA crnntryaabhydhikaa||1003|| prathamAtpaJcAdheguNAzcatuguNottaravihInabhAgena / bhaktaM naraizcaturbhiH paJcadazonaM zatacatuSkam // 1013 // samAnupAtI bhAga sambandhI niyama, jahA~ mana se cunI huI kucha pUrNAMka rAziyoM ko jor3anA athavA ghaTAnA hotA hai dI gaI kula rAzi ko joDI jAne vAlI pUNAMka rAziyoM dvArA hAsita kiyA jAtA hai, athavA ghaTAI jAnevAlI pUrNAka dhanAtmaka rAziyoM meM milAyA jAtA hai| taba isa pariNAmI rAzi kI sahAyatA se samAnupAtI bhAga kI kriyA ko jAtI hai, aura pariNAmI samAnupAtI bhAgoM ko kramazaH unameM jor3I jAnevAlI pUrNAka rAziyoM se milA diyA jAtA hai| athavA, ve una ghaTAI jAnevAlI pUrNAMka rAziyoM dvArA kramazaH hvAsita kI jAtI haiM // 971 // ___ udAharaNArtha prazna cAra manuSyoM ne uttarottara dviguNita samAnupAtI bhAgoM meM aura uttarottara dviguNita antaroM vAle yoga meM apane hissoM ko prApta kiyaa| prathama manuSya ko eka hissA milA / 67 bA~TI jAne vAlI rAzi hai| pratyeka ke hisse kyA haiM ? // 98 // 78 kI rakama ina cAra manuSyoM meM aise samAnupAtI bhAgoM meM vitarita kI jAtI hai jo uttarottara prathama se Arambha hokara pratyeka pUrvavartI se 13 guNe haiM aura (yoga meM ) jinakA antara eka se Arambha hokara tigunA vRddhi rUpa hai| pratyeka ke dvArA prApta bhAgoM ke mAna batalAo / // 993 // pA~ca manuSyoM ke hisse kramikarUpeNa prathama se Arambha hokara pratyeka pUrvavartI se 13 gune haiM, aura yoga meM antara kI rAziyA~ ve haiM jo uttarottara (pUrvavartI antara ) se 23 guNI haiN| 53 vibhAjita kI jAne vAlI kula rAzi hai| pratyeka ke dvArA prApta bhAgoM ke mAna batalAo // 1003 // 400 RNa 15 ko cAra manuSyoM ke bIca aise bhAgoM meM vibhAjita kiyA jAtA hai jo pahile se Arambha hokara pratyeka pUrvavartI se 21 guNe haiM, aura jo una aMtaroM dvArA hAsita haiM jo uttarottara pUrvavartI aMtara se 4 gune haiM / vibhinna bhAgoM ke mAnoM ke prApta karo // 1013 // (973) samAnupAtI bhAga kI kriyA yahA~ 873 se 893 meM diye gaye niyamoM meM se kisI bhI eka ke anusAra kI jA sakatI hai| (981 ) hissoM meM jor3I jAnevAlI aMtara rAzi yahA~ 1 hai jo dUsare manuSya ke saMbaMdha meM hai| yaha do zeSa manuSyoM meM se pratyeka ke liye pUrvavartI aMtara kI dugunI hai| yaha aMtara dUsare manuSya ke liye spaSTa rUpa se ullikhita nahIM hai jaisA ki isa udAharaNa meM 1 ullikhita hai| 1001 vI gAthA aura 1011vI gAthA ke udAharaNa meM bhI spaSTa ullekha nahIM hai|

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112] gaNitasArasaMgrahaH [ 6. 1023 samadhanArghAnayanatajjyeSThadhanasaMkhyAnayanasUtramjyeSThadhanaM saikaM syAt svavikraye'ntyArdhaguNamapaikaM tat / krayaNe jyeSThAnayanaM samAnayet karaNaviparItAt // 102 // atroddezakaH dvAvaSTau SaTUtriMzanmUlaM nRNAM SaDeva caramArthaH / ekArgheNa krItvA vikrIya ca samadhanA jAtAH // 1033 // sArdhaikamardhamardhadvayaM ca saMgRhya te trayaH puruSAH / krayavikrayau ca kRtvA SabhiH pazcArghAtsamadhanA jAtAH / / 1043 / / ( vyApAra meM lagAI gaI ) sabase U~cI rakama jyeSTha dhana kA mAna tathA becane kI tulya rakameM utpanna karane vAlI kImatoM ke mAna ko nikAlane ke liye niyama lagAyA gayA sabase bar3A dhana, 1 meM milAne para ( becI jAne vAlI ) vastu ke vikraya kI dara ho jAtA hai / vahI ( becane kI dara ) jaba zeSa vastu kI ( dI gaI ) becane kI kImata dvArA guNita hokara eka dvArA hAsita kI jAtI hai taba kharIdane kI dara utpanna hotI hai / isa vidhi ko viparyasita (ulTA ) karane para kArabAra meM lagAyA gayA sabase bar3A dhana nikAlA jA sakatA hai / / 1023 // udAharaNArtha prazna tIna manuSyoM ne kramazaH 2, 8 aura 36 rakameM lagAIM / 6 vaha kImata hai jisa para zeSa vastueM becI jAtI haiN| usI dara para kharIda kara aura beca kara ve tulya dhana vAle bana jAte haiM / kharIda aura becane kI kImatoM ko nikAlo / / 1033 / / unhIM tIna manuSyoM ne kramazaH 12, re aura 23 dhanoM ko vyApAra meM lagAyA aura unhIM kImatoM para usI vastu kA kraya aura vikraya kiyaa| aMta meM, zeSa ko 6 dvArA nirUpita rAzi meM becane para ve samAna dhana vAle bana gaye / kharIdane aura becane ke dAmoM ko nikAlo / / 1043 // samAna dhana vAlI rAzi 41 hai / jisa kImata para anta meM zeSa vastueM becI 1023 ) isa niyama para kiye jAnevAle praznoM meM, vibhinna mUla rakamoM se kisI sAdhAraNa dara para koI vastu kharIdI huI samajha lI jAtI hai| taba isa taraha kharIdI huI vastu koI anya sAdhAraNa dara para becI jAtI hai / vyApAra meM lagAye gaye dhana kI ikAI meM becI jAne ke liye paryApta na hone ke kAraNa jitanI vastu kI mAtrA baca rahatI hai vaha yahA~ para 'zeSa' kahalAtI hai| jisa kImata para yaha 'zeSa' becI jAtI hai use avaziSTa-mUlya ( aMtyArdha) kahate haiM / pratIka rUpase, mAnalo a, a + ba aura a+ba+samUladhana / yahA~ antima ( a+ba+ sa ) jyeSThadhana arthAt sabase bar3A dhana hai / mAnalo pa caramArgha ( antyArgha ) athavA avaziSTa mUlya hai; taba isa niyamAnusAra a+ba+ sa + 1 = becane kI dara; aura ( a+ba+ sa + 1 ) pa - 1 = kharIdane kI dara hotI haiN| yaha saralatApUrvaka dikhalAyA jA sakatA hai ki vastu ko becane kI dara para aura zeSa ko avaziSTa mUlya para becane se jo rakameM prApta hotI haiM unakA yoga pratyeka dazA meM ekasA hotA hai| yaha AlokanIya hai ki kharIdane kI dara, isa niyama para Azrita praznoM meM, samadhana athavA samAna vikrayodaya ( bikrI kI rakamoM) ke mAna ke samAna hotI hai /

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- 6. 1093 ] mizrakaMvyavahAraH catvAriMzat saikA samadhanasaMkhyA SaDeva caramAghaH / AcakSva gaNaka zIghraM jyeSThadhanaM kiM ca kAni mUlAni // 1053 // samadhanasaMkhyA paJcatriMzadbhavanti yatra dInArAH / catvArazvaramArghe jyeSThadhanaM kiM ca gaNaka kathaya tvam // 106 // caramArghabhinnajAtau samadhanArghAnayanasUtramtulyApacchedadhanAntyArghAbhyAM vikrayakrayAca prAgvat / chedacchedakRtighnAvanupAtAt samadhanAni bhinne'ntyArdhe // 1073 / / atripAdabhAgA dhanAni SaTapaJcamAMza kAzcaramArghaH / ekArgheNa krItvA vikrIya ca samadhanA jAtAH / / 1083 / / punarapi antyArghe bhinne sati samadhanAnayanasUtram - jyeSThAMzadviharahatiH sAntyaharA vikrayo'ntyamUlyannaH / naikodvaya khilaharaghnaH syAtkraya saMkhyAnupAto'tha // / 1093 / / [ 113 jAtI haiM vaha 6 hai / he aMkagaNitajJa ! mujhe zIghra batalAo ki kauna sI sabase UMcI lagAI gaI rakama hai aura vibhinna anya rakameM kauna-kauna haiM ? / / 1053 / / usa dazA meM jaba ki 35 dInAra samAna dhana rAzi hai, aura 4 vaha kImata hai jisa para zeSa vastueM becI jAtI haiM, he gaNitajJa ! mujhe batalAo ki sabase UMcI lagAI jAne vAlI rakama kyA hai ? / / 1062 / / jaba avaziSTa kImata ( antya ardha ) bhinnIya rUpa meM hoM taba samAna becane kI rakameM utpanna karane vAlI kImatoM ke mAna nikAlane ke liye niyama samAna hara vAlA banA kara / taba iSTa becane aura kharIdane avaziSTa - kImata ( antya argha ) bhinnIya hone para becane aura kharIdane kI daroM ko pahile kI bhA~ti prApta karate haiM jaba ki lagAI gaI rakamoM aura avaziSTa kImata ko upayoga meM lAte haiM / yaha hara isa samaya upekSita kara diyA jAtA hai kI daroM ko prApta karane ke liye ina becane aura kharIdane kI daroM ko guNita karate haiM / taba samAna vikrayodaya ( becane kI rakamoM) ko karate haiM / / 1073 / / isa hara aura hara ke varga dvArA trairAzika ke niyama dvArA prApta udAharaNArtha prazna kisI vyApAra meM 2, 3, tIna vyaktiyoM dvArA lagAI gaI rakameM haiN| avaziSTa kImata ( antyArdha ) 6 hai / unhIM kImatoM para kharIdane aura becane para ve samAna dhana rAzi vAle bana jAte haiM / becane ko kImata aura kharIdane kI kImata tathA samAna vikraya-dhana nikAlo / / 1083 // jaba avaziSTa kImata ( antyArdha ) bhinnIya ho taba samAna vikrayodaya ( becane kI rakamoM ) ko nikAlane ke liye dUsarA niyama sabase bar3e aMza, do aura ( lagAI gaI mULa rakamoM ke prApya ) haroM kA saMtata guNanaphala jaba avaziSTa mUlya ke mAna ke hara meM jor3A jAtA hai taba becane kI dara utpanna hotI hai| jaba ise avaziSTa - mUlya ( andhyArgha ) se guNita kara aura 1 dvArA hAsita kara aura phira uttarottara do tathA samasta haroM dvArA guNita kiyA jAtA hai, taba kharIdane kI dara prApta hotI hai| tatpazcAt trairAzika kI sahAyatA se becane kI rakama ( sale-proceeds ) kA sAdhAraNa mAna prApta hotA hai / / 1093 // " 1053 ) yahA~ AlokanIya hai ki isa niyamAnusAra kevala sabase bar3I rakama nikAlI jAtI hai / anya rakameM mana se cuna lI jAtI haiM, tAki ve sabase bar3I rakama se choTI hoM / ga0 sA0 saM0-15

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114] gaNitasArasaMgrahaH [6.103atroddezakaH adhaM dvau vyaMzau ca trIn pAdAMzAMzca' saMgRhya / vikrIya krItvAnte paJcabhiraMdhyaMzakaiH samAnadhanAH / / 110 // ___iSTaguNeSTasaMkhyAyAmiSTasaMkhyAsamarpaNAnayanasUtramantyapade svaguNahRte kSipedupAntyaM ca tasyAntam / tenopAntyena bhajedyallabdhaM tadbhavenmUlam // 111 / / atroddezakaH kazcicchAvakapuruSazcaturmukhaM jinagRhaM samAsAdya / pUjAM cakAra bhaktyA surabhINyAdAya kusumAni // 1123 // dviguNamabhUdAdyamukhe triguNaM ca caturguNaM ca pazcaguNam / sarvatra paJca paJca ca tatsaMkhyAmbhoruhANi kAni syuH // 1133 / / dvitricaturbhAgaguNAH pazcArdhaguNAtripaJcasaptASTau / bhaktairbhaktyAhebhyo dattAnyAdAya kusumaani||114|| iti mizrakavyavahAre prakSepakakuTTIkAraH samAptaH / 1. M meM zloka krama 1103 ke pazcAt nimnalikhita zloka jor3A gayA hai, jo B meM prApya nahIM hai: ardhatripAdabhAgA dhanAni SaTpaJcamAMzakAntyAH / ekArpaNa krItvA vikrIya ca samadhanA jaataaH|| udAharaNArtha prazna ,,, kramazaH vyApAra meM lagAkara vahI vastu kharIdane aura becane tathA avaziSTa-mUlya se tIna vyApArI aMta meM samAna vikrayodaya (becane kI rakama) vAle ho jAte haiN| kharIda kI kImata becane kI kImata aura bikrI kI tulya rakameM kyA kyA haiM ? // 110 // . aise prazna ko hala karane ke liye niyama jisameM mana se cunI huI saMkhyA bAra cune gaye apavayoM meM mana se cunI huI rAziyA~ samarpita ko ( dI) gaI hoM: upaaMtima rAzi ko, aMtima rAzi kI hI saMvAdI apavartya saMkhyA dvArA vibhAjita aMtima rAzi meM jor3A jaave| isa kriyA se prApta phala ko usa apavarya saMkhyA dvArA vibhAjita kiyA jAve jo ki isa dI gaI upaaMtima rAzi se saMyavita (associated) hai| saba vibhinna dI gaI rAziyoM ke sambandha meM isa kriyA ko karane para iSTa mUla rAzi prApta hotI hai / // 1113 // udAharaNArtha prazna kisI zrAvaka ne cAra daravAjoM vAle jina maMdira meM (apane sAtha ) sugaMdhita phUla lejAkara unheM pUjana meM isa prakAra bhakti pUrvaka bheMTa kiye-cAra daravAjoM para kramazaH ve dugane ho gaye, taba tigune ho gaye, taba caugune ho gaye aura taba pA~cagune ho gaye / pratyeka dvAra para usane 5 phUla arpita kiye batalAo ki usake pAsa kula kitane kamala ke phUla the? // 12-1133 // bhaktoM dvArA bhakti pUrvaka phUla prApta kiye gaye aura pUjana meM Ta kiye gaye / phUla jo isa prakAra bheMTa kiye gaye uttarottara 3, 5, 7, aura 8 the| unakI saMvAdI apavarI rAziyA~ kramazaH... aura thiiN| phUloM kI kula mUla saMkhyA kyA thIM? // 1143 // isa prakAra, mizraka vyavahAra meM prakSepaka kuTTIkAra nAmaka prakaraNa samApta huA /

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- 6. 1155 ] mizraka vyavahAraH kAkuTTIkAra itaH paraM vallikAkuTTIkAragaNitaM vyAkhyAsyAmaH / kuTTIkA re vallikAgaNitanyAyasUtram - chittvA chedena rAzi prathamaphalamapohyAptamanyonyabhaktaM sthApyordhvAdharyato'dho matiguNamayujAlpe'vaziSTe dhanarNam / chittvAdhaH svoparighnopariyutahara bhAgo'dhikAgrasya hAraM chittvA chedena sAmrAntaraphalamadhikAgrAnvitaM hAraghAtam / / 1153 / / [ 115 vallikA kuTTIkAra isake pazcAt hama vallikA kuTTIkAra* nAmaka gaNanA vidhi kI vyAkhyA kareMge / kuTTIkAra sambandhI vallikA nAmaka gaNanA vidhi ke liye niyama do gaI rAzi ( samUha vAcaka saMkhyA ) ko diye gaye bhAjaka dvArA vibhAjita karo / prathama bhajanaphala ko alaga kara do / taba ( vibhinna pariNAmo zeSoM dvArA vibhinna pariNAmI bhAjakoM ke uttarottara bhAga se prApta vibhinna ) bhajanaphaloM ko eka dUsare ke nIce rakho, aura phira isake nIce mana se cunI huI saMkhyA rakho jisase ki ( uttarottara bhAga kI uparyukta vidhi meM ) ayugma sthiti kramavAle alpatama zeSa ko guNita kiyA jAtA hai; aura taba isake nIce isa guNanaphala ko ( praznAnusAra dI gaI jJAta saMkhyA dvArA ) bar3hAkara yA hAsita kara aura taba ( uparyukta uttarottara bhAga kI vidhi meM antima bhAjaka dvArA ) bhAjita kara rkho| isa prakAra vallikA arthAt beli sarIkhI aMkoM kI zRGkhalA prApta hotI hai / isameM zRGkhalA kI nimnatama saMkhyA ko, ( isake ThIka Upara kI saMkhyA meM Upara ke ThIka Upara kI saMkhyA kA guNana karane se prApta ) guNanaphala meM jor3ate haiN| aisI rIti ko taba taka karate jAte zRGkhalA samApta nahIM ho jAtI hai / yaha yoga pahile hI diye gaye bhAjaka se bhAjita [ isa antima bhAjana meM 'zeSa' guNaka bana jAtA hai jisameM, ( isa prazna meM vibhAjita yA vitarita kI jAne vAlI rAzi ko prApta karane ke liye, pahile dI gaI rAzi ( samUha vAcaka saMkhyA) kA guNA kiyA jAtA hai / parantu, jo eka se adhika bAra bar3hAI gaI athavA hAsita kI gaI hoM, aisI dI gaI rAziyoM ( samUha vAcaka saMkhyAoM ) ko eka se adhika samAnupAta meM vibhAjita karanA par3atA hai / yahA~ do viziSTa vibhAjanoM meM se koI eka ke sambandha meM prApta ] adhika bar3A samUha vAcaka mAna sambandhI bhAjaka ko ( choTe samUha vAcaka mAna sambandhI ) bhAjaka dvArA Upara batalAye anusAra bhAjita kiyA jAtA hai tAki uttarottara bhajanaphaloM kI latA ke samAna zRGkhalA pUrva krama anusAra isa dazA meM bhI prApta ho jAve / isa zrRMkhalA meM nimnatama bhajanaphala ke nIce, isa antima uttarottara meM bhAga meM ayugma sthiti kramavAle alpatama zeSa ke mana se cune hue guNaka ko rakhA jAtA hai; aura phira isake nIce pahile batalAe hue samUha vAcaka mAnoM ke antara ko Upara mana se cune hue guNaka dvArA guNita kara, *vallikA kuTTIkAra kahane kA kAraNa yaha hai ki isa niyama meM samajhAI gaI kuTTIkAra kI vidhi latA samAna aMkoM kI zRMkhalA para AdhArita hotI hai / ( 1153) gAthA 1173 vIM kA prazna sAdhita karane para yaha niyama spaSTa ho jAvegA / yahA~ kathana kiyA gayA hai ki 7 alaga phaloM sahita 63 keloM ke Dhera 23 manuSyoM meM ThIka-ThIka bhAjana yogya haiM / eka Dhera meM phaloM kI saMkhyA nikAlanA hai / yahA~ 63 ko 'samUha vAcaka saMkhyA ' ( rAzi ) kahA jAtA hai, aura pratyeka meM sthita phaloM ke saMkhyAtmaka mAna ko 'samUha vAcaka mAna' kahA jAtA hai| isI 'samUha jaba taka ki pUrI kiyA jAtA hai / batalAI gaI vidhi meM )

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116] gaNitasArasaMgrahaH [-6. 1153 12 5 antima ayugma sthiti krama vAle alpatama zeSa meM jor3akara pariNAmI yogaphala ko Upara kI bhAjana zrRMkhalA ke antima bhAjaka dvArA vibhAjita karane ke pazcAt prApta saMkhyA ko rakhanA cAhiye / isa prakAra isa bAda vAcaka mAna' ko nikAlanA iSTa hotA hai| aba isa niyama ke anusAra hama pahile rAzi athavA samUhavAcaka saMkhyA 63 ko cheda athavA bhAjaka 23 dvArA bhAjita karate haiM, aura taba hama jisa prakAra do saMkhyAoM kA mahattama samApavartya nikAlate haiM usI prakAra kI bhAga vidhi ko yahA~ jArI rakhate haiM / 23 ) 63 (2 yahA~ prathama bhajanaphala 2 ko upekSita kara diyA 46 jAtA hai; anya bhajanaphala bAjU ke stambha meM eka paMkti meM 17) 23 (1 eka ke nIce eka likhe gaye haiN| aba hameM eka aisI 6) 17 (2 saMkhyA cunanA par3atI hai jo jaba antima zeSa 1 ke dvArA guNita kI jAtI hai, aura phira 7 meM jor3I jAtI hai, to vaha antima bhAjaka 1 ke dvArA bhAjana yogya hotI hai / isaliye, hama 1 ko cunate haiM, jo zrRMkhalA meM antima aMka 1)5 / 4 ke nIce likhA huA hai| isa cunI huI saMkhyA ke nIce, phirase cunI huI saMkhyA kI sahAyatA se, uparyukta bhAga meM prApta bhajanaphala likhA jAtA hai / isa prakAra hameM bAjU meM yahA~ hama pA~caveM zeSa ke sAtha hI prathama stambha ke aMkoM meM zRMkhalA athavA vallikA prApta bhAga roka dete haiM, kyoMki vaha bhAjana ho jAtI hai| taba hama zRMkhalA ke nIce upa antima aMka ko zreDhiyoM meM ayugma sthiti krama vAlA arthAt 1 ko likhakara usake Upara ke aMka 4 dvArA guNita alpatama zeSa hai| karate haiM, aura 8 jor3ate haiN| yaha 8, zRkhalA kI aMtima saMkhyA hai| pariNAmI 12 isa taraha likha diyA jAtA hai 2-38 tAki vaha 4 ke saMvAdI sthAna meM ho / tatpazcAt isa 12 ko 1-13 vallikA zRMkhalA meM usake Upara ke aMka 1 dvArA guNita karate 4-12 hai aura 1 jor3ane para (jo ki usake usI prakAra nIce hai) hameM 13 eka ke saMvAdI sthAna meM prApta hotA hai / isI prakAra, kriyA ko jArI rakhakara hameM 38 aura 51 bhI prApta hote haiM jo 2 aura 1 ke saMvAdI sthAna meM prApta kiye jAte haiN| isa 51 ko 23 dvArA bhAjita kiyA jAtA hai; aura zeSa 5 eka gucche meM phaloM ko alpatama saMkhyA dRSTigata hotI hai| nimnalikhita bIjIya nirUpaNa dvArA isa niyama kA mUlabhUta siddhAnta ( rationale) spaSTa ho jAvegA 14kha ( jo eka pUrNAka hai )=pha, ka+pa., jahA~ pa. -( bA-Apha, ) ka+ba A ... Apa,-ba .( jahA~ ra. =bA-Apha, jo prathama zeSa hai)=pha, pa, +., jahA~ para bhA = 22 15-1, aura phara dUsarA bhajanaphala hai tathA ra, dUsarA zeSa hai / aura pha tIsarA isaliye, pa, = ra, pa2 +4 = pha, pa. +pa, jahA~ para = ra 12 + bhajanaphala tathA ra, tIsarA zeSa hai|

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-6. 1153] mizrakavyavahAraH ke mizrita prazna ke hala ke liye iSTa latA samAna aMkoM kI zRGkhalA prApta kI jAtI hai| yaha zRGkhalA pahile kI bhA~ti nIce se Upara kI ora bartI jAtI hai aura, pahile kI taraha, pariNAmI saMkhyA ko isa isI taraha, pa. = 12 13 = pha4 pa +pa., jahA~ pa = 24 para hai; pa = ra3 para + va = pha. pa. + pa., jahA~ pa. = 25 pa ba hai / isa prakAra hameM nimnalikhita sambandha prApta hote haiM. ka= phara pa.+pa3, pa, =pha pa3+pa; pa. =pha pa +pa pa pha pax+pa ___54 kA mAna isa taraha cunate haiM tAki ratha paraba ( joki upara batalAe anusAra pa, kA mAna ha), eka pUrNAka bana jAve / isa prakAra, zrRMkhalA phA, phA, phApa, aura parako jamAte haiM jisase ka kA mAna prApta ho jAtA hai: arthAta UparI rAzi kI guNana vidhi ko tathA zRMkhalA kI nimnatara rAzi kI jAr3a vidhi ko sabase Upara kI rAzi taka le jAkara ka kA mAna prApta karate haiN| ka kA mAna isa prakAra prApta kara, use A ke dvArA vibhAjita karate haiN| prApta zeSa, ka kI alpatama arhA ko nirUpita karatA hai: kyoMki ka ke ve mAna jo samIkAra bAka+ba = koI pUrNAka, kA samAdhAna karate haiM, saba samAntara A zredi meM hote haiM jahA~ pracaya ( common difference ) A hotA hai / isa niyama ke dvArA ve prazna bhI hala kiye jA sakate haiM jahA~ do yA do se adhika dazAyeM dI gaI rahatI haiN| aise prazna gAthAoM 1211 se lekara 1299 taka diye gaye haiN| 1213 vI gAthA kA prazna isa niyama ke anusAra isa prakAra hala kiyA jA sakatA hai diyA gayA hai ki phaloM kA eka Dhera jaba 7 dvArA hAsita kiyA jAtA hai taba vaha 8 manuSyoM meM ThIka-ThIka bhAjana yogya ho jAtA hai, aura vahI Dhera jaba 3 dvArA hAsita kiyA jAtA hai taba 13 manuSyoM meM ThIka-ThIka bhAjana yogya ho jAtA hai| aba uparyukta rIti dvArA sabase pahile phaloM kI alpatama saMkhyA ko nikAlA jAtA hai jo prathama dazA kA samAdhAna kare, aura taba phaloM kI vaha saMkhyA nikAlI jAtI hai jo dUsarI dazA kA samAdhAna kre| isa prakAra, hameM kramazaH 15 aura 16 samUha vAcaka mAna prApta hote haiN| aba adhika bar3e samUha vAcaka mAna sambandhI bhAjaka ko choTe samUha vAcaka mAna sambandhI bhAjaka dvArA vibhAjita kiyA jAtA hai tAki nayI vallikA (zraMkhalA) prApta ho jAve / isa prakAra, 13 ko 8 dvArA vibhAjita karane para aura bhAga ko jArI rakhane para hameM nimnalikhita prApta hotA hai8)13(1 isake dvArA vallikA zRMkhalA isa prakAra prApta hotI hai5)8(1 1 ko 'mati' cunakara, aura pahile hI prApta do samUha mAnoM ke aMtara (16-15 ) ko arthAt 1 ko mati aura aMtima bhAjaka ke guNanaphala meM jor3ate haiN| isa yoga ko aMtima bhAjaka dvArA bhAjita karane para hameM 2 prApta hotA hai jise vallikA (zRMkhalA) meM mati ke nIce 2)3(1 likhanA hotA hai| taba, vallikA ke sAtha pahile kI rIti karane para hameM 11 prApta hotA hai, jise prathama bhAjaka 8 dvArA bhAjita karane para zeSa 3 baca rahatA hai| ise adhika bar3e samUhamAna sambandhI bhAjaka 13 dvArA guNita kara, adhika bar3e samUhamAna meM jor3a diyA jAtA hai (1343+ 1655) / isa prakAra Dhera meM phaloM kI saMkhyA 55 prApta hotI hai| 12(1

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118] gaNitasArasaMgrahaH [6. 1152 antima bhAjana zRGkhalA ke prathama bhAjaka dvArA vibhAjita karate haiM / (isa kriyA meM prApta) zeSa ko (adhika bar3e samUha vAcaka mAna sambandhI) bhAjaka dvArA guNita karate haiM, aura pariNAmI guNanaphala meM isa adhikabar3e samUha vAcaka mAna ko jor3a dete haiN| (isa prakAra dI gaI samUha saMkhyA ke iSTa guNaka kA mAna prApta kiyA jAtA hai, jo do vicArAdhIna viziSTa vibhAjanoM kA samAdhAna karatA hai ) // 1156 // Aja isa vidhi kA bhUla bhUta siddhAnta ( rationale) nimnalikhita vimarza se spaSTa ho jAvegA( 1 ) bAka + bApUrNAka hai; ( 2 ) bAka + ba2 pUrNAka hai; aura ( 3 ) bAkapUrNAka hai / Ata Ara (1) meM mAnalo ka kA alpatama mAna%sa, hai| (2) meM mAnalo ka kA alpatama mAna % sara hai| (3) meM mAnalo ka kA alpatama mAna =sa, hai / ( 4 ) jaba (1) aura (2) donoM kA samAdhAna karanA par3atA hai, taba daA, + sa, ko kSaAra +sa, ke tulya honA par3atA hai, tAki sa,-sa, kSaA,-daA. ho: arthAta . 1112/ Ara =kSa, ho| ajJAta mAnavAlI rAziyoM da aura kSa sahita hone se anighRta (indeterminate) samIkaraNa (4) se, jaisA ki pahale hI siddha kiyA jA cukA hai usake anusAra, da ke alpatama dhanAtmaka pUrNAka ko prApta kara sakate haiN| da ke isa mAna ko A, dvArA guNita karane, aura taba sa, meM jor3ane para ka kA mAna prApta hotA hai jo (1) aura (2) kA samAdhAna karatA hai| mAnalo yaha ta, hai, aura ina donoM samIkAroM kA samAdhAna karane vAlA ka kA aura adhika bar3A mAna mAnalo tara hai| (5) aba, ta, +naA, ta, hai, (6) aura, ta, +maAra tara hai| .. Apa = ma . isa prakAra, A, = ma. pa, aura A3 = na. pa, jahA~ A, ora Ara kA Arana sabase bar3A sAdhAraNa guNanakhaMDa ( maha. samA.) pa hai| ::ma = Aga, aura na = Ara . (5) athavA (6) meM inakA mAna rakhane para, ta, + A, A2 = ta, hotA hai / isase spaSTa hai ki ka kA dUsarA uccatara mAna jo do samIkaraNoM kA samAdhAna karatA hai vaha A, aura Ara ke laghuttama samApavartya ko nimnatara mAna meM jor3ane para prApta hotA hai| phira se, mAnalo tInoM sabhI samokAroM kA samAdhAna karane vAle ka kA mAna va hai| taba, va = ta, + A A2 4ra, ( jahA~ ra ghanAtmaka pUrNAka hai ) = ( mAnalo) ta, + lara aura va = sa + A = ta, + la ra , .:. ra=Sa A + sa-ta, hogaa| pichale samIkAra meM vallikA kuTTIkAra ke siddhAnta kA prayoga karane para Sa kA mAna prApta ho jAtA

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[119 -6. 1203] mizrakagyavahAraH atroddezakaH jambUjambIrarambhAkramukapanasukharjUrahintAlatAlIpunnAgAmrAdyanekadrubhakusumaphalainamrazAkhAdhirUDham / bhrAmya gAjavApIzukapikakulanAnAdhvanivyAptadikka pAnthAH zrAntA vanAntaM zramanudamamalaM te praviSTAH prhRssttaaH|| 1163 // rAzitriSaSTiH kadalIphalAnAM saMpIDya saMkSipya ca saptabhistaiH / pAnthaitrayoviMzatibhirvizuddhA rAzestvamekasya vada pramANam // 117 // rAzIna punarvAdaza dADimAnAM samasya saMkSipya ca pazcabhistaiH / pAnthainaraiviMzatibhirnirekairbhaktAMstathaikasya vada pramANam // 1183 / / dRSTvAmrarAzIna pathiko yathaikatriMzatsamUhaM kurute trihInam / zeSe hRte saptatibhitrimitrairnarairvizuddhaM kathayaikasaMkhyAm / / 1193 // dRSTAH saptatriMzatkapitthaphalarAzayo vane pthikaiH| saptadazApohya hRte vyekAzItyAMzakapramANaM kim // 1203 // udAharaNArtha prazna kisI vana kA prakAzavAna aura tAjagI lAne vAlA sImAstha (outskirts ) bahuta se aise vRkSoM se pUrNa thA jinakI zAkhAyeM phala-phUla ke bhAra se nIce jhuka gaI thiiN| aise vRkSoM meM jambU, jambIra, rambhA, kramuka, panasa, khajUra, hintAla, tAlI, punnAga aura Ama (samAviSTa) the| vaha sthAna totoM aura koyaloM kI dhvani se vyApta thaa| tote aura koyaleM aise jharanoM ke kinAre para thIM jinameM kamaloM para bhramara bhramaNa kara rahe the| aise banAnta meM kucha thake hue yAtriyoM ne sAnanda praveza kiyA // 111 // keloM kI 63 DheriyA~ aura 7 kele ke phala 23 yAtriyoM meM barAbara-barAbara bA~Ta diye gaye jisase kucha bhI zeSa na bcaa| eka DherI meM phaloM kI saMkhyA btlaao|| 1171 // phira se, anAra kI 12 DheriyA~ aura 5 anAra ke phala uso taraha 19 yAtriyoM meM bA~Te gaye / eka DherI meM kitane anAra the? // 1981 // eka yAtrI ne AmoM kI barAbara phaloM vAlI DheriyA~ dekhiiN| 31 DheriyA~ 3 phaloM dvArA hAsita kara dI gii| jaba zeSaphala 73 vyaktiyoM meM barAbara-barAbara bA~Ta diye gaye to zeSa kucha bhI na rhaa| ina DheriyoM meM se kisI bhI eka meM kitane phala the? // 1193 // vanameM yAtriyoM dvArA 37 kapittha phala kI DheriyA~ dekhI gii| 17 phala alaga kara diye gaye zeSaphala 79 vyaktiyoM meM barAbara-barAbara bA~Tane para kucha bhI zeSa na rhaa| pratyeka ko kitane-kitane phala mile ? // 1201 // hai, aura taba va kA mAna saralatA pUrvaka nikAlA jA sakatA hai| isase yaha dekhA jAtA hai ki jaba va kA mAna nikAlane ke liye hama ta, aura sa ko kuTTIkAra vidhi ke anusAra bartate haiM; taba cheda athavA bhAjaka ko ta, ke sambandha meM A, A3 lenA par3atA hai; athavA, prathama do samIkAroM meM bhAjakoM ke laghuttama samApavartya ko lenA par3atA hai|

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120] gaNitasArasaMgrahaH [ 6. 1213dRSTvAmrarAzimapahAya ca sapta pazcAdbhakte'STabhiH punarapi pravihAya tasmAt / trINi trayodazabhiruddalite vizuddhaH pAnthairvane gaNaka me kathayaikarAzim // 1213 / / dvAbhyAM tribhizcaturbhiH paJcabhirekaH kpitthphlraashiH|| bhakto rUpAgrastatpramANamAcakSva gaNitajJa / / 1223 // dvAbhyAmekastribhiau ca caturbhirbhAjite trayaH / catvAri paJcabhiH zeSaH ko rAzirvada me priya // 1233 // dvAbhyAmekastribhizzuddhazcaturbhirbhAjite trayaH / catvAri pazcabhiH zeSaH ko rAzirvada me priya / / 1243 // dvAbhyAM nirana ekAgrastribhinAyo vibhAjitaH / caturbhiH paJcabhirbhakto rUpAyo rAzireSa kaH // 1253 / / dvAbhyAmekastribhiH zuddhazcaturbhi jite trayaH / niragraH paJcabhirbhaktaH ko rAziH kathayAdhunA // 1266 / / dRSTA jambUphalAnAM pathi pathikajanai rAzayastatra rAzI dvau tryagrau tau navAnAM traya iti punarekAdazAnAM vibhaktAH / pazcAprAste yatInAM caturadhikatarAH paJca te saptakAnAM kaTIkArArthavinme kathaya gaNaka saMcintya rAzipramANama // 1271 // vanAntare dADimarAzayaste pAnthaistrayaH sptbhirekshessaaH| sapta trizeSA navabhirvibhaktAH pazcASTabhiH ke gaNaka dviraprAH // 1283 // vana meM AmoM kI DheriyA~ dekhane ke bAda aura unameM 7 phala nikAlane ke pazcAt unheM 8 yAtriyoM meM barAbara-barAbara bA~Ta diyA gayA / aura jaba, phira se, unhIM DheriyoM meM se 3 phala nikAla liye gaye taba unheM 13 yAtriyoM meM bA~Ta diyA gyaa| donoM dazAoM meM kucha bhI zeSa na rahA / he gaNitajJa ! isa kevala eka DherI kA saMkhyAtmaka mAna (phaloM kI saMkhyA) batalAo // 1.13 // kapittha phaloM kI kevala eka DherI ke phaloM ko 2, 3, 4 athavA 5 manuSyoM meM vibhAjita karane para pratyeka dazA meM zeSa 1 bacatA hai / he gaNita vettA ! usa DherI meM phaloM kI saMkhyA batalAo // 1223 // jaba 2 dvArA bhAjita ho taba zeSa 1 rahatA hai, jaba 3 dvArA bhAjita ho taba zeSa 2, jaba 4 dvArA taba zeSa 3, jaba 5 dvArA taba zeSa 4 hai| he mitra ! aisI DherI meM kitane phala haiM ? // 123 // jaba 3 dvArA bhAjita ho taba zeSa 1 hai, jaba 3 dvArA taba zeSa kucha nahIM hai, jaba 4 dvArA taba zeSa hai, jaba 5 dvArA taba zeSa 4 hai / DherI kA saMkhyAtmaka mAna batalAo // 124 // jaba 2 dvArA bhAjita ho taba zeSa kucha nahIM hai, jaba 3 dvArA taba zeSa 1, jaba 4 dvArA taba zeSa kucha nahIM haiN| aura jaba 5 dvArA bhAjita ho taba zeSa 1 rahatA hai / yaha rAzi kyA hai ? // 1251 // jaba 2 dvArA bhAjita ho taba zeSa 1 hai, jaba 3 dvArA taba zeSa kucha nahIM hai, jaba 4 dvArA taba zeSa 3, aura jaba 5 dvArA bhAjita ho taba zeSa kucha nahIM hai| yaha rAzi kauna hai ? // 126 // rAste meM yAtriyoM ne jambU phaloM kI kucha barAbara DheriyA~ dekhiiN| unameM se 2 DheriyA~ 9 sAdhuoM meM barAbara-barAbara bA~Tane para 3 phala zeSa rahe / phira se, 3 DheriyA~ isI prakAra 11 vyaktiyoM meM bA~Tane para 5 phala zeSa bace, punaH 5 DheriyoM ko 7 vyaktiyoM meM barAbara bA~Tanepara zeSa 4 phala bace / he vibhAjana kI kuTTIkAra vidhi ko jAnane vAle aMkagaNitajJa ! ThIka taraha socakara DherI kA saMkhyAtmaka mAna batalAo // 1273 // vana ke antara meM anAra kI 3 barAbara DheriyA~ 7 yAtriyoM meM barAbara bA~Ta dene para 1 phala zeSaphala hai. aisI DheriyA~ usI prakAra 9 meM bA~Tane para zeSa 3 phala, aura punaH 5 aisI DheriyA~ 8 meM bA~Ta dene para 2 phala bacate haiN| he aMkagaNitajJa ! pratyeka kA saMkhyAtmaka mAna batalAo // 128 //

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-6. 1303] mizrakavyavahAraH [121 lyA vAlI cha na rhaa| aura bhaktA dviyuktA navabhistu paJca yuktAzcaturbhizca SaDaSTabhistaiH / pAnthairjanaiH saptabhirekayuktAzcatvAra ete kathaya pramANam // 1293 / / _ agrazeSavibhAgamUlAnayanasUtramzeSAMzAavadho yuk svAgreNAnyastadaMzakena guNaH / yAvadbhAgAstAvadvicchedAH syustdgrgunnaaH||1303|| samAna phaloM kI saMkhyA vAlI 5 DheriyA~ thIM, jinameM 2 phala milAne ke pazcAt 9 yAtriyoM meM bA~Tane para kucha na rahA / 6 aisI DheriyoM meM 4 phala milAne ke pazcAt usI prakAra 8 meM bA~Tane para, aura 4 DheriyoM meM 1 phala milAkara usI prakAra 7 meM bA~Tane para zeSa kucha na rhaa| DherI kA saMkhyAtmaka mAna batalAo // 1293 // icchAnusAra vitarita mUla rAzi ko nikAlane ke liye niyama, jaba ki kucha viziSTa jJAta rAziyoM ko haTAne para zeSa ko prAsa kiyA jAtA hai : haTAI jAne vAlI ( dI gaI)jJAna rAzi aura ( dI gaI jJAta rAzi ko de cukane para) jo zeSa viziSTa bhinnIya bhAga baca rahatA hai usakA bhinnIya samAnupAta-ina donoM kA guNanaphala prApta karo / isake bAda ko rAzi, isa guNanaphala meM pichale zeSa meM se nikAlI jAne vAlI viziSTa jJAta rAzi ko jor3akara prApta kI jAtI hai / aura, isa pariNAmI yoga ko usI prakAra ke Upara kathita zeSa ke zeSa rahane vAle bhinnIya samAnupAta dvArA guNita kiyA jAtA hai| yaha utane bAra karanA par3atA hai jitane ki vitaraNa karane par3ate haiN| tatpazcAt isa taraha prApta rAziyoM ke haroM ko alaga kara denA caahiye| hara rahita rAziyoM aura zeSa ke Upara kathita zeSa rahane vAle bhinnIya samAnupAta ke uttarottara guNanaphaloM ko jJAta rAzi aura (anya tatva, jaise, ajJAta rAzi kA guNAMka) apavartya ( tathA bhAjaka ke nAma se vallikA kuTTokAra ke prazna meM) upayoga meM lAte haiM // 1303 // (1302) yahA~ haTAI jAne vAlo jJAta rAzi agra kahalAtI hai| aba ke haTAne ke pazcAt jo baca rahatA hai vaha zeSa' kahalAtA hai| jo diyA athavA liyA jAtA hai aise zeSa ke bhinna ko agrAMza kahate haiM, aura agrAMza ke diye athavA liye jAnepara jo zeSa baca rahatA hai vaha zeSAMza athavA zeSa kA zeSa rahanevAlA bhinnIya samAnupAta kahalAtA hai, jaise, jahA~ ka kA mAna nikAlanA par3atA hai, aura 'a' vibhAjita hue bhinnIya samAnupAta 3 ko lekara prathama vibhAjana sambandhI agra hai, vahA~ agrAMza hai aura ( ka - 4 )- zeSAMza hai / 1322 - 1336 vI gAthA ke prazna ko hala karane para yaha niyama spaSTa ho jAvegA yahA~ 1 pahilA agra hai, aura / pahilA agrAMza hai; isaliye ( 1 - ) yA 3 zeSAMza hai / aba, agra aura zeSAMza kA guNanaphala 14 yA 3 hai / ise do sthAnoM meM likho, yathA .................................... aba rAziyoM, {2/3 } kI punarAvRtti karo; kisI eka rAzi meM dUsare agra 1 ko jor3a do / taba hameM {2/31 prApta hotA hai / donoM ko dUsare zeSAMza arthAt 1 - 3 yA 3 dvArAguNita karo, tAki {19/9 } prApta ho|...... .............(2) ina aMkoM ko lekara pahile kI taraha tIsare agra 1 ko jor3o jisase 1199 / prApta hogA / ga0 sA0 saM0-16 /B .

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122] gaNitasArasaMgrahaH [ 6. 1313 atroddezakaH AnItavatyAmraphalAni puMsi prAgekamAdAya punastadardham / gate'graputre ca tathA jaghanyastatrAvazeSArdhamatho tamanyaH // 1313 / / pravizya jainaM bhavanaM tripUruSaM prAgekamabhyarcya jinasya paade'| zeSatribhAgaM prathame'numAne tathA dvitIye ca tRtIyake tathA // 1323 // zeSatribhAgadvayatazca zeSatryaMzadvayaM cApi tatastribhAgAn / kRtvA caturviMzatitIrthanAthAna samarcayitvA gatavAn vizuddhaH // 1333 / iti mizrakavyavahAre sAdhAraNakuTTIkAraH samAptaH / 1. hastalipi meM pAdau zabda hai jo yahA~ zuddha pratIta nahIM hotA hai| B meM pAde ke liye ke jJAn pATha hai| udAharaNArtha prazna kisI manuSya dvArA ghara para Amra phaloM ko lAne para usake bar3e putra ne pahile eka phala liyA aura taba zeSa ke Adhe liye| bar3e lar3ake ke jAne para, choTe lar3ake ne bhI zeSa meM se usI prakAra phala liye / ( usane, tatpazcAt , jo zeSa rahA usakA AdhA liyA ); aura anya putra ne zeSa Adhe liye| pitA ke dvArA lAye hae phaloM kI saMkhyA nikaalo| // 1313 // koI manuSya phUla lekara aise jinamaMdira meM gayA jo manuSya kI U~cAI se tigunA U~cA thaa| pahile usane ina phUloM meM se pUjana meM jina bhagavAn ke caraNoM meM eka phUla car3hAyA, aura taba pUjana meM zeSa phUloM ke eka tihAI jina bhagavAn kI prathama U~cAI-mApa vAlI pratimA ke caraNoM meM bheMTa kiye| zeSa do tihAI phUloM meM se usane usI prakAra dvitIya U~cAI-mApa vAlI pratimA ke caraNoM meM bheMTa kiye, aura taba usI prakAra tIsarI U~cAI-mApa vAlI pratimA ke caraNoM meM bheMTa kiye| aMta meM jo do tihAI bace ve bhI tIna barAbara bhAgoM meM bA~Te gaye; aura ina bhAgoM meM se eka-eka bhAga ATha-ATha tIrthaMkaroM ko (isa prakAra kula 24 tIrthaMkaroM ko) bheMTa karane para usake pAsa eka bhI phUla na bcaa| batalAo usake pAsa kitane phUla the? // 1322-1333 // isa prakAra, mizraka vyavahAra meM, sAdhAraNa kuTTIkAra nAmaka prakaraNa samApta huaa| dUsare zeSAMza 1- yA dvArA aura antima za yA dvArA guNita karo jisase TATa prApta / 8/81 hogaa|........... ...........(3) (1), (2), (3) dvArA darzAye gaye bhinnoM kI ina tIna rAziyoM meM prathama bhinnoM ke haroM ko alaga kara dete haiM, aura za vallikA kuTTIkAra meM RNAtmaka agra nirUpita karate haiM jahA~ una rAziyoM meM dUsare bhinnoM meM se pratyeka aMza aura hara kramazaH bhAjya, guNaka aura bhAjaka kA nirUpaNa karate haiM / isa 8 ka-38 prakAra, pUrNAka prApta hote haiM / ina tIna dazAoM 4kaUmar. . .pUNAkA aura 81 ko samAdhAnita karanevAlA ka kA mAna, phUloM kI saMkhyA hotI hai|

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-6. 1353] mizrakavyavahAraH [123 viSamakuTTIkAraH itaH paraM viSamakaTokAra vyAkhyAsyAmaH / viSamakuTrIkArasya sUtramamatisaMguNitau chedau yojyonatyAjyasaMyutau rAzihRtau / bhinne kuTTIkAre guNakAro'yaM samuddiSTaH / / 1343 / / atroddezakaH rAziH SaTkena hato dazAnvito navahato niravazeSaH / dazabhirdAnazca tathA tadguNako' ko mamAzu saMkathaya / / 1353 / / 1. B gunnkaarau| viSama kuTTIkAra* isake pazcAt hama viSama kuTTIkAra ko vyAkhyA kareMge / viSama kuTTIkAra sambandhI niyama : diyA huA bhAjaka do sthAnoM meM likha liyA jAtA hai, aura pratyeka sthAna meM mana se cunI huI saMkhyA dvArA guNita kiyA jAtA hai| (isa prazna meM ) jor3ane ke liye dI gaI (jJAta) rAzi ina sthAnoM ke kisI eka guNanaphala meM se ghaTAI jAtI hai| ghaTAI jAne ke liye dI gaI rAzi anya sthAna meM likhe hue guNanaphala meM jor3a dI jAtI hai| isa prakAra prApta donoM rAziyA~ (praznAnusAra vibhAjita kI jAne vAlI ajJAta rAziyoM ke ) jJAta guNAMka (guNaka) dvArA bhAjita kI jAtI haiN| isa taraha prApta pratyeka bhajanaphala iSTa rAzi hotI hai, jo bhinna kuTTIkAra kI rIti meM diye gaye guNaka dvArA gaNita kI jAtI hai / // 134 // udAharaNArtha prazna koI rAzi 6 dvArA guNita hokara, taba 10 dvArA bar3hAI jAkara aura taba 9 dvArA bhAjita hokara kucha bhI zeSa nahIM chodd'tii| isI prakAra, ( koI dUsarI rAzi 6 dvArA guNita hokara ), taba 10 dvArA hAsita hokara ( aura taba 9 dvArA bhAjita hokara ) kucha zeSa nahIM chodd'tii| una do rAziyoM ko zIghra batalAo ( jo diye gaye guNaka se yahA~ isa prakAra guNita kI jAtI haiM / ) // 1353 // isa prakAra, mizraka vyavahAra meM, viSama kuTTIkAra nAmaka prakaraNa samApta huaa| * viSama aura bhinna donoM zabda kuTTIkAra ke saMbaMdha meM upayoga meM lAye gaye haiM aura donoM ke spaSTataH eka se artha haiN| ye ina niyamoM ke praznoM meM Ane vAlI bhAjya (dividend) rAziyoM ke bhinnIya rUpa ko nirdezita karate haiN|

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124] gaNitasArasaMgrahaH [6.136:sakalakuTTIkAraH sakalakuTTIkArasya sUtrambhAjyacchedAnazeSaiH prathamahRtiphalaM tyAjyamanyonyabhaktaM nyasyAnte sAgramUrdhvarupariguNayutaM taiH samAnAsamAne / svarNanaM vyAptahArau guNadhanamRNayozcAdhikAgrasya hAraM hRtvA hRtvA tu sAmAntaradhanamadhikAgrAnvitaM hAraghAtam // 1363 / / sakala kuTTIkAra sakala kuTTIkAra sambandhI niyama : vibhAjita kI jAne vAlI ajJAta rAzi ke bhAjya guNaka dvArA agranayanita (carried on) tathA bhAjaka aura uttarottara pariNAmI zeSoM dvArA agranayanita bhAjanoM meM prathama ke bhajanaphala ko alaga kara diyA jAtA hai| isa pArasparika bhAjana dvArA, jo ki bhAjaka aura zeSa ke samAna ho jAne taka kiyA jAtA hai, anya bhajanaphala prApta kiye jAte haiM, jo UrdhvAdhara zrRMkhalA meM antima tulya zeSa aura bhAjaka ke sAtha likhe jAte haiM / isa zrRMkhalA ke nimnatama aMka meM bhAjaka dvArA vibhAjita kI gaI jJAta rAzi se prApta zeSa ko jor3anA par3atA hai| (taba, zrRMkhalA meM ina saMkhyAoM dvArA,) vaha yoga prApta karate hai, jo uttarottara nimnatama saMkhyA meM usake ThIka Upara kI do saMkhyAoM kA guNanaphala jor3ane para prApta hotA hai / (yaha vidhi taba taka kI jAtI hai jaba taka ki zrRMkhalA kA uccatama aMka bhI kriyA meM zAmila nahIM ho jaataa|) usake bAda yaha pariNAmI yoga aura prazna meM diyA gayA bhAjaka, do zeSoM ke rUpa meM, ajJAta rAzi ke do mAnoM ko utpanna karatA hai| isa rAzi ke mAnoM ko prazna meM diye gaye bhAjya guNaka dvArA guNita kiyA jAtA hai| isa prakAra prApta hone vAle do mAna yA to jor3I jAne vAlI dI gaI jJAta rAzi se sambandhita rahate haiM athavA ghaTAI jAne vAlI dI gaI jJAta rAzi se sambandhita rahate haiM, jaba ki Upara kathita bhajanaphaloM kI zrRMkhalA kI aMka paMkti kI saMkhyA kramazaH yugma athavA ayugma hotI hai| (jahA~ diye gaye samUha eka se adhika prakAra se bar3hAye jAne para athavA ghaTAye jAne para eka se adhika anupAta meM vitarita kiye jAnA hote haiM vahA~ ) adhika bar3e samUhamAna se sambandhita bhAjaka (jise Upara samajhAye anusAra do viziSTa vibhAjanoM meM se kisI eka ke sambandha meM prApta kiyA jAtA hai) ko Upara ke anusAra bAra-bAra choTe samUha mAna se saMbaMdhita bhAjaka dvArA bhAjita kiyA jAtA hai, tAki uttarottara bhajanaphaloM kI latA samAna zrRMkhalA isa dazA meM bhI prApta ho sake / isa zrRMkhalA ke nimnatama bhajanaphala ke nIce isa aMtima uttarottara bhAga meM ayugma sthiti kramavAle alpatama zeSa ke mana se cune hue guNaka ko rakhA jAtA hai| phira isake nIce vaha saMkhyA rakhI jAtI hai, jo do samUha-mAnoM ke aMtara ko Upara kathita mana se cune hue guNaka se guNita ayugya sthiti kramavAle alpatama zeSa ke guNanaphala meM jor3anepara, aura taba isa pariNAmI yoga ko Upara kI bhAjana zrRMkhalA ke aMtima bhAjaka dvArA bhAjita karane para prApta hotI hai| isa prakAra latA sadRza aMkoM kI zrRMkhalA prApta hotI hai, jisakI AvazyakatA isa pichale prakAra ke prazna ke sAdhana ke liye hotI hai| yaha zrRMkhalA nIce se Upara taka pahile kI bhA~ti bartI jAtI hai, aura pariNAmI saMkhyA pahile kI taraha isa aMtima bhAjana zrRMkhalA meM prathama bhAjaka dvArA bhAjita kI jAtI hai| isa kriyA se prApta zeSa ko adhika bar3e samUha-mAna se sambandhita bhAjaka dvArA guNita kiyA jAnA cAhiye / pariNAmI guNanaphala meM yaha adhika bar3A samUhamAna jor3a denA caahiye| ( isa prakAra, diye gaye samUhamAna ke iSTa guNaka kA mAna prApta karate haiM tAki vaha vicArAdhIna do ullikhita vibhAjanoM kA samAdhAna kare ) / 136 // (1363 ) yaha niyama 1373 vI gAthA meM diye gaye prazna ko hala karane para spaSTa ho jAvegA

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67 -6. 1373] mizrakavyavahAraH [ 125 atroddezakaH saptottarasaptatyA yutaM zataM yojyamAnamaSTatriMzat / saikazatadvayabhaktaM ko guNakAro bhavedatra // 1373 // udAharaNArtha prazna ajJAta guNanakhaMDa kA bhAjya (dividend ) guNaka 177 hai| 240, sva meM jor3e jAnevAle athavA ghaTAye jAne vAle guNanaphala se sambandhita jJAta rAzi hai; pUrI rAzi ko 201 dvArA bhAjita karane para zeSa kucha nahIM rhtaa| yahA~ ajJAta guNanakhaNDa kauna sA hai, jisase kI diyA gayA bhAjyaguNaka guNita kiyA jAnA hai ? // 1371 // 35 aura anya rAziyA~, jo saMkhyA meM 16 haiM, aura uttarottara mAna prazna hai ki jaba 177 ka 24deg pUrNAka hai to ka ke mAna kyA hoMge? sAdhAraNa guNana khaMDoM ko nirasita 201 karane para hameM 57 58deg pUrNAMka prApta hotA hai| lagAtAra kiye jAne vAle bhAga kI iSTa vidhi ko nimnalikhita rUpa meM kAryAnvita karate haiM67)590 prathama bhajanaphala ko alaga kara, anya bhajanaphala, zrRMkhalA meM isa prakAra likhe jAte haiM59)67(1 __ isake nIce 1 aura 1 ko agrima likhA jAtA hai| ye antima bhAjaka aura zeSa 8)59(7 samAna hote haiN| yahA~ bhI jaisA ki vallikA 3)8(2 kuTTIkAra meM hotA hai, yaha dekhane yogya hai ki 1+13-14 antima bhAjana meM koI zeSa nahIM rahatA kyoMki 2)3(1 2 meM 1 kA pUrA-pUrA bhAga calA jAtA hai| parantu cU~ki, antima zeSa, zrRMkhalA ke liye cAhiye, 1)2(1 isaliye vaha antima bhajanaphala choTA se choTA banAkara rakha diyA jAtA hai, aura antima saMkhyA 1 meM yahA~, 13 jor3ate haiM, jo ki 80 meM se 67 kA bhAga dene para prApta hotA hai| isa prakAra 14 prApta kara, use zrRMkhalA ke anta meM nIce likha diyA jAtA hai| isa prakAra zrRMkhalA parI ho jAtI hai / isa zrRMkhalA ke aMkoM ke lagAtAra kiye gaye guNana aura jor3a dvArA, (jaisA ki gAthA 115 ke noTa meM pahile hI samajhAyA jA cukA hai,) hameM 392 prApta hotA hai| ise 67 dvArA vibhAjita kiyA jAtA hai| zeSa 57 ka kA eka mAna hotA hai, jaba ki 80 ko zrRMkhalA meM aMkoM kI saMkhyA ayugma hone ke kAraNa RNAtmaka le liyA jAtA hai| parantu jaba 80 ko dhanAtmaka liyA jAtA hai, taba ka kA mAna (67-57) athavA 10 hotA hai| yadi zrRMkhalA meM aMkoM kI saMkhyA yugma hotI hai, to ka kA prathama 7-345 nikAlA huA mAna dhanAtmaka agra sambandhI hotA hai| yadi yaha mAna bhAjaka meM se 2-47 1-16 ghaTAyA jAtA hai to ka kA RNAtmaka agra sambandhI mAna prApta hotA hai| 1-15 isa vidhi kA siddhAnta usI prakAra hai jaisA ki vallikA kuTTIkAra ke sambandha meM hai| parantu, unameM antara yahI hai ki yahA~ zrRMkhalA meM do antima aMka dUsarI vidhi dvArA prApta kiye jAte haiN| adhyAya 6 kI 115:vI gAthA ke niyama ke noTa

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126] gaNitasArasaMgrahaH [ 6. 1383 pazcatriMzat vyuttaraSoDazapadAnyeva hArAzca / dvAtriMzadvyadhikaikA vyuttarato'grANi ke dhanarNaguNAH / / 1383 / / meM 3 dvArA bar3hatI huI haiM, datta bhAjyaguNaka haiM / diye gaye bhAjaka, 32 ( aura anya ) haiM, jo uttarottara 2 dvArA bar3hate jAte haiM / aura, 1 ko uttarottara 3 dvArA bar3hAte jAne para jJAta dhanAtmaka aura RNAtmaka sambandhita rAziyA~ utpanna hotI haiM / jJAta bhAjya-guNaka ke ajJAta guNanakhaNDoM ke mAna kyA haiM jabaki ve dhanAtmaka yA RNAtmaka jJAta saMkhyAoM ke sAtha yogarUpa se sambandhita haiM ? // 1383 // meM diye gaye mUlabhUta siddhAnta meM ayugma sthiti krama vAle zeSa ke sAtha sambandhita agra ba kA bIjIya cinha vahI hai jo isa prazna meM diyA gayA hai, parantu yugma sthiti kramavAle zeSa ke sAtha sambandhita agra va kA cinha prazna meM jaisA diyA gayA hai usake viparIta hai; isaliye jaba ayugma sthiti kramavAle, zeSa taka lagAtAra bhAjana kiyA jAtA hai taba prApta ka kA mAna usa agra ke sambandha meM hotA hai jisakA cinha aparivartita hai| aura dUsarI ora, jaba lagAtAra bhAjana yugma sthiti kramavAle zeSa taka le jAyA jAtA hai taba vahA~ se prApta ka kA mAna usa agra ke sambandha meM hotA hai jisakA cinha parivartita hai / jaba prApta zeSoM kI saMkhyA ayugma hotI hai, taba zrRMkhalA meM bhajanaphaloM kI saMkhyA yugma hotI hai; aura jaba zeSoM kI saMkhyA yugma hotI hai, taba zrRMkhalA meM bhajanaphaloM kI saMkhyA ayugma hotI hai| kAraNa yaha hai ki isa niyama meM antima zeSa se sambandhita agra hamezA dhanAtmaka liyA jAtA hai, isaliye isa dhanAtmaka agra ke sambandha meM ka kA mAna prApta hotA hai jaba ki aMtima zeSa ayugma sthiti kramameM ho| vaha RNAtmaka agra ke sambandha meM taba prApta hotA hai jaba ki aMtima zeSa yugma sthiti krama meM ho| dUsare zabdoM meM, yadi bhajanaphaloM kI saMkhyA yugma ho, taba dhanAtmaka agra sambandhI mAna prApta hotA hai; aura jaba bhajanaphaloM kI saMkhyA ayugma ho, taba RNAtmaka agra sambandhI mAna prApta hotA hai| isa prakAra, dhanAtmaka aura RNAtmaka agroM ke sambandha meM ka kA mAna prApta karane para dUsarA mAna, isa mAnako prazna ke bhAjaka meM se ghaTAkara prApta karate haiN| yaha nimnalikhita nirUpaNa se spaSTa ho jAvegA:- 4-eka pUrNAka / yahA~ mAnalo ka=Sa: taba, : na ASa+ba - - = eka pUrNAMka / hama bA jAnate haiM ki bhA bhI eka pUrNAka hai / isaliye bAbA jAnate haiM ki AbA sIpako AbA - ASa + bA A (bA-Sa)-ba. " ' bA eka pUrNAka hai / yahA~ yaha dekhane yogya hai, ki tInoM dI gaI saMkhyAtmaka rAziyoM ke sAdhAraNa guNanakhaMDoM ko lagAtAra bhAjana ke Arambha karane ke pUrva hI haTA dete haiM / aMtima bhAjaka aura aMtima zeSa barAbara honA cAhiye isaliye ina meM se pratyeka 1 hotA hai / 'mati' jise vallikA kuTTIkAra ke sambandha meM niyamAnusAra cunanA par3atA hai, aura bhajanaphaloM kI zrRMkhalA ke nIce likhanA par3atA hai, vaha isa niyama meM hamezA 1 rahatI hai| aMtima bhAjaka bhI 1 hotA hai| isaliye vallikA kuTTIkAra meM 'mati' yahA~ aMtima bhAjaka kA sthAna le letI hai| isake bAda dekhA jAyagA ki isa niyama dvArA prApta aMkhalA kA aMtima aMka (1+ agra) utanA hI rahatA hai jitanA ki vallikA kuTTIkAra meM prApta zrRMkhalA kA aMtima aMka / yaha aMtima aMka, aMtima bhAjaka ko agra tathA mati aura aMtima zeSa ke guNanaphala ke yoga dvArA vibhAjita karane para prApta karate haiM / yathA, aMtima aMka = [ aMtima bhAjaka ] + { agra+(mati 4 aMtima zeSa )} bA

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-6. 1433 ] mizrakavyavahAraH [ 127 adhikAlparAzyormUlamizravibhAgasUtramjyeSThanamahArAzerjaghanyaphalatADitonamapanIya / phalavargazeSabhAgo jyeSThA?'nyo guNasya viparItam / / 1393 / / atroddezakaH navAnAM mAtuluGgAnAM kapitthAnAM sugandhinAm / saptAnAM mUlyasaMmizraM saptottarazataM punaH // 1403 / / saptAnAM mAtuluGgAnAM kapitthAnAM sugandhinAm / navAnAM mUlyasaMmizramekottarazataM punaH / / 1413 // mUlye te vada me zIghraM mAtuluGgakapitthayoH / anayogaNaka tvaM me kRtvA samyak pRthak pRthak / / 1422 / / bahurAzimizratanmUlyamizravibhAgasUtramiSTanaphalairUnitalAbhAdiSTAptaphalamasakRt / tairUnitaphalapiNDastacchedA guNayutAstadarghAH syuH // 1433 / / bar3I aura choTI saMkhyAoM vAlI vastuoM kI komatoM ke diye gaye mizra yogoM meM se do bhinna vastuoM kI vinimayazIla bar3I aura choTI saMkhyA kI kImatoM ko alaga-alaga karane ke liye niyama do prakAra kI vastuoM meM se kisI eka kI saMvAdI bar3I saMkhyA dvArA guNita uccatara mUlya-yoga meM se do prakAra kI vastuoM meM se anya sambandhI choTI saMkhyA dvArA guNita nimnatara mUlya-saMkhyA ghttaao| taba, pariNAma ko ina vastuoM sambandhI saMkhyAoM ke vargoM ke antara dvArA bhAjita kro| isa prakAra prApta phala adhika saMkhyA vAlI vastuoM kA mUlya hotA hai| dUsarA arthAt choTI saMkhyA vAlI vastu kA mUlya guNakoM ( multipliers) ko paraspara badala dene se prApta ho jAtA hai // 139 // . udAharaNArtha prazna 9 mAtuluGga ( citron ) aura 7 sugandhita kapittha phaloM kI mizrita kImata 107 hai / punaH 7 mAtuluGga aura 9 sugandhita kapistha phaloM kI kImata 101 hai| he aMkagaNitajJa ! mujhe zIghra batAo ki eka mAtuluGga aura eka kapittha ke dAma alaga-alaga kyA haiM ? // 140-1423 // diye gaye mizrita mUlyoM aura diye gaye mizrita mAnoM meM se vibhinna prakAra kI vastuoM ke vibhinna mizrita parimANoM kI saMkhyAoM aura mUlyoM kI alaga-alaga karane ke liye niyama (vibhinna vastuoM kI) dI gaI vibhinna mizrita) rAziyoM ko mana se cunI huI saMkhyA dvArA guNita kiyA jAtA hai| ina mizrita rAziyoM ke diye gaye mizrita mUlya ko ina guNanaphaloM ke mAnoM dvArA alaga alaga hAsita kiyA jAtA hai| eka ke bAda dUsarI pariNAmI rAziyoM ko mana se cunI huI saMkhyA dvArA bhAjita kiyA jAtA hai aura zeSoM ko phira se mana se cunI huI saMkhyA dvArA bhAjita kiyA jAtA hai / isa vidhi ko bArabAra duharAnA par3atA hai| vibhinna vastuoM kI dI gaI mizrita rAziyoM ko uttarottara UparI vidhi meM saMvAdI bhajanaphaloM dvArA hAsita kiyA jAtA hai| isa prakAra, mizrayogoM meM vibhinna vastuoM ke saMkhyAtmaka mAnoM ko prApta kiyA jAtA hai| mana se cune hue gukI ( multipliers) ko uparyukta lagAtAra bhAga kI vidhi vAle mana se cune hue bhAjakoM meM milAne se prApta rAziyA~ tathA ukta guNaka bhI dI gaI vibhinna vastuoM ke prakAroM meM se kramazaH pratyeka kI eka vastu ke mUlyoM kI saMracanA karate haiM / // 1433 // (1393) bIjIya rupa se, yadi aka+ba kha=ma, aura ba ka + akha na ho, taba aka+a ba kha = ama aura baka+a ba kha =ba na hote haiN| ::.ka (a2 -ba2)=ama-bana, athavA, ka-ama-bana , aba hotA hai| ( 1433 ) gAthAoM 1443 aura 1453 ke prazna ko nimnalikhita prakAra se sAdhita karane para

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gaNitasArasaMgrahaH 128] atroddezakaH atha mAtuluGgakadalIkapitthadADimaphalAni mizrANi / prathamasya saikaviMzatiratha dviramA dvitIyasya // 1443 / / viMzatiratha surabhINi ca punastrayoviMzatistRtIyasya / teSAM mUlyasamAsastrisaptatiH kiM phalaM ko'rghaH // 1453 / / -- udAharaNArtha prazna yahA~, 3 DheriyoM meM sugandhita mAtuluGga, kadalo, kapistha aura dADima phaloM ko ikaTThA kiyA gayA hai| prathama DherI meM 21, dUsarI meM 22, aura tIsarI meM 23 haiN| ina DheriyoM meM se pratyeka kI mizrita kImata 73 hai| pratyeka DherI meM vibhinna phaloM ko saMkhyA aura bhinna prakAra ke phaloM kI kImata nikaalo| // 1443 aura 1453 // niyama spaSTa ho jaavegaa| prathama DherI meM phaloM kI kula saMkhyA 21 hai| dUsarI " " " " 22 hai / tIsarI" " " " 23 hai| mana se koI bhI saMkhyA jaise, 2 cunane para aura usase ina kula saMkhyAoM ko guNita karane para hameM 42, 44, 46 prApta hote haiN| inheM alaga-alaga DheriyoM ke mUlya 73 meM se ghaTAne para zeSa 31, 29 aura 67 prApta hote haiN| inheM mana se cunI huI dUsarI saMkhyA 8 dvArA bhAjita karane para bhajanaphala 3,3,3 aura zeSa 7,5 aura 3 prApta hote haiN| ye zeSa, punaH, mana se cunI huI saMkhyA 2 dvArA bhAjita honepara bhajanaphala 3, 2, 1 aura zeSa 1, 1, 1 utpanna karate haiN| ina aMtima zeSoM ko yahA~ mana se cunI huI saMkhyA 1 dvArA bhAjita karane para bhajanaphala 1, 1, 1 prApta hote haiM aura zeSa kucha bhI nhiiN| pahilI kula saMkhyA ke sambandha meM nikAle gaye bhajanaphaloM ko usameM se ghaTAnA par3atA hai| isa prakAra hameM 21-(3+3+1) = 14 prApta hotA hai| yaha saMkhyA aura bhajanaphala 3, 3, 1 prathama DherI meM bhinna prakAroM ke phaloM kI saMkhyA prarUpita karate haiN| isI prakAra, hameM dUsare samUha meM 16, 3, 2, 1 aura tIsare samUha meM 18, 3, 1,1 vibhinna prakAra ke phaloM kI saMkhyA prApta hotI hai| prathama cunA huA guNaka 2, aura usake anya mana se cune hue guNakoM ke yoga kImateM hotI hai| isa prakAra, hameM krama se ina 4 bhinna prakAroM ke phaloM meM pratyeka kI kImata 2,2+8 yA 10,2+2 yA 4, aura 2+1 yA 3, rUpa meM prApta hotI hai / isa rIti kA mUlabhUta siddhAnta nimnalikhita bIjIya nirUpaNa dvArA spaSTa ho jAvegAaka+va kha+ sa ga+Da gha pa,"""" ......................"(1) ......................../ a + ba+ sa + ha na,.... ...........(2) mAnalo ghaza; taba (2) ko za se guNita karane para hameM za (a+basa+Da)= zana .................(3) prApta hotA hai / .......... (3) ko (1) meM se ghaTAne para hameM a (ka-za)+ba (kha-za)+sa (ga-za)=pa-zana prApta hotA hai| ....... ...."(4) .. . . ... . ..

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-6. 149] mizrakanyavahAraH [129 jaghanyonamilitarAzyAnayanasUtrampaNyahRtAlpaphalonaizchindyAdalpannamUlyahIneSTam / kRtvA tAvatkhaNDaM tadUnamUlyaM jaghanyapaNyaM syAt / / 1463 / / atroddezakaH dvAbhyAM trayo mayUrAstribhizca pArAvatAzca catvAraH / haMsAH paJca caturbhiH paJcabhiratha sArasAH SaT ca / / 1473 / / yatrArghastatra sakhe SaTapaJcAzatpaNaiH khagAn krItvA / dvAsaptatimAnayatAmityuktvA mUlamevAdAt / katibhiH paNestu vihagAH kati vigaNayyAzu jAnIyAH / / 149 / / kula kImata ke diye gaye mizrita mAna meM se, kramazaH, ma~hagI aura sastI vastuoM ke mUlyoM ke saMkhyAtmaka mAnoM ko nikAlane ke liye niyama - (dI gaI vastuoM kI dara-rAziyoM ko) unakI dara-kImatoM dvArA bhAjita kro| ( ina pariNAmI rAziyoM ko alaga-alaga) unameM se alpatama rAzi dvArA hvAsita kro| taba ( uparyukta bhajanaphala rAziyoM meM se ) alpatama rAzi dvArA saba vastuoM kI mizrita kImata ko guNita karo; aura ( isa guNanaphala ko) vibhinna vastuoM kI kula saMkhyA meM se ghttaao| taba (isa zeSa ko mana se) utane bhAgoM meM vibhakta karo ( jitane ki ghaTAne ke pazcAt bace hue uparyukta bhajanaphaloM ke zeSa hote haiN)| aura taba, ( ina bhAgoM ko una bhajanaphala rAziyoM ke zeSoM dvArA ) bhAjita karo / isa prakAra, vibhinna sastI vastuoM kI kImateM prApta hotI haiN| inheM kula kImata se alaga karane para kharIdI huI mahaMgI vastu kI kImata prApta hotI hai // 146 // udAharaNArtha prazna "2 paNa meM 3 mora, 3 eNa meM 4 kabUtara, 4 paNa meM 5 haMsa, aura 5 paNa meM 6 sArasa kI daroM ke anusAra, he mitra, 56 paNa ke 72 pakSI kharIda kara mere pAsa laao|" aisA kahakara eka manuSya ne kharIda kI kImata ( apane mitra ko ) de dii| zIghra gaNanA karake batalAo ki kitane paNoM meM usane pratyeka prakAra ke kitane pakSI kharIde // 1473-149 // 3 paNa meM 5 pala zuNThi, 4 paNa meM (4) ko (ka-za) se vibhAjita karane para hameM bhajanaphala a prApta hotA hai, aura zeSa ba (kha-za)+ sa (ga-za ) prApta hotA hai, jahA~ ka-za upayukta pUrNAka hai| isI prakAra, hama yaha kriyA aMta taka le jAte haiN| isa prakAra, yaha dekhane meM AtA hai ki uttarottara cune gaye bhAjaka ka-za, kha - za aura ga-za, jaba za meM milAye jAte haiM, taba ve vibhinna kImatoM ke mAna ko utpanna karate haiM, prathama vastu kI kImata za hI hotI hai, aura yaha ki uttarottara bhajanaphala a, ba, sa aura sAtha hI na-(a+ba+sa) vibhinna prakAroM kI vastuoM ke mAna haiN| isa niyama meM, dI gaI vastuoM ke prakAroM kI saMkhyA se eka kama saMkhyA ke vibhAjana kiye jAte haiM / aMtima bhAjana meM koI bhI zeSa nahIM bacanA cAhie / (1463) agalI gAthA (1473-149) meM diye gaye prazna ko sAdhana karane para niyama spaSTa ho jAvegA-dara-rAziyAM 3, 4, 5, 6 ko kramavAra dara-kImatoM 2, 3, 4, 5 dvArA vibhAjita karate haiM / isa prakAra hameM 3,,5,6 prApta hote haiN| inameM se alpatama6 ko anya tIna meM se alaga ga0 sA0 saM0-17

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gaNita sArasaMgrahaH [ 6.150 130 ] tribhiH paNeH zuNThipalAni paJca caturbhirekAdaza pippalAnAm / aSTAbhirekaM maricasya mUlyaM SaSTyAnayASTottaraSaSTimAzu || 150 // iSTAriSTamUlyairiSTavastupramANAnayanasUtrammUlyannaphalecchA guNapaNAnta reSTannayutiviparyAsaH / dviSThaH svadhaneSTaguNaH prakSepakakaraNamavaziSTam // 151 // - 11 pala lambI mirca, aura 8 paNa meM 1 pala mirca prApta hotI hai / 60 paNa kharIda ke dAmoM meM zIghra hI 68 pala vastuoM ko prApta karo // 150 // icchita rakama ( jo ki kula kImata hai ) meM icchita daroM para kharIdI gaI kucha viziSTa vastuoM ke icchita saMkhyAtmaka mAna ko nikAlane ke liye niyama ( kharIdI gaI vibhinna vastuoM ke ) dara-mAnoM meM se pratyeka ko ( alaga-alaga kharIda ke dAmoM ke ) kulamAna dvArA guNita kiyA jAtA hai |-dr-rkm ke vibhinna mAna alaga-alaga samAna hote haiM / ve kharIdI gaI vastuoM kI kula saMkhyA se guNita kiye jAte haiN| Age ke guNanaphala kramavAra pichale guNanaphaloM meM se ghaTAye jAte haiM / dhanAtmaka zeSa eka paMkti meM nIce likha liye jAte haiM / RNAtmaka zeSa eka paMkti meM unake Upara likhe jAte haiN| sabhI meM rahane vAle sAdhAraNa guNanakhaMDoM ko alaga kara isa sabako alpatama padoM meM prahAsita ( laghukRta ) kara liyA jAtA hai / taba ina prahvAsita aMtaroM meM se pratyeka ko mana se cunI huI alaga rAzi dvArA guNita kiyA jAtA hai| una guNanaphaloM ko jo nIce kI paMkti meM rahate haiM tathA unheM jo Upara kI paMkti meM rahate haiM, alaga-alaga jor3ate haiM, aura yogoM ko Upara nIce likhate haiM / saMkhyAoM kI nIce kI paMkti ke yoga ko Upara likhate haiM aura Upara kI paMkti ke yoga ko nIce likhate haiN| ina yogoM ko unake sarvasAdhAraNa guNanakhaMDa haTAkara alpatama padoM meM prahAlita kara liyA jAtA hai | pariNAmI rAziyoM meM se pratyeka ko nIce dubArA likha liyA jAtA hai, tAki eka ko dUsare ke nIce utanI bAra kiyA jA sake, jitane ki saMvAdI ekAntara yoga meM saMghaTaka tatva hote haiN| ina saMkhyAoM ko isa prakAra do paMktiyoM meM jamAkara, unakI kramavAra dara-kImatoM aura cIjoM ke dara- mAnoM dvArA guNita karate haiN| ( aMkoM kI eka paMkti meM dara-mUlya guNana aura aMkoM kI dUsarI paMkti meM dara-saMkhyA kA guNana karate haiM / ) isa prakAra prApta guNanaphaloM ko phirase unake sarvasAdhAraNa guNanakhaMDoM ko haTAkara alpatama padoM meM prahAsita kara liyA jAtA hai / pratyeka UrdhvAdhara ( vertical ) paMki ke pariNAmo aMkoM meM se pratyeka ko alaga-alaga unake saMvAdI mana se cune hue guNakoM (multipliers) dvArA guNita karate haiN| guNanaphaloM ko pahile kI taraha do kSaitija paMktiyoM meM likha liyA jAnA cAhiye / guNanaphaloM kI UparI paMkti kI saMkhyAyeM usa anupAta meM hotI haiM, jisameM ki krayadhana vitarita kiyA gayA hai| aura, jo saMkhyAyeM guNanaphaloM kI nimna paMkti meM rahatI haiM ve usa anupAta meM hotI haiM jisameM ki saMvAdI kharIdI gaI vastue~ vitarita kI jAtI haiN| isaliye aba jo zeSa rahatI hai vaha kevala prakSepaka karaNa kI kriyA hI hai / (prakSepaka karaNa kriyA meM trairAzika niyama ke anusAra AnupAtika vibhAjana hotA hai // 151 // alaga ghaTAne para hameM de aura prApta hote haiM / uparyukta alpatama rAzi ko dI gaI mizrita kImata 56 se se guNita karane para 56 x 6 prApta hotA hai / kula pakSiyoM kI saMkhyA 72 meM se ise ghaTAte haiN| zeSa 24 ko tIna bhAgoM meM bA~Tate haiM; aura 3 / inheM kramazaH aura 20 dvArA bhAjita karane para hameM prathama tIna prakAra ke pakSiyoM kI kImateM 14, 12 aura 36 prApta hotI haiM / ina tInoM kImatoM ko kula 56 meM se ghaTAkara pakSiyoM ke cauthe prakAra kI kImata prApta kI jA sakatI hai / ( 151 ) gAthA 152 - 153 meM diye gaye prazna kA sAdhana nimnalikhita rIti se karane para sUtra

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-6. 153] mizrakavyavahAraH atroddezakaH tribhiH pArAvatAH paJca paJcabhiH sapta sArasAH / saptabhinava haMsAzca navabhiH shikhinstryH||152|| krIDArthaM nRpaputrasya zatena zatamAnaya / ityuktaH prahitaH kazcit tena kiM kasya dIyate / / 153 // udAharaNArtha prazna kabUtara 5 prati 3 paNa kI dara se bece jAte haiM, sArasa pakSI 7 prati 5paNa kI dara se, haMsa 9 prati 7 paNa ko dara se, aura more 3 prati 9 paNa kI dara se becI jAtI haiN| kisI manuSya ko yaha kaha kara bhejA gayA ki vaha rAjakumAra ke manoraMjanArtha 72 paNa meM 100 pakSiyoM ko laave| batalAo ki pratyeka prakAra ke pakSiyoM ko kharIdane ke liye use kitane-kitane dAma denA par3eMge ? // 152-153 // . spaSTa ho jAvegA-dara-vastuoM aura dara-kImatoM ko do paMktiyoM meM isa prakAra likho ki eka ke nIce dUsarI ho| 500 700 900 300 inheM kramazaH kula kImata aura vastuoM kI kula saMkhyA 300 500 700 900 dvArA guNita kro| taba ghttaao| sAdhAraNa guNanakhaMDa . . . 600 100 ko httaao| cunI huI saMkhyAyeM 3, 4, 5, 6 dvArA 20. 200 2000 guNita kro| pratyeka kSaitija paMkti meM saMkhyAoM ko jor3o aura sAdhAraNa guNanakhaMDa 6 ko httaao| ina aMkoM kI sthiti ko badalo, aura ina do paMktiyoM ke pratyeka aMka ko utane bAra likho jitane ki badalI sthiti ke saMvAdI yoga meM saMghaTaka tatva hote haiN| do paMktiyoM ko dara-kImatoM aura dara-vastuoM dvArA kramazaH guNita kro| taba sAdhAraNa guNanakhaMDa 6 ko httaao| aba pahile se cunI huI saMkhyAoM 3, 4, 5, 6 dvArA guNita kro| do paMktiyoM kI saMkhyAyeM una anupAtoM ko prarUpita karatI haiM, jinake anu sAra kula kImata aura vastuoM kI kula saMkhyA vitarita ho 30 42 jAtI hai| yaha niyama anirdhArita (indeterminate) 42 54 12 samIkaraNa sambandhI hai, isaliye uttaroM ke kaI saMgha ( sets) ho sakate haiN| ye uttara mana se cunI huI guNaka ( multiplier ) rUpa rAziyoM para nirbhara rahate haiN| 20 35 36 yaha saralatApUrvaka dekhA jA sakatA hai ki, jaba 15 28 45 12 / kucha saMkhyAoM ko mana se cune hue guNaka ( multip ___liers ) mAna lete haiM, taba pUrNAka uttara prApta hote haiM / anya dazAoM meM, avAJchita bhinnIya uttara prApta hote haiN| isa vidhi ke mUlabhUta siddhAnta ke spaSTIkaraNa ke liye adhyAya ke anta meM diye gaye noTa (TippaNa) ko dekhiye / 36

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132 gaNita sArasaMgrahaH vyastArghapaNyapramANAnayanasUtram ' paNyaikyena paNaikyamantaramataH paNyeSTapaNyAntarairichandyAtsaMkramaNe kRte tadubhayorarghau bhavetAM punaH / paye te khalu paNyayogavivare vyastaM tayorarghayo:praznAnAM viduSAM prasAdanamidaM sUtraM jinendroditam / / 154 // atroddezakaH - [ 6. 154 AdyamUlyaM yadekasya candanasyAgarostathA / palAni viMzatirmizraM caturasrazataM paNAH / / 155 / / kAlena vyatyayArghaH syAtsaSoDazazataM paNAH / tayorarghaphale brUhi tvaM SaDaSTa pRthak pRthak / / 156 / / 1. upalabdha hastalipiyoM meM prApya nahIM / jinake mUlyoM ko paraspara badala diyA gayA hai aisI do datta vastuoM ke parimANa ko prApta karane ke liye niyama - yoga ke saMkhyAtmaka mAna do datta vastuoM kI becane kI kImatoM aura kharIdane kI kImatoM ke ko dI gaI vastuoM ke yoga ke saMkhyAtmaka mAna dvArA bhAjita kiyA jAtA hai| taba una uparyukta becane aura kharIdane kI kImatoM ke aMtara ko ( dI gaI vastuoM ke diye gaye ) yoga meM se kisI mana se cunI huI vastu rAzi ko ghaTAne para prApta hue aMtara ke saMkhyAtmaka mAna dvArA bhAjita kiyA jAtA hai / yadi inake sAtha ( arthAt Upara kI prathama kriyA meM prApta bhajanaphala aura dUsarI kriyA meM prApta kaI bhajanaphaloM meM se kisI eka ke sAtha ) saMkramaNa kriyA kI jAya, to ve dareM prApta hotI haiM jina para ki ye vastue~ kharIdI jAtI haiM / yadi vastuoM ke yoga aura unake antara ke sambandha meM vahI saMkramaNa kriyA kI jAve to vaha vastuoM ke saMkhyAtmaka mAna ko utpanna karatI hai / uparyukta kharIda-daroM ke ekAntaraNa se becane kI dareM utpanna hotI haiM / isa prakAra ke praznoM ke sAdhana kA pratipAdana vidvAnoM ne kiyA hai aura sUtra bhagavAn jinendra ke nimitta se udaya ko prApta huA hai // 154 // udAharaNArtha prazna caMdana kASTa ke eka Tukar3e kI mUla kImata aura agaru kASTha ke eka Tukar3e kI kImata milAne se 104 paNa meM 20 pala vajana kI ve donoM prApta hotI haiN| jaba ve apanI pArasparika badalI huI komatoM para becI jAtI haiM to 116 paNa prApta hote haiM / niyamAnusAra 6 aura 8 alaga-alaga mana se cuno huI saMkhyAe~ lekara vastuoM kI kharIda evaM becane kI dara tathA unakA saMkhyAtmaka mAna nikAlo / / 155-156 // ( 154 ) isa niyama meM varNita vidhi kA bIjIya nirUpaNa gAthA 155 - 156 ke prazna ke sambandha meM isa prakAra diyA jA sakatA hai: mAnalo aya + bara = 104,. ara + baya = 116,. 1 ) . ( 2 ) a + ba = 20.. ( 1 ) aura ( 2 ) kA yoga karane para, ( a + ba ) ( ya + ra ) = 220,.. .( 3 ) 4 ) .. ya + ra = 11.. .. (5) punaH (1) ko ( 2 ) meM se ghaTAne para, ( a - ba ) ( ra ya ) = 12 prApta hotA hai / aba 2ba ko manase 6 ke tulya mAna lete haiN| isa prakAra, a + ba - 2 ba athavA a-ba = 20 - 6 = 14......(6)

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--6. 161 ] mizraka vyavahAraH sUryarathAzveSTayogayojanAnayanasUtram - akhilAptAkhilayAjanasaMkhyA paryAyayojanAni tAnISTayogasaMkhyA nighnAnyekaikagamanamAnAni // 157 // syuH / atroddezakaH . ravirathaturagAH sapta hi catvAro'zvA vahanti dhUryuktAH / yojanasaptatigatayaH ke vyUDhAH ke caturyogAH / / 158 // sarvadhaneSTahInazeSapiNDAt svasvahastagatadhanAnayanasUtram - rUponanarairvibhajet piNDIkRtabhANDasAramupalabdham / sarvadhanaM syAttasmAduktavihInaM tu hastagatam / / 159 / / atroddezaH vaNijaste catvAraH pRthak pRthak zaulkikena paripRSTAH / kiM bhANDasAramiti khalu tatrA hai ko vaNika zreSThaH // 160 // AtmadhanaM vinigRhya dvAviMzatiriti tataH paro'vocat / tribhiruttarA tu viMzatiratha caturadhikaiva viMzatisturyaH // 161 / / [ 133 sUryaratha ke azvoM ke iSTa yoga dvArA yojanoM meM taya kI gaI dUrI nikAlane ke lie niyama - kula yojanoM kA nirUpaNa karane vAlI saMkhyA kula azvoM kI saMkhyA dvArA vibhAjita hokara pratyeka azva dvArA prakrama meM taya kI jAnevAlI dUrI ( yojanoM meM ) hotI hai / yaha yojana saMkhyA jaba prayukta azvoM kI saMkhyA dvArA guNita kI jAtI hai to pratyeka azva dvArA taya kI jAnevAlI dUrI kA mAna prApta hotA hai / / 157 // udAharaNArtha prazna yaha prasiddha hai ki sUrya ratha ke azvoM kI saMkhyA 7 hai / ratha meM kevala 4 azva prayukta kara unheM 70 yojana kI yAtrA pUrI karanA par3atI hai| batalAo ki unheM 4, 4 ke samUha meM kitane bAra kholanA par3atA hai aura kitane bAra jotanA par3atA hai ? // 158 // samasta vastuoM ke kula mAna meM se jo bhI iSTa hai use ghaTAne ke pazcAt bace hue mizrita zeSa meM se saMyukta sAjhedArI ke svAmiyoM meM se pratyeka kI hastagata vastu ke mAna ko nikAlane ke lie niyamavastuoM ke saMyukta ( conjoint ) zeSoM ke mAnoM ke yoga ko eka kama manuSyoM kI saMkhyA dvArA bhAjita karo; bhajanaphala samasta vastuoM kA kula mAna hogA / isa kula mAna ko viziSTa mAnoM dvArA hAsita karane para saMvAdI dazAoM meM pratyeka svAmI kI hastagata vastu kA mAna prApta hotA hai || 159 // udAharaNArtha prazna cAra vyApAriyoM ne milakara apane dhana ko vyApAra meM lgaayaa| una logoM meM se pratyeka se alaga-alaga, mahasUla padAdhikArI ne vyApAra meM lagAI gaI vastu ke mAna ke viSaya meM puuchaa| unameM se eka zreSTha vaNika ne, apanI lagAI huI rakama ko ghaTAkara 22 batalAyA / taba, dUsare ne 23, anya ne 24 12 2.ra - ya = 14 ..(7) yahA~ ( 7 ) aura ( 5 ) tathA ( 6 ) aura ( 3 ) ke sambandha meM saMkramaNa kriyA karate haiM, jisase ya, ra, a aura ba ke mAna prApta ho jAte haiN|

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124 ] gaNitasArasaMgrahaH saptottaraviMzatiriti samAnasArA nigRhya sarve'pi / UcuH kiM brUhi sakhe pRthak pRthagbhANDasAraM me // 162 // anyo'nyamiSTaratna saMkhyAM dattvA samadhanAnayanasUtram - puruSasamAsena guNaM dAtavyaM tadvizoddhaya paNyebhyaH / zeSaparaspara guNitaM svaM svaM hitvA maNermUlyam // 163 / / atroddezakaH prathamasya zakranIlAH SaT sapta ca marakatA dvitIyasya / vajrANyaparasyASTAvekaikA rghaM pradAya samAH // 164 // prathamasya zakranIlAH SoDaza daza marakatA dvitIyasya / vajrAstRtIyapuruSasyASTau dvau tatra datvaiva / / 165 / / teSvekaiko'nyAbhyAM samadhanatAM yAnti te trayaH puruSAH / tacchatranIlamara katavatrANAM kiMbidhA arthAH // 166 // aura caube ne 20 btlaayaa| isa prakAra kathana karane meM pratyeka ne apanI-apanI lagAI huI rakamoM ko vastu ke kulamAna meM se ghaTA liyA thA / he mitra ! batalAo ki pratyeka kA usa paNyadravya meM kitanAkitanA bhANDasAra ( hissA ) thA ? // 160-162 // kisI bhI iSTa saMkhyA ke ratnoM kA pArasparika vinimaya karane ke pazcAt samAna ratnamayI rakamoM ko nikAlane ke lie niyama diye jAne vAle ratnoM ko saMkhyA ko badale meM bhAga lenevAle manuSyoM kI kula saMkhyA dvArA guNita karo vaha guNagaphala alaga-alaga ( pratyeka ke dvArA hastagata) bece jAnevAle ranoM kI saMkhyA meM se ghaTAyA jAtA hai / isa taraha prApta zeSoM kA saMtata guNana pratyeka dazA meM ratna kA mUlya utpanna karatA hai, jaba ki usase sambandhita zeSa isa prakAra ke guNanaphala ko prApta karane meM tyAga diyA jAtA hai // 163 // udAharaNArtha prazna - [ 6. 162 prathama manuSya ke pAsa ( samAna mUlya vAle ) zakra nIla rana the, dUsare manuSya ke pAsa ( usI prakAra ke ) 7 marakata ( mInA emeralds ) the, aura anya (tIsare manuSya) ke pAsa 8 ( usI prakAra ke) Dore the| unameM se pratyeka ne zeSa anya meM se pratyeka ko apane pAsa ke eka ratna ke mUlya ko cukAyA jisase vaha dUsaroM ke samAnadhana vAlA bana gayA / pratyeka prakAra ke ratna kA mUlya kyA-kyA hai ? // 164 // prathama manuSya ke pAsa 16 zakra nIla ratna, dUsare ke pAsa 10 marakata haiM, aura tIsare manuSya ke pAsa 8 hIre haiN| unameM se pratyeka dUsaroM meM se pratyeka ko khuda ke hI ranoM ko de detA hai, jisase tInoM manuSya samAna dhanavAle bana jAte haiN| batalAo ki una zakra nIla ratna, marakata tathA hIroM ke alaga-alaga dAma kyA-kyA haiM ? / / 165-166 // (163) mAna lo 'ma', 'na', 'pa', kramazaH tIna prakAra ke ratnoM kI saMkhyAe~ hai jinake tIna bhinna manuSya svAmI hai / mAnalo paraspara vinimita ratnoM kI saMkhyA 'a' hai, aura 'ka' 'kha', 'ga', kisI eka ratna kI kramazaH tIna prakAroM meM kImateM haiM taba saralatA pUrvaka prApta kiyA jA sakatA hai ki ka ( na 3 a ) ( pa - 3a ); = kha = ( ma - 3a ) ( pa - 3 a ); ga (ma-3a) (na- 3a ).

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-6. 169] gaNitasArasaMgrahaH [135 krayavikrayalAbhaiH mUlAnayanasUtramanyo'nyamUlaguNite vikrayabhakte krayaM yadupalabdhaM / tenaikonena hRto lAbhaH pUrvoddhRtaM mUlyam // 167 / / atroddezakaH tribhiH kroNAti saptava vikroNAti ca paJcabhiH / / nava prasthAna vaNik kiM syAllAbho dvAsaptatidhanam // 168 / / iti mizrakavyavahAre sakalakuTTIkAraH samAptaH / suvarNakuTTIkAraH ____ itaH paraM suvarNagaNitarUpakuTTIkAraM vyAkhyAsyAmaH / samasteSTavargarekIkaraNena saMkaravarNAnayanasUtramkanakakSayasaMvargo mizrasvarNAhRtaH kSayo jJeyaH / paravaNepravibhaktaM suvarNaguNitaM phalaM hemnaH // 169 // kharIda kI dara, becane kI dara aura prApta lAbha dvArA, lagAI gaI rakama kA mAna prApta karane ke liye niyama vastu ko kharIdane aura becane kI daroM meM se pratyeka ko, eka ke bAda eka, mUlya daroM dvArA guNita kiyA jAtA hai / kharIda kI dara kI sahAyatA se prApta guNanaphala ko becane kI dara se prApta guNanaphala dvArA bhAjita kiyA jAtA hai| lAbha ko eka kama pariNAmI bhajanaphala dvArA vibhAjita karane para lagAI gaI mUla rakama utpanna hotI hai // 167 // udAharaNArtha prazna kisI vyApArI ne 3 paNa meM prastha anAja kharIdA aura 5 paNa meM 9 prastha kI dara se becaa| isa taraha use 72 paNa kA lAbha huaa| isa vyApAra meM lagAI gaI rakama kauna sI hai? // 168 // isa prakAra, mizraka vyavahAra meM sakala kuTTIkAra nAmaka prakaraNa samApta huaa| suvarNa kuTTIkAra isake pazcAt hama usa kuTTIkAra kI vyAkhyA kareMge jo svarNa gaNita sambandhI hai| icchita vibhinna vargoM ke sone ke vibhinna prakAra ke ghaTakoM ko milAne se prApta hue saMkara (mizrita) svarNa ke varNa ko prApta karane ke lie niyama yaha jJAta karanA par3atA hai ki vibhinna svarNamaya ghaTaka parimANoM ke (vibhinna ) guNanaphaloM ke yoga ko kramazaH unake varNoM se guNita kara, jaba mizrita svarNa kI kula rAzi dvArA vibhAjita kiyA jAtA hai taba pariNAmI varNa utpanna hotA hai| kisI saMghaTaka bhAga ke mUla varNa ko jaba bAda ke kula mile hue pariNAmI varNa dvArA vibhAjita kara, aura usa saMghaTaka bhAga meM datta svarNa parimANa dvArA guNita karate haiM taba mizrita svarNa kI aisI saMvAdI rAzi utpanna hotI hai, jo mAna meM usI saMghaTaka bhAga ke barAbara hotI hai| // 169 // . (167) yadi kharIda kI dara ba meM a vastue~ ho, aura becane kI dara da meM sa vastue~ ho, tathA vyApAra meM lAbha ma ho, to lagAI gaI rakama ada -ma / hotI hai| basa

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136] mizrakavyavahAraH / 6.170atroddezakaH ekakSayamekaM ca dvikSayamekaM trivarNamekaM ca / varNacatuSke ca dve paJcakSayikAzca catvAraH // 170 // sapta caturdazavarNAstriguNitapazcakSayAzcASTau / etAnekIkRtya jvalane kSiptvaiva mizravaNaM kim / etamizrasuvarNa pUrvairbhaktaM ca kiM kimekasya // 1713 / / iSTavarNAnAmiSTasvavarNAnayanasUtramsvaiHsvaivarNahataimizraM svarNamizreNa bhAjitam / labdhaM varNa vijAnIyAttadiSTAptaM pRthaka pRthaka // 1723 // atroddezakaH viMzatipaNAstu SoDaza varNA dshvrnnprimaannaiH| parivartitA vada tvaM kati hi purANA bhavantyadhunA // 1733 / / aSTottarazatakanakaM varNASTAMzatrayena saMyuktam / ekAdazavarNaM caturuttaradazavarNakaiH kRtaM ca kiM hema // 1743 / / ajJAtavarNAnayanasUtramkanakakSayasaMvarga mizraM svarNanamizrataH zoddhadham / svarNena hRtaM varNa varNavizeSeNa kanakaM syAt / / 1753 // . ___ udAharaNArtha prazna svarNa kA eka bhAga 1 varNa kA hai, eka bhAga 2 vargoM kA hai, eka bhAga 3 varNoM kA hai, 2 bhAga 4 varNoM ke haiM, 4 bhAga 5 vargoM ke haiM, 7 bhAga 14 vargoM ke hai, aura 8 bhAga 15 vargoM ke haiN| inheM agni meM DAlakara eka piNDa banA liyA jAtA hai| batalAo ki isa prakAra mizrita svarNa kisa varNa kA hai? yaha mizrita svarNa una bhAgoM ke svAmiyoM meM vitarita kara diyA jAtA hai| pratyeka ko kyA milatA hai ? // 170-1713 // jo mAna meM diye gaye varNoM vAlI datta svarNa kI mAtrAoM ke tulya hai aise kisI vAnchita varNa vAle svarNa kA ( icchita ) vajana nikAlane ke liye niyama svarNa kI dI gaI mAtrAoM ko alaga-alaga unake hI varNa dvArA kramavAra guNita kiyA jAtA hai, aura guNanaphaloM ko jor3a diyA jAtA hai| pariNAmI yoga ko mizrita svarNa ke kula vajana dvArA bhAjita kiyA jAtA hai| bhajanaphala ko pariNAmI ausata varNa samajha liyA jAtA hai| yaha uparyukta guNanaphaloM kA yoga, isa svarNa ke samAna (icchita ) vajana ko lAne ke liye, alaga-alaga vAnchita varNoM dvArA bhAjita kiyA jAtA hai // 1723 // udAharaNArtha prazna 16 varNa ke 20 paNa vajanavAle svarNa ko 10 varNa vAle svarNa se badalA gayA hai; batalAo ki aba vaha vajana meM kitane paNa ho jAvegA ? // 1733 // 111 varNa vAlA 108 vajana kA svarNa 14 varNa vAle svarNa se badalA jAne para kitane vajana kA ho jAvegA ? // 17 // ajJAta varNa ko nikAlane ke liye niyama svarNa kI kula mAtrA ko mizraNa ke pariNAmI varNa se guNita kro| prApta guNaphala meM se usa yoga ko ghaTAo jo svarNa kI vibhinna ghaTaka mAtrAoM ko unake nija ke varNoM dvArA guNita karane se prApta guNanaphaloM ko jor3ane para prApta hotA hai / jaba zeSa ko ajJAta varNa vAle svarNa kI jJAta ghaTaka mAtrA se vibhAjita kiyA jAtA hai, taba iSTa varNa utpanna hotA hai; aura jaba vaha zeSa pariNAmI varNa tathA ( svarNa ko ajJAta ghaTaka mAtrA ke ) jJAta varNa ke aMtara dvArA bhAjita kiyA jAtA hai, taba usa svarNa kA iSTa vajana utpanna hotA hai // 1753 //

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-6. 181] mizrakavyavahAra: [ 137 ajJAtavarNasya punarapi sUtramsvasvarNavarNavinihatayogaM svarNaikyadRDhahatAcchodhyam / ajJAtavarNahemnA bhaktaM varNaM budhAH prAhuH // 1763 / / atroddezakaH 'SaDjaladhivahnikanakaistrayodazASTartuvarNakaiH kramazaH / ajJAtavarNahemnaH paJca vimizrakSayaM ca saikadaza / ajJAtavarNasaMkhyAM brUhi sakhe gaNitatattvajJa // 178 / / caturdazaiva varNAni sapta svarNAni tatkSaye / catussvarNe dazotpannamajJAtakSayakaM vada // 179 / / - ajJAtasvarNAnayanasUtram -- svasvarNavarNavinihatayogaM svarNaikyaguNitadRDhavarNAt / tyaktvAjJAtasvarNakSayadRDhavarNAntarAhRtaM kanakam / / 180 / / atroddezakaH dvitricatuHkSayamAnAstristriH kanakAstrayodazakSayikaH / varNayutirdaza jAtA hi sakhe kanakaparimANam / / 181 // 1. yahA~ ranala ke sthAna meM vahni, aura STAvRtukSayeH ke sthAna meM STartuvarNakaiH Adezita kiyA gayA hai, tAki pATha vyAkaraNa kI dRSTi se aura uttama ho jAve / 2. hastalipi meM pATha tatkSaya hai, jo spaSTarUpa se azuddha hai| ajJAta varNa ke sambandha meM eka aura niyama svarNa kI vibhinna saMghaTaka mAtrAoM ko unake kramavAra varNoM se (respectively) guNita karate haiM / prApta guNanaphaloM ke yoga ko pariNAmI varNa tathA svarNa kI kulamAtrA ke guNanaphala meM se ghaTAte haiN| buddhimAna vyakti kahate haiM ki yaha zeSa jaba ajJAta varNavAle svarNa ke vajana dvArA bhAjita kiyA jAtA hai taba iSTa varNa utpanna hotA hai // 1763 // udAharaNArtha prazna kramazaH 13, 8 aura 6 varNa vAle 6, 4 aura 3 vajana vAle svarNa ke sAtha ajJAta varNa vAlA 5 vajana kA svarNa milAyA jAtA hai| mizrita svarNa kA pariNAmI varNa hai| he gaNanA ke bhedoM ko jAnane vAle mitra ! mujhe isa ajJAta varNa kA saMkhyAtmaka mAna batalAo // 1771-178 // diye gaye namUne kA 7 vajana vAlA svarNa 14 varNa vAlA hai| 4 vajana vAlA anya svarNa kA namUnA (prAdarza) usameM milA diyA jAtA hai / pariNAmI varNa 10 hai| dUsare namUne ke svarNa kA ajJAta varNa kyA hai ? // 179 // svarNa kA ajJAta vajana nikAlane ke liye niyama svarNa kI vibhinna saMghaTaka mAtrAoM ko nija ke varNoM dvArA guNita karate haiN| prApta guNanaphaloM ke yoga ko, svarNa ke jJAta bhAroM ko abhinava dRr3ha (durable) pariNAmI varNa dvArA guNita karane se prApta guNanaphaloM ke yoga meM se ghaTAte haiN| zeSa ko svarNa kI ajJAta mAtrA ke jJAta varNa tathA mizrita svarNa ke dRr3ha ( durable) pariNAmI varNa ke antara dvArA bhAjita karane para svarNa kA vajana prApta hotA hai // 18 // udAharaNArtha prazna svarNa ke tIna Tukar3e jinameM se pratyeka vajana meM 3 hai, kramazaH 2, 3 aura 4 varNa vAle haiN| ye 13 varNa vAle ajJAta vajana ke svarNa meM galAye jAte haiN| pariNAmI varNa 10hotA hai / he mitra ! mujhe batalAo ki ajJAta bhAravAle svarNa kA mApa kyA hai ? // 18 // ga0 sA0 saM0-18

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138] gaNitasArasaMgrahaH [6.182 ___ yugmavarNamizrasuvarNAnayanasUtramjyeSThAlpakSayazodhitapakvavizeSAptarUpakaiH prAgvat / prakSepamataH kuyodevaM bahuzo'pi vA sAdhyam // 182 / / punarapi yugmavarNamizrasvarNAnayanasUtramiSTAdhikAntaraM caiva hIneSTAntarameva ca / ubhe te sthApayevyastaM svarNa prakSepataH phalam / / 183 // atroddezakaH dazavarNasuvaNaM yat SoDazavarNena saMyutaM pakkam / dvAdaza cetkanakazataM dvibhedakanake pRthak pRthagbRhi // 184 // bahusuvarNAnayanasUtramvyekapadAnAM kramazaH svarNAnISTAni kalpayeccheSam / avyaktakanakavidhinA prasAdhayet prAktanAyeva // 185 // diye gaye varNoM vAle svarNa ke do diye gaye namUnoM ke mizraNa ke jJAta vajana aura jJAta varNa dvArA do diye gaye varNoM ke saMvAdI svarNa ke bhAroM ko nikAlane ke liye niyama mizraNa ke pariNAmI varNa aura ( ajJAta saMghaTaka mAtrAoM vAle svarNa ke) jJAta uccatara aura nimnatara varNoM ke antaroM ko prApta kro| 1 ko ina antaroM dvArA kramavAra bhAjita kro| taba pahile kI bhA~ti prakSepa kriyA ( athavA ina vibhinna bhajanaphaloM kI sahAyatA se samAnupAtika vibhAjana ) kro| isa prakAra, svarNa kI aneka saMghaTaka mAtrAoM kI arthI ko bhI prApta kiyA jA sakatA hai / / 182 / / punaH, diye gaye varNa vAle svarNa ke do diye gaye namUnoM ke mizraNa ke jJAta vajana aura jJAta varNa dvArA do diye gaye vargoM ke saMvAdI svarNa ke bhAroM ko nikAlane ke liye niyama pariNAmI varNa tathA ( svarNa kI do saMghaTaka mAtrAoM vAle do diye gaye vargoM ke ) uccatara varNa ke antara ko aura sAtha hI pariNAmI varNa tathA (do diye gaye vargoM ke ) nimnatara varNa ke antara ko viloma krama meM likho| ina viloma krama meM rakhe hue antaroM kI sahAyatA se samAnupAtika vitaraNa kI kriyA karane para prApta kiyA gayA pariNAma (saMghaTaka mAtrAoM vAle) svarNa ( ke iSTa bhAroM) ko utpanna karatA hai| // 18 // udAharaNArtha prazna yadi 10 varNa vAlA svarNa, 16 varNa vAle svarNa se milAyA jAne para 12 varNa vAlA 100 vajana kA svarNa utpanna karatA hai, to svarNa ke do prakAroM ke vajana ke mApoM ko alaga-alaga prApta karo // 18 // jJAta varNa aura jJAta vajanavAle mizraNa meM jJAta varNa ke bahuta se saMghaTaka mAtrAoM vAle svarNa ke bhAroM ko nikAlane ke liye niyama ____eka ko chor3akara sabhI jJAta saMghaTaka vargoM ke sambandha meM mana se cune hue bhAroM ko le liyA jAtA hai| taba, jo zeSa rahatA hai use pahile jaisI dI gaI dazAoM ke sambandha meM ajJAta bhAra vAle svarNa ke nizcita karane ke niyama dvArA hala karanA par3atA hai / / / 185 / / [185] yahA~ diyA gayA niyama Upara dI gaI gAthA 180 meM upalabdha hai|

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mizrakavyavahAraH atroddezakaH varNAH zarartunagavasumRDavizve nava ca pakkaMvarNaM hi / kanakAnAM SaSTizcet pRthaka pRthak kanakamA kiM syAt // 986 // dvayanaSTavarNAnayanasUtramsvarNAbhyAM hRtarUpe suvarNavarNAhate dviSThe / svasvarNahRtaikena ca hInayute vyastato hi varNaphalam / / 187 // atroddezakaH -6. 188 ] SoDazadazakanakArbhyAM varNaM na jJAyate ' pakkam / varNaM caikAdaza cedvarNau tatkanakayorbhavetAM kau // 188 // 1. B meM yahA~ yate jur3A hai / [ 139 udAharaNArtha prazna saMghaTaka rAziyoM vAle svarNa ke diye gaye varNa kramazaH 5, 6, 7, 8, 11 aura 13 haiM; aura pariNAmI varNa 9 hai / yadi svarNa kI samasta saMghaTaka mAtrAoM kA kula bhAra 60 ho to svarNa kI vibhinna saMghaTaka mAtrAoM ke vajana meM vibhinna bhApa kauna-kauna hoMge ? / / 186 / / jaba mizraNa kA pariNAmI varNa jJAta ho, taba svarNa kI do jJAta mAtrAoM ke naSTa arthAt ajJAta varNoM ko nikAlane ke liye niyama 1 ko svarNa ke diye gaye do vajanoM dvArA alaga-alaga bhAjita kro| isa prakAra prApta bhajanaphaloM meM se pratyeka ko alaga-alaga svarNa kI saMgata mAtrA ke bhAra dvArA tathA pariNAmI varNa dvArA bhI guNita kro| isa prakAra prApta donoM guNanaphaloM ko do bhinna sthAnoM meM likho / ina do kulakoM ( sets ) meM se pratyeka ke ina phaloM meM se pratyeka ko yadi una rAziyoM dvArA hAsita kiyA jAya athavA jor3A jAya, jo 1 ko saMgata prakAra ke svarNa ke jJAta bhAra dvArA bhAjita karane para prApta hotI haiM, to iSTa varNoM kI prApti hotI hai // 187 // udAharaNArtha prazna yadi saMghaTaka varNa jJAta na ho, aura kramazaH 16 aura 10 bhAra vAle do bhinna prakAra ke svarNoM kA pariNAmI varNa 11 ho, to ina do prakAra ke svarNa ke varNa kauna kauna haiM, batalAo // 188 // (187 ) gAthA 188 ke prazna ko nimna rIti se sAdhita karane para yaha sUtra spaSTa ho jAvegA16 1611 aura 10 x 10 x 11 do sthAnoM meM likha diyA jAtA hai / likhane para, isa prakAra; 11 11 11 11 aura ko do kulakoM meM pratyeka ke ina phaloM meM se pratyeka ko kramAnusAra 1 ko varNa dvArA bhAjita karane se prApta rAziyoM dvArA jor3A aura ghaTAyA jAtA hai- 11 {{+} aura {{{7 isa prakAra uttaroM ke do kulaka ( sets ) prApta hote haiM /

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140] gaNitasArasaMgrahaH [6, 189 punarapi dvayanaSTavarNAnayanasUtramekasya kSayamiSTaM prakalpya zeSa prasAdhayet praagvt|| bahukanakAnAmiSTaM vyekapadAnAM tataH prAgvat / / 189 / / atroddezakaH dvAdazacaturdazAnAM svarNAnAM samarasIkRte jAtam / / varNAnAM dazakaM syAt tadvau brUhi saMcintya / / 190 // aparAdhasyodAharaNam saptanavazikhidazAnAM kanakAnAM saMyute pakkaM / dvAdazavarNaM jAtaM kiM hi pRthaka pRthagvarNam // 191 / / parIkSaNazalAkAnayanasUtramparamakSayAptavarNAH sarvazalAkAH pRthak pRthagyojyAH / svarNaphalaM tacchodhyaM zalAkapiNDAt prapUraNikA // 192 / / atroddezakaH vaizyAH svarNazalAkAzcikIrSavaH svarNavarNajJAH / cakruH svaNezalAkA dvAdazavarNaM tadAdyasya / / 193 / / punaH, jaba mizraNa kA pariNAmI varNa jJAta ho, taba do jJAta mAtrAoM vAle svarNoM ke ajJAta varNoM ko nikAlane ke liye niyama do dI gaI mAtrAoM ke svarNa meM se eka ke sambandha meM varNa mana se cuna lo / jo nikAlanA zeSa ho use pahile kI bhA~ti prApta kiyA jA sakatA hai| eka ko chor3a kara samasta prakAra ke svarNa kI jJAta mAtrAoM ke sambandha meM varNa mana se cuna liye jAte haiM, aura taba pahile kI taraha apanAI gaI rIti se agrasara hote haiM // 18 // udAharaNArtha prazna kramazaH 12 aura 14 vajana vAle do prakAra ke svarNa ko eka sAtha galAyA gayA, jisase pariNAmI varNa 10 banA / una do prakAra ke svarNa ke varNoM ko socakara batalAo // 19 // niyama ke uttarArddha ko nidarzita karane ke liye udAharaNArtha prazna kramazaH 7, 9, 3 aura 10 bhAravAle cAra prakAra ke svarNa ko galAkara 12 varNa vAlA svarNa banAyA gayA / pratyeka prakAra ke saMghaTaka svarNa ke vargoM ko alaga-alaga batalAo // 19 // svarNa kI parIkSaNa zalAkA kI arhA kA anumAna lagAne ke liye niyama pratyeka zalAkA ke varNa ko, alaga-alaga, diye gaye mahattama varNa dvArA vibhAjita karanA par3atA hai| isa prakAra prApta ( sabhI) bhajanaphaloM ko jor3A jAtA hai| pariNAmI yoga zuddha svarNa kI iSTa mAtrA kA mApa hotA hai| sabhI zalAkAoM ke bhAroM kA yoga karane para, prApta yogaphala meM se pichale pariNAmI yoga ko ghaTAte haiN| jo zeSa bacatA hai vaha prapUrNikA ( arthAt nimna zreNI kI mizrita dhAtu ) kI mAtrA hotI hai // 192 // udAharaNArtha prazna svarNa ke varNa ko pahicAnane vAle 3 vyApArI svarNa kI parIkSaNa zalAkAoM ko banAne ke icchuka the| unhoMne aisI svarNa-zalAkAe~ bnaaii| pahile vyApArI kA svarNa 12 varNa vAlA, dUsare kA

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-6. 1983 ] mizrakavyavahAraH [ 141 caturuttaradazavarNaM SoDazavarNaM tRtIyasya / kanakaM cAsti prathamasyaikonaM ca dvitIyasya // 194 // ardhArdhanyUnamatha tRtIyapuruSasya pAdonam / paravarNAdArabhya prathamasyaikAntyameva ca vyantyam / / 195 / / tryantyaM tRtIyavaNijaH sarvazalAkAstu mASamitAH / zuddhaM kanakaM kiM syAt prapUraNI kA pRthak pRthak tvaM me / AcakSva gaNaka zIghraM suvarNagaNitaM hi yadi vetsi / / 1963 / / vinimaya varNasuvarNAnayanasUtram - krayaguNasuvarNavinimaya varNeSTanAntaraM punaH sthApyam / vyastaM bhavati hi vinimayavarNAntarahRtphalaM kanakam // 1973 // atroddezakaH SoDazavarNaM kanakaM saptazataM vinimayaM kRtaM labhate / dvAdazadazavarNAbhyAM sASTasahasraM tu kanakaM kim / / 1983 / / 14 varNa vAlA aura tIsare kA 16 varNa vAlA thA / pahile vyApArI kI parIkSaNa zalAkAoM ke vibhinna namUne, niyamita krama se, varNa meM 1 kama hote jAte the| dUsare ke I aura re kama aura tIsare ke niyamita krama meM kama hote jAte the / pahile vyApArI ne parIkSaNa svarNa ke namUne ko mahattama varNavAle se Arambhakara 1 varNa vAle taka banAye; usI taraha se dUsare vyApArI ne 2 varNa vAlI taka kI zalAkAe~ banAI aura tIsare ne bhI mahattama varNa vAlI se Arambha kara 3 varNa vAlI taka kI parIkSaNa zalAkAe~ / pratyeka parIkSaNa zalAkA bhAra meM 1 mAzA thI / he gaNitajJa ! yadi tuma vAstava meM svarNa gaNanA ko jAnate ho, to zIghra batalAo ki yahA~ zuddha svarNa kA mApa kyA hai, tathA prapUrNikA (nimna zreNI kI milI huI dhAtu ) kI mAtrA kyA hai ? // 193 - 1163 // do diye gaye varNa vAle aura badale meM prApta svarNa ke bhinna bhAroM ko nikAlane ke liye niyamapahile badale jAne vAle diye gaye svarNa ke bhAra ko diye gaye varNa dvArA guNita karate haiM, aura badale meM prApta svarNa kA bhAra tathA badale hue svarNa ke do namUnoM meM se pahile ke varNa dvArA guNi karate haiM / prApta guNanaphaloM ke aMtara ko eka ora likha liyA jAtA hai| uparyukta prathama guNanaphala ko badale meM prApta svarNa kA bhAra tathA badale hue svarNa ke do namUnoM meM se dUsare ke varNa dvArA guNita karane se prApta guNanaphala dvArA hAsita karane se prApta aMtara ko dUsarI ora likha liyA jAtA hai| yadi taba, sthiti meM badala diye jAya~, aura badale hue svarNa ke do prakAroM ke do viziSTa varNoM ke aMtara ke dvArA bhAjita kiye jAya~, to ( badale meM prApta do prakAra ke ) svarNa kI do iSTa mAtrAyeM hotI haiM // 1973 // udAharaNArtha prazna 16 varNa vAlA 700 bhAra kA svarNa badale jAne para, 12 aura 10 varNa vAle do prakAra kA kula 1008 bhAra vAlA svarNa utpanna karatA hai / aba svarNa ke ina do prakAroM meM se pratyeka prakAra kA bhAra kitanA kitanA hai ? // 1983 // ( 1973 ) yaha niyama gAthA 1983 ke prazna kA sAdhana karane para spaSTa ho jAvegA - 700x16 - 1008x10 aura 1008x12 - 700x16 kI sthitiyoM ko badala kara likhane se 896 aura 1120 prApta hote haiN| jaba inheM 12 - 10 arthAt 2 dvArA bhAjita karate haiM, to kramazaH 10 aura 12 varNa vAle svarNa ke 448 aura 560 bhAra prApta hote haiM /

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gaNitasArasaMgrahaH [ 6. 1993__ bahupadavinimayasuvarNakaraNasUtramvarNanakanakamiSTasvarNenAptaM dRDhakSayo bhavati / prAgvatprasAdhya labdhaM vinimayabahupadasuvarNAnAm // 1993 / / atroddezakaH varNacaturdazakanakaM zatatrayaM vinimayaM prakurvantaH / varNAdazadazavasunagaizca zatapaJcakaM svarNam / eteSAM varNAnAM pRthak pRthaka svarNamAnaM kim / / 201 / / _ vinimayaguNavarNakanakalAbhAnayanasUtramsvarNaghnavarNayutihRtaguNayutimUlakSayanarUponena / AptaM labdhaM zodhyaM mUladhanAccheSavittaM syAt / / 202 // tallabdhamUlayogAdvinimayaguNayogabhAjitaM labdham / prakSepakeNa guNitaM vinimayaguNavarNakanakaM syAt / / 203 / / kaI viziSTa prakAra ke badale ke pariNAma svarUpa prApta svarNa ke vibhinna bhAroM ko nikAlane ke liye niyama yadi badale jAne vAle datta svarNa ke bhAra ko usake hI varNa dvArA guNita kara use badale meM prApta iSTa svarNa kI mAtrA se bhAjita kiyA jAya, to samAMga ausata varNa utpanna hotA hai| isake pazcAt , pUrva kathita kriyAoM ko prayukta karane para, prApta pariNAma badale meM prApta vibhinna prakAra ke svarNa ke iSTa bhAroM ko utpanna karatA hai // 1993 // udAharaNArtha prazna eka manuSya 14 varNa vAle 300 bhAra ke svarNa ke badale meM 500 bhAra ke vibhinna varNa vAle 12,10,8 aura 7 varNa vAle svarNa ke prakAroM ko prApta karatA hai| batalAo ki ina bhinna vargoM meM se pratyeka kA saMgata alaga-alaga svarNa kitane-kitane bhAra kA hotA hai ? // 2003-201 // badale meM prApta svarNa ke vibhinna aise bhAroM ko nikAlane ke liye niyama, jo jJAta varNa vAle haiM aura nizvita guNajoM ( multiples ) ke samAnupAta meM haiM dI gaI samAnupAtI guNaja (multiple) saMkhyAoM ke yoga ko, ( dI gaI samAnupAtI mAtrAoM vAle vibhinna prakAra ke badale meM prApta ) svarNa kI mAtrAoM ko, (unake viziSTa ) varNoM dvArA guNita karane para, prApta guNanaphaloM ke yoga dvArA bhAjita karate haiN| pariNAmI bhajanaphala ko badale jAne vAle svarNa ke mUla varNa dvArA guNita kiyA jAtA hai| yadi isa guNanaphala ko 1 dvArA hvAsita kara isake dvArA badale meM prApta svarNa ke bhAra meM jo baDhatI huI hai use bhAjita kareM, aura prApta bhajanaphala ko svarNa ke mUla bhAra meM se ghaTAyeM, to (jo badalA nahIM gayA hai aise ) svarNa kA zeSa bhAra prApta hotA hai| yaha zeSa bhAra mUla svarNa ke bhAra tathA badale ke kAraNa bhAra meM huI vRddhi ke yoga meM se ghaTAyA jAtA hai| isa prakAra prApta pariNAmI zeSa ko badale se sambandhita samAnupAtI guNaja ( multiple ) saMkhyAoM ke yoga dvArA bhAjita kiyA jAtA hai, aura taba una samAnupAtI saMkhyAoM meM se pratyeka dvArA alaga-alaga guNita kiyA jAtA hai| taba badale meM prApta svarNa ke viziSTa varNa vAle aura viziSTa anupAta vAle vibhinna bhAroM kI prApti hotI hai // 202-2.3 // ( 1991 ) yahA~ ullikhita kriyA 185 vI gAthA se milatI hai|

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mizraka vyavahAraH atroddezakaH kazcidvaNi phalArthI SoDazavarNa zatadvayaM kanakam / yatkiMcidvinimayakRtamekAdyaM dviguNitaM yathA kramazaH || 204 || dvAdazavasunavadazakakSayakaM lAbho dviragrazatam / zeSaM kiM syAdvinimayakAMsteSAM cApi me kathaya || 205 || dRzya suvarNavinimaya suvarNairmUlAnayanasUtram - vinimayavarNenAtaM svAMzaM sveSTakSayannasaMmizrAt / aMzaikyanenAptaM dRzyaM phalamatra bhavati mUladhanam ||206 || atroddezakaH -6. 208 ] vaNijaH kaMcit SoDazavarNaka sauvarNagulakamAhRtya / tricatuHpaJcamabhAgAn krameNa tasyaiva vinimayaM kRtvA // 207 // dvAdazadazavarNaiH saMyujya ca pUrvazeSeNa / mUlena vinA dRSTaM svarNasahasraM tu kiM mUlam // 208 // [ 143 udAharaNArtha prazna koI vyApArI lAbha prApta karane kA icchuka hai, aura usake pAsa 16 varNa vAlA 200 bhAra kA svarNa hai / usakA eka bhAga, 12, 8, 9 aura 10 varNa vAle cAra prakAra ke svarNa se badalA jAtA hai, jinake bhAra aise anupAta meM haiM jo 1 se Arambha hokara niyamita rUpa se 2 dvArA guNita kiye jAte haiM / isa badale ke vyApAra ke phalasvarUpa svarNa ke bhAra meM 102 lAbha hotA hai / zeSa ( binA badale hue ) svarNa kA bhAra kyA hai ? una uparyukta varNoM ke saMgata ( corresponding ) svarNa- prakAroM ke bhAroM kobhI batalAo, jo badale meM prApta hue haiM // 204-205 // jisakA kucha bhAga badalA gayA hai aise svarNa kI sahAyatA se, aura badale ke kAraNa bar3hatA dekhA gayA hai aise svarNa ke bhAra kI sahAyatA se svarNa kI mUla mAtrA ke bhAra ko nikAlane ke liye niyamabadale jAne vAle mUla svarNa ke pratyeka viziSTa bhAga ko usake badale ke saMgata varNa dvArA bhAjita kiyA jAtA hai / pratyeka dazA meM, pariNAmI bhajanaphala diye gaye mUla svarNa ke mana se cune hue varNa dvArA guNita kiye jAte haiM; aura taba ye saba guNanaphala jor3e jAte svarNa ke vibhinna bhinnIya badale hue bhAgoM ke svarNa ke bhAra kI bar3hatI ko isa pariNAmI zeSa dvArA bhAjita kiyA jAya, hotA hai // 206 // haiN| isa yoga meM se mUla yoga ko ghaTAyA jAtA hai / aba yadi badale ke kAraNa to mUla svarNa dhana prApta udAharaNArtha prazna kisI vyApArI kI 16 varNa sone kI bhAga kramazaH 12, 10 aura 9 varNa vAle svarNa se ke svarNoM ke bhAroM ko mUla svarNa ke zeSa bhAga lekhA meM se haTAne se bhAra meM 1000 bar3hatI eka choTI geMda lI jAtI hai; tathA usake 3, aura de badala diye jAte haiM / ina badale hue vibhinna prakAra jor3a diyA jAtA hai / taba mUla svarNa ke bhAra ko dekhI jAtI hai / isa mUla svarNa kA bhAra batalAo meM // 207-208 //

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6.209 144] gaNitasArasaMgrahaH ___ iSTAMzadAnena iSTavarNAnayanasya tadiSTAMzakayoH suvarNAnayanasya ca sUtramaMzAptakaM vyastaM kSiptveSTannaM bhavet suvrnnmyii| sA gulikA tasyA api parasparAMzAptakanakasya / / 209 / / svadRDhakSayeNa varNI prakalpayetprAgvadeva yathA / evaM tadvayayorapyubhayaM sAmyaM phalaM bhavedyadi cet // 210 // prAkkalpaneSTavI gulikAbhyAM nizcayau bhavataH / no cetprathamasya tadA kiMcinnyUnAdhiko kSayau kRtvA // 211 // tatkSayapUrvakSayayorantarite zeSamatra saMsthApya / trairAzikavidhilabdhaM varNoM tenonitAdhiko spaSTau / / 212 // dUsare vyakti ke pAsa ke vAnchita bhinnIya bhAga vAle svarNa kI pArasparika dAna kI sahAyatA se iSTa varNa nikAlane ke liye, tathA una mana se cune hue diye gaye bhAgoM ke saMgata svarNoM ke bhAroM ko kramazaH nikAlane ke liye niyama (do viziSTa rUpa se ) diye gaye bhAgoM meM se pratyeka ke saMkhyAtmaka mAna dvArA ko bhAjita kara vyutkrama meM likhA jAtA hai| yadi isa prakAra prApta bhajanaphaloM meM se pratyeka ko mana se cunI huI rAzi dvArA guNita kiyA jAya, to vaha sone kI do choTI geMdoM meM se pratyeka ke bhAra ko utpanna karatA hai| sone kI ina choTI geMdoM meM se pratyeka kA varNa, tathA vyApAra meM dUsare manuSya ke dvArA diye gaye svarNa ko, pratyeka dazA meM, diye gaye antima ausata varNa kI sahAyatA se prApta karanA par3atA hai| yadi isa prakAra se prApta uttara donoM kulaka (sets) prazna ke iSTa mAnoM se mela khAte haiM, to mana se cunI huI saMkhyA se prApta do varNa, (do diye gaye choTe svarNa kI geMdoM ke sambandha meM ), kathita satyApita varNa ho jAte haiM / yadi ye uttara mela nahIM khAte, to uttaroM ke prathama kulaka ke varNoM ko AvazyakatAnusAra choTA yA kucha bar3A banAnA par3atA hai| taba sudhAre hue saMghaTaka varSoM ke saMgata ausata varNa ko Age prApta karanA par3atA hai| isake pazcAt , isa ausata varNa aura pahile prApta (binA mela khAnevAle ausata) varNa ke antara ko likha liyA jAtA hai aura iSTa samAnupAtika rAziyA~ trairAzika niyama dvArA prApta kI jAtI haiN| pahilI cunI haI saMkhyA ke anusAra prApta varNoM ko jaba ina do rAziyoM meM se kramazaH eka dvArA hAsita aura dUsarI dvArA jor3A jAtA hai, taba yahA~ iSTa varNoM kI prApti hotI hai / // 209-212 // (209-212 ) gAthA 213-215 ke prazna kA sAdhana nimna bhA~ti karane para niyama spaSTa ho jAvegA 1 ko aura dvArA bhAjita karane para hameM kramazaH 2, 3 prApta hote haiN| unakI sthiti badala kara unheM kisI cunI huI saMkhyA (mAnalo 1) dvArA guNita karane se hameM 3, 2 prApta hote haiN| ye do saMkhyAeM kramazaH do vyApAriyoM kI svarNa mAtrAoM kA prarUpaNa karatI haiN| 9 ko prathama vyApArI ke svarNa kA varNa cunakara, hama usake dvArA prastAvita badale (vinimaya) meM se, dUsare vyApArI ke svarNa ke varNa 13 ko saralatA pUrvaka prApta kara sakate haiM / ye varNa 9 aura 13, dUsare vyApArI dvArA prastAvita badale meM, ausata varNa ko utpanna karate haiM, jaba ki prazna meM diyA gayA ausata varNa 12 athavA hotA hai| isaliye varNa 9 aura 13 ko badalanA par3atA hai| yadi 9 ke sthAna para 8 cunA jAya to 13

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-6. 216 ] mizrakavyavahAra [145 atroddezakaH svarNaparIkSakavaNijau parasparaM yAcitau tataH prathamaH / adhaM prAdAt tAmapi gulikAM svasuvarNa Ayojya / / 213 / / varNadazakaM karImItyaparo'vAdIt tribhaagmaatrtyaa| labdhe tathaiva pUrNa dvadAzavaNaM karomi galikAmyAma // 214 // ubhayoH suvarNamAne vau~ saMcintya gaNitatattvajJa / sauvarNagaNitakuzalaM yadi te'sti nigadyatAmAzu // 215 / / iti mizrakavyavahAre suvarNakuTTIkAraH samAptaH / _ vicitrakuTTIkAraH itaH paraM mizrakavyavahAraM vicitrakuTTIkAraM vyAkhyAsyAmaH / satyAnRtasUtrampuruSAH saikeSTaguNA dviguNeSTonA bhavantyasatyAni / puruSakRtistairUnA satyAni bhavanti vacanAni / 216 / ___ udAharaNArtha prazna svarNa ke mUlya ko parakhane meM kuzala do vyApAriyoM ne eka dUsare se svarNa badalane ke liye kahA / pahile ne dUsare se kahA, "yadi apanA AdhA svarNa mujhe de do, to use maiM apane svarNa meM milAkara kula svarNa ko 10 varNa vAlA banA luuNgaa|" taba dUsare ne kahA, "yadi maiM tumhArA kevala bhAga svarNa prApta karalU~, to maiM pUre svarNa ko do goliyoM kI sahAyatA se 12 varNa vAlA banA luuNgaa|" he gaNita tatvajJa ! yadi tuma svarNa gaNita meM kuzala ho to socavicAra kara zIghra batalAo ki unake pAsa kitane-kitane varNa vAlA kitanA-kitanA svarNa ( bhAra meM ) hai ? // 213-215 // isa prakAra, mizraka vyavahAra meM suvarNa kuTTIkAra nAmaka prakaraNa samApta huaa| ___ vicitra kuTTIkAra isake pazcAt , hama mizraka vyahAra meM vicitra kuTTIkAra kI vyAkhyA kreNge| ( aisI paristhiti meM jaisI ki nIce dI gaI hai, jahA~ donoM bAteM sAtha hI sAtha sambhava haiM,) satya aura asatya vacanoM kI saMkhyA jJAta karane ke liye niyama manuSyoM kI saMkhyA ko unameM se cAhe gaye manuSyoM kI saMkhyA ko dvArA bar3hAne se prApta saMkhyA dvArA guNita karo, aura taba use cAhe gaye manuSyoM kI saMkhyA kI dugunI rAzi dvArA hAsita karo / jo saMkhyA utpanna hogI vaha asatya vacanoM kI saMkhyA hogii| saba manuSyoM kA nirUpaNa karanevAlI saMkhyA kA varga ina asatya vacanoM kI saMkhyA dvArA hAsita hokara satya vacanoM kI saMkhyA utpanna karatA hai // 216 // ko pahile badale meM 16 taka bar3hAnA par3atA hai| ina do vargoM 8 aura 16 ko, dUsare badale meM prayukta karane se, hameM ausatavarNa ke badale meM prApta hotA hai / / isa prakAra, dUsare badale meM hama dekhate haiM ki bhAra aura varNa ke guNanaphaloM ke yoga meM (4035) athavA 5 kI bar3hatI hai, jabaki pUrva ke cune hue vargoM ke sambandha meM ghaTatI aura bar3hatI kramazaH 9-8-1 aura 16 - 13 =3 haiN| parantu dUsare badale meM bhAra aura varNa ke guNanaphaloM ke yoga meM bar3hatI 36 -35 = 1 hai / trairAzika ke niyama kA prayoga karane para hameM vargoM meM saMgata ghaTatI aura baDhatI aura prApta hotI haiN| isaliye varNa kramazaH 9-2 yA 86 aura 13+3= 136 haiN| (216) isa niyama kA mUla AdhAra gAthA 217 meM diye gaye prazna ke nimnalikhita bIjIya ga0 sA0 saM0-19

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gaNitasArasaMgrahaH atroddezakaH kAmukapuruSAH paJca hi vezyAyAzca priyAstrayastatra / pratyekaM sA brUte tvabhiSTa iti kAni satyAni // 217 / / prastArayogabhedasya sUtram - ekAkottarataH padamUrdhvAdharyataH kramotkramazaH / sthApya pratilomaghnaM pratilomannena bhAjitaM sAram || 218 || 146 ] pA~ca kAmuka vyakti haiM / pratyeka se alaga-alaga kahatI hai, lakSita ) vacana satya haiM ? // 217 // udAharaNArtha prazna unameM se tIna vyakti vAstava meM vezyA dvArA cAhe jAte haiN| vaha "maiM kevala tumheM cAhatI hU~ / " usake kitane ( vyakta aura upa dI huI vastuoM meM (sambhava ) saMcayoM ke prakAroM sambandhI niyama-- eka se Arambhakara, saMkhyAoM ko dI gaI vastuoM kI saMkhyA taka eka dvArA bar3hAkara, niyamita krama meM aura vyastakrama meM ( kramazaH) eka Upara aura eka nIce kSaitijapaMkti meM likho / yadi Upara kI paMkti meM dAhine se bAIM ora ko liyA gayA ( eka, do, tIna athavA adhika saMkhyAoM kA ) guNanaphala, nIce kI paMkti meM bhI dAhine se bAIM ora ko liye gaye ( eka, do, tIna athavA adhika saMkhyAoM ke saMgata ) guNanaphala dvArA bhAjita kiyA jAya, to pratyeka dazA meM aise saMcaya kI iSTa rAzi phalasvarUpa prApta hotI hai / 218 // nirUpaNa se spaSTa ho jAvegA - mAnalo kula manuSyoM kI saMkhyA a hai jinameM se ba cAhe jAte haiM / vacanoM kI saMkhyA a hai, aura pratyeka vacana a manuSyoM ke bAre meM hai, isaliye vacanoM kI kula saMkhyA aXa = are hai / aba ina a manuSyoM meM se ba manuSya cAhe jAte haiM, aura a-ba cAhe nahIM jAte / jaba ba manuSyoM meM se pratyeka ko yaha kahA jAtA hai, 'kevala tumhIM cAhe jAte ho', taba pratyeka dazA meM asatya vacana ba - 1 haiM; isaliye asatya vacanoM kI ba vacanoM meM kula saMkhyA ba ( ba - 1 ) hai .. 1 ) jaba phira se vahI kathana a-ba manuSyoM meM se pratyeka ko kahA jAtA hai taba pratyeka dazA meM asatya kathanoM kI saMkhyA ba+ 1 hai / isaliye a-ba vacanoM meM kula asatya vacanoM kI saMkhyA ( a - ba ) (ba + 1) hai... (2) (1) aura (2) kA yoga karane para, hameM ba (ba-1) + (aba) (ba + 1) = a (ba + 1) - 2 ba prApta hotA hai / yaha asatya vacanoM kI kula saMkhyA ko nirUpita karatI hai| ise ara meM se ghaTAne para, jo ki saba satya aura asatya vacanoM kI kula saMkhyA hai, hameM satya vacanoM kI saMkhyA prApta hotI hai / ( 218 ) yaha niyama saMcaya ( combination ) ke prazna se sambandha rakhatA hai| yahA~ diyA gayA sUtra yaha hai na (na - 1) (na - 2)... (nara + 1) aura yaha spaSTa rUpa se ra 1 2 3......ra ( 226 ) niyama meM diyA gayA sUtra bIjIya rUpa se nimna prakAra hai ka = [ 6.217 adA 2 2 adA' - abada (dA - da ) dA- da na na-ra - ke tulya hai / jahA~ ka = nikAlI jAne vAlI majadUrI "

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-6. 222] mizrakavyavahAraH [147 atroddezakaH varNAzcApi rasAnAM kaSAyatiktAmlakaTukalavaNAnAm / madhurarasena yutAnAM bhedAn kathayAdhunA gaNaka // 219 / / vanendranIlamarakatavidrumamuktAphalaistu rcitmaalaayaaH| kati bhedA yutibhedAt kathaya sakhe samyagAzu tvam // 220 // ketakyazokacampakanIlotpalakusumaracitamAlAyAH / kati bhedA yutibhedAtkathaya sakhe gaNitatattvajJa // 221 // jJAtAjJAtalAbhairmUlAnayanasUtramlAbhonamizrarAzeH prakSepakataH phalAni saMsAdhya / tena hRtaM tallabdhaM mUlyaM tvajJAtapuruSasya // 222 / / udAharaNArtha prazna he gaNitajJa ! mujhe batalAo ki chaH rasa-kaSAyalA, kaDuA, khaTTA, tIkhA, khArA aura mIThA diye gaye hoM to saMcaya ke prakAra aura saMcaya rAziyAM kyA hogI? // 219 // he mitra ! hIrA, nIla, marakata, vidruma aura muktAphala se racI haI aMtahIna dhAge kI mAlA ke saMcaya meM parivartana hone se kitane prakAra prApta ho sakate haiM, zIghra batalAo // 220 // he gaNita tatvajJa sakhe ! mujhe batalAo ki ketakI, azoka, campaka aura nIlotpala ke phUloM kI mAlA banAne ke liye saMcayoM meM parivartana karane para kitane prakAra prApta ho sakate haiM ? kisI vyApAra meM jJAta aura ajJAta kAbhoM kI sahAyatA se ajJAta mUla dhana prApta karane ke liye niyama samAnupAtika vibhAjana kI kriyA dvArA samasta lAbhoM ke mizrita yoga meM se jJAta lAbha ghaTAkara ajJAta lAbhoM ko nizcita karate haiN| taba ajJAta rakama lagAne vAle vyakti kA mUladhana, usake lAbha ko Upara samAnupAtika vibhAjana kI kriyA meM prayukta usI sAdhAraNa guNanakhaNDa dvArA bhAjita karane para, prApta karate haiM // 222 // aDhoyA jAne vAlA kula bhAra, dA% kula dUrI, da = taya kI huI (jo calI jA cukI hai aisI) dUrI, aura ba = nizcita kI gaI kula majadUrI hai| yaha AlokanIya hai ki yAtrA ke do bhAgoM ke liye majadUrI kI dara eka sI hai, yadyapi yAtrA ke pratyeka bhAga ke liye cukAI gaI rakama pUrI yAtrA ke lie nizcita kI gaI dara ke anusAra nahIM hai / prazna ke nyAsa (data datta sAmagrI ) sahita nimnalikhita samIkaraNa se sUtra saralatApUrvaka prApta kiyA jA sakatA hai ada (a-ka) (dA-da), jahA~ ka ajJAta hai|

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148] gaNitasArasaMgrahaH [6.223 atroddezakaH samaye kecidvaNijastrayaH kraya vikrayaM ca kurvIran / prathamasya SaT purANA aSTau mUlyaM dvitIyasya // 223 // na jJAyate tRtIyasya vyAptistainaraistu SaNNavatiH / ajJAtasyaiva phalaM catvAriMzaddhi tenAptam // 224 // kastasya prakSepo vaNijorubhayorbhavecca ko lAbhaH / pragaNayyAcakSva sakhe prakSepaM yadi vijAnAsi / / 225 // bhATakAnayanasUtram-- bharabhRtigatagamyahatiM tyaktvA yojanadalaghnabhArakRteH / tanmUlonaM gamyacchinnaM gantavyabhAjitaM sAram // 226 / / atroddezakaH panasAni dvAtriMzannItvA yojanamasau dalonASTau / gRhNAtyantarbhATakamadhe bhagno'sya kiM deyam / / 227 // 1M aura B meM yahA~ ta jahA hai; chaMda kI dRSTi se yaha azuddha hai| udAharaNArtha prazna samajhaute ke anusAra tIna vyApAriyoM ne kharIdane aura becane kI kriyA kii| unameM se pahile kI rakama 6 purANa, dUsare kI 8 purANa tathA tIsare kI ajJAta thii| una saba tIna manuSyoM ko 96 purANa lAbha prApta huaa| tIsare vyakti dvArA ajJAta rakama para 40 purANa lAbha prApta kiyA gayA thA / vyApAra meM usane kitanI rakama lagAI thI ? anya do vyApAriyoM ko kitanA-kitanA lAbha huA ? he mitra ! yadi samAnupAtika vibhAjana kI kriyA se paricita ho to bhalIbhA~ti gaNanA kara uttara do // 223-225 // kisI dI gaI dara para kisI nizcita dUrI ke kisI bhAga taka kucha dI gaI vastue~ le jAne ke kirAye ko nikAlane ke liye niyama le jAye jAne vAle bhAra ke saMkhyAtmaka mAna aura yojana meM nApI gaI taya dUrI kI aI rAzi ke guNanaphala ke varga meM se le jAye jAne vAle bhAra ke saMkhyAtmaka mAna, taya kiyA gayA kirAyA, pahu~cI huI dUrI, ina saba ke saMtata guNanaphala ko ghttaao| taba yadi le jAye jAne vAle bhAra ke bhinnIya bhAga ( arthAt yahA~ AdhA bhAga) ko taya kI gaI pUrI dUrI dvArA guNita kara, aura taba uparyukta aMtara ke vargamUla dvArA hAsita kara, taya kI jAne vAlI (jo abhI zeSa hai aisI) dUrI ke dvArA bhAjita kiyA jAya, to iSTa uttara prApta hotA hai| udAharaNArtha prazna yahA~ eka manuSya aisA hai, jise 32 panasa phaloM ko 1 yojana dUra le jAne para majadUrI meM 73 phala milate haiN| vaha AdhI dUra jAkara baiTha jAtA hai| use taya kI gaI majadUrI meM se kitanI milanA cAhiye ? // 227 //

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[149 -6. 230] mizrakavyavahAraH dvitIyatRtIyayojanAnayanasyasUtrambharabhATakasaMvargo'dvitIyabhRtikRtivivarjitazchedaH / tabhRtyantarabharagatihatergatiH syAd dvitIyasya // 228 // atroddezakaH panasAni caturviMzatimA nItvA paJcayojanAni naraH / labhate tabhRtimiha nava SaDabhRtiviyute dvitIyanRgatiH kA // 229 // bahupada' bhATakAnayanasya sUtramsaMnihitanarahRteSu prAguttaramizriteSu mArgeSu / vyAvRttanaraguNeSu prakSepakasAdhitaM mUlyam // 230 // 1. B meM yahA~ 'pada' chUTa gayA hai / jaba pahilA athavA dUsarA bojha Dhone vAlA thaka kara baiTha jAtA hai, taba dUsare athavA tIsare bojha Dhone vAle ke dvArA yojanoM meM taya kI gaI dUriyoM ko nikAlane ke liye niyama le jAye jAne vAle kula vajana aura taya kI gaI majadUriyoM ke mAna ke guNanaphala meM se prathama Dhone vAle ko dI gaI majadUrI ke varga ko ghttaao| isa antara ko taya kI gaI majadUrI aura pahile hI de dI gaI majadUrI ke antara, DhoyA jAne vAlA pUrA vajana, aura taya kI jAnevAlI pUrI dUrI ke saMtata guNanaphaka ke sambandha meM bhAjaka ke rUpa meM upayoga meM lAte haiN| pariNAmI bhajanaphala dUsare majadUra dvArA taya kI jAne vAlI dUrI hotA hai // 228 // udAharaNArtha prazna kisI manuSya ko 24 panasa phala 5 yojana dUra le jAne ke liye 9 phala majadUrI ke rUpa meM prApta ho sakate haiN| yadi prathama manuSya ko inameM se 6 phala majadUrI ke rUpa meM diye jA cuke hoM, to dUsare Dhone vAle ko aba kitanI dUrI taya karanA hai, tAki vaha zeSa majadUrI prApta karale ? // 229 // vibhinna dazAoM kI saMgata majadUriyoM ke mAnoM ko nikAlane ke liye niyama, jaba ki vibhinna majadUra una vibhinna dUriyoM taka diyA gayA bojha le jAveM-- manuSyoM kI vibhinna saMkhyAoM dvArA taya kI gaI dUriyoM ko vahA~ Dhone kA kAma karane vAle manuSyoM kI saMkhyA dvArA bhAjita kro| prApta bhajanaphaloM ko isa prakAra saMyukta karanA par3atA hai, ki unameM se pahilA alaga rakha liyA jAtA hai, aura taba bAda ke bhajanaphaloM (1, 2, 3 Adi ) ko usameM jor3a diyA jAtA hai| ina pariNAmI rAziyoM ko kramazaH vibhinna sthAnoM para baiTha jAne vAle manuSyoM kI saMkhyA dvArA guNita karanA par3atA hai| taba ina pariNAmI guNanaphaloM ke sambandha meM prakSeSaka kriyA (samAnupAtika vibhAjana kI kriyA) karane se vibhinna sthAnoM para chor3ane ( baiThane ) vAle manuSyoM kI majadUriyA~ prApta hotI haiM // 230 // (228) bIjIya rUpa se : dA-da = (ba-ka) adA, jo pichale noTa ke samIkaraNa se saralatA aba-kara pUrvaka prApta kiyA jA sakatA hai / yahA~ ka ajJAta rAzi hai|

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150] gaNitasArasaMgrahaH [6. 231 atroddezakaH zibikA nayanti puruSA viMzatiratha yojanadvayaM teSAm / vRttirdInArANAM viMzatyadhikaM ca saptazatam // 231 // krozadvaye nivRttau dvAvubhayoH krozayostrayazcAnye / paJca naraH zeSArdhAbyAvRtAH kA bhRtisteSAm // 232 // iSTaguNitapoTTalakAnayanasUtramsaikaguNA svasveSTaM hitvaanyonynshessmitiH| apavartya yojya mUlaM (viSNoH) kRtvA vyekena mUlena // 233 // pUrvApavartarAzIna hatvA pUrvApavartarAziyuteH / pRthageva pRthak tyaktvA hastagatAH svadhanasaMkhyAH syuH // 234 / / tAH svasvaM hitvaiva tvazeSayogaM pRthak pRthak sthApya / svaguNanAH svakaragatairUnAH poTTalakasaMkhyAH syuH / / 235 // udAharaNArtha prazna 20 manuSyoM ko koI pAlakI 2 yojana dUra le jAne para 720 dInAra milate haiN| do manuSya do kroza dUra jAkara ruka jAte haiM; do kroza dUra aura jAne para anya tIna ruka jAte haiM, tathA zeSa kI AdhI dUrI jAne para 5 manuSya ruka jAte haiN| Dhone vAle vibhinna majadUroM ko kyA-kyA majadUrI milatI hai ? // 231-232 // kisI thailI meM bharI huI rakama ko nikAlane ke liye niyama, jo kucha manuSyoM meM se pratyeka ke hAtha meM jitanI rakama hai usameM jor3I jAne para, anya ke hAthoM meM rakhI huI rakamoM ke yoga kI viziSTa guNaja ( multiple) bana jAtI hai prazna meM viziSTa guNaja ( multiple) saMkhyAoM meM se pratyeka meM eka jor3akara yoga rAziyAM prApta karate haiN| ina yogoM ko eka dUsare se, pratyeka dazA meM, vizeSa ullikhita guNaja ke sambandhI yoga ko upekSita karate hue, guNita karate haiN| inheM, sAdhAraNa guNanakhaMDoM ko haTA kara, alpatama padoM meM pravAsita (laghukRta) karate haiN| taba ina prahAsita (laghukRta) rAziyoM ko jor3A jAtA hai / isa pariNAmI yoga kA vargamUla prApta kiyA jAtA hai, jisameM se eka ghaTA diyA jAtA hai| uparyukta prahAsita rAziyoM ko isa / dvArA hAsita vargamUla dvArA guNita kiyA jAtA hai| taba inheM alaga-alaga unhIM prahvAsita rAziyoM ke yoga meM se ghaTAyA jAtA hai / isa prakAra, kaI vyaktiyoM meM se pratyeka ke hAtha kI rakameM prApta hotI haiM / una vyaktiyoM meM se kevala eka ke pAsa ke dhana ke mAna ko pratyeka dazA meM jor3a se vazcita kara, ina saba hAtha kI rakamoM kI rAziyoM ko eka dUsare meM jor3anA par3atA hai| isa prakAra prApta kaI yoga alaga-alaga likhe jAte haiN| inheM kramazaH uparyukta ullikhita guNaja rAziyoM dvArA guNita kiyA jAtA hai| isa prakAra prApta kaI guNanaphaloM meM se hAtha kI rakamoM ko alaga-alaga ghaTAyA jAtA hai| taba hAtha meM kaI rakamoM meM se pratyeka ke sambandha meM alaga-alaga thailI kI rakama kA vahI mAna prApta hotA hai // 233-235 // ( 233-235 ) gAthA 236-237 meM diye gaye prazna meM, mAnalo ka, kha, ga hAtha meM rakhI huI tIna vyApAriyoM kI rakameM haiM; aura thailI meM ya rakama hai|

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-6. 236 ] mizrakanyavahAraH [151 atroddezakaH mArga tribhirvaNigbhiH poTTalakaM dRSTamAha tatraikaH / poTTalakamidaM prApya dviguNadhano'haM bhaviSyAmi // 236 // udAharaNArtha prazna tIna vyApAriyoM ne sar3aka para eka thailI par3I huI dekhI / eka ne zeSa una se kahA, "yadi mujhe yaha thailI mila jAya, to tumhAre hAtha meM jitanI rakameM haiM unake hisAba se maiM tuma donoM logoM se dugunA dhanavAna ho jaauuNgaa|" taba dUsare ne kahA, "maiM tigunA dhanavAna ho jaauuNgaa|" taba tIsare ne kahA, "maiM pAMca gunA dhanavAna ho jaauuNgaa|" thailI kI rakama tathA pratyeka ke hAtha kI rakamoM ko alaga-alaga batalAo // 236 // hAtha kI rakamoM ke mAna tathA thailI kI rakama nikAlane ke liye niyama, jabaki thailI kI rakama kA vizeSa ullikhita bhinnIya bhAga datta-saMkhyA ke manuSyoM meM, pratyeka ke hAtha kI rakama meM kramazaH jor3ane para, pratyeka dazA meM unake dhana kI hAtha kI rakama ke vahI guNaja ( multiple ) ho jAveMtaba ya+ ka = a (kha+ga), ya+kha = ba (ga+ka), jahA~ a, ba, sa prazna meM guNajoM kA nirUpaNa karate haiM / ya+ga = sa (ka+kha), ) aba ya+ka+kha+ga =(a+1) (kha+ga) = (ba+ 1) (ga+ka) = (sa+1) (ka+ kha). (a+ 1) (ba+ 1) (sa + 1)(kha + ga) = (ba+ 1) (sa + 1),......(1) tA jahA~ tA-ya+ka+kha+ga hai| isI prakAra, (ja (a+ 1) (ba+ 1) (sa + 1) x (ga+ka) = (sa + 1) (a+ 1)......(2) tA hI (a+ 1) (ba+ 1) (sa + 1)x(ka+kha) = (a+ 1) (ba+ 1)......(3) tA (1), ( 2 ) aura ( 3 ) ko jor3ane para, (a+ 1) (ba+ 1) (sa+ 1)42 (ka+kha+ga) tA = (ba + 1) (sa+1) + (sa + 1) (a+ 1) + (a+ 1) (ba+ 1) = zA......(4) (1), (2) aura (3) ko alaga-alaga 2 dvArA guNita karake (4) meM se ghaTAne para(a+1) (ba+1) (sa+1) 42 ka zA -2 (ba+ 1) (sa+1), tA (a+1) (ba+1) (sa+1) 42 kha-zA-2 (sa+1) (a+ 1), tA (a+1)(ba+1) (sa +1). 42 ga = zA - 2 (a+ 1) (ba+ 1), taba

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152 ] gaNita sArasaMgrahaH hastagatAbhyAM yuvayostriguNadhano'haM dvitIya Aheti / paJcaguNo'haM tvaparaH poTTalahastasthamAnaM kim ||237|| sarvatulyaguNakapoTTalakAnayanahastagatAnayanasUtram vyekapadaghnavyekaguNeSTazivadhonitAMzayutiguNaghAtaH / hastagatAH syurbhavati hi pUrvavadiSTAMzabhAjitaM poTTalakam // 238 // prazna meM diye gaye sabhI ullikhita bhinnoM ke yoga ke hara kI upekSA kara, use (ullikhita sAdhAraNa ) apavartya saMkhyA ( multiple ) dvArA guNita kiyA jAtA hai| isa guNanaphala meM se ve rAziyAM alagaalaga ghaTAI jAtI haiM, jo sAdhAraNa hara meM prahvAsita uparyukta bhinnoM meM se pratyeka ko eka kama manuSyoM ke mAmaloM kI saMkhyA aura ullikhita apavartya ke guNanaphala ko eka dvArA hAsita karane se prApta rAzi dvArA guNita karane se prApta hotI / pariNAmI zeSa, hAtha kI rakamoM ke alaga-alaga mAnoM ko sthApita karate haiM / pahile kI taraha kriyAyeM karane para aura taba prazna meM vizeSa ullikhita bhinnIya bhAga dvArA vibhAjana karane para thailI kI rakama kA mAna prApta ho jAtA hai // 238 // [ 6. 237 .. ka : kha : ga : : zA- 2 (ba+1) (sa+1) : zA-2 ( sa + 1) (a+1) : zA-2 (a+1) (ba+1). samAnupAta ke dAhinI ora, (yadi koI ho to) sAdhAraNa guNanakhaMDoM ko haTAne se, hameM ka, kha, ga ke sabase choTe pUrNokamAna prApta hote haiM / yaha samAnupAta niyama meM sUtra ke rUpa meM diyA gayA hai / yaha dekhane yogya hai ki niyama meM kathita vargamUla kevala gAthA 236 - 237 meM diye gaye prazna se sambandhita hai| yadi zuddha rUpa se likhA jAya, to "vargamUla" ke sthAna meM '3' honA cAhiye / yaha saralatA pUrvaka aura .ke koI bhI do dekhA jA sakatA hai ki yaha prazna tabhI sambhava hai, jaba ki 1 1 a + 1' ba + 1 1 sa + 1 kA yoga tIsare se bar3A ho / ( 238 ) niyama meM diyA gayA sUtra yaha hai-- ka = ma ( a + ba + sa ) - a ( 2ma- 1 ), kha = ma ( a + ba + sa ) - ba (2 ma - 1 ), ga = ma ( a + ba + sa ) - sa ( 2ma - 1 ), ye mAna agale samIkAroM se saralatA pUrvaka nikAle jA sakate haiM / pA. a + ka = ma ( kha + ga ), pA. ba + kha= ma ( ga + ka), aura pA. sa + ga = ma ( ka + kha ), jahA~ pA, thailI kI rakama hai / jahA~ ka, kha, ga hAtha kI rakameM haiM, ma sAdhAraNa guNaja (multiple ) hai, aura a, ba, sa diye gaye ullikhita bhinnIya bhAga 1

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--6. 241] mizrakanyavahAraH atroddezakaH vaizyaiH paJcabhirekaM poTTalakaM dRSTamAha caikaikaH / / poTalakaSaSThasaptamanavamASTamadazamabhAgamAptvaiva // 239 / / svasvakarasthena saha triguNaM triguNaM ca zeSANAm / gaNaka tvaM me zIghraM vada hastagataM ca poTralakam / / 240 // iSTAMzeSTaguNapoTTalakAnayanasUtramiSTaguNAnAnyAMzAH seSTAMzAH saikanijaguNahRtA yuktAH / ghanapadaneSTAMzanyUnAH saikeSTaguNahRtA hastagatAH // 241 / / udAharaNArtha prazna pA~ca vyApAriyoM ne eka thailI dekhii| unhoMne ( eka ke bAda dUsare se ) isa prakAra kahA ki thailI kI rakama kA kramazaH 1.1.1 aura bhAga pAne para vaha apane hAtha kI rakama milAkara anya vyApAriyoM ke kula dhana se tigunA dhanI ho jAyagA / he gaNitajJa ! unake hAthoM kI alaga-alaga rakama tathA thailI meM bharI huI rakama ko zIghra hI batalAo // 239-240 // thailI kI rakama prApta karane ke liye niyama, jaba ki ullikhita bhinnIya bhAgoM ko, kramazaH una vyaktiyoM ke hAtha kI rakama jor3ane para, pratyeka anya kI kula rakamoM ke mAna se viziSTa guNA dhanI bana jAve (dRSTa manuSya ke bhAga ko chor3akara,) zeSa sabhI se sambandhita ullikhita bhinnIya bhAgoM ko sAdhAraNa hara meM pravAsita kara hara ko upekSita kara diyA jAtA hai| inheM ( alaga-alaga dRSTa manuSya sambandhI ) nirdiSTa apavayaM ( multiple) dvArA guNita karate haiM / ina guNanaphaloM meM usa dRSTa manuSya ke bhinnIya bhAga ko jor3ate haiN| pariNAmI yogoM meM se pratyeka ko alaga-alaga usake saMgata ullikhita apavartya ( multiple) se eka adhika rAzi dvArA bhAjita karate haiN| taba ina bhajanaphaloM ko bhI jor3A jAtA hai| alaga-alaga dazAoM sambandhI isa prakAra prApta yogoM ko, do kama dazAoM kI saMkhyA dvArA guNita kara, nirdiSTa bhinnIya bhAga dvArA hvAsita karate haiN| antara ko eka adhika nirdiSTa apavarya dvArA bhAjita karate haiM / yaha phala (isa viziSTa dazA meM) hAtha kI rakama hai // 24 // ( 241) niyama meM diyA gayA sUtra isa prakAra hai - [a + maba + a + masa + a + mada + ...-(za-2 ) a} (ma + 1) ' na+1 'ya+1 'ra+1 ' ba+ naa.ba+ nasa ba+ nada. . . ma+1 ya+1 +1 jahA~ ka, kha,........ .... hAtha kI rakameM haiM; a, ba, sa, da minIya bhAga haiM; ma, na, ya, ra,............vibhinna apavartya saMkhyAyeM haiM; aura za vyApAra sambandhI vyaktiyoM kI saMkhyA hai| ga0 sA0 saM0-20

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gaNitasArasaMgrahaH atrodezakaH pathi pathikAbhyAM poTTalakaM dRSTamAha tatraikaH / asya saMprApya dviguNadhano'haM bhaviSyAmi // 242 // aparastryaMzadvitayaM triguNadhanastvatkarasthadhanAt / makaradhanena sahitaM hastagataM kiM ca poTTalakam / / 243 / / dRSTaM pathi pathikAya poTTalakaM tadgRhItvA ca / dviguNamabhUdAdyastu svakarasthadhanena cAnyasya // hastasthadhanAdanyastriguNaM kiM karagataM ca poTTalakam // 244 // mArge naraizcaturbhiH poTTalakaM dRSTamAha tatrAdyaH / poTTakamidaM labdhvA hyaSTaguNo'haM bhaviSyAmi // 2453 // svakarasthadhanenAnyo navasaMguNitaM ca zeSadhanAt / daza guNadhanavAnaparastvekAdazaguNitadhanavAn syAt / poTTalakaM kiM karagatadhanaM kiyad brUhi gaNakAzu || 247 / / mArge naraiH poTTalakaM caturbhirdRSTaM hi tasyaiva tadA babhUvuH / paJcAMzapAdArdhatRtIyabhAgAstadvitripaJcannacaturgeNAzca' / / 248 / / 1. M aura B meM syuH pATha hai, jo spaSTarUpa se anupayukta hai / 154] [ 6. 242 udAharaNArtha prazna do yAtriyoM ne sar3aka para dhana se bharI huI thailI dekhii| unameM se eka ne dUsare se kahA, "thailI kI AdhI rakama prApta hone para mai tumase dugunA dhanI ho jAU~gA / " dUsare ne kahA, "isa thailI kI 2/3 rakama mila jAne para maiM hAtha kI rakama milAkara tumhAre hAtha kI rakama se tigunI rakamavAlA ho jAU~gA / " hAtha kI alaga-alaga rakameM tathA thailI kI rakama batalAbho // 242 - 243 // do yAtriyoM ne rAste para par3I huI dhana se bharI thailI dekhii| eka ne use uThAyA aura kahA, "isa dhana aura hAtha ke dhana ko milAkara maiM tumase dugunA dhanI hU~ / " dUsare ne thailI ko lekara kahA, "maiM isa dhana aura hAtha ke dhana ko milAkara tumase tigunA dhanI hU~ / " hAtha kI rakameM aura thailI kI rakama alaga-alaga batalAo / // 244-2443 // cAra manuSyoM ne dhana se bharI eka thailI rAste meM dekhI / pahile ne kahA, "yadi mujhe yaha thailI mila jAya, to maiM kula dhana milAkara tuma sabhI ke dhana se AThagunA dhanavAna ho jaauuN|" dUsare kahA, "yadi yaha thailI mujhe mila jAya to merA kuladhana tumhAre kuladhana se 9 gunA ho jAya / " tIsare ne kahA, "maiM 10 gunA dhanI ho jAU~gA / " aura cauthe ne kahA, "maiM 11 gunA dhanI ho jAU~gA / " he gaNitajJa ! thailI kI rakama aura unameM se pratyeka ke hAtha kI rakameM batalAo // 2453 - 247 // cAra manuSyoM ne rakama bharI thailI rAste meM dekhii| taba jo kucha pratyeka ke hAtha meM thA, yadi usameM thailI kA kramazaH pe hai, 2 aura 3 bhAga milAyA jAtA, to vaha dUsaroM ke kuladhana se kramazaH dugunA, tigunA, pA~ca gunA aura cAragunA dhana ho jAtA / thailI kI rakama aura unameM se pratyeka ke hAtha kI rakameM batalAo // 248 // tIna vyApAriyoM ne rAste meM dhana se bharI huI thailI dekhI / pahile ne ( zeSa ) unase

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[ 155 -6. 2523 ] mizrakavyavahAra mArge tribhirvaNigbhiH poTTalakaM dRSTamAha tatrAdyaH / yadyasya caturbhAgaM labhe'hamityAha sa yuvayordviguNaH // 249 // Aha tribhAgamaparaH svahastadhanasahitameva ca triguNaH / asyAdhaM prApyAhaM tRtIyapuruSazcaturgradhanavAn syAm / AcakSva gaNaka zIghraM kiM hastagataM ca poTTalakam // 2503 // yAcitarUpairiSTaguNakahastagatAnayanasya sUtramyAcitarUpaikyAni svasaikaguNavardhitAni taiH prAgvat / hastagatAnAM nItvA ceSTaguNanneti sUtreNa // 2513 / / sahazacchedaM kRtvA saikeSTaguNAhRteSTaguNayutyA / rUponitayA bhaktAna tAneva karasthitAn vijAnIyAt // 2523 // kahA, "yadi mujhe isa thailI kA dhana mila jAya, to maiM apane hAtha kI rakama milAkara tuma sabhI ke kuladhana se dugune dhanavAlA ho jaauuN|" dUsare ne kahA, "yadi mujhe thailI kA dhana mila jAya, to use milAkara maiM tuma sabhI ke kula dhana se tigune dhanavAlA ho jaauuN|" tIsare ne kahA, "yadi mujhe thailI kA AdhA dhana mila jAya to use milAkara maiM tuma donoM ke kula dhana se caugune dhanavAlA ho jaauuN|" he gaNitajJa ! zIghra hI unake hAtha kI rakameM tathA thailo kI rakama alaga-alaga batalAo // 249-2501 // hAtha kI aisI rakama nikAlane kA niyama, jo dUsare se mA~ge hue dhana meM milane para dUsaroM ke hAtha kI rakamoM kA nirdiSTa apavartya bana jAtI hai: mAMgI huI rakamoM ko alaga-alaga nija kI saMgata, apavartya ( multiple) rAzi meM eka jor3ane se prAptaphala dvArA guNita karate haiN| ina guNanaphaloM kI sahAyatA se gAthA 241 meM diye gaye niyama dvArA hAtha kI rakamoM ko prApta kara lete haiN| isa prakAra prApta ina rAziyoM ko sAdhAraNa haravAlI banAte haiN| pratyeka eka dvArA bar3hAI gaI apavayaM ( multiple ) rAziyoM dvArA kramazaH nirdiSTa apavartya rAziyoM ko bhAjita karate haiN| taba sAdhAraNa haravAlI rAziyoM ko alaga-alaga ina prApta phaloM ke ekona yoga dvArA bhAjita karate haiN| ina pariNAmI bhajanaphaloM ko vibhinna manuSyoM ke hAthoM kI rakameM samajhanA cAhiye / / 2515-2523 / / ( 2513-2523 ) bIjIya rUpa se, [ [(a + ba) (ma + 1) + ma (sa + da) (na + 1) / - na+1 (a+ba) (ma+1)+ma(i + pha) (pa+ 1).......... pa+1 ...+ ityAdi-(za - 2) (a+ba) (ma + 1) } + (ma + 1) | (#+++44-1) isI prakAra kha, ga ke liye, ityaadi| yahA~ a, ba, sa, da, i, pha eka dUsare se mA~gI huI rakameM haiN|

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156 ] gaNitasArasaMgrahaH atroddezakaH vaizyaikhibhiH parasparahastagataM yAcitaM dhanaM prathamaH / catvAryatha dvitIyaM paJca tRtIyaM naraM prAthyaM // 2533 / / dviguNo'bhavadvitIyaH prathamaM catvAri SaT tRtIyamagAt / triguNaM tRtIyapuruSaH prathamaM paJca dvitIyaM ca // 2543 // SaTa prArthyAbhUtpazcakaguNaH svahastasthitAni kAni syuH| kathayAzu citrakuTTImizraM jAnAsi yadi gaNaka / / 2553 / / puruSAstrayo'tikuzalAzcAnyonyaM yAcitaM dhanaM prathamaH / sa dvAdaza dvitIyaM trayodaza prAthya tatriguNaH / / 2563 / / prathamaM daza trayodaza tRtIyamabhyayaM ca dvitIyo'bhUta / paJcaguNito dvitIyaM dvAdaza daza yAcayitvAdyam // 2573 / / saptaguNitastRtIyo'bhavannaro vAJchitAni labdhAni / kathaya sakhe vigaNayya ca teSAM hastasthitAni kAni syuH / / 2583 / / antyasyopAntyatulyadhanaM dattvA samadhanAnayanasUtramvAJchAbhaktaM rUpaM sa upAntyaguNaH sruupsNyuktH| zeSANAM guNakAraH saiko'ntyaH karaNametatsyAt / / 2593 / / udAharaNArtha prazna tIna vyApAriyoM ne eka dUsare se unake pAsa kI rakamoM meM se rakameM maaNgii| pahilA vyApArI dUsare se 4 aura tIsare se 5 mA~gakara zeSa ke kula dhana se dugunA dhana vAlA bana gayA / dUsarA pahile se 4 aura tIsare se 6 mAMga kara zeSa ke kula dhana se tigunA dhanavAlA bana gyaa| tIsarA pahile se 5 aura dUsare se 6 mAMga kara una donoM se pA~cagunA dhanavAlA bana gyaa| he gaNitajJa, yadi tuma vicitra kuTTIkAra vidhi se paricita ho, to mujhe zIghra hI unake hAthoM kI rakameM batalAo // 2531-2559 // tIna atikuzala puruSa the| unhoMne eka dUsare se rakameM maaNgii| pahilA puruSa dUsare se 12 aura tIsare se 13 lekara una donoM se 3 gunA dhanavAlA bana gyaa| dUsarA pahile se 10 aura tIsare se 13 lekara zeSa donoM se 5 gunA dhanavAlA bana gayA tIsarA dUsare se 12 aura pahile se 10 lekara zeSa donoM se 7 gunA dhanavAlA bana gyaa| unakI vAcchAeM pUrNa ho gii| he mitra! gaNanA kara unake hAthoM kI rakamoM ko batalAo // 2563-258 // samAna dhana rAziyoM ko nikAlane ke liye niyama.jaba ki antima manuSya apane khuda ke dhana meM se upaantima ko usI ke dhana ke barAbara de detA hai| aura phira, yaha upAMtima manuSya bAda meM AnevAle manuSya ke sambandha meM yahI karatA hai, ityAdi ____eka ke dvArA dUsare ko diye jAnevAle dhana ke sambandha meM mana se cunI huI guNaja ( multiple ) rAzi dvArA 1 ko vibhAjita kro| yaha upaaMtima manuSya ke dhana ke sambandha meM guNaja ho jAtA hai| yaha guNaja eka dvArA bar3hAyA jAkara dUsare ke hastagata dhanoM kA guNaja bana jAtA hai / isa antima vyakti ke isa prakAra prApta dhana meM 1 jor3A jAtA hai / yahI rIti upayoga meM lAI jAtI hai // 259 // ( 2593 ) gAthA 2633 ke prazna ko nimnalikhita rIti se hala karane para yaha niyama spaSTa ho

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-6. 2633 ] mizrakavyavahAra [157 atroddezakaH vaizyAtmajAtrayaste mArgagatA jyeSThamadhyamakaniSThAH / svadhane jyeSTho madhyamadhanamAtraM madhyamAya dadau / / 2603 // sa tu madhyamo jaghanyajaghanamAtraM yacchati smAsya / samadhanikA: syasteSAM hastagataM brahi gaNaka saMcintya / / 2613 / / vaizyAtmajAzca paJca jyeSThAdanujaH svakIyadhanamAtram / lebhe sarve'pyevaM samavittAH kiM tu hastagatam // 2623 // vaNijaH paJca svasvAdadhu pUrvasya dattvA tu / samavittAH saMcintya ca kiM teSAM hi hastagatam / / 2633 / / udAharaNArtha prazna kisI vyApArI ke tIna lar3ake the| bar3A, ma~jhalA aura choTA, tInoM kisI rAste se kahIM jA rahe the| bar3e ne apane dhana meM se ma~jhale ko utanA dhana diyA jitanA ki maeNjhale ke pAsa thaa| isa maMjhale ne apane dhana meM se choTe ko utanA diyA jitanA ki choTe ke pAsa thaa| aMta meM unake pAsa barAbara-barAbara dhana ho gyaa| he gaNitajJa ! socakara batalAo ki Arambha meM unake pAsa (kramazaH) kitanA-kitanA dhana thA? // 2601-2613 // kisI vyApArI ke pA~ca lar3ake the / dvitIya putra ne bar3e se utanA dhana liyA jitanA ki usakA hastagata dhana thaa| bAkI sabhI ne aisA hI kiyaa| aMta meM una sabake pAsa barAbara-barAbara dhana ho gyaa| batalAo ki Arambha meM unake pAsa kitanI-kitanI rakama thI? // 2623 // pA~ca vyApArI samAna dhana vAle ho gaye, jaba ki unameM se pratyeka ne apanI khuda kI rakama meM se, jo usake sAmane AyA, use usI ke dhana se AdhA de diyaa| socakara batalAo ki unake pAsa Arambha meM kitanA-kitanA dhana thA ? // 263 // 6 vyApArI the| bar3oM ne, jo kucha unake hAtha meM jAvegA-- 1 yA 2 upaaMtima manuSya ke dhana ke sambandha meM guNaja ( multiple ) hai / yaha 2 eka se milAne para 3 ho jAtA hai, jo dUsaroM ke dhanoM ke saMbaMdha meM guNaja athavA apavartya ( multiple ) ho jAtA hai| aba.......... upaaMtima 1 ko 2 se guNita kara aura anya ko 3 dvArA guNita karane se hameM yaha prApta hotA hai.......... """""2, 3 / anta ke aMka meM 1 jor3ane para yaha prApta hotA hai.............2,4|| aba yaha likhate haiM...... ..................2, 4,4 / upaaMtima 4 ko 2 dvArA aura anya ko 3 dvArA guNita kara aura aMta ke aMka meM jor3ane para hameM yaha prApta hotA hai|''.. ......."6, 8, 13 / punaH " """.................. .........................6, 8, 13, 13 / upara kI taraha, phira se unhIM kriyAoM ko duharAne para hameM yaha prApta hotA hai:18, 24, 26, 40, 54, 72, 78,80, 121 / aMtima paMkti kI saMkhyAe~ 5 vyApAriyoM kI alaga-alaga hastagata rakamoM kA nirUpaNa karatI haiN| bIjIya rUpa se :-a-3 ba=3 ba-3 sa=3 sa-3.da =3 da- -3 jahA~ a, ba, sa, da, i pA~ca vyApAriyoM kI hastagata rakameM haiN| '''''''''"

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158] gaNitasArasaMgrahaH [ 6. 2643 vaNijaH SaT svadhanAdvitribhAgamAtraM krameNa tajjyeSThAH / svasvAnujAya dattvA samavittAH kiM ca hastagatam // 2643 // parasparahastagatadhanasaMkhyAmAtradhanaM dattvA samadhanAnayanasUtramvAJchAbhaktaM rUpaM padayutamAdAvuparyuparyetat / saMsthApya saikavAJchAguNitaM rUponamitareSAm / / 2653 / / atroddezakaH vaNijastrayaH parasparakarasthadhanamekato'nyonyam / dattvA samavittAH syuH kiM syAddhastasthitaM dravyam / / 2663 / / thA. apane se choToM ko kramazaH 3 rakama ( usakI jo unake hAthoM meM alaga-alaga thI) kramAnusAra dii| bAda meM ve saba samAna dhana vAle ho gaye / una sabake pAsa alaga-alaga hAtha meM kauna-kauna sI rakameM thiiN| // 2643 // hAtha kI samAna rakamoM ko nikAlane ke liye niyama, jaba ki kucha ( saMkhyA ke ) manuSya eka se dUsare ko Apasa meM hI utanA dhana dete haiM, jitanA ki kramazaH unake hAtha meM taba rahatA hai prazna meM mana se cunI huI guNaja ( multiple ) rAzi dvArA eka ko bhAjita karate haiM / isameM isa vyApAra meM bhAga lenevAle manuSyoM kI saMgata saMkhyA jor3ate haiN| isa prakAra prathama manuSya ke hAtha kA prArambhika dhana prApta hotA hai| yaha aura usake bAda ke phala krama meM likhe jAte haiM, aura unameM se pratyeka ko eka dvArA bar3hAI gaI mana se cunI huI saMkhyA dvArA guNita kiyA jAtA hai, aura phala ko taba eka dvArA hAsita karate haiM / isa prakAra, pratyeka ke pAsa kA ( Arambha meM unake hAtha kA ) dhana ( jitanA thA, utanA ) prApta hotA jAtA hai / / 2653 // udAharaNArtha prazna 3 vyApAriyoM meM se pratyeka ne dUsaroM ko jitanA unake pAsa usa samaya thA utanA diyaa| taba ve samAna dhanavAna bana gye| unameM se pratyeka ke pAsa alaga-alaga Arambha meM kitanI-kitanI rakama thii||266||caar vyApArI the| unameM se pratyeka ne dUsaroM se utanI rakama prApta kI jitanI ki usake ( 2653 ) gAthA 2663 meM diye gaye prazna ko nimnarIti se hala karane para niyama spaSTa ho jAvegA __ 1 ko mana se cune hue guNaja ( multiple ) dvArA bhAjita karate haiN| isameM manuSyoM kI saMkhyA 3 jor3ane para 4 prApta hotA hai| yaha prathama vyakti ke hAtha kI rakama hai| yaha 4, mana se cune hue guNaja 1 ko 1 dvArA bar3hAne se prApta 2 dvArA guNita hokara, 8 bana jAtA hai / jaba isameM se 1 ghaTAyA jAtA hai, to hameM 7 prApta hotA hai, jo dUsare AdamI ke hAtha kI rakama hai // 25 // yaha 7 Upara kI taraha 2 dvArA guNita hokara, aura phira eka dvArA hAsita hokara 13 hotA hai. jo tIsare AdamI ke hAtha kI rakama hai| yaha hala nimnalikhita samIkaraNa se saralatA pUrvaka prApta ho sakatA hai4 (a-ba-sa)-262 ba-(a-ba-sa)-2 sa }= 4 sa-2 (a-ba-sa) {2 ba-(a-ba-sa)-2 sa}

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-6. 2703] mizrakavyavahAraH [159 vaNijazcatvAraste'pyanyonyadhanArdhamAtramanyasmAt / svIkRtya parasparataH samavittAH syuH kiyatkarasthadhanam // 2673 // ___ jayApajayayo bhAnayanasUtram - svasvachedAMzayutI sthApyordhvAdharyataH kramotkramazaH / anyonyacchedAMzakaguNitau vajrApavartanakramazaH / / 2683 / / chedAMzakramavasthitatadantarAbhyAM krameNa saMbhaktau / svAMzaharanAnyaharau vAJchAnau vyastataH karasthAmitiH / / 2693 / / atroddezakaH dRSTvA kukuTayuddhaM pratyekaM tau ca kukkuttikau| uktau rahasyavAkyairmantrauSadhazaktimanmahApuruSeNa // 2703 / / pAsa kI AdhI usa ( rakama dene ke ) samaya thii| taba ve saba samAna dhanavAle bana gye| Arambha meM pratyeka ke pAsa kitanI-kitanI rakama thI ? // 2673 // (kisI jue meM ) jIta aura hAra se ( barAbara ) lAbha nikAlane ke liye niyama (prazna meM dI gaI do bhinnIya guNaja ) rAziyoM ke aMzoM aura haroM ke do yogoM ko eka dUsare ke nIce niyamita krama meM likhA jAtA hai, aura taba vyutkrama meM likhA jAtA hai| (do yogoM ke kulakoM ( sets) meM se pahile kI) ina rAziyoM ko vajrApravartana kriyA ke anusAra hara dvArA guNita karate haiM, aura dUsare kulaka kI rAziyoM ko usI vidhi se dUsarI saMkalita (summed up) rAzi kI saMgata bhinnIya rAzi ke aMza dvArA guNita karate haiN| prathama kulaka sambandhI prApta phaloM ko haroM ke rUpa meM likha liyA jAtA hai, tathA dUsare kulaka sambandhI prApta phaloM ko aMzoM ke rUpa meM likha liyA jAtA hai| pratyeka kalaka ke hara aura aMza kA aMtara bhI likha liyA jAtA hai| taba ina aMtaroM dvArA ( prazna meM diye gaye pratyeka guNaja bhinnoM ke ) aMza aura hara ke yoga ko dUsare ke hara se guNita karane se prApta phaloM ko kramazaH bhAjita kiyA jAtA hai / ye pariNAmI rAziyA~, iSTa lAbha ke mAna se guNita hone para, (dA~va para lagAne vAle juAr3iyoM ke ) hAtha kI rakamoM ko vyutkrama meM utpanna karatI haiM // 2682-269 // udAharaNArtha prazna mantra aura auSadhi kI zakti vAle kisI mahApuruSa ne murgoM kI lar3AI hotI huI dekhI, aura murgoM ke svAmiyoM se alaga-alaga rahasyamayI bhASA meM mantraNA kii| usane eka se kahA, "yadi tumhArA pakSI jItatA hai, to tuma mujhe dA~va meM lagAyA huA dhana de denA / yadi tuma hAra jAoge, to maiM tumheM dA~va meM lagAye hue dhana kA 3 de duuNgaa|" vaha phira dUsare mujhe ke svAmI ke pAsa gayA, jahA~ usane (2683-2693 ) bIjIya rUpa se, . (sa+da) ba (a+ba) da _xpa, jahA~ _xpa, aura khasibada-(sa+da) a| (sa+da) ba-(a+ba) sa " (a+ba) da-(sa+da) a." ka aura kha juAr3iyoM ke hAtha kI rakameM haiM, aura bhasa, unameM se liye gaye minnIya bhAga haiM, aura pa lAbha hai / ise samIkAra se bhI prApta kiyA jA sakatA hai, yathA kha-aka, jahA~ ka aura kha ajJAta rAziyA~ haiM / ka

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[ 6.2713 160 ] gaNitasArasaMgrahaH jayati hi pakSI te me dehi svarNaM hyavijayo'si dadyA te / tadvitrayaMzakamadyetyaparaM ca punaH sa saMsRtya // 2713 / / tricaturthaM prativAJchatyubhayasmAd dvAdazaiva lAbhaH syAt / tatkukkuTikakarasthaM brUhi tvaM gaNakamukhatilaka / / 2723 / / rAzilabdhacchedamizravibhAgasUtramnizrAdUnitasaMkhyA chedaH saikena tena zeSasya / bhAgaM hRtvA labdhaM lAbhonitazeSa eva rAziH syAt / / 2733 / / ___ atroddezakaH kenApi kimapi bhaktaM sacchedo rAzimizrito lAbhaH / pazcAzattribhiradhikA tacchedaH kiM bhavellabdham / / 2743 / / iSTa saMkhyAyojyatyAjyavargamUlarAzyAnayanasUtram - yojyatyAjyayutiH sarUpaviSamAgraghnArdhitA vargitA vyamA bandhahRtA ca rUpasahitA tyAjyaikyazeSAprayoH / unhIM dazAoM meM dA~va meM lagAye gaye dhana kA hai dhana dene kI pratijJA kI / pratyeka dazA meM use donoM se kevala 12 (svarNa ke Tukar3e) lAbha ke rUpa meM mile| he gaNaka mukha tilaka ! batalAo ki pratyeka pakSI ke svAmI ke pAsa dA~va meM lagAne ke liye hAtha meM kitanA-kitanA dhana thA ? // 270-2726 // ajJAta bhAjya saMkhyA, bhajanaphala aura bhAjaka ko unake mizrita yoga meM se alaga-alaga karane ke liye niyamaH koI bhI suvidhAjanaka manase cunI huI saMkhyA jise diye gaye mizrita yoga meM se ghaTAnA par3atA hai prazna meM bhAjaka hotI hai| isa bhAjaka ko 1 dvArA bar3hAne se prApta rAzi dvArA, mana se cunI huI saMkhyA ko diye gaye mizrita yoga meM se ghaTAne se prApta zeSa ko, bhAjita kiyA jAtA hai| isase iSTa bhajanaphala prApta hotA hai / vaho ( uparyukta ) zeSa, isa bhajanaphala se hAsita hokara, iSTa bhAjya saMkhyA bana jAtA hai // 2733 // udAharaNArtha prazna koI ajJAta rAzi kisI anya ajJAta rAzi dvArA bhAjita hotI hai / yahA~ bhAjaka, bhAjya saMkhyA aura bhajanaphala kA yoga 53 hai / vaha bhAjaka kyA hai, tathA bhajanaphala kyA hai ? // 2743 // usa saMkhyA ko nikAlane ke liye niyama, jo mUla saMkhyA meM koI jJAta saMkhyA ko jor3ane para, vargamUla bana jAtI hai; athavA jo mUla saMkhyA meM se dUsarI jJAta saMkhyA ghaTAI jAne para, vargamUla bana jAtI hai jor3I jAne vAlI rAzi aura ghaTAI jAnevAlI rAzi ke yoga ko usa yoga kI nikaTatama yugma saMkhyA se Upara ke atireka (excess above the even number) meM eka jor3ane se prApta phalA dvArA guNita karate haiM / pariNAmI guNanaphala ko AdhA kiyA jAtA hai, aura taba vargita kiyA jAtA hai| isa vargita rAzi meM se uparyukta sambhava Adhikya ( yoga kI nikaTatama yugma saMkhyA se Upara kA atireka-excess) ghaTAte haiN| yaha phala 4 dvArA bhAjita kiyA jAtA hai, aura taba 1 meM jor3A jAtA

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-6. 2743] mizrakavyavahAra [161 zeSaikyAyutonitA phalamidaM rAzirbhavedvAJchayostyAjyAtyAjyamahattvayoratha kRtemUlaM dadAtyeva saH / / 2753 / / atroddezaka: rAziH kazciddazabhiH saMyuktaH saptadazabhirapi hInaH / mUlaM dadAti zuddhaM taM rAzi syAnmamAzu vada gaNaka / / 2763 / / rAziH saptabhirUno yaH so'STAdazabhiranvitaH kazcit / mUlaM yacchati zuddhaM vigaNayyAcakSva taM gaNaka // 2773 / / rAziva'itryaMzonatrisaptabhAgAnvitassa eva punH| mUlaM yacchati ko'sau kathaya vicintyAzu taM gaNaka / / 2783 / / hai| pariNAmI rAzi ko kramazaH aisI do rAziyoM ke Adhe antara meM jor3A jAtA hai, athavA arddha aMtara meM se ghaTAyA jAtA hai, jinheM ki ayugma banAnevAlI atireka rAzi dvArA una dazAoM meM hAsita kiyA jAtA hai athavA bar3hAyA jAtA hai, jaba ki ghaTAI jAnevAlI dI gaI mUla rAzi jor3I jAnevAlI dI gaI mUla rAzi se bar3I athavA choTI hotI hai| isa prakAra prApta phala vaha saMkhyA hotI hai, jo datta rAziyoM se icchAnusAra sambandhita hokara, nizcita rUpa se vargamUla ko utpanna karatI hai / / 2753 // udAharaNArtha prazna koI saMkhyA jaba 10 se bar3hAI athavA 17 se ghaTAI jAtI hai, taba vaha yathArtha vargamUla bana jAtI hai| yadi sambhava ho to, he gaNitajJa, mujhe zIghra hI vaha saMkhyA batalAo / / 2763 // koI rAzi jaba 7 dvArA hAsita kI jAtI hai athavA 18 dvArA bar3hAI jAtI hai, to vaha yathArtha vargamUla bana jAtI hai / he gaNaka ! usa saMkhyA ko gaNanA ke pazcAt batalAo // 2773 // koI rAzi dvArA hAsita hokara, athavA dvArA bar3hAI jAkara yathArtha vargamUla utpanna karatI hai / he gaNaka, socakara zIghra hI vaha sambhava saMkhyA batalAo // 2783 / 4 (2753 ) bIjIya rUpa se, mAnalo nikAlI jAnevAlI rAzi ka hai, aura usameM joDI jAnevAlI athavA usameM se ghaTAI jAnevAlI rAziyAM kramazaH a, ba hai, taba isa niyama kA nirUpaNa karanevAlA sUtra nimnalikhita hogA* { { (a + ba) 4 (1+1)* 212 - 1 } + 1 + a + 1; isakA mUlabhUta siddhAnta isa prakAra nikAlA jA sakatA hai / (na + 1)2 - na = 2 na + 1 jo ayugma saMkhyA hai; aura (na + 2)2 - na=4na+4 jo yugma saMkhyA hai| jahA~ 'na' koI bhI pUrNAka hai| niyama batalAtA hai ki hama 2na+1 aura 4na+ 4 se kisa prakAra na+a prApta kara sakate haiM, jaba ki hama jAnate haiM ki rana +1 athavA 4na+4 ko a+ba ke barAbara honA caahiye| (2781 ) gAthA 2751 ke noTa meM ba aura a dvArA nirUpita saMkhyAyeM (jo vAstava meM 3 aura hai), isa prazna meM bhinnIya hone ke kAraNa, yaha Avazyaka hai ki diye gaye niyama ke anusAra unheM * ise raMgAcArya ne nimna prakAra diyA hai jo niyama se nahIM milatA hai| { (a+by+{1+ 1) + 2 }-1+1+arbal ga0 sA0 saM0-21

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162 ] gaNitasArasaMgrahaH [ 6. 2793 iSTasaMkhyAhInayuktavargamUlAnayanasUtramuddiSTo yo rAzistva/kRtavargito'tha rUpayutaH / yacchati mUlaM sveSTAtsaMyukta cApanIte ca // 2793 // atroddezakaH dazabhiH saMmizro'yaM dazabhistairvarjitasta sNshddhm| yacchati mUlaM gaNaka prakathaya saMcintya rAziM me // 2803 / / iSTavargIkRtarAzidvayAdiSTaghnAdantaramUlAdiSTAnayanasUtramsaikeSTavyekeSTAva(kRtyAtha vargitau rAzI / etAviSTanAvatha tadvizleSasya mUlamiSTaM syAt // 2813 / / ___ jo kisI jJAta saMkhyA dvArA bar3hAI athavA hAsita kI jAtI hai, aisI ajJAta saMkhyA ke vargamUla ko nikAlane ke liye niyama dI gaI jJAta rAzi ko AdhA karake vargita kiyA jAtA hai aura taba usameM eka jor3A jAtA hai| pariNAmI saMkhyA ko, jaba yA to icchita dI huI rAzi dvArA bar3hAte haiM athavA usI dI huI rAzi dvArA dvAsita karate haiM, taba yathArtha vargamUla prApta hotA hai // 2793 // udAharaNArtha prazna eka saMkhyA hai, jo jaba 10 dvArA bar3hAI jAtI hai athavA 10 dvArA hAsita kI jAtI hai, to yathArtha vargamUla ko detI hai / he gaNaka, ThIka taraha soca kara vaha saMkhyA batAo // 2803 // jJAta saMkhyA dvArA guNita iSTa varga rAziyoM kI sahAyatA se, aura sAtha hI ina guNanaphaloM ke aMtara ke vargamUla ke mAna ko utpanna karane vAlI usI jJAta saMkhyA kI sahAyatA se, unhIM do iSTa varga rAziyoM ko nikAlane ke niyamaH dI gaI saMkhyA ko 1 dvArA bar3hAyA jAtA hai, aura usI dI gaI saMkhyA ko dvArA hAsita bhI kiyA jAtA hai| pariNAmI rAziyoM ko jaba AdhA kara vargita kiyA jAtA hai, to do iSTa rAziyA~ utpanna hotI haiN| yadi inheM alaga-alaga dI gaI rAzi dvArA guNita kiyA jAve, to ina guNanaphaloM ke aMtara ke vargamUla se dI huI rAzi utpanna hotI hai // 2811 // hala karane kI kriyA dvArA haTA diyA jAya / isake liye ve pahile eka se hara vAlI banA lI jAtI haiM aura kramazaH30 aura 1 dvArA nirUpita kI jAtI haiN| taba ina rAziyoM ko (21) dvArA guNita kiyA jAtA hai, jisase 294 tathA 189 ahIe~ prApta hotI haiM, jo prazna meM ba aura amAna lI gaI haiN| ina mAnI huI ba aura a rAziyoM ke dvArA prApta phala ko (21)2 dvArA bhAjita kiyA jAtA hai, aura bhajanaphala hI prazna kA uttara hotA hai| (2793 ) yaha gAthA 275 meM diye gaye niyama kI kevala eka viziSTa dazA hai, jahA~ a ko ba ke barAbara liyA jAtA hai| ( 2813 ) bIjIya rUpa se, jaba dI gaI saMkhyA da hotI hai, taba (da ) aura (2) iSTa vargita rAziyA~ hotI haiN|

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-6. 286] mizrakamyavahAraH [ 163 atroddezakaH yaukocidvargIkRtarAzI guNitau tu saikasaptatyA / sadvizleSapadaM syAdekottarasaptatizca rAzI ko| vigaNayya citrakuTrikagaNitaM yadi vetsi gaNaka me brahi / / 283 // yutahInaprakSepakaguNakArAnayanasUtramsaMvargiteSTazeSaM dviSTaM rUpeSTayutaguNAbhyAM tat / viparItAbhyAM vibhajetprakSepau tatra hInau vA // 284 // atroddezakaH trikapaJcakasaMvargaH paJcadazASTAdazaiva ceSTamapi / iSTaM caturdazAtra prakSepaH ko'tra hAnirvA // 285 / / viparItakaraNAnayanasUtrampratyutpanne bhAgo bhAge guNito'dhike punaH zodhyaH / varge mUlaM mUle vargo viparItakaraNamidam / / 286 // udAharaNArtha prazna do ajJAta vargita rAziyoM ko 71 dvArA guNita kiyA jAtA hai| ina do pariNAmI guNanaphaloM ke aMtara kA vargamUla bhI 71 hotA hai| he gaNaka, yadi citra kuTTIkAra se paricita ho, to gaNanA kara una do ajJAta rAziyoM ko mujhe batalAo // 2821-283 // kisI diye gaye guNya aura diye gaye guNakAra ( multiplier ) ke sambandha meM iSTa bar3hatI yA ghaTatI ko nikAlane ke liye niyama ( tAki datta guNanaphala prApta ho) iSTa guNanaphala aura diye gaye guNya tathA guNaskAra kA pariNAmI guNanaphala (ina donoM guNanaphaloM) ke aMtara ko do sthAnoM meM likhA jAtA hai| pariNAmI guNanaphala ke guNAvayavoM meM se kisI eka meM 1 jor3ate haiM, aura dasare meM iSTa guNanaphala jor3ate haiN| Upara do sthAnoM meM icchAnusAra likhA gayA vaha aMtara alaga-alaga isa prakAra prApta hone vAle yogoM dvArA vyasta krama meM bhAjita kiyA jAtA hai| ye una rAziyoM ko utpanna karate haiM, jo kramazaH diye gaye guNya aura guNakAra athavA kramazaH unameM se ghaTAI jAne vAlI rAziyoM meM jor3I jAtI haiM // 284 // udAharaNArtha prazna 3 aura 5 kA guNanaphala 15 hai / iSTa guNanaphala 18 hai, aura vaha 14 bhI hai| guNya aura guNakAra meM yahA~ kauna sI tIna rAziyA~ jor3I jA~ya athavA unameM se ghaTAI jA~ya ? // 285 // viparItakaraNa (working backwards) kriyA dvArA iSTa phala prApta karane ke lie niyama jahA~ guNana hai vahA~ bhAjana karanA, jahA~ bhAjana hai vahA~ guNana karanA, jahA~ jor3a kiyA gayA hai vahA~ ghaTAnA karanA, jahA~ varga kiyA gayA hai vahA~ vargamUla nikAlanA, jahA~ vargamUla diyA gayA hai vahA~ varga karanA-yaha viparItakaraNa kriyA hai / / 286 / / ( 284 ) jor3I jAnevAlI aura ghaTAI jAnevAlI rAziyA~ ye haiMda aba da aba da+ba bhAra a+ kyoMki (a+ ) (ba+da na) = da, jahA~ a aura ba diye gaye guNanakhaMDa haiM, aura - 'da+ba) da iSTa guNaja hai| 1

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164] gaNitasArasaMgrahaH [6. 287 atroddezakaH saptahRte ko rAzistriguNo vargIkRtaH zarairyuktaH / triguNitapaJcAzahRtastvardhitamUlaM ca pazcarUpANi // 287 / / sAdhAraNazaraparidhyAnayanasUtramzaraparidhitrikamilanaM vargitametatpunastribhiH sahitam / dvAdazahRte'pi labdhaM zarasaMkhyA syAtkalApakAviSTA / / 288 / / udAharaNArtha prazna vaha kauna sI rAzi hai, jo 7 dvArA bhAjita hokara, taba 3 dvArA guNita hokara, taba vagita kI jAkara, taba 5 dvArA bar3hAI jAkara, taba dvArA bhAjita hokara; taba AdhI hokara, aura taba vargamUla nikAle jAne para, 5 hotI hai ? // 287 / / tarakaza ke sAdhAraNa paridhyAna ( common circumferential layer ) kI saMracanA karanevAle tIroM kI yugma saMkhyA kI sahAyatA se kisI tarakaza meM rakhe hue bANoM kI saMkhyA nikAlane ke liye niyama paridhyAna banAne vAlI bANoM kI saMkhyA meM 3 jor3o, taba isa pariNAmI yoga ko vargita karo, aura usa vargita rAzi meM phira se 3 jodd'o| yadi prAptaphala 12 dvArA bhAjita kiyA jAya, to bhajanaphala tarakaza ke tIroM kI saMkhyA kA pramANa bana jAtA hai // 28 // ( 288 ) tIroM kI kula saMkhyA prApta karane ke liye, yahA~ diyA gayA sUtra (na + 3) + 3 hai: 12 jahA~ 'na' paridhyAna zaroM kI saMkhyA hai / yaha sUtra nimnalikhita rIti se bhI prApta ho sakatA hai rekhAgaNita ( jyAmiti ) se siddha kiyA jA sakatA hai ki kisI vRtta ke cAroM ora kevala 6 vRtta khIMce jA sakate haiN| aise sabhI vRtta tulya hote haiM, tathA pratyeka vRtta do Asanna vRttoM ko sparza karatA huA bIca ke ( kendrIya ) vRtta ko bhI sparza karatA hai| ina vRttoM ke cAroM ora phira se utane hI nApake 12 vRtta usI prakAra khIMce jA sakate haiM, aura phira se ina vRttoM ke cAroM ora kevala aise hI 18 vRtta khIMce jAnA sambhava haiM, ityAdi / isa prakAra, prathama ghere meM 6 vRtta, dUsare meM 12, tIsare meM 18 hote haiM, ityAdi / isaliye paveM ghere meM 6 pa vRtta hoNge| aba pa gheroM meM vRttoM kI kula saMkhyA ( kendrIya vRtta se ginI jAkara) 1+146+246+346+ ......+pa46=1+6 (1+2+3+......+pa) = 1+6 pa (pa+1) = 1 + 3 pa (pa+ 1 ) hogI / yadi 6 pa kA mAna 'na' diyA gayA ho, to kula vRttoM kI saMkhyA 1 +34 na ( + 1 ) hogI, jo isa noTa ke Arambha meM diye gaye sUtra rUpa meM prahrAsita kI jA sakatI hai|

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-6. 291 ] mizrakavyavahAraH atrodezakaH ke syuH I paridhizarA aSTAdaza tUNIrasthAH zarAH gaNitajJa yadi vicitre kuTTIkAre zramo'sti te kathaya / / 289 / / iti mizrakavyavahAre vicitrakuTTIkAraH samAptaH / zreDhIbaddhasaMkalitam itaH paraM mizrakagaNita zreDhIbaddhasaMkalitaM vyAkhyAsyAmaH / hInAdhikacayasaMkalitadhanAnayanasUtramvyekA padonAdhikacayaghAtonAnvitaH punaH prabhavaH / gacchAbhyasto hInAdhikacayasamudAya saMkalitam // 290 // atroddezakaH caturuttaradaza cAdirhInacayastrINi paJca gacchaH kim / dvAvAdirvRddhicayaH SaT padamaSTau dhanaM bhavedatra // 299 // [ 165 udAharaNArtha prazna paridhyAna zaroM kI saMkhyA 18 hai / kula milAkara tarakaza meM kitane zara haiM, he gaNitajJa, yadi tumane vicitra kuTTIkAra ke sambandha meM kaSTa kiyA hai, to ise hala karo // 289 // isa prakAra, mizraka vyavahAra meM vicitra kuTTIkAra nAmaka prakaraNa samApta huA / zreDhIbaddha saMkalita ( zreNiyoM kA saMkalana ) isake pazcAt hama gaNita meM zreNiyoM ke saMkalana kI vyAkhyA kareMge / dhanAtmaka athavA RNAtmaka pracayavAlI samAntara zreNI ke yoga ko nikAlane ke liye niyama : prathamapada usa guNanaphala ke dvArA yA to ghaTAyA athavA bar3hAyA jAtA hai, dhanAtmaka pracaya meM zreNI ke eka kama padoM kI saMkhyA kI arddha rAzi kA guNana karane se taba yaha prAptaphala zreNI ke padoM kI saMkhyA se guNita kiyA jAtA hai / isa prakAra, RNAtmaka pracayavAlI samAntara zreNI ke yoga ko prApta kiyA jAtA hai // 290 // jo RNAtmaka yA prApta hotA hai / dhanAtmaka athavA udAharaNArtha prazna prathama pada 14 hai; RNAtmaka pracaya 3 hai; padoM kI saMkhyA 5 hai / prathamapada 2 hai; ghanAtmaka pracaya 6 hai; aura padoM kI saMkhyA 8 hai / ina dazAoM meM se pratyeka meM zreNI kA yoga batalAo / / 291 // ( 290 ) bIjIya rUpa se, (na'badeg a) na = za, jahA~ na padoM kI saMkhyA hai, a prathama pada hai; ba pracaya hai, aura za zreNIkA yoga hai /

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gaNitasArasaMgrahaH adhikahInottara saMkalitadhane AdyuttarAnayanasUtram - gacchavibhakte gaNite rUponapadArdhaguNitacayahIne | AdiH padahRtavittaM cAdyUnaM vyekapadadalahRtaH pracayaH / / 292 / / atroddezakaH 166 ] catvAriMzadgaNitaM gacchaH paJca trayaH pracayaH / na jJAyate'dhunAdiH prabhavo dviH pracayamAcakSva / / 293 || zreDhIsaMkalita gacchAnayanasUtram - AdivihIno lAbhaH pracayArdhahRtaH sa eva rUpayutaH / gaccho lAbhena guNo gacchaH sasaMkalitadhanaM ca saMbhavati // 294 // atrodezakaH trINyuttaramAdi vanitAbhizcotpalAni bhaktAni / estar bhAgo'STau kati vanitAH kati ca kusumAni / / 295 / / dhanAtmaka athavA RNAtmaka pracayavAlI samAntara zreNI ke yoga ke sambandha meM prathamapada aura pracaya nikAlane ke liye niyama zreNI ke diye gaye yoga ko padoM kI saMkhyA dvArA bhAjita karo, aura pariNAmI bhajanaphala meM se pracaya dvArA guNita eka kama padoM kI saMkhyA kI AdhIrAzi ko ghaTAo / isa prakAra, zreNI kA prathamapada prApta hotA hai| zreNI ke yoga ko padoM kI saMkhyA dvArA bhAjita karate haiN| isa pariNAmI bhajanaphala meM se prathama pada ghaTAte haiN| zeSa ko jaba 1 kama padoM kI saMkhyA kI AdhI rAzi dvArA bhAjita karate haiM, to pracaya prApta hotA hai ||292 // udAharaNArtha prazna zreNI kA yoga 40 hai; padoM kI saMkhyA 5 hai; pracaya 3 hai; prathamapada ajJAta hai / use nikaalo| yadi prathamapada 2 ho, to pracaya prApta karo // 293 // jo yoga ko padoM kI ajJAta saMkhyA se bhAjita karane para bhajanaphala ke rUpa meM prApta hotA hai, aise jJAta lAbha kI sahAyatA se samAntara zreNI meM yoga aura padoM kI saMkhyA nikAlane ke liye niyamalAbha ko prathama pada ( Adipada ) dvArA hAsita kiyA jAtA hai, aura taba pracaya kI AdhI rAzi dvArA bhAjita kiyA jAtA hai / pariNAmI rAzi meM 1 jor3ane para zreNI ke padoM kI saMkhyA prApta hotI hai / zreNI ke padoM kI saMkhyA ko lAbha dvArA guNita karane para zreNI kA yoga prApta hotA hai // 294 // udAharaNArtha prazna samAntara zreNI ke yoga prarUpaka, koI saMkhyA ke, utpala phUla liye gaye / 2 prathamapada hai, 3 pracaya hai / koI saMkhyA kI striyoM ne Apasa meM ye phUla barAbara-barAbara bA~Te / pratyeka strI ko 8 phUla hisse meM mileM / striyA~ kitanI thIM, aura phUla kitane the ? // 295 // 1 ( 292 ) bIjIya rUpa se, za na - 1 na 2 (294) bIjIya rUpa se, na = ( 295 ) striyoM kI saMkhyA hI a = ba; aura ba = na - 1 ( ~ ~ ~ ~ ) / 7 = 2 - a = na [ 6. 292 la - a ba/ 2 isa prazna meM padoM kI saMkhyA hai / na + 1, jahA~ la = jo lAbha hai /

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-6. 298 ] mizrakavyavahAraH vargasaMkalitAnayanasUtram-- saiSTakRtirdvinA saikeSTo neSTadalaguNitA / kRtidhanacitisaMghAtastrikabhakto vargasaMkalitam // 296 // atroddezakaH aSTASTAdazaviMzatiSaSTyekAzItiSaTakRtInAM ca / kRtighanaciti saMkalitaM vargacitiM cAzu me kathaya / / 297 / / iSTAdyuttarapadavargasaMkalitadhanAnayanasUtram dviguNaikona padottara kRtihatiSaSThAMzamukhacayahatayutiH / vyekapadannA mukhakRtisahitA padatADiteSTakRticitikA / / 298 / / eka se Arambha hone vAlI dI gaI saMkhyA kI prAkRta saMkhyAoM ke vargoM kA yoga nikAlane ke liye niyama - dI gaI saMkhyA ko eka dvArA bar3hAte haiM, aura taba vargita karate haiN| yaha vargita rAzi 2 se guNita kI jAtI hai, aura taba eka dvArA bar3hAI gaI datta rAzi dvArA hAsita kI jAtI hai| isa prakAra prApta zeSa ko datta saMkhyA kI AdhI rAzI dvArA guNita karate haiM / yaha pariNAma usa yoga ke tulya hotA hai jo dI gaI saMkhyA ke varga, dI gaI saMkhyA ke dhana aura dI gaI saMkhyA kI prAkRta saMkhyAoM ko jor3ane para prApta hotA hai / isa mizrita yoga ko 3 dvArA bhAjita karane para ( dI gaI saMkhyA kI ) prAkRta saMkhyAoM ke varga kA yoga prApta hotA hai / / 296 // [ 167 udAharaNArtha prazna prAkRta saMkhyAoM vAlI kucha zreNiyoM meM, prAkRta saMkhyAoM kI saMkhyA (krama se ) 8, 18, 20, 60, 81 aura 36 hai / pratyeka dazA meM vaha yogaphala batalAo, jo dI gaI saMkhyA kA varga, usakA ghana, aura prAkRta saMkhyAoM kA yoga jor3ane para prApta hotA hai / do gaI saMkhyA vAlI prAkRta saMkhyAoM ke vargoM kA yoga bhI batalAo // 297 // samAntara zreNI meM kucha padoM ke vargoM kA yoga nikAlane ke liye niyama, jahA~ prathamapada, pracaya aura padoM kI saMkhyA dI gaI ho --- padoM kI saMkhyA kI dugunI rAzi 1 dvArA hAsita kI jAtI hai, taba pracaya ke varga dvArA guNita kI jAtI hai, aura taba 6 dvArA bhAjita kI jAtI hai / prAptaphala meM prathamapada aura pracaya ke guNanaphala ko jor3ate haiM / pariNAmI yoga ko eka dvArA hAsita padoM kI saMkhyA se guNita karate haiM / isa prakAra prApta guNanaphala meM prathamapada kI vargita rAzi ko jor3A jAtA hai| prApta yoga ko padoM kI saMkhyA se guNita karane para dI gaI zreDhi ke padoM ke vargoM kA yoga prApta hotA hai / / 298 // I saMkhyAoM ke varga kA yoga hai / +1) na ( 296 ) bIjIya rUpa se, { 2 (na + 13 (na + 1) 3 = zaaa21 jo na taka kI prAkRta ( 298 ) [ { (zna - 1) ba* + aba } (na - 1)+* + aba } (na - 1 ) + a ] na = samAntara zreNI ke padoM ke - bara 6 vargoM kA yoga /

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[6.299 168] gaNitasArasaMgrahaH punarapi iSTAdyuttarapadavargasaMkalitAnayanasUtramdviguNaikonapadottarakRtihatirekonapadahatAGgahRtA / vyekapadAdicayAhatimukhakRtiyuktA padAhatA sAram / / 299 / / atroddezakaH trINyAdiH paJca cayo gacchaH paJcAsya kathaya kRticitikAm / pazcAdistrINi cayo gacchaH saptAsya kA ca kRticitikA // 300 / / ghanasaMkalitAnayanasUtramgacchArdhavargarAzI rUpAdhikagacchavargasaMguNitaH / ghanasaMkalitaM proktaM gaNite'smin gaNitatattvajJaiH / / 301 / / atroddezakaH SaNNAmaSTAnAmapi saptAnAM paMcaviMzatInAM ca / SaTpaMcAzanmizritazatadvayasyApi kathaya ghanapiNDam // 302 / / punaH samAntara zreNI meM koI saMkhyA ke padoM ke vargoM kA yoga nikAlane ke liye anya niyama, jahA~ prathama pada, pracaya, aura padoM kI saMkhyA dI gaI ho zreNI ke padoM kI saMkhyA kI dugunI rAzi eka dvArA hAsita kI jAtI hai, aura taba pracaya ke varga dvArA guNita kI jAtI hai| prAptaphala eka kama padoM kI saMkhyA dvArA guNita kiyA jAtA hai| yaha guNanaphala 6 dvArA bhAjita kiyA jAtA hai| isa pariNAmI bhajanaphala meM, prathama pada kA varga tathA eka kama padoM kI saMkhyA kA yoga, prathama pada, aura pracaya, ina tInoM kA saMtata guNanaphala jor3A jAtA hai / isa prakAra prApta phala, padoM kI saMkhyA dvArA guNita hokara, iSTa phala ko utpanna karatA hai // 299 // udAharaNArtha prazna kisI samAntara zreNI meM prathama pada 3 hai, pracaya 5 hai, tathA padoM kI saMkhyA 5 hai / zreNI ke padoM ke vargoM ke yoga ko nikaalo| isI prakAra, dUsarI samAntara zreDhi meM prathama pada 5 hai, pracaya 13 hai, aura padoM kI saMkhyA 7 hai| isa zreNI ke padoM ke vargoM kA yoga kyA hai ? / / 300 / / / kisI dI huI saMkhyA kI prAkRta saMkhyAoM ke ghanoM ke yoga ko nikAlane ke liye niyama padoM kI dI gaI saMkhyA kI arddharAzi ke varga dvArA nirUpita rAzi ko 1 adhika padoM kI saMkhyA ke yoga ke varga dvArA guNita karate haiM / isa gaNita meM, yaha phala gaNitatasvajJoM dvArA (dI huI saMkhyA kI) prAkRta saMkhyAoM ke ghanoM kA yoga kahA gayA hai / 301 / / ___ udAharaNArtha prazna pratyeka dazA meM 6, 8, 7, 25 aura 256 padoM vAlI prAkRta saMkhyAoM ke dhanoM kA yoga batalAo // 302 // (301 ) bIjIya rUpa se, (na/3)2 (na+1)2 = zA, jo na padoM taka kI prAkRta saMkhyAoM ke ghanoM kA yoga hai|

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-6, 303 ] mizrakavyavahAraH iSTAdyuttara gacchaghana saMkalitAnayanasUtram - cityAdihAtirmukhacayazeSaghnA pracayanighnacitivarge / Adau pracayAdUne viyutA yuktAdhike tu dhanacitikA / / 303 / / atroddezakaH Adi dvau gacchaH paJcAsya ghanacitikA / pazcAdiH saptacayo gacchaH SaT kA bhavecca ghanacitikA / / 304 || [ 169 saMkalita saMkalitA nayanasUtram - dviguNaiko padottarakRtihatiraGgAhRtA cayArdhayutA / AdicayAhatiyuktA vyekapadannAdiguNitena // saikaprabhavena yutA padadalaguNitaiva citicitikA / / 3053 // jahA~ prathama pada, pracaya aura padoM kI saMkhyA ko mana se cunA gayA hai, aisI samAntara zreTi ke padoM ke ghanoM ke yoga ko nikAlane ke liye niyama ( dI huI zreTi ke sarala padoM ke ) yoga ko prathama pada dvArA guNita kara, prathama pada aura pracaya ke aMtara dvArA guNita karate haiM / taba zreTi ke yoga ke varga ko pracaya dvArA guNita karate haiM / yadi prathama pada pracaya se choTA ho, to Upara prApta guNanaphaloM meM se pahile ko dUsare guNanaphala meM se ghaTAyA jAtA / yadi prathama pada pracaya se bar3A ho, to Upara prApta prathama guNanaphala ko dUsare guNanaphala meM jor3a dete haiM / isa prakAra ghanoM kA iSTa yoga prApta hotA hai / / 303 // udAharaNArtha prazna art kA yoga kyA ho sakatA hai, jaba ki prathama pada 3 hai, pracaya 2 hai, aura padoM kI saMkhyA 5 athavA prathama pada 5 hai, pracaya 7 hai, aura pardoM kI saMkhyA 6 ? / / 304 // aisI kI dI huI saMkhyA ke padoM kA yoga nikAlane ke lie niyama, jahA~ pada uttarottara 1 se lekara nirdiSTa sImA taka prAkRta saMkhyAoM ke yoga hoM, tathA ye sImita saMkhyAyeM dI huI samAntara zreDi ke pada hoM samAntara zreDhi meM dI gaI zreDhi kI padoM kI saMkhyA kI dugunI rAzi ko eka dvArA kama karate haiM, aura taba pracaya ke varga dvArA guNita karate haiM / yaha guNanaphala 6 dvArA bhAjita kiyA jAtA / prApta phala pracaya kI arddharAzi meM jor3A jAtA hai, aura sAtha hI prathama pada aura pracaya ke guNanaphala meM bhI jor3A jAtA hai / isa prakAra prApta yoga ko eka kama padoM kI saMkhyA dvArA guNita kiyA jAtA hai| prApta guNanaphala ko prathama pada tathA 1 meM prathama pada jor3ane se prAtarAzi ke guNanaphala meM jor3A jAtA hai| isa prakAra prApta rAzi ko jaba zreTi ke padoM kI saMkhyA kI arddha rAzidvArA guNita kiyA jAtA hai, to aisI zreDhi kA iSTa yoga prApta hotA hai, jisake svapada hI nirdiSTa zreDhi ke yoga hote haiM / / 305 - 3052 // (303 ) bIjIya rUpa se, + za a ( a ba ) + za ba = samAntara zreTi ke padoM ke ghanoM kA yoga, jahA~ za zredi ke sarala padoM kA yoga hai| sUtra meM prathama pada kA cihna yadi aba ho, to + (dhana); aura yadi aba ho, to - (RNa) hotA hai| ga0 sA0 saM0-22

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gaNitasArasaMgrahaH atroddezakaH AdiH SaT paJca cayaH padamapyaSTAdazAtha saMdRSTam / ekAkottaracitisaMkalitaM kiM padASTadazakasya // 3063 // caturasaMkalitAnayanasUtram - saikapadArdhapadAha tirazvairnihatA padonitA tryAptA / saikapadaghnA citiciticitikRtighanasaMyutirbhavati / / 3073 / / 170 ] udAharaNArtha prazna yaha dekhA jAtA hai ki kisI zreDhi kA prathama pada 6 hai, pracaya 5 hai, aura padoM kI saMkhyA 18 | zreDhiyoM ke yogoM ke yoga ko batalAo, jo ki 1 prathama pada ina 18 padoM ke sambandha meM, una vibhinna vAlI aura 1 pracaya vAlI haiM // 3063 / / ( nIce nirdiSTa aura kisI dI huI saMkhyA dvArA nirUpita ) cAra rAziyoM ke yoga ko nikAlane ke liye niyama dI gaI saMkhyA 1 dvArA bar3hAI jAkara, AdhI kI jAtI hai, aura taba nija ke dvArA tathA 7 dvArA guNita kI jAtI hai / isa pariNAmI guNanaphala meM se vahI datta saMkhyA ghaTAI jAtI hai| pariNAmI zeSa ko 3 dvArA bhAjita kiyA jAtA hai / isa prakAra prApta bhajanaphala jaba eka dvArA bar3hAI gaI usI datta saMkhyA dvArA guNita kiyA jAtA hai, taba cAra nirdiSTa rAziyoM kA iSTa yoga prApta hotA hai| aisI cAra nirdiSTa rAziyA~, kramazaH dI huI saMkhyA taka kI prAkRta saMkhyAoM kA yoga, dI gaI saMkhyA taka kI prAkRta saMkhyAoM ke yogoM ke yoga, dI gaI saMkhyA kA varga aura dI gaI saMkhyA kA ghana hotI haiM ||3073 // vAlI pada hai / [ 6.3063 ( 305-3053 ) bIjIya rUpa se, [{{2 na81) ba e+va+aba } (na- 1 ) +a (a+1)] na yaha samAntara zredi kA yoga hai, jahA~ prathamapada kisI sImita saMkhyA taka kI prAkRta saMkhyAoM ke yoga kA nirUpaNa karatA hai-aisI sImita saMkhyA jo kisI samAntara zreTi kA hI eka ( 3073 ) bIjIya rUpa se, na X (na + 1) X 7 2 - na -X ( na + 1 ) 3 isa niyama meM, nirdiSTa cAra rAziyoM kA yoga hai / yahA~ cAra nirdiSTa rAziyA~, kramazaH, ye haiM :( 1 ) 'na' prAkRta saMkhyAoM kA yoga, ( 2 ) 'na' taka kI vibhinna prAkRta saMkhyAoM dvArA kramazaH sImita vibhinna prAkRta saMkhyAoM ke yoga, ( 3 ) 'na' kA varga aura ( 4 ) 'na' kA ghana /

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-6. 3103] mizrakavyavahAraH atroddezakaH saptASTanavadazAnAM SoDazapaJcAzadekaSaSThInAm / brUhi catuHsaMkalitaM sUtrANi pRthak pRthak kRtvA // 3083 / / ___ saMghAtasaMkalitAnayanasUtramgacchastrirUpasahito gacchacaturbhAgatADitaH saikaH / sapadapadakRtivinino bhavati hi saMghAtasaMkalitam / / 3093 / / __ atroddezakaH saptakRteH SaSaSTyAstrayodazAnAM caturdazAnAM ca / paJcAyaviMzatInAM kiM syAt saMghAtasaMkalitam / / 3106 // bhinnaguNasaMkalitAnayanasUtramsamadalaviSamakharUpaM guNaguNitaM vargatADitaM dviSTham / udAharaNArtha prazna dI huI saMkhyAe~ 7,8, 9, 10, 16, 50 aura 61 haiM / Avazyaka niyamoM ko vicArakara. pratyeka dazA meM, cAra nirdiSTa rAziyoM ke yoga ko batalAo // 30 // (pUrva gyavahRta cAra prakAra kI zreDhiyoM ke ) sAmUhika yoga ko nikAlane ke liye niyama padoM kI saMkhyA ko 3 meM jor3ate haiM, aura prAptaphala ko padoM kI saMkhyA ke caturtha bhAga dvArA guNita karate haiM / taba usameM eka jor3A jAtA hai| isa pariNAmI rAzi ko jaba padoM kI saMkhyA ke varga ko padoM kI saMkhyA dvArA bar3hAne se prAptarAzi dvArA guNita kiyA jAtA hai, taba vaha iSTa sAmUhika yoga ko utpanna karatI hai // 309 / / udAharaNArtha prazna 49, 16, 13, 14 aura 25 dvArA nirUpita vibhinna zreDhiyoM ke sambandha meM iSTa sAmUhika yoga kyA hogA ? // 310 // guNottara zreDhi meM bhinnoM kI zreDhi ke yoga ko nikAlane ke liye niyama zreDhi ke padoM kI saMkhyA ko alaga-alaga stambha meM, kramazaH, zUnya tathA 1 dvArA cihnita (marked) kara liyA jAtA hai| cihnita karane kI vidhi yaha hai ki yugmamAna ko AdhA kiyA jAtA hai, aura ayugma mAna meM se 1 ghaTAyA jAtA hai| isa vidhi ko taba taka jArI rakhA jAtA hai, jaba taka ki antatogatvA zUnya prApta nahIM hotaa| taba isa zUnya aura 1 dvArA banI huI prarUpaka zreDhi ko, kramavAra, antima 1 se upayoga meM lAte haiM, tAki yaha 1 sAdhAraNa niSpatti dvArA guNita ho / jahA~ / abhidhAnI pada (denoting item) rahatA hai, vahA~ ise phira se sAdhAraNa niSpatti dvArA guNita karate haiN| aura jahA~ zUnya abhidhAnI pada hotA hai, vahA~ varga prApta karane ke liye use sAdhAraNa niSpatti dvArA (3093 ) bIjIya rUpa se, { (na+3) - +1 (na' + na ) yogoM kA sAmUhika yoga hai, arthAt niyama 296, 3.1 aura 305 se 3053 meM batalAI gaI zreTiyoM ke yogoM tathA 'na' taka kI prAkRta saMkhyAoM ke yoga ( ina saba yogoM) kA sAmUhika yoga hai|

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172 ] gaNita sArasaMgrahaH aMzAptaM vyekaM phalamAdyanyannaM guNonarUpahRtam / / 3113 / / atroddezakaH [ 6.3113 dInArArdhaM paJcasu nagareSu cayastribhAgo'bhUta / AdistrayaMzaH pAdo guNottaraM sapta bhinnaguNacitikA / kA bhavati kathaya zIghraM yadi te'sti parizramo gaNite / / 313 // adhikahInaguNasaMkalitAnayanasUtram - guNacitiranyAdihatA vipadAdhikahIna saMguNA bhaktA / vyekaguNenAnyA phalarahitA hIne'dhike tu phalayuktA // 314 // 1 guNita karate / isa kriyA kA phala do sthAnoM meM likhA jAtA hai / isa prakAra prApta, eka sthAna meM rakhe hue, phala ke aMza ko phala dvArA hI bhAjita karate haiN| taba usameM se 1 ghaTAyA jAtA hai| pariNAmI rAzi koTi ke prathamapada dvArA guNita kiyA jAtA hai, aura taba dUsare sthAna meM rakhI huI rAzi dvArA guNita kiyA jAtA hai / isa prakAra prApta guNanaphala jaba 1 dvArA hAsita sAdhAraNa niSpatti dvArA bhAjita kiyA jAtA hai, taba kA iSTa yoga utpanna hotA hai // 3112 // udAharaNArtha prazna 5 nagaroM ke sambandha meM, prathama pada re dInAra hai, aura sAdhAraNa niSpatti 3 / una sabameM prApta dInAroM ke yoga ko nikaalo| prathamapada hai, sAdhAraNa niSpatti hai aura padoM kI saMkhyA 7 hai / yadi 4 tumane gaNanA meM parizrama kiyA ho, to yahA~ guNottara bhinnIya zreDhi kA yoga batalAo // 3122- 313 // guNottara zreDhi kA yoga nikAlane ke liye niyama, jahA~ kisI dI gaI jJAta rAzi dvArA kisI nirdiSTa rIti se pada yA to bar3hAye yA ghaTAye jAte hoM jisake sambandha meM prathamapada, sAdhAraNa niSpatti aura padoM kI saMkhyA dI gaI hai aisI zuddha guNotara zreDhi ke yoga ko do sthAnoM meM likhA jAtA hai| inameM se eka ko diye gaye prathamapada dvArA bhAjita kiyA jAtA hai / isa pariNAmI bhajanaphala meM se padoM kI dI gaI saMkhyA ko ghaTAyA jAtA hai| pariNAmI zeSa kI prastAvita zredi ke padoM meM jor3I jAnevAlI athavA unameM se ghaTAI jAnevAlI datta rAzi dvArA guNita kiyA jAtA hai| isa prakAra prApta rAzi ko 1 dvArA hAsita sAdhAraNa niSpatti dvArA bhAjita kiyA jAtA hai / dUsare sthAna meM rakhe hue yoga ko isa antima pariNAmI bhajanaphala rAzi dvArA hAsita kiyA jAtA hai, jabaki zreTha ke padoM meM se dI gaI rAzi ghaTAI jAtI ho / para, yadi vaha jor3I jAtI ho, to dUsare sthAna meM rakhe hue guNottara zreDhi ke yoga ko ukta pariNAmI bhajanaphala dvArA bar3hAyA jAtA hai / pratyeka dazA meM prAptaphala nirdiSTa zreDhi kA iSTa yoga hotA hai // 314 // ( 3113 ) isa niyama meM, bhinnIya sAdhAraNa niSpatti kA aMza hamezA 1 le liyA jAtA hai / adhyAya 2 kI 94 vIM gAthA tathA usakI TippaNI dRSTavya hai / ( 314 ) bIjIya rUpa se, +- (yathA- na ) ma + (ra - 1 ) + za; yaha nimnalikhita rUpavAlI zredi kA yoga hai a, ara+ma, (ara+ma) ra ma, 1 (ara + ma) ra ma ra ma ityAdi /

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-6. 318] mizrakanyavahAraH [173 atroddezakaH pazca guNottaramAdidvau trINyadhikaM padaM hi catvAraH / adhikaguNottaracitikA kathaya vicintyAzu gaNitatattvajJa / / 315 // AdistrINi guNottaramaSTau hInaM dvayaM ca daza gcchH| hInaguNottaracitikA kA bhavati vicintya kathaya gaNakAzu / / 316 / / AdyuttaragacchadhanamizrAdyuttaragacchAnayanasUtram - mizrAduddhRtya padaM rUponecchAdhanena saikena / labdhaM pracayaH zeSaH sarUpapadabhAjitaH prabhavaH // 317 / / atroddezakaH AdyuttarapadamizraM paJcAzaddhanami haiva saMdRSTam / gaNitajJAcakSva tvaM prabhavottarapadadhanAnyAzu // 318 / / saMkalitagatidhvagatibhyAM samAnakAlAnayanasUtramadhruvagatirAdivihInazcayadalabhaktaH sarUpakaH kAlaH / udAharaNArtha prazna sAdhAraNa niSpatti 5 hai, prathamapada 2 hai, vibhinna padoM meM jor3I jAnevAlI rAzi 3 hai, aura padoM kI saMkhyA 4 hai / he gaNita tatvajJa, vicAra kara zIghra hI (nirdiSTa rIti ke anusAra nirdiSTa rAzi dvArA bar3hAe jAte haiM pada jisake aisI) guNottara zreDhi ke yoga ko btlaao|| 315 // prathamapada 3 hai, sAthAraNa niSpatti 8 hai, padoM meM se ghaTAI jAnevAlI rAzi 2 hai, aura padoM kI saMkhyA 10 hai| aisI zreDhi kA, he gaNitajJa, yoga nikAlo // 3 // 6 // prathamapada, pracaya, padoM kI saMkhyA aura kisI samAntara zredi ke yoga ke mizrita yoga meM se prathama pada. pracaya aura padoM kI saMkhyA nikAlane ke liye niyama zreDhi ke padoM kI saMkhyA kA nirUpaNa karanevAlI mana se cunI huI saMkhyA ko diye gaye mizrita yoga meM se ghaTAyA jAtA hai| taba se Arambha hone vAlI aura eka kama padoM kI (mana se cunI huI ) saMkhyAvAlI prAkRta saMkhyAoM kA yoga dvArA bar3hAyA jAtA hai| isa pariNAmI phala ko bhAjaka mAna kara, upara kathita mizrita yoga se prApta zeSa ko bhAjita karate haiM / yaha bhajanaphala iSTa pracaya hotA hai, aura isa bhAjana kI kriyA meM jo zeSa bacatA hai use jaba eka adhika (mana se cunI huI) padoM kI saMkhyA dvArA bhAjita karate haiM, to iSTa prathamapada prApta hotA hai // 317 / / udAharaNArtha prazna yaha dekhA jAtA hai ki kisI samAntara zreDhi kA yoga, prathamapada, pracaya aura padoM kI saMkhyA meM milAye jAne para, 50 hotA hai| he gaNaka, zIghahI prathamapada, pracaya, padoM kI saMkhyA aura zreDhi ke yoga ko batalAo // 318 // saGkalita gati tathA dhrava gati se gamana karane vAle do vyaktiyoM ( ko eka sAtha ravAnA hone para eka jagaha phira se milane ke liye samaya kI samAna sImA nikAlane ke liye niyama aparivartanazIla gati ko samAntara zreDhi vAlI gatiyoM ke prathama pada dvArA hAsita karate haiM, aura taba pracaya kI arddha rAzi dvArA bhAjita karate haiN| isa pariNAmI rAzi meM jaba 1 jor3ate haiM, taba milane (317 ) adhyAya do kI gAthAe~ 80-82 tathA unake noTa dekhiye / * samAntara zredi ke padoM ke rUpa meM prarUpita uttarottara gatiyoM rUpa gati /

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174] gaNitasArasaMgrahaH [6.319 dviguNo mArgastadgatiyogahRto yogakAlaH syAt // 319 / / ___ atroddezakaH kazcinnaraH prayAti tribhirAdA uttaraistathASTAbhiH / niyatagatirekaviMzatiranayoH kaH prAptakAlaH syAt / / 320 / / aparA|dAharaNam / SaD yojanAni kazcitpuruSastvaparaH prayAti ca trINi / ubhayorabhimukhagatyoraSTottarazatakayojanaM gamyam / pratyekaM ca tayoH syAtkAlaH kiM gaNaka kathaya me zIghram // 3213 / / saMkalitasamAgamakAlayojanAnayanasUtram - ubhayorAdyoH zeSazcayazeSahRto dvisaMguNaH saikaH / yugapatprayANayoH syAnmArge tu samAgamaH kAlaH // 3223 / / kA iSTa samaya prApta hotA hai| (jaba do manuSya nizcita gati se viraddha dizAoM meM cala rahe hoM, taba unameM se kisI eka ke dvArA taya kI gaI ausata dUrI kI dugunI rAzi pUrI taya kI jAnevAlI yAtrA hotI hai / jaba yaha unakI gatiyoM ke yoga dvArA bhAjita kI jAtI hai, taba unake milane kA samaya prApta hotA hai|)|| 319 // udAharaNArtha prazna koI manuSya Arambha meM 3 kI gati se aura uttarottara 8 pracaya dvArA niyamita rUpa se bar3hAne vAlI gati se jAtA hai / dUsare manuSya kI nizcita gati 21 hai / yadi ve eka hI dizA meM, eka samaya, usI sthAna se prasthAna kareM, to unake milane kA samaya kyA hogA ? / / 320 // ( Upara kI gAthA ke ) uttarArddha ke liye udAharaNArtha prazna ____eka manuSya 6 yojana kI gati se aura dUsarA 3 yojana kI gati se yAtrA karatA hai| unameM se kisI eka ke dvArA taya kI gaI ausata dUrI 100 yojana hai| he gaNaka, unake milane kA samaya nikAlo / / 321-3211 // yadi do vyakti eka hI sthAna se, eka hI samaya tathA vibhinna saMkalita gatiyoM se prasthAna kareM, to unake milane kA samaya aura taya kI gaI dUrI nikAlane ke liye niyama ukta do prathama padoM kA aMtara jaba ukta do pracayoM ke aMtara se bhAjita hokara aura taba 2 se guNita hokara 1 dvArA bar3hAyA jAya, to yugapat yAtrA karane vAle vyaktiyoM ke milane kA samaya utpanna hotA hai / / 3223 // + 1 = sa, jahA~ va nizcala vega hai, ba pracaya hai, (319) bIjIya rUpa se, (va - a) aura sa samaya hai| (3211) bIjIya rUpa se, na% araa12+1. ba-bala

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mizrakavyavahAraH [175 -6. 3263 ] atroddezakaH catvAryAdyaSTottarameko gacchatyatho dvitIyo naa| dvau pracayazva dazAdiH samAgame kastayoH kAlaH // 3233 // vRdhdyuttarahInottarayoH samAgamakAlAnayanasUtramzeSazcAdyorubhayozcayayutadalabhaktarUpayutaH / yugapatprayANakRtayormArge saMyogakAlaH syAt / / 3243 / / atroddeshkH| paJcAdyaSTottarataH prathamo nAtha dvitIyanaraH / AdiH paJcananava pracayo hIno'STa yogakAlaH kaH / / 3253 / / zIghragatimandagatyoH samAgamakAlAnayanasUtrammandagatizIghragatyorekAzAgamanamatra gamyaM yat / tadgatyantarabhaktaM labdhadinaistaiH prayAti zIghro'lpam // 3263 / / ___ udAharaNArtha prazna eka vyakti 4 se Arambha hone vAlI aura uttarottara pracaya 8 dvArA bar3hane vAlI gatiyoM se yAtrA karatA hai / dUsarA vyakti 10 se Arambha hone vAlI aura uttarottara 2 pracaya dvArA bar3hane vAlI gatiyoM se yAtrA karatA hai / unake milane kA samaya kyA hai? // 3233 / / eka hI sthAna se ravAnA hone vAle aura eka hI dizA meM samAntara zreDhi meM bar3hanevAlI gatiyoM se yAtrA karane vAle do vyaktiyoM ke milane kA samaya nikAlane ke lie niyama, jaba ki prathama dazA meM pracaya dhanAtmaka hai, aura dUsarI dazA meM RNAtmaka hai : ukta do prathama padoM ke aMtara ko ukta do diye gaye pracayoM kA prarUpaNa karanevAlI saMkhyAoM ke yoga kI arddha rAzi dvArA bhAjita karane ke pazcAt prApta phala meM 1 jor3A jAtA hai| yaha una do yAtriyoM ke milane kA samaya hotA hai // 324 // udAharaNArtha prazna prathama vyakti 5 se Arambha hone vAlI aura uttarottara pracaya dvArA bar3hanevAlI gatiyoM se yAtrA karatA hai| dUsare vyakti kI Arambhika gati 45 hai aura pracaya RNa 8 hai| unake milane kA samaya kyA hai ? // 325 // bhinna samayoM para ravAnA honevAle aura kramazaH tIvra aura maMda gati se eka hI dizA meM calanevAle do manuSyoM ke milane kA samaya nikAlane ke lie niyama maMdagati aura tIvragati vAle donoM eka hI dizA meM gamanazIla haiN| taya kI jAnevAlI dUrI ko yahA~ una do gatiyoM ke aMtara dvArA bhAjita kiyA jAtA hai| isa bhajanaphala dvArA prarupita dinoM meM, tIvra gativAlA maMdagati vAle kI ora jAtA hai // 326 // ( 3243 ) isakI tulanA 3223 vIM gAthA meM diye gaye niyama se kro|

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gaNitasArasaMgrahaH atroddezakaH navayojanAni kazcitprayAti yojanazataM gataM tena / pratidUto vrajati punastrayodazApnoti kairdivasaiH || 3273 // viSamabANaistUNIravANaparidhikaraNasUtram - pariNAhastribhiradhiko dalito vargIkRta stribhirbhaktaH / saikaH zarAstu parigherAnayane tatra viparItam || 3283 // atroddezakaH 176 ] nava paridhistu zarANAM saMkhyA na jJAyate punasteSAm / tryuttaradazabANAstatpariNAhazarAMzca kathaya me gaNaka || 3293 || Dhobaddhe iSTakAnayanasUtram - taravargo rUponastribhirvibhaktastareNa saMguNitaH / tara saMkalite sveSTapratADite mizrataH sAram ||3303 // udAharaNArtha prazna koI vyakti 9 yojana pratidina kI gati se yAtrA karatA hai| usake dvArA 100 yojana kI dUrI pahile hI taya kI jA cukI hai| eka saMdezavAhaka usake pIche 13 yojana prati dina kI gati se bhejA gayA / yaha kitane dinoM meM usase jAkara milegA ? tarakaza meM bhare hue jJAta ayugma saMkhyA ke zaroM kI sahAyatA se tarakaza ke zaroM kI paridhyAnasaMkhyA nikAlane ke liye ( tathA viloma krameNa ) niyama // 3273 // paridhyAna zaroM kI saMkhyA ko 3 dvArA bar3hAkara AdhA kiyA jAtA hai| ise vargita kiyA jAtA hai, aura taba 3 dvArA bhAjita kiyA jAtA hai| isa pariNAmI rAzi meM 1 jor3ane para tarakaza ke zaroM kI saMkhyA prApta hotI hai / jaba paridhyAna zaroM kI saMkhyA nikAlanI hotI hai, to viparIta kriyA karanI par3atI hai / / 3283 / / udAharaNArtha prazna zaroM kI paridhyAna saMkhyA 9 hai / unakI kula saMkhyA ajJAta hai / vaha kauna sI hai ? tarakaza meM kula zaroM kI saMkhyA 13 hai / he gaNitajJa, paridhyAna zaroM kI saMkhyA batalAo || 3693 / / kisI bhavana kI zreNIbaddha ( eka ke Upara dUsarI ) iSTakAoM ( IMToM) kI saMkhyA nikAlane ke liye niyama satahoM kI saMkhyA ke varga ko 1 dvArA hAsita kara 3 dvArA bhAjita kiyA jAtA hai, aura taba satahoM kI saMkhyA dvArA guNita kiyA jAtA hai| isa prakAra prApta rAzi meM vaha guNanaphala jor3ate haiM, jo sabase Upara kI sataha kI IMToM ko prarUpita karanevAlI ( mana se cunI huI ) saMkhyA aura eka se AraMbha hokara dI gaI satahoM kI saMkhyA taka kI prAkRta saMkhyAoM ke yoga kA guNana karane se prApta hotA iSTa uttara hotA hai ||3302 // / prAptaphala (3303) bIjIya rUpa se, na 2 [ 6.327 3 saMkhyA hai; jahA~ 'na' satahoM kI saMkhyA hai, na ( na + 1) 2 , yaha, banAvaTa kI kula IMToM kI aura 'a' sarvocca sataha meM IMToM kI mana se cunI huI saMkhyA hai / X na + a x

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- 6. 3333] mizrakavyavahAraH [177 atroddezakaH paJcataraikenAgraM vyavaghaTitA gaNitavinmizre / samacaturazrazreDhI katISTakAH syurmamAcakSva // 3313 / / nandyAvartAkAraM catustarAH SaSTisamaghaTitAH / sarveSTakAH kati syuH zreDhobaddhaM mamAcakSva // 332 / / chandaH zAstroktaSaTpratyayAnAM sUtrANisamadalaviSamakharUpaM dviguNaM vargIkRtaM ca padasaMkhyA / saMkhyA viSamA saikA dalato gurureva samadalataH // 3333 / / udAharaNArtha prazna 5 satahavAlI eka vargAkAra banAvaTa taiyAra kI gaI hai| sabase Upara kI sataha meM kevala : iMTa hai| he prazna kI gaNanA jAnane vAle mitra, isa banAvaTa meM kula kitanI iMTeM haiM ? // 331 / / nandyAvarta ke AkAra kI eka banAvaTa uttarottara iMToM kI satahoM se taiyAra kI gaI hai| eka paMkti meM sabase Upara kI iMToM kA saMkhyAtmaka mAna 60 hai, jisake dvArA 4 sataheM sammitIya banAI gaI haiN| batalAo isameM kula kitanI IMTeM lagAI gaI haiM ? // 3323 // chanda (prosody ) zAstrokta chaH pratyayoM ko jAnane ke liye niyama diye gaye zabdAMzika chanda meM zabdAMzoM ( akSaroM) athavA padoM kI yugma aura ayugma saMkhyA ko alaga stambha meM kramazaH 0 aura 1 dvArA cinhita kiyA jAtA hai| (cinhita karane kI vidhi isI adhyAya ke 3111 ve sUtra meM dekhiye / ) vaha isa prakAra hai : yugmamAna ko AdhA kiyA jAtA hai, aura ayugma mAna meM se 1 ghaTAyA jAtA hai / isa vidhi ko taba taka jArI rakhA jAtA hai, jaba taka ki aMtatogatvA zUnya prApta nahIM hotA / isa prakAra prApta aMkoM kI zraGkhalA meM aMkoM ko dugunA kara diyA jAtA hai, aura taba zraGkhalA kI talI se zikhara taka kI saMtata guNana kriyA meM, ve aMka, jinake Upara zUnya AtA hai, vargita kara diye jAte haiM / isa saMtata guNana kA pariNAmI guNanaphala chanda ke vibhinna sambhava zlokoM kI saMkhyA hotA hai // 3333 // isa prakAra prApta sabhI prakAra ke zlokoM meM laghu aura guru kisI bhI sataha kI lambAI athavA caur3AI para IToM kI saMkhyA, agrima nimna (nIcI ) sataha kI IToM se 1 kama hotI hai| ( 3323 ) gAthA meM nirdiSTa nandyAvarta AkRti yaha hai- ' (3331-336.) guru aura laghu zabdAMzoM ( syllables) ke bhinna-bhinna vinyAsa ke saMvAdI kaI vibheda utpanna hote haiM, kyoMki zloka ( stanza) ke eka cauthAI bhAga ko banAnevAle pada (line) meM pAyA jAnevAlA pratyeka zabdAMza yA to laghu athavA guru ho sakatA hai| ina vibhedoM ke vinyAsoM ke liye koI nizcita krama upayoga meM lAyA jAtA hai / yahA~ diye gaye niyama hameM nimnalikhita ko nikAlane meM sahAyaka hote haiM, (1) nirdiSTa zabdAMzoM kI saMkhyA vAle chanda meM sambhava vibhedoM kI saMkhyA, (2) ina prakAroM meM zabdAMzoM ke vinyAsa kI vidhi, (3) svakramasUcaka sthiti dvArA nirdiSTa kisI vibheda meM zabdAMzoM kA vinyAsa, (4) zabdAzoM ke nirdiSTa vinyAsa kI kramasUcaka sthiti, (5) nirdiSTa saMkhyA ke guru aura laghu zabdAMzoM vAle vibhedoM kI saMkhyA, aura (6) kisI vizeSa chanda ke vibhedoM kA pradarzana karane ke liye udagra (lamba rUpa) jagaha kA parimANa / ga0 sA0 saM0-23

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2/2 178] gaNitasArasaMgrahaH [ 6. 3343syAllaghurevaM kramazaH prastAro'yaM vinirdiSTaH / naSTAGkA laghuratha tassaikadale guruH punaH punaH sthAnam // 334 / / akSaroM ( syllables ) ke vinyAsa ko isa prakAra nikAlate haiM se Arambha honevAlI tathA diye gaye chandoM meM zlokoM kI mahattama sambhava saMkhyA ke mApa meM aMta honevAlI prAkRta saMkhyAe~ likhI jAtI haiN| pratyeka ayugma saMkhyA meM 1 jor3A jAtA hai, aura taba use AdhA kiyA jAtA hai| jaba yaha kriyA kI jAtI hai, taba guru akSara (syllable) nizcita pUrvaka sUcita hotA hai / jahA~ saMkhyA yugma hotI hai vaha tatkAla hI AdhI kara dI jAtI hai, jisase vaha laghu pratyaya (syllable) ko sUcita karatI hai| isa prakAra, dazA ke anusAra ( usI samaya saMvAdI guru aura laghu zloka 3373 meM diye gaye praznoM ko nimnalikhita rUpa meM hala karane para ye niyama spaSTa ho jAveMge(1) chanda meM 3 zabdAMza hote haiM; aba hama isa prakAra Age bar3hate haiM3-1 1 dAhine hAtha kI zrRMkhalA ke aGkoM ko 2 dvArA guNita karane para hameM * prApta 2 1 hotA hai| adhyAya 2ke 94 veM zloka (gAthA) kI TippaNI meM samajhAye anusAra guNana aura varga karane kI vidhi dvArA hameM 8 prApta hotA hai| yahI vibhedoM kI saMkhyA hai| (2) pratyeka vibheda meM zabdAMzoM ke vinyAsa kI vidhi isa prakAra prApta hotI haiprathama prakAra : 1 ayugma hone ke kAraNa guru zabdAMza hai; isaliye prathama zabdAMza guru hai / isa 1 meM (vibheda) 1 jor3o, aura yoga ko 2 dvArA bhAjita kro| bhajanaphala ayugma hai, aura dUsare guru zabdAMza ko darzAtA hai| phira se, isa bhajana phala 1 meM 1 jor3ate haiM, aura yoga ko 2 dvArA bhAnita karate haiM; pariNAma phira se ayugma hotA hai, aura tIsare guru zabdAMza ko darzAtA hai| isa prakAra, prathama prakAra meM tIna guru zabdAMza hote haiM, jo isa prakAra darzAye jAte haiM / dvitIya prakAra: 2 yugma hone ke kAraNa laghu zabdAMza sUcita karatA hai / jaba isa 2 ko 2 dvArA (vibheda) bhAjita karate haiM, to bhajanaphala 1 hotA hai jo ayugma hone ke kAraNa guru zabdAMza ko sUcita karatA hai| isa 1 meM 1 jor3o, aura yoga ko 2 dvArA bhAjita karo; bhajanaphala ayugma hone ke kAraNa guru zabdAMza ko sUcita karatA hai| isa prakAra, hameM yaha prApta hotA hai / isI prakAra anya vibhedoM ko prApta karate haiN| (3) udAharaNa ke liye, pA~cavA~ prakAra (vibheda ) upara kI taraha prApta kiyA jA sakatA hai| (4) udAharaNa ke liye, prakAra (vibheda ) kI kramasUcaka sthiti nikAlane ke liye hama yaha rIti apanAte haiM / / / 124 ina zabdAMzoM ke nIce, jisakI sAdhAraNa niSpatti 2 hai aura prathamapada 1 hai aisI guNottara zredi likho| laghu zabdAMzoM ke nIce likhe aMka 4 aura 1 jor3o, aura yoga ko 1 dvArA bddh'aao| hameM 6 prApta

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-6. 3363 mizrakavyavahAraH [179 rUpAddviguNottaratastUddiSTe lAGkasaMyutiH saikA / ekAdyakottarataH padamUrdhvAdharyataH kramotkramazaH // 3353 / / sthApya pratilomannaM pratilomannena bhAjitaM sAram / syAllaghugurukriyeyaM saMkhyA dviguNaikavarjitA sAdhvA / / 336 / / akSara dekhate hue), 1 jor3ane athavA nahIM jor3ane ke sAtha AdhI karane kI kriyA, niyamita rUpa se, taba taka jArI rakhanA cAhiye, jaba taka ki, pratyeka dazA meM chanda ke pratyayoM kI yathArtha saMkhyA prApta nahIM ho jaatii| yadi svAbhAvika krama meM kisI prakAra ke pada kA prarUpaNa karanevAlI saMkhyA, (jahA~ akSaroM kA vinyAsa jJAta karanA hotA hai ) yugma ho to vaha AdhI kara dI jAtI hai aura laghu akSara ko sUcita karatI hai / yadi vaha ayugma ho, to usameM 1 jor3A jAtA hai aura taba use AdhA kiyA jAtA hai aura yaha guru akSara darzAtI hai| isa prakAra guru aura laghu akSaroM ko unakI kramavAra sthitimeM bArabAra rakhanA par3atA hai jaba taka ki pada meM akSaroM kI mahattama saMkhyA prApta nahIM ho jaatii| yaha, zloka ( stanza) ke iSTa prakAra meM, guru aura laghu akSaroM ke vinyAsa ko detA hai // 33 // jahA~ kisI vizeSa prakAra kA zloka diyA hone para usakI nirdiSTa sthiti ( chanda meM sambhava prakAroM ke ilokoM meM se ) nikAlanA ho, vahA~ eka se Arambha honevAlI aura 2 sAdhAraNa niSpatti vAlI guNottara zreDhi ke padoM ( terms ) ko likha liyA jAtA hai, ( yahA~ zreDhi ke padoM kI saMkhyA, diye gaye chandoM meM akSaroM kI saMkhyA ke tulya hotI hai)| ina padoM ( terms) ke Upara saMvAdI guru yA laghu akSara likha liye jAte haiN| taba laghu akSaroM ke ThIka nIce kI sthiti vAle sabhI pada (terms) jor3e jAte haiN| isa prakAra prApta yoga eka dvArA bar3hAyA jAtA hai / yaha iSTa nirdiSTa kramasaMkhyA hotI hai| 1 se Arambha hone vAlI (aura chanda meM diye gaye akSaroM kI saMkhyA taka jAne vAlI) prAkata saMkhyAe~, niyamita krama aura myutkrama meM, do paMktiyoM meM, eka dUsare ke nIce likha lI jAtI haiM / paMkti kI saMkhyAe~ 1, 2,3 ( athavA eka hI bAra meM inase adhika) dvArA dAe~ se bAe~ ora guNita kI jAtI haiN| isa prakAra prApta Upara kI paMkti sambandhI guNanaphala nIce kI paMkti sambandhI saMvAdI guNanaphaloM dvArA bhAjita kiye jAte haiN| taba prApta bhajanaphala, kavitA ( verse ) meM 1,2,3 yA inase adhika, choTe yA bar3e akSaroM vAle ( diye gaye chanda meM ) zlokoM ( stanzas) ke prakAroM kI saMkhyA kI prarUpaNA karatA hai / ise hI nikAlanA iSTa hotA hai| diye gaye chanda ( metre ) meM zlokoM ke vibhedoM kI sambhava saMkhyA ko do dvArA guNita kara eka dvArA hAsita kiyA jAtA hai| yaha phala adhvAna kA mApa detA hai| yahA~. chanda ke pratyeka do uttarottara vibhedoM ( prakAroM ) ke bIca zloka (stanzas) ke talya aMtarAla ( interval ) kA honA mAnA jAtA hai / / 3353-3363 / / hotA hai| isaliye aisA kahate haiM ki tri-zabdAMzika chanda meM yaha chaThavA~ prakAra (vibheda ) hai| (5) mAnalo prazna yaha hai : 2 choTe zabdAMzoM vAle vibheda kitane haiM? prAkRta saMkhyAoM ko niyamita aura viloma krama meM eka dUsare ke nIce isa prakAra rakhoH 123 dAhine ora se bAI ora ko, Upara se aura nIce se do pada ( terms ) lekara, hama pUrvavartI guNanaphala

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180] gaNitasArasaMgrahaH [ 6. 3373atroddezakaH saMkhyA prastAravidhiM naSToddiSTe lagakriyAdhvAnau / SaTpratyayAMzca zIghra tryakSaravRttasya me kathaya // 3372 / / iti mizrakavyavahAre zreDhIbaddhasaGkalitaM samAptam / iti sArasaMgrahe gaNitazAstre mahAvIrAcAryasya kRto mizrakagaNitaM nAma paJcamavyavahAraH samAptaH / / udAharaNArtha prazna 3 akSaroM (syllables ) vAle chanda ke sambandha meM 6 pratyayoM ko batalAo-. (.) chanda ke sambhava zlokoM ( stanzas) kI mahattama saMkhyA, (2) una zlokoM meM akSaroM ke vinyAsa kA krama, (3) kisI diye gaye prakAra ke zlokoM meM akSaroM (zabdAMzoM) kA vinyAsa, jahA~ chanda meM sambhava prakAroM kI kramasUcaka sthiti jJAta hai, (4) diye gaye zloka kI kramasUcaka sthiti, (5) kisI dI gaI laghu yA guru akSaroM ( zabdAMzoM) kI saMkhyAvAle diye gaye chanda ( metre) meM ilokoM kI saMkhyA, aura ( 6 ) adhvAna nAmaka rAzi // 3373 // isa prakAra, mizraka vyavahAra meM zreDhibaddha saMkalita nAmaka prakaraNa samApta huaa| isa prakAra, mahAvIrAcArya kI kRti sArasaMgraha nAmaka gaNitazAstra meM mizraka nAmaka paJcama vyavahAra samApta huaa| ko uttaravartI guNanaphala dvArA bhAjita karate haiM / bhajanaphala 3 iSTa uttara hai| (6) aisA kahA gayA hai ki chanda ke kisI bhI prakAra ke guru aura laghu zabdAMzoM ke nirUpaNa karanevAle pratIka, eka aMgula udagra ( vertical) jagaha le lete haiM, aura koI bhI do vibhedoM ke bIca kA aMtarAla (jagaha) bhI eka aMgula honA caahiye| isaliye, isa chanda ke 8 prakAroM (vibhedoM) ke liye iSTa udagra ( vertical ) jagaha kA parimANa 248-1 athavA 15 aMgula hotA hai|

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7. kSetragaNita vyavahAraH siddhebhyo niSThitArthebhyo variSThebhyaH kRtAdaraH / abhipretArthasiddhayarthaM namaskurve punaH punaH // 1 // itaH paraM kSetragaNitaM nAma SaSThagaNitamudAhariSyAmaH / tadyathAkSetraM jinapraNItaM phalAzrayAdvayAvahArika sUkSmamiti / / bhedAd dvidhA vicintya vyavahAraM spaSTametadabhidhAsye // 2 // tribhujacaturbhajavRttakSetrANi svasvabhedabhinnAni / gaNitANavapAragatairAcAryaiH samyaguktAni // 3 // tribhuja tridhA vibhinnaM caturbhujaM paJcadhASTadhA vRttam / avazeSakSetrANi hyeteSAM bhedabhinnAni // 4 // tribhujaMtu samaM dvisamaM viSamaM caturazramapi samaM bhavati / dvidvisamaM dvisamaM syAtrisamaM viSamaM budhAH prAhuH // 5 // samavRttamardhavRttaM cAyatavRttaM ca kambukAvRttam / nimnonnataM ca vRttaM bahirantazcakravAlavRttaM ca / / 6 / / 7. kSetra-gaNita vyavahAra (kSetraphala ke mApa sambandhI gaNanA ) apane iSTa artha kI siddhi ke liye maiM mana, vacana, kAya se kRtakRtya aura sarvotkRSTa siddhoM ko vAraMvAra sAdara namaskAra karatA hU~ // 1 // isake pazcAt hama kSetra gaNita nAmaka viSaya kI chaH prakAra kI gaNanA kI vyAkhyA kareMge jo nimnalikhita hai jina bhagavAna ne kSetraphala kA do prakAra kA mApa praNIta kiyA hai, jo phala ke svabhAva para AdhArita hai; arthAt eka vaha jo vyAvahArika prayojanoM ke liye anumAnataH liyA jAtA hai, aura dUsarA vaha jo sUkSma rUpa se zuddha hotA hai| ise vicAra meM lekara maiM isa viSaya ko spaSTa rUpa se samajhAU~gA // 2 // gaNita rUpI samudra ke pAragAmI AcAryoM ne samyaka ( ThIka ) rUpa se vividha prakAra ke kSetraphaloM ke viSaya meM kahA hai| una kSetraphaloM meM tribhuja, caturbhuja aura vRtta ( vakrarekhIya ) kSetroM ko inhIM kramavAra prakAroM meM varNita kiyA hai // 3 // tribhuja kSetra ko tIna prakAra meM, caturbhuja ko pA~ca prakAra meM, aura vRtta ko ATha prakAra meM vibhAjita kiyA gayA hai| zeSa prakAra ke kSetra vAstava meM inhIM vibhinna prakAroM ke kSetroM ke vibhinna bheda haiM // 4 // buddhimAna loga kahate haiM ki tribhuja kSetra, samatribhuja, dvisama tribhuja ( samadvibAhu tribhuja ) aura viSama tribhuja ho sakatA hai, aura caturbhuja kSetra bhI samacaturazra (varga), dvidvisamacaturazra (Ayata), dvisamacaturazra (samalamba caturbhuja jisakI do asamAnAntara bhujAyeM barAbara nApakI hoM), trisamacaturazca (samalamba caturbhuja, jisakI tIna bhujAyeM barAbara nApakI hoM), viSama caturazca ( sAdhAraNa caturbhuja kSetra ) ho sakatA hai // 5 // vakrasarala kSetra, samavRtta (vRtta), avRtta, AyatavRtta (unendra athavA aMDAkAra kSetra ), kambukAvRtta (zaMkhAkAra kSetra), nimnAvRtta ( natodara vRttIya kSetra), unnatAvRtta (unnatodara vRttIya kSetra), bahizcakravAla vRtta (bAhara sthita karaNa), evaM aMtazcakravAla vRtta (bhItara sthita karaNa) ho sakatA hai // 6 // (5-6) ina gAthAoM meM kathita vibhinna prakAra kI AkRtiyA~ agale pRSTha para darzAI gaI haiM

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182 ] tribhujacaturbhujakSetra phalAnayanasUtram - tribhujacaturbhuja bAhuprati bAhu samAsadalahataM gaNitam / merbhujayutyadhaM vyAsaguNaM tatphalArdhamiha bAlendoH // 7 // sama tribhuja ( 4 ) vyAvahArika gaNita ( anumAnataH mApasambandhI gaNanA ) tribhuja aura caturbhuja kSetroM ke kSetraphala ( anumAnataH ) nikAlane ke liye niyama - sammukha bhujAoM ke yogoM kI arddharAziyoM kA guNanaphala, tribhuja aura caturbhuja kSetroM ke kSetraphala kA mApa hotA hai / kaGkaNa saharA AkRti ke cakra kI kinAra ( rim ) kA kSetraphala bhItara aura ( 1 ) ( 2 ) ( 3 ) samacaturazra ( 7 ) gaNitasArasaMgrahaH vyAvahArikagaNitam trisama caturazra ( 10 ) arddhavRtta dvisama tribhuja (5) dvidvi samacaturazra ( 8 ) viSama caturazra ( 11 ) [ 7. 7 Ayata (nendra ) viSama tribhuja ( 6 ) dvisamacaturazra ( 9 ) OFE samavRtta ( 12 ) D kambukAvRtta ( zaMkha ke AkAra kI AkRti )

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kSetra gaNitavyavahAraH atroddezakaH tribhujakSetrasyASTau bAhupratibAhubhUmayo daNDAH / tadvayAvahArikaphalaM gaNayitvAcakSva me zIghram // 8 // bAhara kI paridhiyoM ke yoga kI arddharAzi ko kaGkaNa kI caudAI se guNita karane para prApta hotA hai / isa phala kA yahA~ bAlacandramA sadRza AkRti kA kSetraphala hotA hai // 7 // udAharaNArtha prazna tribhuja ke sambandha meM, bhujA, sammukha bhujA, aura AdhAra kA mApa 8 daMDa hai; mujhe zIghra hI batalAo ki isakA vyAvahArika kSetraphala kyA hai ? // 8 // do barAbara bhujAoM vAle tribhuja ke sambandha ( 13 ) ( 14 ) -7. 8 ] nimnavRtta ( natodara vRttIya kSetra ) ( 15 ) [ 183 unnata vRtta (unnatodara vRttIya kSetra ) ( 16 ) O bahizcakravAla vRtta ( bAhara sthiti kaGkaNa ) aMtazcala vAlavRtta ( bhItara sthita kaGkaNa ) caturbhuja kSetroM ke kSetraphala aura anya mApoM ke diye gaye niyamoM para vicAra karane para jJAta hogA ki yahA~ kahe gaye caturbhuja kSetra cakrIya ( vRtta meM antalikhita ) haiM / isaliye samacaturazra yahA~ varga hai, dvi-dvipsamacaturazra Ayata hai, aura dvisamacaturazra tathA trisamacaturazra kI UparI bhujAe~ AdhAra ke samAnAntara haiN| ( 7 ) yahA~ tribhuja ko aisA caturbhuja mAnA gayA hai, jisake AdhAra kI sammukha bhujA itanI choTI hotI hai ki vaha upekSaNIya hotI hai / isa dazA meM tribhuja kI bAjU ko do bhujAe~, sammukha bhujAe~ bana jAtI haiM, aura UparI bhujA mAna meM nahIM ke barAbara lI jAtI hai| isaliye niyama meM tribhujIya kSetra ke sambandha meM bhI sammukha bhujAoM kA ullekha kiyA gayA hai; tribhuja do bhujAoM ke yoga kI arddharAzi samasta dazAoM meM U~cAI se bar3I hotI hai, isaliye isa niyama ke anusAra prApta kSetraphala kisI bhI udAharaNa meM sUkSma rUpa se ThIka nahIM ho sakatA / caturbhuja kSetroM ke sambandha meM isa niyama ke anusAra prApta kSetraphala varga aura Ayata ke viSaya meM ThIka ho sakatA hai, parantu anya dazAoM meM kevala sthUlarUpeNa zuddha hotA hai / jinakA eka hI kendra hotA hai, aise do vRttoM kI paridhiyoM ke bIca kA kSetra nemikSetra kahalAtA hai / yahA~ diye gaye niyama ke anusAra nemikSetra ke vyAvahArika kSetraphala kA mApa zuddha mApa hotA hai / bAlendu jaisI AkRti kA isa niyamAnusAra prApta kSetraphala kevala anumAnita hI hotA hai /

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184]] gaNitasArasaMgrahaH [7.9dvisamatribhujakSetrasyAyAmaH saptasaptatirdaNDAH / vistAro dvAviMzatiratha hastAbhyAM ca saMmizrAH // 9 // tribhujakSetrasya bhujastrayodaza pratibhujasya paJcadaza / bhUmizcaturdazAsya hi daNDA viSamasya kiM gaNitam / / 10 / / gajadantakSetrasya ca pRSThe'STAzItiratra saMdRSTAH / dvAsaptatirudare tanmUle'pi triMzadiha' daNDAH // 11 / / kSetrasya daNDaSaSTirbAhupratibAhukasya gaNayitvA / samacaturazrasya tvaM kathaya sakhe gaNitaphalamAzu // 12 // Ayatacaturazrasya vyAyAmaH saikaSaSTiriha dnnddaaH| vistAro dvAtriMzabyavahAraM gaNitamAcakSva // 13 // daNDAstu saptaSaSTivisamacaturbAhukasya cAyAmaH / vyAsazcASTatriMzat kSetrasyAsya trayastriMzat // 14 // kSetrasyASTottarazatadaNDA bAhutraye mukhe cASTau / hastaitribhiyutAstastrisamacaturbAhukasya vada gaNaka // 15 // viSamakSetrasyASTatriMzaddaNDAH kSitirmukhe dvAtriMzat / pazcAzatprati bAhu SaSTistvanyaH kimasya cturshre||16|| paridhodarastu daNDAtriMzatpRSThaM zatatrayaM dRSTam / navapazcaguNo vyAso nemikSetrasya kiM gaNitam // 17 // 1. B aura M donoM meM triMzatiH pATha hai ! chaMdakI AvazyakatAnusAra ise triMzadiha rUpa meM zuddha kara rakhA gayA hai| 2. B meM "prati" ke liye "deka" pATha hai| meM do bhujAoM dvArA prarUpita lambAI 77 daMDa hai, aura AdhAra dvArA nApI gaI caur3AI 22 daMDa aura 2 hasta hai; kSetraphala nikAlo // 9 // viSama tribhuja ke sambandha meM eka bhujA 13 daMDa, sammukha bhujA 15 daMDa, aura AdhAra 14 daMDa hai / isa AkRti ke kSetraphala kA mApa kyA hai ? // 10 // hAthI ke dA~ta ke madhya se phAr3e hue cheda ( section ) kI AkRti ke bAharI vakra kI lambAI 88 daMDa hai, bhItarI vakra kI lambAI 72 daMDa hai, aura jar3a ke pAsa kI muTAI 30 daMDa hai; kSetraphala nikAlo // 11 // samAyata (varga) ke sambandha meM, jisakI bhujAoM meM se pratyeka 60 daMDa hai, he mitra, zIghrahI kSetraphala kA pariNAmI nApa batalAo // 12 // Ayata caturazra kSetra ke sambandha meM yahA~ lambAI 61 daMDa hai aura caur3AI 32 daMDa hai / vyAvahArika kSetraphala batalAo // 13 // do samAna bAhuoM vAle caturbhujoM kI pratyeka samAna bhujA kI lambAI 67 daMDa hai, caur3AI ( AdhAra para ) 38 hai aura ( Upara ) 33 daMDa hai| kSetraphala kA mApa batalAo // 14 // tIna barAbara bhujAoM vAle caturbhuja kSetra kI pratyeka samAna bhujA 108 daMDa kI hai, aura zeSa (mukha athavA UparI ) bhujAyeM 8 daMDa 3 hasta haiN| he gaNitajJa, isa kSetra ke kSetraphala kA mApa batalAo // 15 // viSama caturbhuja kA AdhAra 38 daMDa, UparI mukha-bhujA 32 daMDa, bAjU kI eka bhujA (pratibAha) 50 daMDa aura dUsarI 60 daMDa kI hai| isa AkRti kA kSetraphala kyA hai ? // 16 // kiso kaMkaNa meM bhItarI vRttAkAra sImA 30 daMDa kI hai, bAharI vRttAkAra sImA 300 daMDa hai aura kaGkaNa kI caur3AI 45 hai| isa kaGkaNa (nemi kSetra) kA kSetraphala nikAlo // 17 // bAlacA~da sadRza eka AkRti kI caur3AI 2 hasta hai| bAharI vakra 68 hasta aura (11) isa gAthA meM kathita AkRti kA AkAra bAjU meM dI gaI AkRti ke samAna hotA hai / prayojana yaha hai ki ise tribhujIya kSetra ke samAna vartA jAve, aura taba isakA kSetraphala tribhujIya kSetroM sambandhI niyama dvArA nikAlA jAya /

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-7. 22] kSetragaNitavyavahAraH [185 hastau dvau viSkambhaH pRSThe'STASaSTiriha ca saMdRSTAH / udare tu dvAtriMzadbAlendoH kiM phalaM kathaya / / 18 // . vRttakSetraphalAnayanasUtram-. triguNIkRtaviSkambhaH paridhiA sArdhavargarAzirayam / triguNaH phalaM same'rdhe vRtte'dhaM prAhurAcAryAH // 19 // atroddezakaH vyAso'STAdaza vRttasya paridhiH kaH phalaM ca kim / vyAso'STAdaza vRttArdhe gaNitaM kiM vadAzu me // 20 // AyatavRttakSetraphalAnayanasUtramvyAsAdheyuto dviguNita AyatavRttasya paridhirAyAmaH / viSkambhacaturbhAgaH pariveSahato bhavetsAram // 21 // atroddezakaH kSetrasyAyatavRttasya viSkambho dvAdazaiva tu / AyAmastatra SaTtriMzat paridhiH kaH phalaM ca kim // 22 / / bhItarI vakra 32 hasta hai| batalAo kI pariNAmI kSetraphala kyA hai ? // 18 // vRtta kA vyAvahArika kSetraphala nikAlane ke liye niyama vyAsa ko 3 dvArA guNita karane se paridhi prApta hotI hai, aura vyAsa (viSkambha ) kI arddha rAzi ke varga ko 3 dvArA guNita karane se pUrNa vRtta kA kSetraphala prApta hotA hai| AcArya kahate haiM ki arddhavRtta kA kSetraphala aura paridhi kA mApa inase AdhA hotA hai / / 19 // udAharaNArtha prazna vRtta kA vyAsa 18 hai| usakI paridhi aura pariNAmI kSetraphala kyA hai? arddhavRtta kA vyAsa 18 hai / zoghra kaho ki usake kSetraphala aura paridhi kyA haiM ? // 20 // Ayata vRtta (janendra athavA aMDAkAra) AkRti kA kSetraphala nikAlane ke liye niyama baDe vyAsa ko choTe vyAsa kI arddha rAzi dvArA bar3hAkara aura taba 2 dvArA guNita karane para AyatavRtta ( janendra ) kI paridhi kA AyAma ( lambAI ) prApta hotA hai| choTe vyAsa kI eka caudhAI rAzi ko paridhi dvArA guNita karane para kSetraphala kA mApa prApta hotA hai // 21 // udAharaNArtha prazna Unendra AkRti (elliptical figure ) ke sambandha meM choTA vyAsa 12 hai aura bar3A gyAsa 36 hai| paridhi aura pariNAmI kSetraphala kyA hai ? // 22 // ( 19) paridhi aura kSetraphala kA mApa yahA~ ( / paridhi 7 ) kA mAna 3 lekara diyA gayA hai| ( 21 ) anendra ( AyatavRtta yA aMDAkRti ) kI paridhi ke liye diyA gayA sUtra spaSTa rUpa se koI bhinna prakAra kA anumAna hai| Unendra kA kSetraphala (ja. a. ba.) hotA hai, jahA~ a aura bahasa Ayata vRtta kI kramazaH bar3I aura choTI ardhAkSa (semiaxes ) haiN| yadi kA mAna 3 leM taba 7. a.ba = 3 a.ba hotA hai| parantu isa gAthA meM diye gaye sUtra se kSetraphala kA mApa 2 ba=2 aba+bara hotA hai| ga. sA. saM0-24

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186] gaNitasArasaMgrahaH [7. 23 zaGkhAkAravRttasya phalAnayanasUtramvadanA?no vyAsastriguNaH paridhistu kambukAvRtte / valayAkRtitryaMzo mukhArdhavargatripAdayutaH // 23 // atroddezakaH vyAso'STAdaza hastA mukhavistAro'yamapi ca catvAraH / kaH paridhiH kiM gaNitaM kathaya tvaM kambukAvRtte // 24 // nimnonnatavRttayoH phalAnayanasUtramparidhezca caturbhAgo viSkambhaguNaH sa viddhi gaNitaphalam / catvAle kUrmanibhe kSetre nimnonnate tasmAt // 25 // zaMkha ke AkAra kI vakrarekhIya AkRti kA pariNAmI kSetraphala nikAlane ke liye niyama zaMkha ke AkAra ke vakrarekhIya ( curvilinear ) AkRti ke sambandha meM, sabase bar3I caur3AI ko mukha kI arda rAzi dvArA hAsita aura 3 dvArA guNita karane para parimiti (paridhi) prApta hotI hai| isa parimiti kI arddharAzi ke varga ke eka tihAI bhAga ko mukha kI arddharAziyoM ke varga ko tIna cauthAI rAzi dvArA hAsita karate haiN| isa prakAra kSetraphala prApta hotA hai // 23 // udAharaNArtha eka prazna zaMkha (kambukAvRtta) kI AkRti ke sambandha meM caur3AI 18 hasta aura mukha 4 hasta hai| usakI parimiti tathA kSetraphala nikAlo // 24 // natodara aura unnatodara vartula taloM ke kSetraphala nikAlane ke liye niyama samajho ki paridhi kI eka cauthAI rAzi ko vyAsa dvArA guNita karane para pariNAmI kSetraphala prApta hotA hai| isa prakAra catvAla aura kachuve kI pITha jaise natodara aura unnatodara kSetroM kA kSetraphala prApta karanA par3atA hai // 25 // (23) yadi a vyAsa ho aura ma mukha kA mApa ho, taba 3 (a-3 ma) paridhi kA mApa hotA hai aura 13 ( a-3 ma) | degx3+ 3x (ma) kSetraphala kA mApa hotA hai / diye hue varNana se AkRti kA AkAra spaSTa nahIM hai| parantu paridhi aura kSetraphala ke liye diye gaye mAnoM se vaha eka hI vyAsa para do aura bhinna-bhinna vyAsa vAle vRttoM ko khIMcakara prApta huI AkRti kA AkAra mAnA jA sakatA hai, jo 6 vIM gAthA ke noTa meM 12 vI AkRti meM batalAyA gayA hai| (25) yahA~ nirdiSTa kSetraphala golIya khaMDa kA jJAta hotA hai| pratIka rUpa se yaha kSetraphala (C4 va ) ke barAbara hai, jahA~ pa chedIya vRtta (kinAra ) kI paridhi hai aura va vyAsa hai / parantu isa paridhi prakAra ke golIya khaMDa ke tala kA kSetraphala (2xnxxxu) hotA hai, jahA~ nita tra = kendrIya vRtta ( kinAra ) kI trijyA, aura u golIya khaMDa kI U~cAI hai / 4 vyAsa,

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-7.30] kSetragatiNavyavahAraH [187 atroddezakaH catvAlakSetrasya vyAsastu bhasaMkhyakaH paridhiH / SaTpaJcAdazadRSTaM gaNitaM tasyaiva kiM bhavati // 26 / / kUrmanibhasyonnatavRttasyodAharaNamaviSkambhaH paJcadaza dRSTaH paridhizca SaTtriMzat / kUrmanibhe kSetre kiM tasmin vyavahArajaM gaNitam / / 27 // antazcakravAlavRttakSetrasya bahizcakravAlavRtrakSetrasya ca vyavahAraphalAnayanasUtram - nirgamasahito vyAsastriguNo nirgamaguNo bahirgaNitam / rahitAdhigamavyAsAdabhyantaracakravAlavRttasya / / 28 // atroddezakaH vyAso'STAdaza hastAH punarbahirnirgatAtrayastatra / vyAso'STAdaza hastAzcAntaH punaradhigatAstrayaH kiM syAt / / 29 / / ___ samavRttakSetrasya vyAvahArikaphalaM ca paridhipramANaM ca vyAsapramANaM ca saMyojya etatsaMyogasaMkhyAmeva svIkRtya tatsaMyogapramANa rAzeH sakAzAt pRthaka paridhivyAsa phalAnAM saMkhyAnayanasUtramgaNite dvAdazaguNite mizraprakSepakaM catuHSaSTiH / tasya ca mUlaM kRtvA paridhiH prakSepakapadonaH / / 30 / / ___udAharaNArtha prazna catvAla ( homa vedI kA agni kuNDa ) kSetra ke kSetraphala ke sambandha meM gyAsa 27 hai aura paridhi 56 hai| isa kuNDa kA kSetraphala nikAlo // 26 // kachuve kI pITha kI taraha unnatodara vartulatala ke liye udAharaNArtha prazna gyAsa 15 hai aura paridhi 36 hai| kachuve kI pITha kI bhAMti isa kSetra kA vyAvahArika kSetraphala nikAlo // 27 // bhItarI kaTTaNa aura bAharI kaGkaNa ke kSetraphala kA vyAvahArika mAna nikAlane ke liye niyama bhItarI vyAsa ko kaGkaNakSetra kI caur3AI dvArA bar3hAkara jaba 3 dvArA guNita kiyA jAtA hai, aura kaGkaNakSetra kI caur3AI dvArA guNita kiyA jAtA hai, taba bAharI kaGkaNa kA kSetraphala utpanna hotA hai / isI prakAra bhItarI kaGkaNa ke kSetraphala ko kaGkaNa kI caur3AI dvArA bAsita nyAsa dvArA guNita karane se prApta karate haiM // 28 // udAharaNArtha prazna vyAsa 18 hasta hai, aura bAharI kaGkaNa kSetra kI caur3AI 3 hai; vyAsa 18 hasta hai, aura phira se bhItarI karaNa kI caur3AI 3 hasta hai| pratyeka dazA meM kakSaNa kA kSetraphala nikAlo // 29 // vRtta AkRti kI paridhi, vyAsa aura kSetraphala nikAlane ke liye niyama, jabaki kSetraphala, paridhi aura vyAsa kA yoga diyA gayA ho 12 dvArA guNita ukta tIna rAziyoM ke mizrita yoga meM prakSepita 64 jor3ate haiM, aura isa yoga kA vargamUla nikAlate haiM / taduparAMta isa vargamUla rAzi ko prakSepita 64 ke vargamUla dvArA hAsita karane se paridhi kA mApa prApta hotA hai // 30 // (28 ) antazcakravAla vRttakSetra aura bahizcakravAla vRttakSetra ke AkAra 7 vI gAthA ke noTa meM kathita nemikSetra ke AkAra ke samAna haiN| isaliye vaha niyama jo ina saba AkRtiyoM ke kSetraphala nikAlane ke liye hai, vyavahAra meM samAna sAdhita hotA hai / (30) yaha niyama nimnalikhita bIjIya nirUpaNa se spaSTa ho jAvegA

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188] gaNitasArasaMgrahaH [7. 31 - atroddezakaH paridhivyAsaphalAnAM mizraM SoDazazataM sahastrayutaM / kaH paridhiH kiM gaNitaM vyAsaH ko vA mamAcakSva // 31 // yavAkAramardalAkArapaNavAkAravajrAkArANAM kSetrANAM vyAvahArikaphalAnayanasUtramayavamurajapaNavazakrAyudhasaMsthAnapratiSThitAnAM tu / mukhamadhyasamAsArdhaM tvAyAmaguNaM phalaM bhavati / / 32 / / ___ atroddezakaH yavasaMsthAnakSetrasyAyAmo'zItirasya viSkambhaH / madhyazcatvAriMzatphalaM bhavetkiM mamAcakSva // 33 // AyAmo'zItirayaM daNDA mukhamasya viMzatimadhye / catvAriMzatkSetre mRdaGgasaMsthAnake behi // 34 // udAharaNArtha prazna kisI vRtta kI paridhi, vyAsa aura kSetraphala kA yoga 1116 hai, usa vRtta kI paridhi, gaNanA kiyA huA kSetraphala aura vyAsa ke mApoM ko prApta karo // 31 // lambAI kI ora se phAr3ane se prApta ( anvAyAma cheda ke ) (1) yavadhAnya (2) mardala (3) paNava aura (4) vajra AkAra kI vastuoM ke vyAvahArika kSetraphala nikAlane ke liye niyama yavadhAnya, muraja, paNava aura vajra ke AkAra ke kSetraphaloM ke sambandha meM iSTa mApa vaha hai jo aMta aura madhya mApa ke yoga kI arddharAzi ko lambAI dvArA guNita karane para prApta hotA hai // 32 // udAharaNArtha prazna kisI mRdaMga ke AkAra ke kSetra kA kSetraphala nikAlo jo lambAI meM 80 daMDa aura aMta (mukha ) meM 20 tathA madhya meM 40 daMDa ho // 34 // kisI kSetra ke sambandha meM jisakA AkAra paNava samAna mAnalo pa vRtta kI paridhi hai| cUMki 7 kA mAna 3 liyA gayA hai, isaliye vyAsa =1 aura 3. pravRtta kA kSetraphala hai / yadi paridhi, vyAsa aura vRtta ke kSetraphala, ina tInoM, kA mizrita yoga ma ho, to niyama meM diye gayA sUtra pa=/ 12 ma + 64-V64 ko samIkaraNa pa+ +3 =ma dvArA saralatApUrvaka prApta kara sakate haiN| (32) muraja kA artha mardala tathA mRdaMga bhI hotA hai| gAthA meM kathita vibhinna AkRtiyoM ke AkAra nimnalikhita haiM yavAkAra kSetra murajAkAra kSetra paNavAkAra kSetra vajrAkAra kSetra samasta AkRtiyoM ke kSetraphala ke mApa isa gAthA meM diye gaye niyamAnusAra anumAnataH ThIka haiM, kyoMki niyama isa mAnyatA para AdhArita hai ki pratyeka sImAvartI vakrarekhA una sarala rekhAoM ke yoga ke barAbara hai, jo vakroM ke siroM (choroM athavA antoM) ko madhya bindu ke milAne se prApta hotI haiN|

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-7. 39 ] kSetragaNita vyavahAraH [ 189 paNavAkArakSetrasyAyAmaH saptasaptatirdaNDAH / mukhayorvistAro'STau madhye daNDAstu catvAraH / / 35 / / vajrAkRtestathAsya kSetrasya SaDagranavatirAyAmaH / madhye sUcirmukhayotrayodaza tryaMzasaMyutA daNDAH || 36 // ubhayaniSedhAdikSetra phalAnayanasUtram - vyAsAtsvAyAmaguNAdviSkambhArdhannadIrghamutsRjya / tvaM vada niSedhamubhayostadardhaparihINamekasya / / 37 / / atroddezakaH AyAma: SaTtriMzadvistaro'STAdazaiva daNDAstu | ubhayaniSedhe kiM phalamekaniSedhe ca kiM gaNitam // 38 // bahuvidhAkArANAM kSetrANAM vyAvahArikaphalA nayanasUtram - rajjvardhakRtitryaM zo bAhuvibhakto nirekabAhuguNaH / sarveSAmazratratAM phalaM hiM bimbAntare caturthAMzaH // 39 // hai, lambAI 77 daMDa, donoM mukhoM meM pratyeka kA mApa 8 daMDa aura madhya kA mApa 4 daMDa hai / isake kSetra - phala kA mApa batalAo / / 35 / / isI prakAra, kisI vajrAkAra kSetra kI lambAI 96 daMDa, madhya meM kevala madhya bindu hai; aura mukhoM meM se pratyeka kA mApa 13 daMDa hai / isakA kSetraphala kyA hai ? / / 36 / / ubhayaniSedha kSetra ke kSetraphala ko nikAlane ke liye niyama - lambAI aura caur3AI ke guNanaphala meM se lambAI aura AdhI caur3AI ke guNanaphala ko ghaTAne para ubhayaniSedha kSetraphala prApta hotA hai / jo lambAI aura AdhI caur3AI ke guNanaphala meM se usI ghaTAI jAne vAlI rAzi kI arddharAzi ghaTAI jAne para prApta hotA hai, vaha ekaniSedha AkRti kA kSetraphala hotA hai / / 37 / / udAharaNArtha prazna lambAI 36 hai, caur3AI kevala 18 daMDa hai / ubhayaniSedha tathA eka niSedha kSetra ke kSetraphaloM ko alaga alaga nikAlo / / 38 / / bahuvidhavajra ke AkAra kI rUparekhA vAle kSetroM ke vyAvahArika kSetraphala ke mApa ko nikAlane ke liye niyama parimiti kI arddharAzi ke varga kI eka tihAI rAzi ko bhujAoM kI saMkhyA dvArA bhAjita kara, aura taba eka kama bhujAoM kI saMkhyA dvArA guNita karane para, bhujAoM se bane hue samasta kSetroM ke vajrAkAra) kSetraphala kA mApa prApta hotA hai| isa phala kA caturthAMza saMsparzI ( eka dUsare ko sparza karane vAle ) vRttoM dvArA ghire hue kSetra kA kSetraphala hotA hai / / 39 / / ( 37 ) isa gAthA meM kathita AkRtiyA~ nIce dI gaI haiMye AkRtiyA~ kisI caturbhujakSetra ko usake do vikarNo dvArA cAra tribhujoM meM bA~Ta dene para prApta huI dikhAI detI haiM ! ubhayaniSedha AkRti, isa caturbhuja ke do sammukha tribhujoM ko haTAne para prApta hotI hai, aura ekaniSedha AkRti aise kevala eka tribhuja ko haTAne para prApta hotI hai| XX ( 39 ) isa gAthA meM kathita niyama koI bhI saMkhyA kI bhujAoM se banI huI AkRtiyoM kA

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19.1 gaNitasArasaMgrahaH atroddezakaH SaDbAhukasya bAhoviSkambhaH paJca cAnyasya / vyAsastrayo bhujasya tvaM SoDazabAhukasya vada / / 40 / / tribhujakSetrasya bhujaH paJca pratibAhurapi ca sapta dharA SaT / anyasya SaDazrasya hyekAdiSaDantavistAraH // 41 / / maNDalacatuSTayasya hi navaviSkambhasya madhyaphalam / SaTpaJcacatuLasA vRttatritayasya madhyaphalam // 42 // dhanurAkArakSetrasya vyAvahArikaphalAnayanasUtramkRtveSuguNasamAsaM bANAdhaguNaM zarAsane gaNitam / zaravargAtpazcaguNAjjyAvargayutAtpadaM kASTham / / 43 // udAharaNArtha prazna ___ cha: bhujAoM vAlI AkRti kI eka bhujA 5 hai, aura 16 bhujAoM vAlI AkRti kI eka bhujA 3 hai| pratyeka dazA meM kSetraphala batAo // 40 // tribhuja ke sambandha meM eka bhujA 5 hai, sammukha (dUsarI ) bhujA 7 hai, aura AdhAra 6 hai| dUsarI chaH bhujAkAra AkRti meM bhujAe~ kramavAra 1 se 6 taka haiM / pratyeka dazA meM kSetraphala kyA hai ? // 41 // jinameM se pratyeka kA gyAsa 9 hai, aise cAra samAna eka dUsare ko sparza karane vAle vRttoM dvArA ghire hue kSetra kA kSetraphala kyA hai? tIna eka dUsare ko sparza karane vAle kramazaH 6, 5 aura 4 mApa ke vyAsavAle vRttoM ke dvArA ghire hue kSetra kA kSetraphala bhI btlaao|| 42 // dhanuSa ke AkAra kI rUparekhA hai jisakI aise AkAra vAlI AkRti kA vyavahArika kSetraphala nikAlane ke liye niyama bANa aura jyA (kRti yA DorI) ke mApoM ko jor3akara yogaphala ko bANa ke mApa kI arddha rAzi dvArA guNita karane se, dhanuSAkAra kSetra kA kSetraphala prApta hotA hai| bANa ke mApa ke varga ko 5 dvArA guNita kara, aura taba usameM kRti (DorI) ke varga ko milAne se prApta rAzi kA vargamUla dhanuSa kI dhanuSAkAra kASTha kI lambAI hotI hai / / 43 // kSetraphala detA hai | yadi bhujAoM ke mApoM ke yoga kI AdhI rAzi ya ho, aura bhujAoM kI saMkhyA na ho, to kSetraphala ='x' hotA hai / yaha sUtra tribhuja, caturbhuja, SaTabhuja, aura vRtta ko ananta bhujAoM kI AkRti mAnakara, unake sambandha meM vyAvahArika kSetraphala kA mAna detA hai| niyama kA dUsarA bhAga eka dUsare ko sparza karane vAle vRttoM ke dvArA ghire kSetra ke viSaya meM hai| isa niyamAnusAra prApta kSetraphala bhI AnumAnika hotA hai| pArzva meM diyA gayA citra, cAra saMsparzI vRttoM dvArA sImita kSetra hai| (43) dhanuSAkAra kSetra rUparekhA meM, vAstava meM, vRtta kI avadhA (khaNDa ) jaisA hotA hai| yahA~ dhanuSa cApa hai, dhanuSa kI DorI ( jyA) cApakarNa hai, aura bANa cApa tathA DorI ke bIca kI mahattama lamba rUpa dUrI hotI hai| yadi ca, ka aura la ina tInoM rekhAoM kI lambAIyoM ko nirUpita karate hoM, to gAthA 43 aura 45 meM diye niyamoM ke anusAra yahA~

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kSetragaNitavyavahAraH atroddezakaH jyA SaDviMzatireSA trayodazeSuzca kArmukaM dRSTam / kiM gaNitamasya kASThaM kiM vAcakSvAzu me gaNaka // 44 // bANaguNapramANAnayanasUtram - -7. 46 ] guNacApakRtivizeSAt paJcahRtAtpadamiSuH samuddiSTaH / zaravargAtpaJcaguNAdUnA dhanuSaH kRtiH padaM jIvA // 45 // atroddezakaH asya dhanuH kSetrasya zaro'tra na jJAyate parasyApi / na jJAyate ca maurvI tadvayamAcakSva gaNitajJa // 46 // udAharaNArtha prazna eka dhanuSAkAra kSetra kI DorI 26 evaM bANa 13 hai / he gaNaka, zIghrahI mujhe isake kSetraphala aura jhuke hue kASTha kA mApa batalAo // 44 // dhanuSAkAra kSetra ke sambandha meM bANasApa aura guNa ( DorI ) pramANa nikAlane ke liye niyamaDho aura jhuke hue dhanuSa ke vargoM ke antara ko 5 dvArA bhAjita karate haiM / pariNAmI bhajana phala kA vargamUla bANa kA iSTa mApa hotA hai / bANa ke varga ko 5 dvArA guNita kara, prApta guNanaphala ko dhanuSa ke cApa ke varga meM se ghaTAte haiM / isa pariNAmI rAzi kA vargamUla DorI ke saMvAdI mApa ko detA hai // 45 // udAharaNArtha dhanuSAkAra kSetra ke bANa kA mApa ajJAta hai, aura dUsare aise hI kSetra kI DorI kA mApa ajJAta hai / he gaNitajJa, ina donoM mApoM ko nikAlo // 46 // dhanuSa kSetra kA kSetraphala nikAlane ke liye diyA gayA sUtra, cIna kI sambhavataH pustakoM ko 213 IsvI pUrva meM jalAye jAne kI ghaTanA se pUrva ko pustaka cyu - cAMga suAna -cu ( navAdhyAyI aMkagaNita ) meM bhI isI rUpa meM dRSTigata hotA hai / la kSetraphala = ( ka + la )x, dhanuSa kI lambAI = V52 + kara bANa kI lambAI = {V/cara - ka} 1/5 [ 191 punaH dhanuSa kI DorI kI lambAI = jambU dvIpa prajJapti ( 6/9 ) meM tathA triloka diyA gayA hai- jIvA = / ( vyAsa - bANa ) 4 bANa 4 ( bANa ) + ( jIvA ) 2 vyAsa = 4 bANa yahA~ ca = cApa, ka = cApakarNa, la = lamba hai / sUkSma mAnoM ke liye isa adhyAya kI 733 aura 742 vIM gAthAoM ko dekhiye | 2-5 la2 prajJapti ( 4 / 2598 ) meM yaha mAna kramazaH isa prakAra kUlija ke anusAra pAyayegorasa ke sAdhya para AdhArita isa sUtra kA udgama bAbula meM prAyaH 2600 IsvI pUrva sphAnalipi graMthoM meM dRSTi gata huA hai / isa sambandha tiloya paNNattikA gaNita dRSTavya hai /

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192] gaNitasArasaMgrahaH [7.47 bahirantazcaturazrakavRttasya vyAvahArikaphalAnayanasUtrambAhye vRttasyedaM kSetrasya phalaM trisaMguNaM dalitam / abhyantare tadardhaM viparIte tatra caturazre / / 47 / / __ atroddezakaH paJcadazabAhukasya kSetrasyAbhyantaraM bahirgaNitam / caturazrasya ca vRttavyavahAraphalaM mamAcakSva // 48 // iti vyAvahArikagaNitaM samAptam / atha sUkSmagaNitam itaH paraM kSetragaNite sUkSmagaNitavyavahAra mudAhariSyAmaH / tadyathA' AvAdhAvalambakAnayanasUtrambhujakRtyantarabhUhRtabhUsaMkramaNaM tribAhukAbAdhe / tadbhujavargAntarapadamavalambakamAhurAcAryAH // 49 // 1. isake pazcAt M meM nimnalikhita aura jur3A haitribhuja kSetrasya bhujadvayasaMyogasthAnamArabhyaadhassthita bhUmi saMspRSTa rekhAyA nAma avalambakaH syAt / caturbhuja ke bahilikhita aura antalikhita vRtta ke kSetraphala ke nyAvahArika mAna ko nikAlane ke liye niyama-- aMtalikhita caturbhuja ke kSetraphala ke mApa kI tigunI rAzi kI arddharAzi aise bAharI parigata vRtta ke kSetraphala kA mApa hotI hai| usa dazA meM jabaki vRtta antalikhita ho aura caturbhuja bahirgata ho, taba Upara ke prApta mApa kI arddharAzi iSTa rAzi hotI hai // 47 // udAharaNArtha prazna caturbhuja kSetra kI pratyeka bhujA 15 hai| mujhe aMtargata aura bahirgata vRttoM ke vyAvahArika kSetraphala ke mApa batalAo // 48 // isa prakAra kSetragaNita vyavahAra meM vyAvahArika gaNita nAmaka prakaraNa samApta huaa| sUkSma gaNita isake pazcAt hama gaNita meM kSetraphaloM ke mApa sambandhI sUkSma gaNita nAmaka viSaya kA pratipAdana kreNge| vaha isa prakAra hai kisI diye hue tribhuja ke AbAdhAoM (khaMDa jinameM ko AdhAra lamba ke dvArA vibhAjita ho jAtA hai ) aura avalamba (zIrSa se AdhAra para girAyA haA lamba) ke mApa nikAlane ke liye niyama bhujAoM ke vargoM ko bhAdhAra dvArA bhAjita karane se prApta rAzi aura AdhAra ke bIca saMkramaNa kriyA karane se tribhuja kI AbAdhAoM ( AdhAra ke khaMDoM) ke mApa prApta hote haiN| AcArya kahate haiM ki ina AbAdhAoM meM se eka, aura saMvAdI Asanna bhujA ke vargoM ke aMtara kA vargamUla avalamba kA mApa hotA hai // 49 // (47) yahA~ diyA gayA sUtra varga ke sambandha meM ThIka mApa detA hai, parantu anya caturbhujoM ke sambandha meM jaba 7 kA mAna 3 lete haiM, taba kevala AnumAnika mAna prApta hotA hai| (49 ) bIjIya rUpa se prarUpita hone para

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-7. 53] kSetragaNita vyavahAraH sUkSmagaNitAnayanasatramabhujayutyardhacatuSkAdbhujahInAddhAtitAtpadaM sUkSmam / athavA mukhatalayutidalamavalambaguNaM na vissmcturshre|| 50 // atroddezakaH tribhujakSetrasyASTau daNDA bhUrbAhuko samasya tvam / sUkSmaM vada gaNitaM me gaNitavidavalambakAbAdhe / / 51 / / dvisamatribhujakSetre trayodaza syurbhujadvaye daNDAH / daza bhUrasyAbAdhe athAvalambaM ca sUkSmaphalam / / 52 // viSamatribhujasya bhujA trayodaza pratibhujA tu paJcadaza / bhUmizcaturdazAsya hi kiM gaNitaM cAvalambakAbAdhe / / 53 / / tribhuja aura caturbhuja kSetroM ke kSetraphaloM ke sUkSma mApa nikAlane ke liye niyama kramazaH pratyeka bhujA dvArA hAsita bhujAoM ke yoga kI arddharAzi dvArA nirUpita prApta cAra rAziyA~ eka sAtha guNita kI jAtI haiN| isa prakAra prApta guNanaphala kA vargamUla kSetraphala kA sUkSma mApa hotA hai| athavA kSetraphala kA mApa, UparI sire se AdhAra para girAye gaye lamba ko AdhAra aura UparI bhujA ke yoga kI arddharAzi se guNita karane para prApta hotA hai| para yaha bAda kA niyama viSama caturbhuja ke sambandha meM nahIM hai // 50 // udAharaNArtha prazna samatribhuja kI pratyeka bhujA 8 daMDa hai| he gaNitajJa, usake kSetraphala kA sUkSma mApa tathA zIrSa se AdhAra para girAye hue lamba aura isa taraha prApta AdhAra ke khaMDoM ke sUkSma mAnoM ko batalAo / / 5 / / kisI samadvibAhu tribhuja kI barAbara bhujAoM meM se pratyeka 13 daMDa hai aura AdhAra kA mApa 10 hai / kSetraphala, lamba aura AdhAra kI AbAdhAoM ke sUkSma mApoM ko nikAlo // 52 // viSama tribhuja kI eka bhujA 13, sammukha bhujA 15 aura AdhAra 14 hai| isa kSetra kA kSetraphala, lamba aura AdhAra kI AbAdhAoM ke sUkSma mAna kyA haiM ? // 53 // sa6 = ( sa- )x; sa aura la =V a2 - sa, 2 athavA / ba - sa, 2 hotA hai / yahA~ a, ba, sa tribhuja kI bhujAoM kA nirUpaNa karate haiM; sa, sa. aise AdhAra ke do khaMDa haiM, jinakI kula lambAI sa hai, la lamba hai| (50) bIjIya rUpa se nirUpita karane para, saphala V ya (ya-a) (ya-ba) (ya-sa),jahA ya bhujAoM ke yoga kI AdhI rAzi hai| a, ba, sa bhujAoM ke mApa haiN| athavA, kSetraphala = sxla, jahA~ la zIrSa se AdhAra para girAye gaye lamba kA mAna hai| ga0 sA. saM0-25

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194 ] gaNita sArasaMgrahaH itaH paraM paJcaprakArANAM caturazrakSetrANAM karNAnayanasUtram - kSititaviparItabhujau mukhaguNabhuja mizritau guNacchedau / chedaguNau pratibhujayoH saMvargayuteH padaM karNau // 54 // atroddezakaH samacaturazrasya tvaM samantataH paJcabAhukasyAzu | karNa ca sUkSmaphalamapi kathaya sakhe gaNitatattvajJa // 55 // Ayatacaturazrasya dvAdaza bAhuzca koTirapi paJca / karNaH kaH sUkSmaM kiM gaNitaM cAcakSva me zIghram // 56 // dvisamacaturazrabhUmiH SaTatriMzadvAhurekaSaSTizca / so'nyaccaturdazAsyaM karNaH kaH sUkSmagaNitaM kim // 57 // [ 7. 54 isake pazcAt pA~ca prakAra ke caturbhujoM ke vikarNoM ke mAna nikAlane ke liye niyama - AdhAra ko bar3I aura choTI, dAhinI aura bAIM bhujAoM ke dvArA guNita karane se prApta rAziyoM ko kramazaH aisI do anya rAziyoM meM jor3ate haiM, jo UparI bhujA ko dAhinI aura bAIM ora kI choTI aura bar3I bhujAoM dvArA guNita karane se prApta hotI haiN| pariNAmI do yoga, guNaka aura bhAjaka tathA sammukha bhujAoM ke guNanaphaloM ke yoga sambandhI bhAjaka aura guNana kI saMracanA karate haiN| isa prakAra prApta rAziyoM ke vargamUla vikarNoM ke iSTa mApa hote haiM // 54 // udAharaNArtha prazna jisakI cAroM ora kI pratyeka bhujA kA mApa 5 hai, aise samabhuja caturbhuja ke sambandha meM gaNita tatvajJa, vikarNa tathA kSetraphala ke sUkSma mAna zIghra batalAo // 55 // Ayata kSetra ke sambandha meM kSaitija bhujA mApa meM 12 hai, aura lamba rUpa bhujA mApa meM 5 hai / mujhe zIghra batalAo ki vikarNa kA aura kSetraphala kA sUkSma mApa kyA kyA hai ? / / 56 / / samadvibAhu caturbhuja ( samalamba cakrIya caturbhuja ) kI AdhArabhujA 36 hai / eka bhujA 61 hai, aura dUsarI bhI utanI hI hai / UparI bhujA 14 hai / batalAo ki vikarNa aura kSetraphala ke sUkSma mApa kyA haiM ? // 57 // samatribAhu caturbhuja ( cakrIya samatribAhu caturbhuja ) ke sambandha meM 13 kA varga samAna bhujAoM meM se eka kA mApa hotA hai / AdhAra 407 hai / vikarNa kA mApa tathA AdhAra ke khaNDoM kA mApa aura lamba tathA kSetraphala ke mApa kyA kyA haiM ? / / 58 / / kisI viSama caturbhuja kI dAhinI aura bAIM bhujAe~ 13x 15 aura caturbhuja kSetra kA kSetraphala =(ya- a ) ( ya - ba ) ( ya - sa ) ( ya - da ) ; yahA~ ya, bhujAoM ke yoga kI arddharAzi hai, aura a, ba, sa, da caturbhuja kSetra kI bhujAoM ke mApa haiM / athavA, |kSetraphala = -Xla ( usa dazA ke apavAda ko chor3akara jabaki caturbhuja viSama hotA hai, jahA~ la UparI bhujA ke aMtoM se AdhAra para girAye gaye barAbara lamboM meM se kisI eka kA mApa hai / tribhuja kSetroM ke liye diye gaye ye sUtra ThIka parantu jo caturbhuja kSetroM ke liye diye gaye haiM ve kevala cakrIya caturbhujoM ke sambandha meM ThIka haiM, kyoMki unhIM mApoM ke liye kSetraphala tathA lamba kA mAna parivartanazIla ho sakatA hai / (54) bIjIya rUpa se nirUpita caturbhuna kSetra ke vikarNa kA mApa yaha hai-- 'asa + bada ) ( aba + sada) ghtt + kr ba+da 2 athavA asa + bada ) ( ada + basa aba + sada ' ye sUtra kevala

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[195 -7.61] kSetragaNitamyavahAraH vagaistrayodazAnAM trisamacaturbAhuke punarbhUmiH / sapta catuzzatayuktaM karNAbAdhAvalambagaNitaM kim // 58 // viSamacaturazrabAhU trayodazAbhyastapaJcadazaviMzatikau / pazcaghano vadenamadhastrizataM kAnyatra karNamukhaphalAni / / 59 // itaH paraM vRttakSetrANAM sUkSma phalAnayanasUtrANi / tatra samavRttakSetrasya sUkSmaphalAnayana sUtramvRttakSetravyAso dazapadaguNito bhavetparikSepaH / / vyAsacaturbhAgaguNaH paridhiH phalamadhemadhe tat / / 60 / / atroddezakaH samavRttavyAso'STAdaza viSkambhazca SaSTiranyasya / dvAviMzatiraparasya kSetrasya hi ke ca paridhiphale // 61 // 13 4 20 haiN| UparI bhujA (5)3 hai, aura nIce kI bhujA 300 hai / vikarNa se Arambha kara sabake mAna yahA~ kyA kyA haiM ? / / 59 / / isake pazcAt vakrarekhIya kSetroM ke sambandha meM sUkSma mAnoM ko nikAlane ke liye niyama diye jAte haiN| unameM se samavRtta ke sambandha meM sakSama mAna nikAlane ke liye niyama vRtta kA vyAsa 10 ke vargamUla se guNita hokara paridhi ko utpanna karatA hai| paridhi ko eka cauthAI vyAsa se guNita karane para kSetraphala prApta hotA hai| arddhavRtta ke sambandha meM yaha isakA AdhA hotA hai // 60 // udAharaNArtha prazna kisI vRttAkAra kSetra ke sambandha meM vRtta kA vyAsa 18 hai| dUsare ke sambandha meM 60 hai: eka aura anya ke sambandha meM 22 hai| paridhiyAM aura kSetraphala kyA kyA haiM / // 61 // arddhavRttAkAra kSetra cakrIya caturbhujoM ke liye ThIka hai| lamba athavA vikaNoM ke mAnoM ko pahile se binA jAne hue caturbhuja ke kSetraphala ko nikAlane ke prayatna ke viSaya meM bhAskarAcArya paricita the| yaha unakI lIlAvatI grantha kI nimnalikhita gAthA se prakaTa hotA hai-- lambayoH karNayokamanirdizyAparAn katham / pRcchatyaniyatatve'pi niyataM cApi tatphalam // sapRcchakaH pizAco vA vaktA vA nitarAM ttH| yo na vetti caturbAhukSetrasyAniyatAM sthitim // paridhi (60) isa gAthAnusAra yA kA mAna V10 = 3.16...hai| isase bhI sUkSma mAna prApta karane ke liye navIM zatAbdI kI dhavalA TIkA graMthoM meM nimnalikhita rIti dI hai16 (vyAsa)+16 -+3 (vyAsa ) = paridhi / isa sUtra ke vAma pakSa ke prathama pada meM se aMza 113 kA+16 haTA dene para T kA mAna 355 athavA 3.141593 prApta hotA hai, jise cIna meM 476 IsvI pazcAt tsu-zuMga-ciha dvArA upayoga meM lAyA gayA hai / vAstava meM yaha sUtra eka pradeza ke vyAsa ke sambandha meM prayukta huA hai| asaMkhyAta pradezoM vAle aMgula Adi vyAsa ke mApa kI ikAiyoM ke liye + 16 kA mAna nagaNya ho jAtA hai, aura cInI mAna prApta ho jAtA hai| AryabhaTTa dvArA diyA gayA 7 kA mAna 3344 = 314116 hai| bhAskarAcArya dvArA bhI yaha mAna (3139) rUpa meM hAsita kara prarUpita kiyA gayA hai|

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196] gaNitasArasaMgrahaH [7.63 dvAdazaviSkambhasya kSetrasya hi cArdhavRttasya / SatriMzadvathAsasya kaH paridhiH kiM phalaM bhavati / / 62 / / AyatavRttakSetrasya sUkSmaphalAnayanasUtramvyAsakRtiHSaDaguNitA dvisaMguNAyAmakRtiyutA ( padaM ) paridhiH / vyAsacaturbhAgaguNazcAyatavRttasya sUkSmaphalam / / 63 // atroddezakaH AyatavRttAyAmaH SaTtriMzadvAdazAsya viSkambhaH / kaH paridhiH kiM gaNitaM sUkSma vigaNayya me kathaya / 64 // zaGkhAkArakSetrasya sUkSmaphalAnayanasUtramvadanA|no vyAso dazapadaguNito bhavetparikSepaH / mukhadalarahitavyAsArdhavargamukha caraNakRtiyogaH / / 65 / / dazapadaguNitaH kSetre kambunibhe sUkSmaphalametat / / 653 / / kA myAsa 12 hai| dUsare kSetra kA vyAsa 36 hai| batalAo ki paridhi kyA hai aura kSetraphala kyA hai ? // 62 // AyatavRtta (ilipsa ) sambandhI sUkSma mAnoM ko nikAlane ke liye niyama choTe vyAsa kA varga 6 dvArA guNita kiyA jAtA hai, aura bar3e vyAsa kI lambAI kI dugunI rAzi ke varga ko usameM jor3A jAtA hai| isa yoga kA vargamUla paridhi kA mApa hotA hai| jaba isa paridhi ke mApa ko choTe vyAsa kI eka cauthAI rAzi dvArA guNita karate haiM, taba Unendra kA sUkSma kSetraphala prApta hotA hai // 63 // udAharaNArtha prazna ilipsa ke sambandha meM bar3e vyAsa kI lambAI 36 aura choTe vyAsa kI 12 hai, gaNanA ke pazcAt batalAo ki paridhi kyA hai aura sUkSma kSetraphala kyA hai ? // 6 // zaMkha ke AkAra kI AkRti ke sambandha meM sUkSma mAnoM ko nikAlane ke liye niyama AkRti kI sabase bar3I caur3AI ( choTe vyAsa) ko mukha kI caur3AI kI arddharAzi dvArA hAsita kara, aura taba 10 ke vargamUla dvArA guNita karane para parimApa (perimeter ) utpanna hotA hai AkRti kI mahattama caur3AI kI arAzi ke varga ko mukha kI AdhI caur3AI dvArA hvAsita karane se prApta rAzi meM mukha kI caur3AI kI eka cauthAI rAzi ke varga ko jor3ate haiN| pariNAmI yoga ko 10 ke vargamUla dvArA guNita karate haiM / prApta rAzi zaMkha AkRti kA sUkSma kSetraphala hotA hai // 653 // (63) yadi bar3A vyAsa 'a' aura choTA vyAsa 'ba' ho, to isa niyamAnusAra paridhi V632 + 432 hotI hai, aura kSetraphala : baXV672 + 4ara hotA hai| isa gAthA meM (hastalipi meM) paridhi prApta karane ke liye prApta rAzi ke vargamUla nikAlane kA kathana bhUla se chUTa gayA hai| yahA~ diyA gayA kSetraphala kA sUtra kevala eka anumAna hai, aura vaha vRtta ke kSetraphala kI sAmyatA para AdhArita hai, jo xax dvArA prarUpita hotA hai : jahA~ va vyAsa hai aura ( 7va) paridhi hai| (653) bIjIya rUpa se, paridhi = ( a-1 ma)x/10 ; tathA,

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-7.693 ] kSetragaNitavyavahAraH [197 atroddezakaH vyAso'STAdaza daNDA mukhavistAro'yamapi ca catvAraH / kaH paridhiH kiM gaNitaM sUkSma tatkambukAvRtte / / 663 // . bahizcakravAlavRttakSetrasya cAntazcakravAlavRttakSetrasya ca sUkSmaphalAnayanasUtramnirgamasahito vyAso dazapadanirgamaguNo bahirgaNitam / rahito'dhigamenAsAvabhyantaracakravAlavRttasya / / 673 / / atroddezakaH vyAso'STAdaza daNDAH punarbahinirgatAstrayo daNDAH / sUkSmagaNitaM vada tvaM bahirantazcakravAlavRttasya // 683 // vyAso'STAdaza daNDA antaH punaradhigatAzca catvAraH / sukSmagaNitaM vada tvaM cAbhyantaracakravAlavRttasya / / 69 / / udAharaNArtha prazna zaMkha AkRti ke vakrarekhIya kSetra ke saMbaMdha meM mahattama caur3AI 18 daMDa hai, aura mukha kI caur3AI 4 daMDa hai / isakI parimiti aura sUkSma kSetraphala ke mApa kyA haiM ? // 66 // bAhara sthita aura bhItara sthita ( bahizcakravAla aura aMtazcakravAla ) kaMkaNa ke saMbaMdha meM sUkSma mApoM ko nikAlane ke liye niyama bhItarI vyAsa meM cakravAla vRtta kI caur3AI jor3akara, prApta rAzi ko 10 ke vargamUla tathA cakravAla vRtta kI caur3AI dvArA guNita karate haiN| isase bahizcakravAla vRtta kA kSetraphala prApta hotA hai| bAharI vyAsa ko cakravAla vRtta kI caur3AI dvArA hAsita karate haiN| prApta rAzi ko 10 ke vargamUla tathA cakravAla vRtta kI caur3AI dvArA guNita karane se aMtazvakravAla vRtta kA kSetraphala prApta hotA hai // 671 // udAharaNArtha prazna cakravAla vRtta kA bhItarI athavA bAharI vyAsa kA mApa 18 daMDa hai| cakravAla vRtta kI cauDAI 3 daMDa hai| bahizcakravAla vRtta tathA aMtazcakravAla vRtta kA sUkSma mApa batalAo / / 681 // bAharI vyAsa 18 daMDa hai| aMtazcakravAla vRtta kI caur3AI 4 daMDa hai| aMtazcakravAla vRtta kA sUkSma kSetraphala nikAlo // 693 // kSetraphala = [{(a-3 ma)x3} + (5)]x/10 ; jahA~ a mahattama caur3AI kA mApa hai aura ma zaMkha ke mukha kI caur3AI hai| gAthA 23 ke noTa ke anusAra yahA~ bhI isa AkRti ko do asamAna arddhavRttoM dvArA saMracita kiyA gayA hai|

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gaNitasArasaMgrahaH yavAkArakSetrasya ca dhanurAkArakSetrasya ca sUkSmaphalAnayanasUtram - iSupAdaguNazca guNo dazapadaguNitazca bhavati gaNitaphalam / yavasaMsthAnakSetre dhanurAkAre ca vijJeyam // 703 // atrodezakaH dvAdazadaNDAyAmo mukhadvayaM sUcirapi ca vistAraH / catvAro madhye'pi ca yavasaMsthAnasya kiM tu phalam / / 713 / / dhanurAkArasaMsthAne jyA caturviMzatiH punaH / catvAro'syeSuruddiSTaH sUkSmaM kiM tu phalaM bhavet / / 723 / / 198 ] dhanurAkArakSetrasya dhanuH kASThabANapramANAnayanasUtram - zaravargaH SaDguNito jyAvargasamanvitastu yastasya / mUlaM dhanurguNeSuprasAdhane tatra viparItam // 733 / / [ 7.703 yavAkAra kSetra tathA dhanuSAkAra kSetra ke sambandha meM sUkSma mAnoM ko nikAlane ke liye niyamadhanuSa kI DorI ko bANa kI eka cauthAI rAzi dvArA guNita karate haiM / prApta phala ko 10 ke vargamUla dvArA guNita karane para dhanuSAkAra tathA yavAkAra kSetra ke sambandha meM kSetraphala kA sUkSma rUpa se ThIka mAna prApta hotA hai / / 702 // udAharaNArtha prazna yavamanya ko bIca se phAr3ane se prApta kSetra kI AkRti kI mahattama lambAI 12 daMDa hai; do sire suI - bindu haiM, aura bIca meM caudAI 4 daMDa hai| kSetraphala kyA ? // 71 // dhanuSAkAra rUparekhA vAlI AkRti ke saMbaMdha meM DhorI 24 hai tathA bANa 4 hai / kSetraphala kA sUkSma mApa kyA hai ? // 723 // dhanuSa ke vakra kASTha tathA bANa ko nikAlane ke liye niyama, jaba ki AkRti dhanuSAkAra hai ke mApaka varga 6 dvArA guNita kiyA jAtA hai / pariNAmI yoga kA vargamULa dhanuSa ke vakra kASTha kA mApa hotA hai nikAlane ke sambandha meM isakI viparIta kriyA karate haiM // 733 // isameM DorI ke varga ko jor3ate haiM / / DorI kA mApa aura bANa kA mApa ( 703) dhanuSa ke samAna AkRti, vRtta kI avadhA jaisI, spaSTa rUpa se dikhAI detI hai / yahA~ avadhA kA kSetraphala = ka x X/10 hai / yaha zuddha mApa nahIM hai / la 4 usI kI arddhavRtta ke kSetraphala ko prApta karane ke liye jo niyama hai yaha sAmyatA para AdhArita hai| arddhavRtta kA kSetraphala = x 2tra X tra 4 cApakarNa ke donoM ora ke dhanuSa ( vRtta kI avadhAyeM ) milAne se yavAkAra AkRti prApta hotI hai| spaSTa hai ki isa dazA meM bANa kA mApa dugunA ho jAtA hai| isa prakAra yaha sUtra isake liye bhI prayojya hai / ka hai, jahAM tra trijyA hai / sAdhAraNa triloka prajJapti meM (4/2373 bhAga 1, pRSTha 442 para ) avadhA kA kSetraphala sUtra rUpa se yaha hai-- dhanuSakSetra = V ( } bANa jIvA ) 2 x 10

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-7. 753] kSetragaNitamyavahAraH viparItakriyAyA sUtramguNacApakRtivizeSAttakahatAtpadamiSuH samuddiSTaH / zaravargAt SaDguNitAdUnaM' dhanuSaH kRteH padaM jIvA / / 743 / / atroddezakaH dhanurAkArakSetre jyA dvAdaza SaT zaraH kASTham / na jJAyate sakhe tvaM kA jIvA kaH zarastasya / / 753 / / 1. B aura M donoM meM uparyukta pATha hai; para iSTa artha "SaDguNitAdUnAyA dhanuSkRteH padaM jIvA" se nikalatA hai| viparIta kriyA ke sambandha meM niyama DorI ke varga aura dhanuSa ke vakrakASTha ke varga ke antara kI bhAga rAzi kA vargamUla bANa kA mApa hotA hai| dhanuSakASTha ke varga meM se bANa ke varga kI 6 guno rAzi ko ghaTAne se prApta zeSa kA vargamUla DorI kA mApa hotA hai // 743 // ___ udAharaNArtha prazna dhanuSAkAra AkRti kI DorI 12 hai, aura bANa 6 hai| jhukI huI kASTha kA mApa ajJAta hai| he mitra, use nikaalo| isI AkRti ke saMbaMdha meM DorI aura usake bANa ke mApa ko alaga-alaga kisa taraha nikAloge, jaba ki Avazyaka rAziyA~ jJAta hoM ? // 753 // /ca2-kara (733-743) bIjIya rUpa se, cApa = V6 la. + ka2; lamba =V aura cApakarNa = V2 - 6 lare cApakarNa aura bANa ke padoM meM cApa kA mAna samIkaraNa ke rUpa meM dene ke liye arddhavRtta banAnevAle cApa ko AdhAra mAnanA par3atA hai| prApta sUtra ko kisI bhI avadhA (vRtta khaMDa) ke cApa kA mAna nikAlane ke upayoga meM lAte haiN| arddhavRttIya cApa%AXV10V 1.%DV6 12+4tra hotA hai, jahA~ / trijyA athavA arddhavyAsa hai| isI siddhAnta para AdhArita yaha sUtra kisI bhI cApa ke liye hai / yahA~ la = bANa (cApa tathA cApakarNa ke bIca kI mahattama dUrI), aura ka = jIvA (cApakarNa) hai / jambUdvIpa prajJapti ( 2/24, 6/10) meM dhanuSapRSTha kA sUtra mahAvIra ke sUtra samAna hai, dhanuSapRSTha =V6 ( bANa2 ) + { ( vyAsa - bANa) 4 bANa } DV6 (bANa )2 + ( jIvA )2 triloka. prajJapti ( 4/181) meM sUtra isa rUpa meM hai, dhanuSa%DV2 {(vyAsa + bANa)2-(vyAsa )2} bANa nikAlane ke liye jambUdvIpa prajJapti (6/11) tathA triloka prajJapti (4/182 ) meM avatarita sUtra dRSTavya hai|

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200 ] gaNita sArasaMgrahaH atroddezakaH mRdaGganibhakSetrasya ca paNavAkArakSetrasya ca vajrAkAra kSetrasya ca sUkSmaphalAnayanasUtram - mukhaguNitAyAmaphalaM svadhanuH phalasaMyutaM mRdaGganibhe / tatpaNavavajranibhayordhanuHphalonaM tayorubhayoH / / 76 / / atroddezakaH [ 0.042 caturviMzatirAyAmo vistAro'STau mukhadvaye / kSetre mRdaGgasaMsthAne madhye SoDaza kiM phalam / / 773 / / caturviMzatirAyAmastathASTau mukhayordvayoH / catvAro madhyaviSkambhaH kiM phalaM paNavAkRtau / / 783 // caturviMzatirAyAmastathASTau mukhayordvayoH / madhye sUcistathAcakSva vajrAkArasya kiM phalam // 793 // nemikSetrasya ca bAlendvAkAra kSetrasya ca ibhadantAkArakSetrasya ca sUkSmaphalAnayanasUtram-pRSThodara saMkSepaH SaDbhakto vyAsarUpasaMguNitaH / dazamUlaguNo ne merbAle dvibhadantayozca tasyArdham / / 803 // mRdaMgAkAra, paNavAkAra aura vajrAkAra AkRtiyoM ke saMbaMdha meM sUkSma phaloM ko prApta karane ke liye niyama jo mahattama lambAI ko mukha kI caur3AI dvArA guNita karane para prApta hotA hai aise pariNAmI kSetraphala meM saMbaMdhita dhanuSAkRtiyoM ke kSetraphaloM ke mAna ko jor3ate haiM / yaha pariNAmI yoga mRdaMga ke AkAra kI AkRti ke kSetraphala kA mApa hotA hai paNava aura vajra kI AkRti ke ke liye mahattama lambAI aura mukha kI caur3AI ke guNanaphala se prApta kSetraphala ko kSetraphaloM ke mApa dvArA hAsita karate haiN| zeSaphala iSTa kSetraphala hotA hai // 76 // udAharaNArtha prazna / hai 1 mRdaMgAkAra AkRti ke saMbaMdha meM mahattama lambAI 24 hai / do mukhoM meM se pratyeka ke mukha kI caudAI 8 hai / bIca meM mahattama caur3AI 16 hai / kSetraphala kyA hai ? // 77 // paNavAkRti ke saMbaMdha meM mahattama lambAI 24 hai / isI prakAra pratyeka mukha kI caudAI 8 aura kendrIya caudAI 4 hai / kSetraphala kyA hai ? // 78 // vajra ke AkAra kI AkRti ke mahattama lambAI 24 hai / do mukhoM meM se pratyeka kI caur3AI 8 hai / kendra kevala eka bindu mikSetra aura bAlendu samAna kSetra ( hAthI kI khIsa ke phaloM ko nikAlane ke liye niyama saMbaMdha meM kSetraphala nikAlo || 793 // anvAyAma chedAkRti ) ke sUkSma kSetra - / kSetraphala prApta karane dhanuSAkRti saMbaMdhI nemikSetra ke saMbaMdha meM bhItarI aura bAharI vakroM ke mApoM ke yoga ko 6 dvArA bhAjita karate haiM / ise kaMkaNa kI caur3AI se guNita kara phira se 10 ke vargamUla dvArA guNita karate haiM / pariNAmI phala iSTa kSetraphala hotA hai / isakA AdhA bAlendu kA kSetraphala athavA hAthI kI khIsa kI anvAyAma chedAkRti ( ibhadantAkAra kSetra ) kA kSetraphala prApta hotA hai // 80 // to vaha isa ( 763) isa niyama kA mUla AdhAra 32 vIM gAthA meM noTa meM diye gaye citroM se spaSTa ho jAvegA / (803 ) nemikSetra ke liye diyA gayA niyama yadi bIjIya rUpa se prarUpita kiyA jAya, rUpa meM AtA hai, + 2. XXV 10, jahA~ 11, 12 do paridhiyoM ke mApa haiM, aura la nemikSetra 6 pa -

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-7. 833 ] kSetragaNitavyavahAraH [201 atroddezakaH pRSThaM caturdazodaramaSTau nemyAkRtau bhUmau / madhye catvAri ca tadbAlendoH kimibhadantasya // 813 / / caturmaNDalamadhyasthitakSetrasya sUkSmaphalAnayanasUtramviSkambhavargarAzevRttasyaikasya sUkSmaphalam / tyaktvA samavRttAnAmantarajaphalaM caturNA syAt / / 823 / / atroddezakaH golakacatuSTayasya hi parasparasparza kasya madhyasya / sUkSmaM gaNitaM kiM syAccatuSkaviSkambhayuktasya / / 833 // udAharaNArtha prazna nemikSetra ke saMbaMdha meM bAharI vakra 14 hai aura bhItarI 8 hai| bIca meM caudAI 4 hai| kSetraphala kyA hai ? bAlendu kSetra tathA ibhadantAkAra kSetra kI AkRtiyoM kA kSetraphala bhI kyA hogA ? // 13 // cAra, eka dUsare ko sparza karane vAle, vRttoM ke bIca ke kSetra (caturmaNDala madhyasthita kSetra) ke sUkSma kSetraphala ko nikAlane ke liye niyama kiptI bhI eka vRtta ke kSetraphala kA sUkSma mApa yadi usa vRtta ke vyAsa ko vargita karane se prApta rAzi meM se ghaTAyA jAya, to pUrvokta kSetra kA kSetraphala prApta hotA hai // 823 // udAharaNArtha prazna cAra eka dUsare ko sparza karane vAle vRttoM ke bIca kA kSetraphala nikAlo (jaba ki pratyeka vRtta kA gyAsa " hai ) // 832 // (kaMkaNa) kI caur3AI hai| isa nemikSetra ke kSetraphala kI tulanA gAthA 7 meM diye gaye noTa meM varNita AnumAnika mAna se kI jAya, to spaSTa hogA ki yaha sUtra zuddha mAna nahIM detaa| gAthA 7 meM diyA gayA mAna zuddha mAna hai| yaha galatI, eka galata vicAra se udita huI mAlUma hotI hai| isa kSetraphala ke mAna ko nikAlane ke liye, 7 kA upayoga pa, aura pa, ke mAnoM meM apekSAkRta ulaTA kiyA gayA hai| isake sambandha meM jambUdvIpa prajJapti (10/91) aura triloka prajJapti ( 4/2521-2522 ) meM diye gaye sUtra dRSTavya haiN| (823) nimnalikhita AkRti se isa niyama kA mUla | ( 843 ) isI prakAra, yaha AkRti bhI niyama ke kAraNa spaSTa ho jaavegaa| kAraNa ko zIghra hI spaSTa karatI hai| varga sama tribhuja ga. sA. saM0-26

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202] gaNitasArasaMgrahaH [7.843vRttakSetratrayasyAnyo'nyasparzanAjAtasyAntarasthitakSetrasya sUkSmaphalAnayanasUtramviSkambhamAnasamakatribhujakSetrasya sUkSmaphalam / vRttaphalArdhavihInaM phalamantarajaM trayANAM syAt / / 843 / / atroddezakaH viSkambhacatuSkANAM vRttakSetratrayANAM ca / anyo'nyaspRSTAnAmantarajakSetragaNitaM kim // 853 // SaDazrakSetrasya karNAvalambakasUkSmaphalAnayanasUtrambhujabhujakRtikRtivargA dvitritriguNA yathAkrameNaiva / zrutyavalambakakRtidhanakRtayazca SaDazrake kSetre // 863 / / atroddezakaH bhujaSaTakakSetre dvau dvau daNDau pratibhujaM syAtAm / asmin zrutyavalambakasUkSmaphalAnAM ca vargAH ke / / 873 / tIna samAna paraspara eka dUsare ko sparza karanevAle vRttIya kSetroM ke bIca ke kSetra kA sUkSma rUpa se zuddha kSetraphala nikAlane ke liye niyama jisakI pratyeka bhujA vyAsa ke barAbara hotI hai aise sama tribhuja kA sUkSma kSetraphala ina tIna meM se kisI bhI eka ke kSetraphala kI arddharAzi dvArA hAsita kiyA jAtA hai| zeSa hI iSTa kSetraphala hotA hai // 8 // udAharaNArtha prazna paraspara eka dUsare ko sparza karane vAle tathA mApa meM 40 vyAsa vAle tIna vRttoM kI paridhiyoM se ghire hue kSetra kA sUkSma kSetraphala kyA hai ? // 853 / / ____ niyamita SaTbhuja kSetra ke saMbaMdha meM karNa, avalamba (lamba ) aura kSetraphala ke sUkSma rUpa se zuddha mAnoM ko nikAlane ke niyama- - SaTabhuja kSetra ke saMbaMdha meM bhujA ke mApa ko, isa bhujA ke varga ko tathA isI bhujA ke varga ke varga ko kramazaH 2,3 aura 3 dvArA guNita karane para usI krama meM karNa, lamba kA varga aura kSetraphala ke mApa kA varga prApta hotA hai // 86 // udAharaNArtha prazna niyamita SaTabhujAkAra AkRti ke saMbaMdha meM pratyeka bhujA 2 daNDa hai| isa AkRti ke karNa kA varga, lamba kA varga aura sUkSma kSetraphala ke mApa kA varga batalAo / / 873 / / (863) yaha niyama niyamita SaTbhuja AkRti ke liye likhA gayA jJAta hotA hai| yaha sUtra SaTbhuja ke kSetraphala kA mAna V3a detA hai, jahA~ kisI bhI eka bhujA kI lambAI ahai| tathApi zuddha sUtra yaha hai- 24353

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7.893] kSetragaNitavyavahAraH [ 203 vargasvarUpakaraNirAzInAM yutisaMkhyAnayanasya ca teSAM vargasvarUpakaraNirAzInAM yathAkrameNa parasparaviyatitaH zeSasaMkhyAnayanasya ca sUtramakenApyapavartitaphalapadayogaviyogakRtihatAcchedAt / mUlaM padyutiviyutI rAzInAM viddhi karaNigaNitamidam // 883 // __atroddezakaH SoDazaSatriMzacchatakaraNInAM vargamUlapiNDaM me / atha caitatpadazeSa kathaya sakhe gaNitatattvajJa // 893 // iti sUkSmagaNitaM samAptam / kala vargamala rAziyoM ke yoga ke saMkhyAtmaka mAna tathA eka dUsare meM se svAbhAvika krama meM kucha vargamUla rAziyoM ko ghaTAne ke pazcAt zeSaphala nikAlane ke liye niyama samasta vargamUla rAziyA~ eka aise sAdhAraNa guNanakhaMDa dvArA bhAjita kI jAtI haiM, jo aise bhajanaphaloM ko utpanna karatA hai jo vargarAziyA~ hotI haiN| isa prakAra prApta vargarAziyoM ke vargamUloM ko jor3A jAtA hai, athavA unheM svAbhAvika krama meM eka ko dUsare meM se ghaTAyA jAtA hai| isa prakAra prApta yoga aura zeSaphala donoM ko vargita kiyA jAtA hai, aura taba alaga alaga ( pahile upayoga meM lAe hue) bhAjaka guNanakhaMDa dvArA guNita kiyA jAtA hai / ina pariNAmI guNanaphaloM ke vargamUla, prazna meM dI gaI rAziyoM ke yoga aura aMtima aMtara ko utpanna karate haiM / samasta prakAra kI vargamUla rAziyoM ke gaNita ke saMbaMdha meM yaha niyama jAnanA cAhiye // 8 // ___ udAharaNArtha prazna he gaNitatattvajJa sakhe, mujhe 16, 36 aura 100 rAziyoM ke vargamUloM ke yoga ko batalAo. aura taba inhIM rAziyoM ke vargamUloM ke saMbaMdha meM aMtima zeSa bhI btlaao| isa prakAra, kSetra gaNita vyavahAra meM sUkSma gaNita nAmaka prakaraNa samApta huA // 893 // (883) yahA~ AyA huA "karaNI" zabda koI bhI aisI rAzi darzAtA hai jisakA vargamUla nikAlanA hotA hai, aura jaisI dazA ho usake anusAra vaha mUla parimeya (rational, dhanarAzi jo karaNIrahita ho) athavA aparimeya hotA hai| gAthA 893 meM diye gaye prazna ko nimna prakAra se hala karane para yaha niyama spaSTa ho jAvegA V16 +/36 +/100 aura (/ 100)-(/36 - V16) ke mAna nikAlanA haiN| inheM / 4 (/4 +/9 +/25); V4 {/25 -(V9 -V4)} dvArA prarUpita kiyA jA sakatA hai| sAdhita karane para, pUrva rAzi =V4 (2+3+5) ; apara rAzi =V4 15 -(3 - 2)} =V 4 (10) __ " =V 4 (4) =vxx/100 4xv16 =V400 " =V64 -20

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204] gaNitasArasaMgrahaH [7. 903 janyavyavahAraH itaH paraM kSetragaNite jnyvyvhaarmudaahrissyaamH| iSTasaMkhyAbIjAbhyAmAyatacaturazrakSetrAnayanasUtramvargavizeSaH koTiH saMvargo dviguNito bhavedvAhuH / vargasamAsaH karNazcAyatacaturazrajanyasya // 903 / / atroddezakaH ekadvike tu bIje kSetre janye tu saMsthApya / kathaya vigaNayya zIghra koTibhujAkaNamAnAni // 913 // bIje dve trINi sakhe kSetre janye tu saMsthApya / kathaya vigaNayya zIghraM koTibhujAkarNamAnAni // 923 // punarapi bIjasaMjJAbhyAmAyatacaturazrakSetrakalpanAyAH sUtrambIjayutiviyutighAtaH koTistadvargayozca saMkramaNe / bAhuzrutI bhavetAM janyavidhau karaNametadapi / / 933 / / janya vyavahAra isake pazcAt hama kSetraphala mApa sambandhI gaNita meM janya kriyA kA varNana kreNge| mana se cunI haI saMkhyAoM ko bIjoM ke samAna lekara unakI sahAyatA se Ayata kSetra ko prApta karane ke liye niyama mana se prApta Ayata kSetra ke saMbaMdha meM bIja saMkhyAoM ke vargoM kA aMtara laMba bhujA kI saMracanA karatA hai| bIja saMkhyAoM kA guNanaphala 2 dvArA guNita hokara dUsarI bhujA ho jAtA hai, aura bIja saMkhyAoM ke vargoM kA yoga karNa bana jAtA hai // 901 // udAharaNArtha prazna jyAmitIya AkRti ke saMbaMdha meM (jise mana ke anusAra prApta karanA hai) aura 2 likhe jAnevAle bIja haiM / gaNanA ke pazcAt mujhe lamba bhujA, dUsarI bhajA aura karNa ke mApoM ko zIghra batalAo // 11 // he mitra, 2 aura 3 ko, mana ke anusAra kisI AkRti ko prApta karane ke saMbaMdha meM. bIja lekara gaNanA ke pazcAt lamba bhujA, anya bhujA aura karNa zIghra batalAo // 12 // punaH bIjoM dvArA nirUpita saMkhyAoM kI sahAyatA se Ayata caturazra kSetra kI racanA karane ke liye dUsarA niyama bIjoM ke yoga aura aMtara kA guNanaphala lambamApa hotA hai| bIjoM ke yoga aura aMtara ke vargoM kA saMkramaNa anya bhujA tathA karNa ko utpanna karatA hai| yaha kriyA janya kSetra ko ( diye hue bIjoM se ) prApta karane ke upayoga meM bhI lAI jAtI hai // 13 // (903) "janya" kA zAbdika artha "meM se utpanna" athavA "meM se vyutpAdita" hotA hai, isaliye vaha aise tribhuja aura caturbhuja kSetroM ke viSaya meM hai jo diye gaye nyAsa (datta dazAoM) se prApta kiye jA sakate haiM / tribhuja aura caturbhuja kSetroM kI bhujAoM kI lambAI nikAlane ko janya kriyA kahate haiN| bIja, jaisA ki yahA~ varNita hai, sAdhAraNataH dhanAtmaka pUrNAka hotA hai| tribhuja aura caturbhuna kSetroM ko prApta karane ke liye do aise bIja aparivartanIya DhaMga se diye gaye hote haiN| isa niyama kA mUla AdhAra nimnalikhita bIjIya nirUpaNa se spaSTa ho jAvegA yadi "a" aura "" bIja saMkhyAyeM hoM, to a2 - ba2 lamba kA mApa hotA hai / 2 aba dUsarI bhujA kA mApa hotA hai aura a ba karNa kA mApa hotA hai, jaba ki caturbhuja kSetra Ayata ho| isase spaSTa hai ki bIja aisI saMkhyAe~ hotI haiM jinake guNanaphala aura vargoM kI sahAyatA se prApta bhujAoM ke mApoM dvArA samakoNa tribhuja kI racanA kI jA sakatI hai| (933) yahA~ diye gaye niyama meM a2 - ba2, 2 a ba aura a + 2 ko (a + ba) (a - ba),

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mizrakavyavahAraH atrodezakaH tripaJcakabIjAbhyAM janyakSetraM sakhe samutthApya / koTibhujA zrutisaMkhyAH kathaya vicintyAzu gaNitatattvajJa / / 943 / / iSTajanyakSetrAdvIjasaMjJa saMkhyayorAnayanasUtramkoTicchedAvAptyoH saMkramaNe bAhudalaphalacchedau / bIje zrutISTakRtyoryoga viyogArdhamUle te // 953 // atrodezakaH -7. 973 ] [ 205 kasyApi kSetrasya ca SoDaza koTizca bIje ke / triMzadathavAnyAbAhurbIje ke te zrutizcatustriMzat // 963 // koTisaMkhyAM jJAtvA bhujA karNasaMkhyAnayanasya ca bhujasaMkhyAM jJAtvA koTikarNasaMkhyAnayanasya ca karNasaMkhyAM jJAtvA koTibhujA saMkhyAnayanasya ca sUtram - koTikRtezchedAptyoH saMkramaNe zrutibhujau bhujakRtervA / athavA zratISTakRtyorantarapadamiSTamapi ca koTibhuje // 973 // udAharaNArtha prazna he gaNitatatvajJa mitra, 3 aura 5 ko bIja lekara unakI sahAyatA se janya kSetra kI racanA karo, aura tatra soca vicAra kara zIghra hI lamba bhujA, anya bhujA aura karNa ke mApoM ko batalAo // 943 // bIjoM se prApta karane yogya kisI dI gaI AkRti saMbaMdhI bIja saMkhyAoM ko nikAlane ke liye niyama lamba bhujA ke mana se cune hue yathArtha bhAjaka aura pariNAmI bhajanaphala meM saMkramaNa kriyA karane se iSTa bIja utpanna hote haiM / anya bhujA kI bharddharAzi ke mana se cune hue yathArtha bhAjaka aura pariNAmI bhajanaphala bhI iSTa bIja hote haiN| ve bIja kramazaH karNa aura mana se cunI huI saMkhyA kI varNita rAzi ke yoga kI arddharAzi ke vargamULa tathA aMtara kI arddharAzi ke vargamULa hote haiM || 953 // udAharaNArtha prazna kisI raikhikIya AkRti ke saMbaMdha meM lamba 16 hai, batalAo bIja kyA-kyA haiM ? athavA yadi anya bhujA 30 ho, to bIjoM ko batalAo / yadi karNa 34 ho, to ve bIja kauna kauna haiM ? // 963 // anya bhujA aura karNa ke saMkhyAtmaka mAnoM ko nikAlane ke liye niyama, jaba ki lamba bhujA jJAta ho; lamba bhujA aura karNa ko nikAlane ke liye niyama, jaba ki anya bhujA jJAta ho; aura lamba bhujA tathA anya bhujA ko nikAlane ke liye niyama, jaba ki karNa kA saMkhyAtmaka mApa jJAta ho pariNAmI bhajanaphala ke bIca lamba bhujA ke varga ke mana se cunA hue yathArtha bhAjaka aura saMkramaNa kriyA karane para kramazaH karNa aura anya bhujA utpanna hotI haiM / isI prakAra anya bhujA ke ke saMbaMdha meM vahI saMkramaNa kriyA karane se lamba bhujA aura karNa ke mApa utpanna hote haiM / athavA, karNa ke varga aura kisI mana se cunI huI saMkhyA ke varga ke aMtara kI vagarmUla zazi tathA vaha cunI huI saMkhyA kramazaH lamba bhujA aura anya bhujA hotI haiM // 973 // (a+ba) - - (a-)2 2 2 aura (a + ba) + (a-ba) ke dvArA prarUpita kiyA gayA hai / 2 (953) isa niyama meM kathita kriyAeM gAthA 903 meM kathita kriyAoM se viparIta haiM / (973) yaha niyama nimnalikhita sarvasamikAoM ( identities ) para nirbhara hai -

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206 ] gaNita sArasaMgrahaH atrodezakaH kasyApi koTirekAdaza bAhuH SaSTiranyasyaH / zrutirekaSaSTiranyAsyAnuktAnyatra me kathaya // 983 // dvisamacaturazrakSetrasyAnayanaprakArasya sUtram - janyakSetra bhujArdhahAraphalajaprAgjanya koTyoryutirbhUrAsyaM viyutirbhujA zrutirathAlpAlpA hi koTirbhavet / mahatI zrutiH zrutirabhUjjyeSThaM phalaM syAtphalaM bAhuH syAdavalambako dvisamakakSetre caturbAhuke // 993 // udAharaNArtha prazna kisI AkRti ke saMbaMdha meM, lamba bhujA 11 hai, dUsarI AkRti ke saMbaMdha meM anya ( dUsarI ) bhujA 60 hai, aura tIsarI AkRti ke saMbaMdha meM karNa 61 hai / ina tIna dazAoM meM ajJAta bhujAoM ke mApoM ko batalAo // 98 // [ 7.983 diye gaye bIjoM kI sahAyatA se do barAbara bhujAoM vAle caturbhuja kSetra ko prApta karane kI rIti ke saMbaMdha meM niyama diye gaye bIjoM kI sahAyatA se prApta prathama Ayata kI lamba bhujA ko dUsarI AkRti ( jise mUlataH prApta AkRti ke AdhAra kI arddharAzi ke mana se cune hue do guNanakhaMDoM ko bIja mAnakara prApta kiyA gayA hai aisI AkRti ) kI lamba bhujA meM jor3anepara do barAbara bhujAoM vAle caturbhuja kSetra kA AdhAra utpanna hotA hai| ina do lamboM ke mApoM ke antara se caturbhuja kI UparI bhujA utpanna hotI hai| pUrva kathita do prApta AkRtiyoM kA choTA karNaM do barAbara bhujAoM meM se kisI eka kA mApa hotA hai / una do prApta AkRtiyoM ke sambandha meM do lamba bhujAoM meM se choTI bhujA, AdhAra ke usa choTe khaMDa kA mApa hotI hai jo UparI bhujA ke aMtoM meM se kisI eka se AdhAra para lamba girAne se banatA hai / una do prApta AkRtiyoM ke sambandha meM bar3A karNa iSTa karNa kA mApa hotA hai| una do prApta AkRtiyoM meM se bar3e kA kSetraphala iSTa AkRti kA kSetraphala hotA hai; aura una do AkRtiyoM meM se kisI eka kA AdhAra, UparI bhujA ke aMtoM meM se kisI eka se AdhAra para girAye gaye lamba kA mApa hotA hai // 993 // (adeg -bara)deg deg (a-ba)+- } / 2= a + ba' athavA 2 a ba (dazAnusAra ) ( a - ba ) 2 1 ) 2 ) { 3)/(a'+ ba+- (2 a ba ) ra 2 ba ` deg 2 ba' } )+- - ( 2 - (99) isa gAthA meM kathita niyama ke anusAra sAdhana kiyA jAne vAlA prazna yaha hai ki do diye gaye bIjoM kI sahAyatA se do barAbara bhujAoM vAle caturbhuja kSetra kI racanA kisa prakAra karanA lamboM tathA lamba ke kAraNa saMracita do AyatoM meM se nikAlanA par3atI / inameM se prathama Ayata kSetra Upara gAthA 903 meM diye gaye niyamAnusAra banAyA jAtA hai| prathama Ayata ke AdhAra kI lambAI kI arddharAzi ke mana se cune hue do guNanakhaMDoM meM se usI niyama ke anusAra dUsarA Ayata kSetra banatA hai / ( una do guNanakhaMDoM ko bIja mAna lete haiN|) isaliye atra hama prathama Ayata ko, dUsare Ayata kSetra se alaga pahicAnane ke liye, prAthamika AkRti kaheMge / / 2 = a + ba' athavA ara - ba a ba )2 = a' - bara cAhiye / bhujAoM, karNoM aura UparI bhujA ke aMtoM se AdhAra para girAye gaye utpanna hue khaMDoM kI lambAiyoM diye gaye bIjoM kI sahAyatA se

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-7.10.1] kSetragaNitavyavahAraH [207 atroddezakaH caturazrakSetrasya dvisamasya ca paJcaSaTakabojasya / mukhabhUbhujAvalambakakarNAbAdhAdhanAni vada // 1003 / / udAharaNArtha prazna do barAbara bhujAoM vAle tathA 5 aura 6 ko bIja mAnakara unakI sahAyatA se racita caturbhuja kSetra ke saMbaMdha se UparI bhujA. AdhAra. do barAbara bhujAoM meM se eka, UparI bhujA se AdhAra para girAyA gayA laMba, karNa aura AdhAra kA choTA khaMDa tathA kSetraphala ke mApoM ko batalAo // 1001 // isa niyama kA mUla AdhAra gAthA 1001 meM diye gaye prazna ke hala ko citrita karane vAlI nimnalikhita AkRtiyoM se spaSTa ho jAvegA / yahA~ diye gaye bIja 5 aura 6 haiN| prathama Ayata athavA bIjoM se prApta prAthamika AkRti aba sa da hai [noTa-ye AkRtiyA~ paimAne rahita haiM / ] isa AkRti meM AdhAra kI lambAI ko arddharAzi 30 hai| isake do guNanakhaMDa 3 aura 10 cune jA sakate haiN| ina saMkhyAoM kI sahAyatA se ( unheM bIja mAnakara ) saMracita Ayata kSetra ipha ga ha hai do barAbara bhujAoM vAle iSTa caturbhuja kSetra kI racanA ke liye apane karNa dvArA vibhAjita prathama Ayata ke do tribhujoM meM se eka ko dUsare Ayata kI ora, aura vaise hI dUsare tribhuja ke barAbara kSetra ko dUsare Ayata kI dUsarI ora se haTA dete haiM jaisA kI AkRti ha aphasa' se spaSTa hai| yaha kriyA AkRtiyoM kI tulanA se spaSTa ho jaavegii| iSTa caturbhuja kSetra ha aphasa' kA kSetraphala = dUsare Ayata ipha ga ha kA kSetraphala / _AdhAra meM prathama Ayata kI lamba bhujA dhana dUsare Ayata kI lamba bhujA-aba+hapha UparI bhujA ha sa' =dUsare Ayata kI lamba bhujA RNa prathama Ayata kI lamba bhujA-ga ha-sada karNa ha pha= dUsare Ayata kA karNa F

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208] gaNitasArasaMgrahaH trisamacaturazrakSetrasya mukhabhUbhujAvalambakakarNAbAdhAdhanAnayanasUtrambhujapadahatabIjAntarahRtajanyadhanAptabhAgahArAbhyAm / tadbhujakoTibhyAM ca dvisama iva trismcturshre|| 1013 // atroddezakaH caturazrakSetrasya trisamasyAsya dvikatrikasvabojasya / mukhabhUbhujAvalambakakarNAbAdhAdhanAni vada / / 1023 // -- diye gaye bIjoM kI sahAyatA se tIna barAbara bhujAoM vAle caturbhuja kSetra ke saMbaMdha meM UparI bhujA, AdhAra, koI bhI eka barAbara bhujA, Upara se AdhAra para girAyA gayA lamba, karNa, AdhAra kA choTA khaMDa aura kSetraphala ke mApoM ko nikAlane ke liye niyama diye gaye bIjoM kA aMtara, una bIjoM kI sahAyatA se tatkAla prApta caturbhuja kSetra ke AdhAra ke vargamUla dvArA guNita kiyA jAtA hai| isa tatkAla prApta prAthamika caturbhuja ke kSetraphala ko isa prakAra prApta guNanaphala dvArA bhAjita kiyA jAtA hai| taba kriyA meM bIjoM kI taraha upayoga meM lAye gaye pariNAmI bhajanaphala aura bhAjaka kI sahAyatA se prApta dUsarA caturbhuja kSetra racA jAtA hai| tIsarA caturbhuja, tatkAla prApta caturbhuja ke AdhAra aura lamba bhujA ko bIja mAnakara, banAyA jAtA hai| taba ina do aMta meM prApta caturbhujoM kI sahAyatA se tIna barAbara bhujAoM vAle caturbhuja kSetra kI uparyukta bhujAoM Adi ke mApoM ko do barAbara bhujAoM vAle caturbhuja meM prayukta vidhi anusAra prApta kiyA jAtA hai // 1013 // udAharaNArtha prazna tIna barAvara bhujAoM vAle, tathA 2 aura 3 bIja haiM jisake aise, caturbhuja kSetra ke saMbaMdha meM UparI bhujA, AdhAra, tIna barAbara bhujAoM meM se eka, UparI bhujA se AdhAra para girAyA gayA lamba, karNa, adhAra kA choTA khaMDa aura kSetraphaloM ke mApoM ko batalAo // 1023 // AdhAra kA choTA khaMDa arthAt a -prathama Ayata kI laMba bhujA =aba lamba ha i-dUsare athavA prathama Ayata kA AdhAra-basa- phaga bAja kI pratyeka barAbara bhajA a' athavA phasa'-prathama Ayata kA karNa. arthAta , asa (1013) yadi diye gaye bIja aaura ba dvArA nirUpita hoM, to tatkAla prApta caturbhuja kI bhujAoM ke mApa ye hoMge : lAba bhujA = a-bara, AdhAra =2 aba, karNa - a + ba2, kSetraphala =2 a ba (a2 - b)| jaisA ki do barAbara bhujAoM vAle kSetraphala kI racanA ke saMbaMdha meM gAthA 99 kA niyama upayoga kahA gayA hai, usI taraha yaha niyama, do prApta AyatoM kI sahAyatA se, tIna barAbara bhujAoM vAle iSTa caturbhuja kSetra kI saMracanA meM sahAyaka hotA hai| ina AyatoM meM prathama saMbaMdhI bIja ye haiM2aba4(a-ba) arthAta 12, arthAt /2a bax(a+ba) aura / aba x (a-ba) gAthA 903 kA niyama yahA~ prayukta karane para hameM prathama Ayata ke liye nimnalikhita mAna prApta hote haiM lamba bhujA = (a+ba)2x2a ba-(a-ba)242aba athavA 8abara

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[209 -7. 1033] kSetragaNitavyavahAraH __viSamacaturazrakSetrasya mukhabhUbhujAvalambakakarNAbAdhAdhanAnayanasUtramjyeSThAlpAnyonyahInazrutihatabhujakoTI bhuje bhUmukhe te koTyoranyonyadobhyAM hatayutiratha dorghAtayukkoTighAtaH / karNAvalpazrutinAvanadhikabhujakoTyAhatau lambako tAbAbAdhe koTidona vavanivivarake karNaghAtAdhaimarthaH // 1033 // viSama caturbhuja ke saMbaMdha meM, UparI bhujA, AdhAra, bAjU kI bhujAoM, UparI bhujA ke aMtoM se AdhAra para girAye gaye lamboM, kareM. AdhAra ke khaMDoM aura kSetraphala ke mApoM ko nikAlane ke liye niyama---- diye gaye bIjoM ke do kulakoM ( sets ) saMbaMdhI do AyatAkAra prApta caturbhuja kSetroM ke bar3e aura choTe karNoM se AdhAra aura ( unhIM prApta choTI aura bar3I AkRtiyoM kI) lamba bhujA kramazaH guNita kI jAtI haiN| pariNAmI guNanaphala iSTa caturbhuja kSetra kI do asamAna bhujAoM, AdhAra aura UparI bhujA ke mApoM ko dete haiN| prApta AkRtiyoM kI lamba bhujAe~ eka dUsare ke AdhAra dvArA guNita kI jAtI haiN| isa prakAra prApta do guNanaphala jor3e jAte haiN| taba una AkRtiyoM saMbaMdhI do lara bhujAoM ke guNanaphala meM unhoM AkRtiyoM ke AdhAroM kA guNanaphala jor3A jAtA hai| isa prakAra prApta do yoga, jaba una do AkRtiyoM ke do karNoM meM se choTe karNa ke dvArA guNita kiye jAte haiM, taba ve iSTa karNoM ko utpanna karate haiN| ve hI yoga, jaba choTI AkRti ke AdhAra aura lamba bhujA dvArA kramazaH guNita kiye jAte haiM, taba ve karNoM ke aMtoM se girAye gaye lamboM ke mApoM ko utpanna karate haiM; aura jaba ve usI AkRti kI lamba bhujA aura AdhAra dvArA guNita hote haiM, taba ve lamboM dvArA utpanna AdhAra ke khaMDoM ke mApoM ko utpanna karate haiN| ina khaMDoM ke mApa jaba AdhAra ke mApa meM se ghaTAye jAte haiM, taba anya khaMDoM ke mAna prApta hote haiN| uparyukta prApta huI AkRti ke karNoM ke guNanaphala kI arddharAzi, iSTa AkRti ke kSetraphala kA mApa hotI hai // 1033 // AdhAra = 2XV 2aba x(a+4)XV2a ba (a-ba) athavA 4a ba (a2 - bara) karNa %3D (a+)242a ba+ (a-ba)2x2a ba athavA 4 a ba (a+ 2) dUsare Ayata kSetra ke saMbaMdha meM bIja a-ba aura aba haiN| isa Ayata ke saMbaMdha meM: lamba bhujA = 4a ba -(a-ba2)2; AdhAra = 4a ba (a-ba2); karNa = 42 va+ (a-ba2) athavA (a+2)2 ina do AyatoM kI sahAyatA se, iSTa kSetraphala kI bhujAoM, koM, Adi ke mApoM ko gAthA 99 ke niyamAnusAra prApta kiyA jAtA hai| ve ye haiM AdhAra = lamba bhujAoM kA yoga = 8a ba + 4'ba2-(a-ba2)2 UparI bhujA = bar3I lamba bhujA-choTo lAba bhujA-8a2 ba2-142 ba2-(a-ba2)2} =(a + 32)2 bAjU kI koI eka bhujA = choTA karNa = (a+ba2)2 AdhAra kA choTA khaMDa = choTI lamba bhujA = 4a ba -(a2-2) lamba = do kaNoM meM se bar3A karNa = 4a ba (a+ba2) kSetraphala = bar3e Ayata kA kSetraphala = 8a ba244a ba (a2-bara) yahA~ dekhA sakatA hai ki UparI bhujA kA mApa bAjU kI bhujAoM meM se koI bhI eka ke barAbara hai| isa prakAra, tIna bhujAoM vAlA iSTa caturbhuja kSetra prApta hotA hai| (103) nimnalikhita bIjIya nirUpaNa se niyama spaSTa ho jAvegAga0 sA0 saM0-27

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gaNita sArasaMgrahaH atroddezakaH ekadvikadvikatrikajanye cotthApya viSamacaturazre / mukhabhUbhujAvalambakakarNAbAdhAdhanAni vada / / 1043 / / punarapi viSamacaturazrAnayanasUtram - hrasvatikRtiguNito jyeSThabhujaH koTirapi dharA vadanam / karNAbhyAM saMguNitAvubhayabhujAvalpabhujakoTI / / 1053 / / jyeSThabhuja koTiviyutidvidhAlpabhujakoTitAr3itA yuktA / hrasvabhujako TiyutiguNapRthukoTyAtpazrutinakau karNau // 1063 // alpazrutihRtakarNAlpakoTibhujasaMhatI pRthaglambau / tadbhujayutiviyutiguNAtpadamAbAdhe phalaM zrutiguNArdham // 1073 / / 210 ] [ 7.104 udAharaNArtha prazna 1 aura 2 tathA 2 aura 3 bIjoM ko lekara, do AkRtiyA~ prApta kara, viSama caturbhuja ke saMbaMdha meM Upara kI bhujA, AdhAra, bAjU kI bhujAoM, lamboM, karNau, AdhAra ke khaMDoM aura kSetraphala ke mApoM ko batalAo // 104 // viSama caturbhuja ke saMbaMdha meM bhujAoM ke mApa Adi ko prApta karane ke lie dUsarA niyamado prApta AyatoM meM choTI AkRti ke karNaM ke varga ko, alaga-alaga, AdhAra aura bar3e bhAyata kI laMba bhujA dvArA guNita karane se viSama iSTa caturbhuja ke AdhAra aura UparI bhujA ke mApa utpanna hote haiN| choTe Ayata kA AdhAra aura lamba bhujA, pratyeka uttarottara, uparokta Ayata kSetroM ke pratyeka ke karNaM dvArA guNita hokara kramazaH iSTa caturbhuja kI do pArzva bhujAoM ko utpanna karate haiM / bar3I AkRti ( Ayata ) ke AdhAra aura lamba bhujA kA aMtara, alaga-alaga do sthAnoM meM rakhA jAkara, choTI AkRti ke AdhAra aura lamba bhujA dvArA guNita kiyA jAtA / isa kriyA ke do pariNAmI guNanaphala alagaalaga usa guNanaphala meM jor3e jAte haiM, jo choTe Ayata ke AdhAra aura laMba bhujA ke yoga ko bar3e Ayatako lamba bhujA se guNita karane para prApta hotA hai / isa prakAraprApta do yoga jaba choTe Ayata ke karNa dvArA guNita kiye jAte haiM, to iSTa caturbhuja kSetra ke do karNoM ke mApa prApta hote haiM / iSTa caturbhuja kSetra ke karNoM ko alaga-alaga choTe Ayata ke karNa dvArA bhAjita kiyA jAtA 1 isa prakAra prApta bhajanaphaloM ko kramazaH choTe bhAyata kI lamba bhujA aura AdhAra dvArA guNita kiyA jAtA hai | pariNAmI guNanaphala iSTa caturbhuja kSetra ke laMboM ke mApoM ko utpanna karate haiM / ina do laMboM meM ( AdhAra aura UparI bhujA chor3akara ) uparyukta do bhujAoM ke mAnoM ko alaga-alaga jor3A jAtA hai / bar3I bhujA, bar3e lamba meM aura choTI bhujA choTe laMba meM / ina laMboM aura bhujAoM ke aMtara bhI usI krama maiM prApta kiye jAte haiM / uparyukta yoga kramazaH ina aMtaroM dvArA guNita kiye jAte haiN| isa prakAra prApta guNanaphaloM ke vargamUla iSTa caturbhuja saMbaMdhI AdhAra ke khaMDoM ke mAnoM ko utpanna karate haiM / iSTa caturbhuja kSetra ke karNoM ke guNanaphala kI AdhI rAzi usakA kSetraphala hotI hai // 105 - 1073 // mAnalo diye gaye bIjoM ke do kulaka ( sets ) a, ba aura sa, da haiN| taba vibhinna iSTa tattva nimnalikhita hoMge bAjU kI bhujAe~ = 2 a ba (sa e + da e) (a' + ba') aura (are - bara) (sa' + da e) (a + ba+-) AdhAra = 1 sa da ( a' + ba' ) ( a + ba' )

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-7. 1043] kSetragaNitavyavahAraH [21 ekasmAjanyAyatacaturazrAddvisamatribhujAnayanasUtram-- karNe bhujadvayaM syAdvAhurdviguNIkRto bhavedbhUmiH / koTiravalambako'yaM dvisamatribhuje dhanaM gaNitam // 1083 // kevala eka janya Ayata kSetra kI sahAyatA se samadvibAhu tribhuja prApta karane ke liye niyama diye gaye bIjoM kI sahAyatA se saMracita Ayata ke do karNa iSTa samadvibAhu tribhuja ko do barAbara bhujAe~ ho jAte haiM / Ayata kA AdhAra do dvArA guNita hokara iSTa tribhuja kA AdhAra bana jAtA hai / Ayata kI laMba bhujA, iSTa tribhuja kA zIrSa se AdhAra para girAyA huA lamba hotI hai / usa Ayata kA kSetraphala, iSTa tribhuja kA kSetraphala hotA hai // 10 // UparI bhujA=(sara-da) ( a + ba2 ) (a+bara) karNa = { ( a2 - 2 )42 sa da + (sa2 - da2) 2 a ba }x ( a + 2 ); aura {(a -ba )(sa -da2)+4 a ba sa da }x(a +ba2) lamba % { ( a-bara)42 sa da +(sa-da2)2 aba}42 aba; aura {( a -bara) ( sa2 -da2 )+4 a ba sa da}X( a -2) khaMDa avadhAe~ ={ (a2 -2 )42 sa da + (sara-dara )42 a ba} ( a - bara); aura { (a-ba ) (sara-dara )+ 4 a ba sa da }42 a ba. (1053-1071) gAthA 1033 ke noTa meM kathita mAna yahA~ bhI bhujAoM Adi ke liye diye gaye haiM; kevala ve kucha bhinna vidhi se kahe gaye haiN| 1033 vI gAthA ke hI pratIka lekarakarNa = [12 sa da - (sa2 - da2)} 2 a ba +{2 a ba + (a2 - ba)} (sa2 - da2)]x(a + 2); aura [12 sa da - (sa2 -da')} (a2 - ba)+{2 aba+ (a2 - 32)} (sa2 - da2)]x (a+br)| [{2 sada-(sa2 -da')}42 a ba +{2 a ba + (a2 - ba) }(sa2 - da2)] (a+vara) -x (a-ba); (a+ba2) [{2sa da - (sa2 - da2)} (a2 - bara) + {2a ba + (ara-ba)} (sa2 - da2)] (a +2) -42ab| (a+ba) uparyukta cAra bIjavAkya 1035 vI gAthA meM diye gaye karNoM aura laMboM ke mApoM ke rUpa meM prahAsita kiye jA sakate haiN| yahA~ AdhAra ke khaMDoM ke mApa, khaMDa kI sevAdI bhujA aura laMba ke vargoM ke antara ke vargamUla ko nikAlane para prApta kiye jA sakate haiN| lamca: - (1083) isa niyama kA mUla AdhAra isa prakAra nikAlA jA sakatA hai:-mAnalo aba sa da eka Ayata hai aura ada, itaka bar3hAI jAtI hai tAki __ ada%da i| isa ko jodd'o| asa i eka samadvibAhu tribhuja hai jisakI bhujAe~ Ayata ke karmoM ke mApa ke barAbara haiM, aura jisakA kSetraphala Ayata ke kSetraphala ke barAbara hai| pArzva AkRti se yaha bilkula spaSTa ho jaavegaa|

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gaNita sArasaMgrahaH atroddezakaH trikapaJcakabIjotthadvisamatribhujasya gaNaka bAhU dvau / bhUmimavalambakaM ca pragaNayyAcakSva me zIghram / / 1093 / / viSama tribhujakSetrasya kalpanAprakArasya sUtramjanyabhujArthaM chittvA kenApicchedalabdhajaM cAbhyAm / koTiyutirbhUH karNau bhujau bhujA lambakA viSame / / 1103 // atroddezakaH 212 ] dvibIjakasya kSetrabhujArdhena cAnyamutthApya / tasmAdviSamatribhuje bhujabhUmyavalambakaM brUhi / / 1113 // iti janyavyavahAraH samAptaH / udAharaNArtha prazna he gaNitajJa, 3 aura 5 ko bIja lekara unakI sahAyatA se prApta samadvibAhu tribhuja ke saMbaMdha meM do barAbara bhujAoM, AdhAra aura laMba ke mApoM ko zIghra hI gaNanA kara batAo // 1093 // [ 7. 1093 viSama tribhuja kI racanA karane kI vidhi ke liye niyama diye gaye bIjoM se prApta Ayata ke AdhAra ko mana se cune hue guNanakhaMDa mAnakara dUsarA Ayata prApta AdhI rAzi ko dvArA bhAjita karate haiM | bhAjaka aura bhajanaphala kI isa kriyA meM bIja karate haiM / ina do AyatoM kI lamba bhujAoM kA yoga iSTa viSama tribhuja ke AdhAra kA mApa hotA hai / una do AyatoM ke do karNa iSTatribhuja kI do bhujAoM ke mApa hote haiM / una do AyatoM meM se kisI eka kA AdhAra iSTa tribhuja ke laMba kA mApa hotA hai // 1103 // udAharaNArtha 2 aura 3 ko bIja lekara unase prApta Ayata tathA usa Ayata ke Adhe AdhAra se prApta dUsarA Ayata saMracita kara, mujhe isa kriyA kI sahAyatA se viSama tribhuja kI bhujAbhoM, AdhAra aura laMba ke mApoM ko batalAo // 1113 // isa prakAra, kSetra gaNita vyavahAra meM janma vyavahAra nAmaka prakaraNa samApta huA / (1103) pArzvalikhita racanA se niyama spaSTa ho jAvegA - mAnalo a ba sa da aura i pha ga ha do aise janya Ayata haiM ki AdhAra a da= AdhAra iha / ba a ko ka taka itanA a keM bar3hAo ki aka=ipha hoN| yaha saralatA pUrvaka dikhAyA jA sakatA hai ki da ka = iga aura tribhuja badaka kA AdhAra ba ka = ba a +ipha, jo AyatoM kI laMba bhujAyeM kahalAtI haiM / tribhuja kI bhujAyeM unhIM AyatoM ke karNoM ke barAbara hotI haiN|

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-7. 1123] kSetragaNitavyavahAraH [ 213 paizAcikavyavahAraH itaH paraM paishaacikvyvhaarmudaahrissyaamH| samacaturazrakSetre vA AyatacaturazrakSetre vA kSetraphale rajjusaMkhyayA same sati, kSetraphale bAhusaMkhyayA same sati, kSetraphale karNasaMkhyayA same sati, kSetraphale rajjavardhasaMkhyayA same sati, kSetraphale bAhostRtIyAMzasaMkhyayA same sati, kSetraphale karNasaMkhyAyAzcaturthAMzasaMkhyayA same sati, dviguNitakarNasya triguNitabAhozca caturguNitakoTezca rajjossaMyogasaMkhyA dviguNIkRtya tadviguNitasaMkhyayA kSetraphale samAne sati, ityevamAdInAM kSetrANAM koTibhujAkarNakSetraphalarajjuSu, iSTarAzidvayasAmyasya ceSTarAzidvayasyAnyonyamiSTaguNakAraguNitaphalavatakSetrasya bhujAkoTisaMkhyAnayanasya sUtramsvaguNeSTena vibhaktAH sveSTAnAM gaNaka gaNitaguNitena / guNitA bhujA bhujAH syuH samacaturazrAdijanyAnAm // 1123 // paizAcika vyavahAra ( atyanta jaTila prazna) isake pazcAt hama paizAcika viSaya kA pratipAdana kreNge| samAyata (varga) athavA Ayata ke saMbaMdha meM AdhAra aura laMba bhujA kA saMkhyAtmaka mAna nikAlane ke liye niyama jaba ki laMba bhujA, AdhAra, karNa, kSetraphala aura parimiti meM koI bhI do mana se samAna cuna liye jAte haiM, athavA jaba kSetra kA kSetraphala vaha guNanaphala hotA hai jo mana se cune hue guNakoM (multipliers ) dvArA kramazaH uparyukta tatvoM meM se koI bhI do rAziyoM ko guNita karane para prApta hotA hai: arthAt-samAyata (varga) athavA Ayata ke sambandha meM AdhAra aura laMba bhujA kA saMkhyAtmaka mAna nikAlane ke lie niyama jaba ki kSetra kA kSetraphala mAna meM parimiti ke tulya hotA hai; athavA jaba (kSetra kA kSetraphala) AdhAra ke barAbara hotA hai, athavA jaba (kSetra kA kSetraphala) parimiti ke mApakI arddharAziyoM ke tulya hotA hai; athavA jaba (kSetra kA kSetraphala ) AdhAra kI eka tihAI rAzi ke barAbara hotA hai; athavA jaba (kSetra kA kSetraphala) usa dviguNita rAzi ke tulya hotA hai jo usa rAzi ko dugunI karane para prApta hotI hai, aura jise karNa kI dugunI rAzi, AdhAra kI tigunI rAzi, laba bhujA kI caugunI rAzi aura parimiti ityAdi ko jor3ane para pariNAma svarUpa prApta karate haiM kisI mana se cunI huI iSTa AkRti ke AdhAra ke mApa ko ( pariNAmI) cune hue aise guNanakhaMDa dvArA bhAjita karane para, jisakA guNA AdhAra se karane para mana se cunI huI iSTa AkRti kA kSetraphala utpanna hotA hai ), athavA aisI mana se cunI huI iSTa AkRti ke AdhAra ko aise guNanakhaMDa se guNita karane para, (ki jisake diye gaye kSetra ke kSetraphala meM guNA karane para iSTa prakAra kA pariNAma prApta hotA hai) iSTa samabhuja caturazra tathA anya prakAra kI prApta AkRtiyoM ke AdhAroM ke mApa utpanna hote haiM // 12 // (1123) gAthA 1133 meM diyA gayA prathama prazna hala karane para niyama spaSTa ho jAvegA yahA~ prazna meM varga kI bhujA kA mApa tathA kSetraphala kA mAna nikAlanA hai, jaba ki kSetraphala parimiti ke barAbara hai| mAnalo 5 hai bhujA jisakI aisA varga liyA jAve to parimiti 20 hogI aura kSetraphala 25 hogA / vaha guNanakhaMDa jisase parimiti ke mApa 20 ko guNita karane para kSetraphala 25 ho jAve ' hai| yadi 5, varga kI mana se cunI huI bhujA dvArA bhAjita kI jAye, to iSTa caturbhuja kI bhujA utpanna hotI hai|

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gaNitasArasaMgrahaH atroddezakaH rajjurgaNitena samA samacaturazrasya kA tu bhujasaMkhyA | aparasya bAhusadRzaM gaNitaM tasyApi me kathaya / / 1133 // karNo gaNitena samaH samacaturazrasya ko bhavedvAhuH / rajjurdviguNo'nyasya kSetrasya dhanAcca me kathaya / / 1143 // Ayata caturazrasya kSetrasya ca rajjutulyamiha gaNitam / gaNitaM karNena samaM kSetrasyAnyasya ko bAhuH / / 1153 // kasyApi kSetrasya triguNo bAhurdhanAcca ko bAhuH / karNazcaturguNo'nyaH samacaturazrasya gaNita phalAt / / 1163 / / Ayatacaturazrasya zravaNaM dviguNaM triguNo bAhuH / koTicaturguNA tai rajjuyutairdviguNitaM gaNitam // 1173 / / Ayatacaturazrasya kSetrasya ca rajjurana rUpasamaH / koTi ko bAhurvA zIghraM vigaNayya me kathaya // 118 // 214 ] [ 7. 1133 udAharaNArtha prazna varga kSetra ke saMbaMdha meM parimiti kA saMkhyAtmaka mApa kSetraphala ke mApa ke barAbara hai / AdhAra kA saMkhyAtmaka mApa kyA hai ? usI prakAra kI dUsarI AkRti ke saMbaMdha meM kSetraphala kA mApa AdhAra ke mApa ke barAbara hai / usa AkRti ke saMbaMdha meM AdhAra kA mApa batalAo // 113 // kisI samAyata (varga) kSetra ke saMbaMdha meM karNa kA mApa kSetraphala ke mApa ke barAbara hai| AdhAra kA sApa kyA ho sakatA hai ? dUsarI usI prakAra kI AkRti ke saMbaMdha meM parimiti kA mApa, kSetraphala ke mApa kA dugunA hai| AdhAra kA mApa batalAoM // 1142 // Ayata kSetra ke saMbaMdha meM yahA~ kSetraphala kA mApa parimiti ke mApa ke tulya hai, aura dUsare usI prakAra ke kSetra ke saMbaMdha meM kSetraphala kA saMkhyAtmaka mApa karNa ke mApa ke barAbara hai| pratyeka dazA meM AdhAra kA mApa kyA hai ? // 115 // kisI varga kSetra ke saMbaMdha meM AdhAra kA saMkhyAtmaka mAna kSetraphala ke mApa se tigunA hai| dUsare varga kSetra ke saMbaMdha meM karNa kA saMkhyAtmaka mAna kSetraphala ke mApa se caugunA hai| inameM se pratyeka dazA meM AdhAra kA mApa kyA hai ? // 116 // kisI Ayata kSetra meM karNa ke mApa se dugunI rAzi, AdhAra se tigunI rAzi tathA laMba bhujA se caugunI rAzi lekara una meM parimiti kA mApa jor3A jAtA hai / isa prApta yogaphala se dugunI rAzi kSetraphala kA saMkhyAtmaka mApa hotI hai / AdhAra kA mApa batalAo // 1173 // Ayata kSetra ke saMbaMdha meM parimiti kA saMkhyAtmaka mAna 1 hai / gaNanA ke pazcAt yaha niyama dUsarI rIti bhI nirdiSTa karatA hai jo vyAvahArika rUpa meM usI prakAra hai / vaha guNanakhaMDa jisase kSetraphala 25 ko guNita kiyA jAtA hai, tAki vaha parimiti ke mApa 20 ke barAbara ho jAve, hai / yadi mana se cunI huI AkRti kI bhujA ( jo mApa meM 5 mAna lI gaI hai ) ko isa guNanakhaMDa se guNita kiyA jAve to iSTa AkRti kI bhujA kA mApa prApta hotA hai /

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[215 -7. 1223 ] kSetragatiNavyavahAraH karNo dviguNo bAhutriguNaHkoTizcaturguNA mizraH / rajjvA saha tatkSetrasyAyatacatarazrakasya rUpasamaH // 119 // punarapi janyAyatacaturazrakSetrasya bIjasaMkhyAnayane karaNasUtramkoTyUnakaNedalatatkarNAntaramubhayayozca pde| Ayatacaturazrasya kSetrasyeyaM kriyA janye // 1203 // ___ atroddezakaH Ayatacaturazrasya ca koTiH paJcAzadadhikapazca bhujA / sASTAcatvAriMzatrisaptatiH atirathAtra ke bIje // 1213 / / iSTakalpitasaGkhathApramANavatkaNasahitakSetrAnayanasUtramyadyatkSetraM jAtaM bIjaiH saMsthApya tasya karNena / iSTaM karNa vibhajellAbhaguNAH koTidoH karNAH // 1223 // mujhe zIghra batalAo ki lamba bhujA aura AdhAra ke mApa kyA-kyA haiM? // 18 // Ayata kSetra ke saMbaMdha meM karNa se dugunI rAzi. AdhAra se tigunI rAzi aura laMba se caugunI rAzi, ina sabako jor3a kara, jaba parimiti ke mApa meM jor3ate haiM, to yoga phala ho jAtA hai / AdhAra kA mApa batalAo // 1193 // prApta Ayata kSetra ke saMbaMdha meM bIjoM kA nirUpaNa karane vAlI saMkhyA ko nikAlane kI rIti saMbaMdhI niyama Ayata kSetra ke saMbaMdha meM, utpanna karane vAle bIjoM ko nikAlane kI kriyA meM, (.) laMba dvArA hAsita karNa kI arddha rAzi tathA (2) isa rAzi aura karNa kA aMtara, inake dvArA nirUpita do rAziyoM kA vargamUla nikAlanA par3atA hai / / 120 // udAharaNArtha prazna Ayata kSetra ke saMbaMdha meM laMba bhujA 55 hai, AdhAra 48 hai, aura karNa 73 hai| yahA~ bIja kyA-kyA haiM ? // 1213 // iSTa kalpita saMkhyAtmaka pramANa ke karNa vAle Ayata kSetra ko prApta karane ke liye niyama diye gaye bIjoM kI sahAyatA se prApta vibhinna AkRtiyoM meM se pratyeka likha liye (sthApita kiye ) jAte haiM, aura usake karNa ke mApa ke dvArA diyA gayA karNa kA mApa bhAjita kiyA jAtA hai| isa AkRti kI laMba bhujA, AdhAra aura karNa, yahA~ prApta hue bhajanaphala dvArA guNita hokara, iSTa kSetra kI raMba bhujA, AdhAra aura karNa ko utpanna karate haiN| (1203) isa adhyAya kI 953vI gAthA kA niyama Ayata kSetra ke karNa athavA laMba athavA AdhAra se bIjoM ko prApta karane kI rIti pradarzita karatA hai| parantu isa gAthA kA niyama Ayata ke laMba aura karNa se bIjoM ko prApta karane ke viSaya meM rIti nirUpita karatA hai| varNita kI haI rIti nimnalikhita sarvasamikA (identity ) para AdhArita hai/a + ba - (a - bara) .. . baaura ) . .. a+ba2- +-(a jahA~ a + bare karNa kA mApa hai, a-ba Ayata kI lamba-bhujA kA mApa hai| a aura va iSTa bIja haiM / (1223) yaha niyama isa siddhAnta para AdhArita hai ki samakoNa tribhuja kI bhujAeM karNa kI anupAtI hotI haiM / yahA~ karNa ke usI mApake liye bhujAoM ke mAnoM ke vibhinna kulaka (sets) ho sakate haiN| --a,

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gaNita sArasaMgrahaH atroddezakaH ekadvikadvikatrikacatuSkasaptaikasASTakAnAM ca / gaNaka caturNAM zIghraM bIjairutthApya koTibhujAH / / 1233 // AyatacaturazrANAM kSetrANAM viSamabAhukAnAM ca / karNo'tra paJcaSaSTiH kSetrANyAcakSva kAni syuH // / 1243 / / _iSTajanyAyatacaturazrakSetrasya rajjusaMkhyAM ca karNasaMkhyAM ca jJAtvA tajjanyAyatacaturazrakSetrasya 216 ] bhujakoTisaMkhyAnayanasUtram - karNakRtau dviguNAyAM rajjvardhakRtiM vizodhya tanmUlam / rajjvadhe saMkramaNIkRte bhujA koTirapi bhavati / / 1253 / / atroddezakaH paridhiH sa catustriMzat karNazcAtra trayodazo dRSTaH / janyakSetrasyAsya pragaNayyAcakSva koTibhujau / 1263 / / udAharaNArtha prazna he gaNitajJa, diye gaye bIjoM kI sahAyatA se, aise cAra AdhAroM ke mAnoM ko zIghra batalAo, jinake kramazaH 1 aura 2, 8 bIja haiM, tathA jinake AdhAra bhinna bhinna haiM / ( isa prazna meM ) dazAmeM, iSTa kSetroM ke mApoM ko batalAo / / 1233 - 1243 // jisakI parimiti kA mApa aura karNa kA mApa jJAta hai aise janya Ayata kSetra ke AdhAra aura usakI lamba bhujA ke saMkhyAtmaka mAnoM ko nikAlane ke liye niyama - karNa ke varga ko 2 se guNita kro| pariNAmI guNanaphala meM se parimiti kI arddharAzi ke varga ko ghttaao| taba pariNAmI aMtara ke vargamUla ko prApta kro| yadi yaha vargamUla AdhI parimiti ke sAtha saMkramaNa kriyA meM lAyA jAya, to iSTa AdhAra aura lamba bhujA bhI utpanna hotI haiM / / 1253 // Ayata kSetroM kI laMba bhujAe~ aura 2 aura 3, 4 aura 7, tathA 9 aura yahA~ karNa kA mAna 65 hai / isa udAharaNArtha prazna isa dazA meM parimiti 34 hai, aura karNa 13 hai / isa janya AkRti ke saMbaMdha meM laMba bhujA aura AdhAra ke mApoM ko gaNanA ke bAda batalAo // 126 // (1253) yadi kisI Ayata kI bhujAeM a aura ba dvArA prarUpita hoM, to kA mApa hotA hai aura parimiti kA mApa 2a + 2ba hotA hai / yaha saralatApUrvaka hai ki 2 a + 2 ba 2 [ 7. 1233 + 2 a + 2ba '2 ( /a + ba1) - ( 23 2 ba 2 a + 2 ba 2 -N 2 ( Va* + ** )9. - (2 a+ )' } 2 ye do sUtra varNita rIti kA yahAM bIjIya rUpa se nirUpaNa karate haiM / a' +bara karNa dekhA jA sakatA / 2 = a; aura /2=b|

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-7. 1303] kSetragaNitavyavahAraH [217 kSetraphalaM karNasaMkhyAM ca jJAtvA bhujakoTisaMkhyAnayanasUtramkarNakRtau dviguNIkRtagaNitaM hInAdhikaM kRtvA / mUlaM koTibhujau hi jyeSThe hrasvena saMkramaNe // 1273 // atroddezakaH Ayatacaturazrasya hi gaNitaM SaSTistrayodazAsyApi / karNastu koTibhujayoH parimANe zrotumicchAmi // 1283 / / kSetraphalasaMkhyAM rajasaMkhyAM ca jJAtvA Ayatacaturazrasya bhujakoTisaMkhyAnayanasUtramrajjvardhavagairAzergaNitaM caturAhataM vizodhyAtha / mUlena hi rajjvadhaM saMkramaNe sati bhujAkoTI // 1293 / / atroddezakaH saptatizataM tu rajjuH pazcazatottarasahasramiSTadhanam / janyAyatacaturazre koTibhujau me samAcakSva / / 1303 / / jaba AkRti kA kSetraphala aura karNa kA mAna jJAta ho, taba AdhAra aura lamba bhujA ke saMkhyAtmaka mAnoM ko prApta karane ke liye niyama kSetraphala ke mApa se dugano rAzi karNa ke varga meM se ghaTAI jAtI hai| vaha karNa ke varga meM jor3I bhI jAtI hai / isa prakAra prApta aMtara aura yoga ke vargamUloM se iSTa laMba bhujA aura AdhAra ke mApa prApta ho sakate haiM, jabaki vargamUloM meM se bar3I rAzi ke sAtha choTI ( vargamUla rAzi ) ke saMbaMdha meM saMkramaNa kriyA kI jAve / / 127 // ___ udAharaNArtha prazna kisI AyatakSetra ke saMbaMdha meM kSetraphalakA mApa 60 hai, aura karNa kA mApa 13 hai / maiM tumase lamba bhujA aura AdhAra ke mApoM ko sunane kA icchuka hU~ // 12 // jaba Ayata kSetra ke kSetraphala kA tathA parimiti kA saMkhyAtmaka mApa diyA gayA ho, taba usa AkRti ke saMbaMdha meM AdhAra aura lamba bhujA ke saMkhyAtmaka mAnoM ko prApta karane ke liye niyama parimiti kI arddharAzi ke varga meM se 4 dvArA guNita kSetraphala kA mApa ghaTAyA jAtA hai| taba isa pariNAmI aMtara ke vargamUla ke sAtha parimiti kI arddharAzi ke sambandha meM saMkramaNa kriyA karane se iSTa AdhAra aura laMbabhujA sacamuca meM prApta hotI hai / // 129 // udAharaNArtha prazna kisI prApta Ayata kSetra meM parimiti kA mApa 170 hai| diye gaye kSetra kA mApa 1500 haiN| laMba bhujA aura AdhAra ke mAnoM ko batalAo / / 1301 // (1271) gAthA 1251vIM ke noTa ke samAna hI pratIka lekara yahA~ diyA gayA niyama nimralikhita rUpa meM nirUpita hotA hai:--dazAnusAra { ( + va2 ) + 2 a ba+VIV a + ba2)2 - 2 a ba } *2= a athavA ca (1293) yahA~ bhI, 12 a 2 va 23.2- aba } + 2= a athavA ba, jaisI dazA ho| ga. sA. saM0-28

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218] gaNitasArasaMgrahaH [7. 1313AyatacaturazrakSetradvaye rajjusaMkhyAyAM sadRkSAyAM satyAM dvitIyakSetraphalAt prathamakSetraphale dviguNite sati, athavA kSetradvaye'pi kSetraphale sadRze sati prathamakSetrasya rajjusaMkhyAyA api dvitIyakSetrarajjusaMkhyAyAM dviguNAyAM satyAm , athavA kSetradvaye prathamakSetrarajjusaMkhyAyA api dvitIyakSetrasya rajjusaMkhyAyAM dviguNAyAM satyAM dvitIyakSetraphalAdapi prathamakSetraphale dviguNe sati, tattatkSetradvayasyAnayanasUtramsvAlpahRtarajjudhanahatakRtiriSTanaiva koTi:syAt / vyekA dostulyaphale'nyatrAdhikagaNitaguNiteSTam / / 1313 // vyekaM tadUnakoTiH triguNA doH syAdathAnyasya / rajjvardhavargarAzeriti pUrvoktena sUtreNa / tadgaNitarajjumititaH samAnayettadbhujAkoTo // 133 // iSTa Ayata kSetroM ke kramika yugmoM ko prApta karane ke liye niyama (1) jaba ki parimiti ke saMkhyAtmaka mApa barAbara haiM, aura prathama AkRti kA kSetraphala dUsare ke kSetraphala se dugunA haiathavA (2) jaba ki donoM AkRtiyoM ke kSetraphala barAbara haiM, aura dUsarI AkRti kI parimiti kA saMkhyAtmaka mApa prathama AkRti kI parimiti se duganA hai; athavA (3) jaba ki do kSetroM ke saMbaMdha meM dUsarI AkRti kI parimiti kA saMkhyAtmaka mApa, prathama AkRti kI parimiti se dugunA hai, aura prathama AkRtikA kSetraphala dUsarI AkRti ke kSetraphala se dugunA hai do iSTa Ayata kSetroM saMbaMdhI parimitiyoM tathA kSetraphaloM kI dI gaI niSpattiyoM meM bar3I saMkhyAoM ko unakI saMvAdI choTI saMkhyAoM dvArA bhAjita kiyA jAtA hai| pariNAmI bhajanaphaloM ko eka dUsare se paraspara guNita kara vargita kiyA jAtA hai| yahI rAzi jaba diye gaye mana se cune guNakAra (multiplier) dvArA guNita kI jAtI hai, taba laMbabhujA kA mAna utpanna hotA hai| aura usa dazA meM jaba ki do iSTa AkRtiyoM ke kSetraphala barAbara hoM, yaha laMba bhujA kA mApa eka dvArA hAsita hokara, AdhAra kA mApa bana jAtA hai| paraMtu dUsarI dazA meM jaba ki iSTa AkRtiyoM ke kSetraphala barAbara nahIM hote, taba bar3I niSpatti saMkhyA jo kSetraphaloM se saMbaMdhita hotI hai, diye gaye mana se cune guNakAra dvArA guNita kI jAtI hai aura pariNAmI guNanaphala | dvArA hAsita kiyA jAtA hai| Upara prApta laMba bhujA isa pariNAmI rAzi dvArA hAsita kI jAtI hai, aura taba 3 dvArA guNita kI jAtI hai| isa prakAra AdhAra kA mApa prApta hotA hai| tatpazcAt do iSTa caturbhuja kSetroM meM se dUsare caturbhuja ke mApa ko prApta karane ke lie, jJAta kSetraphala aura parimiti kI sahAyatA se, gAthA 1293 meM diye gaye niyamAnusAra usakA AdhAra tathA laMba nikAlanA par3ate haiM // 13 // 3-133 // (1313-133) yadi prathama Ayata kI do Asanna bhujAe~ ka aura kha hoM, tathA dUsare Ayata kI do Asanna bhujAe~ aaura ba hoM, to isa niyama meM dI gaI tIna prakAra kI samasyAoM meM kathita dazAoM ko isa prakAra se prarUpita kiyA jA sakatA hai (1) ka+kha = a+ba, ka kha %2 aba (2)2 (ka+kha) =a+ba, ka kha = aba (3)2 (ka+kha)= a+ba, ka kha 2 aba isa niyama meM diyA gayA hala kevala 134-136 gAthAoM meM diye gaye praznoM kI vizeSa dazAoM ke liye hI upayukta dikhAI detA hai|

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-7. 137] kSetragaNitavyavahAraH [219 atroddezakaH asamavyAsAyAmakSetre dve dvaavthessttgunnkaarH| prathamaM gaNitaM dviguNaM rajjU tulye kimatra koTibhuje // 134 // Ayatacaturazre dve kSetre dvayamevaguNakAraH / gaNitaM sadRzaM rajjurdviguNA prathamAt dvitIyayasya // 135 / / Ayatacaturazre dve kSetre prathamasya dhanamiha dviguNam / dviguNA dvitIyarajjustayorbhujAM koTimapi kathaya / / 136 / / dvisamatribhujakSetrayoH paraspararajjudhanasamAnasaMkhyayoriSTaguNakaguNitarajjudhanavatorvA dvisamatribhujakSetradvayAnayanasUtramrajjukRtighnAnyonyadhanAlpAptaM Sadvighnamalpamekonam / taccheSaM dviguNAlpaM bIje tajjanyayo(jAdayaH prAgvat // 137 // udAharaNArtha prazna do caturbhuja kSetra haiM jinameM se pratyeka asamAna laMbAI aura caur3AI vAlA hai| diyA gayA guNakAra 2 hai| prathama kSetra kA kSetraphala dUsare ke kSetraphala se dugunA hai, aura donoM meM parimitiyA~ barAbara haiN| isa prazna meM laMba bhujAe~ aura AdhAra kyA-kyA haiM ? // 134 // do Ayata kSetra haiM aura diyA gayA guNakAra bhI 2 hai| unake kSetraphala barAbara haiM paraMtu dUsare kSetra kI parimiti pahile kI parimiti se dugunI hai| unakI laMba bhujAe~ aura AdhAroM ko nikAlo // 135 // do Ayata kSetra diye gaye haiN| prathama kA kSetraphala dUsare ke kSetraphala se dugunA hai| dUsarI AkRti kI parimiti pahile kI parimiti se dugunI hai| unake AdhAroM aura laMba bhujAoM ke mAnoM ko prApta karo // 136 // aise samadvibAhu tribhujoM ke yugma ko prApta karane ke liye niyama, jinakI parimitiyA~ aura kSetraphala Apasa meM barAbara hoM athavA eka dUsare ke apavartya hoM iSTa samadvibAhu tribhujoM kI parimitiyoM ke niSpattirUpa mAnoM ke vargoM meM una tribhujoM ke kSetraphala ke niSpattirUpa mAnoM dvArA ekAntara guNana kiyA jAtA hai| isa prakAra prApta do guNanaphaloM meM se bar3hA choTe ke dvArA vibhAjita kiyA jAtA hai| tathA alaga se do ke dvArA bhI guNita kiyA jAtA hai| isa prakAra prApta guNanaphaloM meM se choTA guNanaphala ke dvArA hAsita kiyA jAtA hai| bar3A guNanaphala aura hAsita choTA guNanaphala aise bhAyatakSetra ke saMbaMdha meM do bIjoM kI saMracanA karate haiM, jinase iSTa tribhujoM meM se eka prApta kiyA jAtA hai| uparyukta ina do bIjoM ke aMtara aura ina bIjoM meM choTe kI dugunI rAzi : ye donoM aise Ayata kSetra ke saMbaMdha meM bIjoM kI saMracanA karate haiM, jinase dUsarA iSTa tribhuja prApta kiyA jAtA hai| apane kramavAra bIjoM kI sahAyatA se banI huI do AyatAkAra AkRtiyoM meM se, iSTa tribhujoM saMbaMdhI bhujAe~ aura anya bAteM Upara samajhAye anusAra prApta kI jAtI haiM // 13 // (137) do samadvibAhu tribhujoM kI parimitiyoM kI niSpatti a : ba ho, aura unake kSetraphaloM kI 6basa.2vasa ....4basa niSpatti sa:da ho, taba niyamAnusAra aura 4 -1tathAada adada ada ye bIjoM ke do kulaka ( ts) haiM, jinakI sahAyatA se do samadvibAha tribhujoM ke vibhinna

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220 ] gaNitasArasaMgrahaH atroddezakaH dvisamatribhujakSetradvayaM tayoH kSetrayoH samaM gaNitam / rajjU sametayoH syAt ko bAhuH kA bhavedbhUmiH // 138 // dvisamatribhujakSetre prathamasya dhanaM dvisaMguNitam / rajjuH samA dvayorapi ko bAhuH kA bhavedbhUmiH // 139 // dvisamatribhujakSetre dve rajjudviguNitA dvitIyasya / gaNite dvayoH samAne ko bAhuH kA bhavedbhUmiH // 140 // dvisamatribhujakSetre prathamasya dhanaM dvisaMguNitam / dviguNA dvitIyarajjuH ko bAhuH kA bhavedbhUmiH // 141 // udAharaNArtha do samadvibAhu tribhuja haiN| unakA kSetraphaLa eka sA hai| unakI parimitiyA~ bhI barAbara haiM / bhujAoM aura AdhAroM ke mAna kyA kyA haiM ? / / 138 // do samatribAhu tribhuja haiM / pahile kA kSetraphala dUsare ke kSetraphala se dugunA hai| una donoM kI parimitiyA~ eka sI haiM / bhujAoM aura AdhAroM ke mAna kyA kyA haiM ? // 139 // do samadvibAhu tribhuja haiN| dUsare tribhuja kI parimiti pahile tribhuja kI parimiti se dugunI hai / una do tribhujoM ke kSetraphala barAbara haiN| bhujAoM aura AdhAroM ke mApa kyA kyA haiM ? // 140 // do samadvibAhu tribhuja diye gaye haiM / prathama tribhuja kA kSetraphala dUsare ke kSetraphala se dugunA hai, aura dUsare kI parimiti pahile kI parimiti se bhujAoM aura AdhAroM ke mApa kyA kyA haiM ? // 141 // dugunI hai / iSTa tatvoM ko prApta kara sakate haiM / isa adhyAya kI 108 vIM gAthA ke nikAlI gaI bhujAoM aura U~cAiyoM ke mApoM ko jaba kramazaH parimitiyoM kI vAlI rAziyoM a aura ba dvArA guNita karate haiM, taba do samadvibAhu tribhujoM kI iSTa ke mApa prApta hote haiM / ve nimnalikhita haiM ( 1 ) barAbara bhujA = aX 2 2basa {(2) + (- 1)' } da a 6ba 2 sa sa AdhAra = a x 2x2x XX(11) anusAra, ina bIjoM se niSpatti meM pAI jAne bhujAoM aura U~cAiyoM sa ******* ******* U~cAI = aX {G)-GT-)} 4ba sa a da + 1)' + (-<)'} *} ada ( 2 ) barAbara bhuvA= bax {( AdhAra = bax2x2x (bharada + 1 ) x (+1) (2) basa da [ 7.138 ...... ....... ****** 4ba sa 42 sa U~cAI ba zak =<Page #278
kSetra gaNitavyavahAraH [ 221 ekadvayAdigaNanAtItasaMkhyAsu iSTasaMkhyAmiSTavastuno bhAgasaMkhyAM parikalpya tadiSTavastubhAgasaMkhyAyAH sakAzAt samacaturazrakSetrAnayanasya ca samavRttakSetrAnayanasya ca samatribhujakSetrAnayanasya cAyatacaturazrakSetrAnayanasya ca sUtram - svasamIkRtA vadhRtihRtadhanaM caturnna hi vRttasamacaturazravyAsaH / guNitaM tribhujAyata caturazrabhujArdhamapi koTiH / / 142 / / -7. 142 ] varga, athavA samavRtta kSetra, athavA samatribhuja kSetra, athavA Ayata ko inameM se kisI upayukta AkRti ke anupAtI bhAga ke saMkhyAtmaka mAna kI sahAyatA se prApta karane ke liye niyama, jaba ki 1, 2 Adi se prArambha hone vAlI prAkRta saMkhyAoM meM se koI mana se cunI huI saMkhyA dvArA usa dI gaI uparyukta AkRti ke anupAtI bhAga ke saMkhyAtmaka mAna ko utpanna karAyA jAtA hai ( anupAtI bhAga ke ) kSetraphala ( kA diyA gayA mApa hasta meM ) lie gae ( samucita rUpa se ) anurUpita (similarised ) mApa dvArA bhAjita kiyA jAtA hai / isa prakAra prApta bhajanaphala yadi 4 ke dvArA guNita kiyA jAya, to varga tathA vRtta kI bhI caur3AI kA mApa utpanna hotA hai| vahI bhajanaphala, yadi 6 dvArA guNita kiyA jAya, to samatribhuja tathA Ayata kSetra ke AdhAra kA mApa bhI utpanna hotA hai / isakI arddharAzi Ayata kSetra kI laMba bhujA kA mApa hotI hai // 142 // (142) isa niyama ke antargata diye gaye praznoM ke prakAra meM, vRtta, yA varga, yA samadvibAhu tribhuja, yA Ayata mana cAhe samAna bhAgoM meM vibhAjita kiyA jAtA hai / pratyeka bhAga, eka ora parimiti ke kisI viziSTa bhAga dvArA sImita hotA hai| jo anupAta parimiti ke usa viziSTa bhAga aura pUrI parimiti meM hotA hai vahI anupAta usa sImita bhAga aura AkRti ke pUrNa kSetraphala meM rahanA cAhie | vRtta ke saMbaMdha meM pratyeka khaMDa, dvaitrijya ( sector ) hotA hai; vargAkAra AkRti hone para aura AyatAkAra AkRti hone para vaha bhAga AyatAkAra hotA tathA samatribhuja AkRti hone para vaha tribhuja hotA hai / pratyeka bhAga kA kSetraphala aura mUla parimiti kI lambAI donoM datta mahattA kI hotI haiM / yaha gAthA, vRtta ke vyAsa varga kI bhujAoM, athavA samatribhuja Ayata kI bhujAoM kA mApa nikAlane ke liye niyama kA kathana karatI hai / yadi pratyeka bhAga kA kSetraphala 'ma' ho aura saMpUrNa parimiti kI lambAI kA koI bhAga 'na' ho to niyama meM diye gaye sUtra ye haiM yA ma - X 4 = vRtta kA vyAsa, athavA varga kI bhujA; na ma aura * X 6 = samatribhuja yA Ayata kI bhujA; na aura na na X6 kA arddhabhAga = Ayata kI la~ba bhujA kI lambAI / agale pRSTha para diye gaye samIkAroM se mUla AdhAra spaSTa ho jAvegA, jahA~ pratyeka AkRti ke vibhAjita khaMDoM kI saMkhyA 'ka' hai / vRtta kI trijyA athavA anya AkRti saMbaMdhI bhujA 'a' hai, aura Ayata kI laMba bhujA 'ba' hai /

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gaNita sArasaMgrahaH atroddezakaH svAntaHpure narendraH prAsAdatale nijAGganAmadhye / divyaM sa ratnakambalamapIpatattacca samavRttam // 143 // tAbhirdevIbhirdhRtamebhirbhujayozca muSTibhirlabdham / paJcadazaikasyAH syuH kati vanitAH ko'tra viSkambhaH // 144 // samacaturazrabhujAH ke samatribAhau bhujAcA Ayatacaturazrasya hi tatkoTibhujau sakhe kathaya // 145 // 222 ] kSetraphalasaMkhyAM jJAtvA samacaturazrakSetrAnayanasya cAyatacaturazrakSetrAnayanasya ca sUtram - sUkSmagaNitasya mUlaM samacaturazrasya bAhuriSTahRtam / dhanamiSTaphale syAtAmAyatacaturazra koTibhujau // 146 // udAharaNArtha prazna kisI rAjA ne apane aMtaHpura ke prAsAda meM apanI rAniyoM ke bIca meM Upara se pharza para samavRtta AkAra vAlA utkRSTa ratnakaMbala nIce giraayaa| vaha una deviyoM dvArA hAtha meM grahaNa kara liyA gayA / unameM se pratyeka ne apanI donoM bhujAoM kI muTTiyoM meM paMdraha paMdraha daMDa kSetraphala kA kaMbala grahaNa kara rakhA / yahA~ batalAo ki isa narendra kI vanitAyeM kitanI haiM, aura vRttAkAra kaMbala kA vyAsa ( viSkaMbha ) kitanA hai ? yadi yaha kaMbala vargAkAra ho, to isakI pratyeka bhujA kitane mApa kI hogI ? yadi vaha samatribhujAkAra ho to usakI bhujA kitanI hogI ? he mitra, mujhe batalAo ki yadi kaMbala AyatAkAra ho, to usakI laMba bhujA aura AdhAra kA mApa kyA hogA ? // 143 - 145 // vargAkAra AkRti athavA AyatAkAra AkRti prApta karane ke liye niyama, jabaki AkRti ke kSetraphala kA saMkhyAtmaka mAna jJAta ho / diye gaye kSetraphala ke zuddha mApa kA vargamUla iSTa vargAkAra AkRti kI bhujA kA mApa hotA hai| diye gaye kSetraphala ko mana se cunI huI ( kevala kSetraphala ke chor3akara ) koI bhI rAzi dvArA bhAjita karane para pariNAmI bhajanaphala aura yaha mana se Ayata kSetra ke saMbaMdha meM kramazaH AdhAra aura laMba bhujA kI racanA karatI haiM // 146 // Ayata kI dazA meM, ara a = " ka X ma vRtta kI dazA meM, kaXna kaXma a varga kI dazA meM, =- ; ka X na 4a _Xma_a / 2 samatribhuja kI dazA meM, kaXna = 3a aXba ka X ma liyA gayA jahA~ ba = = a 2 1 , Xna 2 ( a + ba) adhyAya kI 7 vIM gAthA meM diye gaye niyama ke anusAra samabhuja tribhuja ke kSetraphala kA vyAvahArika mAna yahA~ upayoga meM lAyA gayA hai / anyathA, isa niyama meM diyA gayA sUtra ThIka siddha nahIM hotA / (143 - 145) isa prazna meM muTThIbhara kA artha cAra aMgula pramANa hotA hai / vargamUla ko cunI huI rAzi jahA~ T = [ 7. 143 paridhi vyAsa ;

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-7.148] kSetragaNitavyavahAraH [223 atroddezakaH kasya hi samacaturazrakSetrasya phalaM catuSSaSTiH / phalamAyatasya sUkSmaM SaSTiH ke vAtra koTibhuje // 147 / / ___iSTadvisamacaturazrakSetrasya sUkSmaphalasaMkhyA jJAtvA, iSTasaMkhyAM guNakaM parikalpya, iSTasaMkhyAkabIjAbhyAM janyAyatacaturazrakSetraM parikalpya, tadiSTadvisamacaturazrakSetraphalavadiSTadvisamacaturazrAnayanasUtramtaddhanaguNiteSTakRtijanyadhanonA bhujAhRtA mukhaM kottiH| dviguNA samukhA bhUrdolambaH karNau bhuje tadiSTahRtAH // 148 // udAharaNArtha prazna 64 kSetraphala vAlI vargAkAra AkRti vAstava meM kauna sI hai ? Ayata kSetra ke kSetraphala kA zuddha mAna 60 hai| batalAo ki yahA~ laMba bhujA aura AdhAra ke mAna kyA kyA haiM ? // 147 // do barAbara bhujAoM vAle aise caturbhuja kSetra ko prApta karane ke liye niyama, jise bIjoM kI sahAyatA se Ayata kSetra ko prApta karane para aura sAtha hI kisI dI huI saMkhyA ko iSTa guNakAra kI taraha upayoga meM lAkara prApta karate haiM, tathA jaba (do barAbara bhujAoMvAle) aise caturbhuja kSetra ke kSetraphala ke barAbara jJAta sUkSma kSetraphala vAle caturbhuja kA kSetraphala hotA hai diye gaye guNakAra kA varga diye gaye kSetraphala dvArA guNita kiyA jAtA hai| pariNAmI guNanaphala, diye gaye bIjoM se prApta Ayata ke kSetraphala dvArA hAsita kiyA jAtA hai| zeSaphala jaba isa Ayata ke AdhAra dvArA bhAjita kiyA jAtA hai, taba UparI bhujA kA mApa utpanna hotA hai| prApta Ayata kI laMba bhujA kA mAna, jaba 2 dvArA guNita hokara (pahile hI) prApta UparI bhujA ke mAna meM jor3A jAtA hai, taba AdhAra kA mAna utpanna hotA hai| isa Ayata kSetra ke AdhAra kA mAna UparI bhujA ke aMtaroM se AdhAra para girAye gaye laMba ke samAna hotA hai, tathA vyutpAdita Ayata kSetra ke karNoM kA mAna bhujAoM ke mAna ke samAna hotA hai| isa prakAra prApta do samAna bhujAoM vAle caturbhuja ke ye tattva diye gaye guNakAra dvArA bhAjita kiye jAte haiM, tAki do samAna bhujAoM vAlA iSTa caturbhuja prApta ho // 14 // (148) yahA~ diye gaye kSetraphala aura do barAbara bhujAoM vAle caturbhuja kI racanA saMbaMdhI prazna kA vivecana kiyA gayA hai / isa hetu mana se koI saMkhyA cunI jAtI hai| do bIjoM kA eka kulaka (set) bhI diyA gayA rahatA hai| isa niyama meM varNita rIti dUsarI gAthA meM diye gaye prazna meM prayukta karane para spaSTa ho jaavegii| ullikhita bIja yahA~ 2 aura 3haiN| diyA gayA kSetraphala 7 hai, tathA mana se cunI huI saMkhyA 3 hai|

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gaNitasArasaMgrahaH atroddezakaH sUkSmadhanaM sapteSTaM trikaM hi bIje dvike trike dRSTe / dvisamacaturazrabAhu mukhabhUmyavalambakAn brUhi / / 149 // 224 ] udAharaNArtha prazna diye gaye kSetraphala kA ThIka mApa 7 hai, mana se cunA huA guNakAra 3 hai, aura datta bIja 2 aura 3 haiN| do barAbara bhujAoM vAle caturbhuja kSetra ko barAbara bhujAoM, UparI bhujA, AdhAra aura laMba ke mAnoM ko prApta karo / / 149 // noTa - AkRtiyoM ke mApa anumApa ( scale ) rahita haiM / sabase pahile isa adhyAya kI 903 vIM gAthAnusAra diye gaye bIjoM kI sahAyatA se Ayata kI racanA karate haiM / usa Ayata kI choTI bhujA kA mApa 5 aura bar3I bhujA kA mApa 12 tathA karNa kA mApa 13 hotA hai / usakA kSetraphala mAna meM 60 hotA hai| aba isa prazna meM diye gaye kSetraphala ko prazna meM dI gaI mana se cunI huI saMkhyA ke varga dvArA guNita karate haiM, jisase hameM 7 X 3 2 = 63 prApta hotA hai / isa 63 meM se hameM diye gaye bIjoM se saMracita Ayata kA kSetraphala 60 ghaTAnA par3atA hai, jisase 3 zeSa prApta hotA hai / 3 kSetraphala vAlA eka Ayata banAnA par3atA hai, jisakI eka bhujA bIjoM se prApta Ayata kI bar3I bhujA ke barAbara hotI hai / yaha bar3I bhujA mApa meM 12 hai, isaliye isa Ayata kI choTo 132383 bhujA AkRti meM dikhalAye anusAra hai mApa ko hotI hai / bIjoM se prApta Ayata ke do bhAga karNa dvArA prApta karate haiM, jo do tribhuja hote haiN| ina do tribhujoM ko, AkRti meM dikhAye anusAra, x 12 kSetraphala vAle Ayata ke donoM ora jamAte haiM, tAki laMbI bhujAe~ saMpAtI hoM / isa prakAra aMta meM hameM do barAbara 13 mApavAlI bhujAoM kA caturbhuja prApta hotA hai, jisakI UparI bhujA hai aura AdhAra 101 hotA hai| isakI sahAyatA se prazna meM iSTa caturbhuja kI bhujAoM ke mApa, mana se cunI huI saMkhyA 3 dvArA, bhujAoM ke mApa 13, 4, 13 aura 104 ko bhAjita kara, prApta kara sakate haiM / 13 [ 7. 149- 12 12 13

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kSetragaNitavyavahAraH [225 iSTasUkSmagaNitaphalavatrisamacaturazrakSetrAnayanasUtramiSTadhanabhaktadhanakRtiriSTayutArdhaM bhujA dviguNiteSTam / vibhujaM mukhamiSTAptaM gaNitaM yavalambakaM trisamajanye // 150 // __ atroddezakaH kasyApi kSetrasya trisamacaturbAhukasya sUkSmadhanam / SaNNavatiriSTamaSTau bhUbAhumukhAvalambakAni vada // 151 / / tIna barAbara bhujAoM vAle jJAta kSetraphala ke caturbhuja kSetra ko prApta karane ke liye niyama jaba ki guNaka ( multiplier ) diyA gayA ho diye gaye kSetraphala ke varga ko diye gaye guNaka ke dhana dvArA bhAjita kiyA jAtA hai / taba diye gaye guNakAra ko pariNAmI bhajanaphala meM jor3A jAtA hai| isa prakAra prApta yoga kI arAzi barAbara bhujAoM meM se kisI eka kA mApa detI hai| diyA gayA guNaka 2 se guNita hokara, aura taba prApta barAbara bhujA ( jo abhI prApta huI hai aisI samAna bhujA) dvArA hAsita hokara, UparI bhujA kA mApa detA hai| diyA gayA kSetraphala diye gaye guNaka dvArA bhAjita hokara, tIna barAbara bhujAoM vAle iSTa caturbhuja kSetra ke saMbaMdha meM UparI bhajA ke aMtoM se AdhAra para girAye gaye samAna laMboM meM se kisI eka kA mAna detA hai // 150 // udAharaNArtha prazna kisI 3 barAbara bhujAoM vAle caturbhuja kSetra ke saMbaMdha meM kSetraphala kA zuddha mAna 96 hai| diyA gayA guNaka 8 hai| AdhAra, bhujAoM, UparI bhujA aura laMba ke mApoM ko batalAo // 151 // (150) niyama meM kathana hai ki diye gaye kSetraphala ko mana se cunI huI datta saMkhyA dvArA bhAjita karane para iSTa AkRti saMbaMdhI laMca prApta hotA hai| kSetraphala kA mAna. AdhAra aura UparI bhujA ke yoga kI arddharAzi tathA laMba ke guNanaphala ke barAbara hotA hai| isaliye dI gaI cunI huI saMkhyA UparI bhujA aura AdhAra ke yoga kI arddharAzi kA nirUpaNa karatI hai| yadi aba sa da tIna barAbara bhujAoM vAlA caturbhuja hai, aura sa i, sa se ada para girAyA gayA laMba hai, to a i, a da aura ba sa ke yoga kI AdhI hotI hai, aura dI gaI cunI huI saMkhyA ke barAbara hotI hai| yaha saralatA pUrvaka dikhAyA jA sakatA hai ki adaxai=(sa i)+ (sa i2 aha) . bhaTa (sa i) + (ma i)2 _ (sa i)2 ...ada% a i . (a ) + 2a i ai (saha-aha) +ai - - + . (a )9 +ai yahA~ sai ai-caturbhuja kA diyA gayA kSetraphala hai| yaha aMtima sUtra, prazna meM tIna barAbara bhujAoM vAle caturbhuja kI koI bhI eka barAbara bhujA kA mAna nikAlane ke liye diyA gayA hai| ga0 sA0 saM0-29

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gaNitasArasaMgrahaH [ 7. 152 sUkSmaphalasaMkhyAM jJAtvA caturbhiriSTacchedaizca viSamacaturazrakSetra syamukhabhUbhujApramANasaMkhyAna yanasUtram - dhanakRtiriSTacchedaizcaturbhirAptaiva labdhAnAm / yutidalacatuSTayaM tairUnA viSamAkhyacaturazrabhujasaMkhyA / / 152 / / 226 ] atroddezakaH navatirhi sUkSmagaNitaM chedaH paJcaiva navaguNaH / dazadhRtitriMzatiSaTkRtihataH kramAdviSamacaturazre // bhUmibhujA saMkhyA vigaNayya mamAzu saMkathaya / / 1533 // 4 diye gaye bhAjakoM kI sahAyatA se, jaba ki iSTa caturbhuja kSetra kA kSetraphala jJAta hai, viSama caturbhuja kSetra ke saMbaMdha meM UparI bhujA, AdhAra aura anya bhujAoM ke saMkhyAtmaka mAna nikAlane ke liye niyama diyA gayA kSetraphala kA varga alaga alaga cAra diye gaye bhAjakoM dvArA bhAjita kiyA jAtA hai, aura cAra pariNAmI bhajanaphaloM ko alaga-alaga likhA jAtA hai / ina bhajanaphaloM ke yoga kI arddhazako cAra sthAnoM meM likhA jAtA hai, aura krama meM Upara likhe hue bhajanaphaloM dvArA kramazaH hAsita kiyA jAtA hai| isa prakAra prApta zeSa, viSama caturbhuja kI asamAna nAmaka bhujAoM ke saMkhyAtmaka mAna ko utpanna karate haiM // 152 // udAharaNArtha prazna viSama caturbhuja ke saMbaMdha meM kSetraphala kA zuddha mApa 90 hai / 5 ko kramazaH 9, 10, 18, 20 aura 36 dvArA guNita karane para cAra diye gaye bhAjakoM kI utpatti hotI hai / gaNanA ke pazcAt UparI bhujA, AdhAra aura anya bhujAoM ke saMkhyAtmaka mAnoM ko zIghra batalAo // 153-1533 // (152) asamAna bhujAoM vAle caturbhuja kSetra kA kSetraphala pahile hI batAyA jA cukA hai : Vya (ya - a) (ya - ba ) ( ya sa ) (ya-da) = caturbhuja kA kSetraphala, jahA~ ya = parimiti kI arddharAzi hai, aura a, ba, sa aura da bhujAoM ke mApa haiM ( isI adhyAya kI 50 vIM gAthA dekhiye ) / isa niyama ke anusAra kSetraphala ke mAna ko vargita kara, aura taba cAra mana se cune hue bhAjakoM dvArA alaga-alaga bhAjita karate haiM / yadi (ya - a) (ya- ba ) ( ya - sa ) ( ya - da ) ko aise cAra upayukta cune hue bhAjakoM dvArA bhAjita kiyA jAya ki ya- a, yaba, ya-sa aura ya-da bhajanaphala prApta hoM, to ina bhajanaphaloM ko jor3akara, aura unake yoga ko AdhA karane para, ya prApta hotA hai / yadi ya ko krama se ya-a, yaba, yasa aura ya - da hAsita kiyA jAya, to zeSa kramazaH viSama caturbhuja kI bhujAoM ke mAnoM kI prarUpaNA karate haiM /

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-7. 1563 ] kSetragaNitavyavahAraH [ 227 sUkSmagaNitaphalaM jJAtvA tatsUkSmagaNitaphalavatsamatribAhukSetrasya bAhusaMkhyAnayanasUtramgaNitaM tu caturguNitaM vargIkRtvA bhajet tribhilabdham / tribhujasya kSetrasya ca samasya bAhoH kRtervargam // 1543 // atroddezakaH kasyApi samatryakSetrasya ca gaNitamuddiSTam / rUpANi trINyeva behi pragaNayya me bAhum // 1553 // sUkSmagaNitaphalasaMkhyAM jJAtvA tatsUkSmagaNitaphalavadvisamatribAhukSetrasya bhujabhUmyavalambakasaMkhyAnayanasUtram - icchAptadhanecchAkRtiyutimUlaM doH kSitirdviguNitecchA / icchAptadhanaM lambaH kSetre dvisamatribAhujanye syAt // 1563 / / 1. vargIkRtvA ke sthAna meM vargIkRtya honA cAhie; para isa rUpa meM vaha chaMda ke upayukta nahIM hotA hai| sUkSma rUpa se jJAta kSetraphala vAle samabhuja tribhuja kI bhujAoM ke saMkhyAtmaka mAnoM ko nikAlane ke liye niyama diye gaye kSetraphala kI caugunI rAzi vargita kI jAtI hai| pariNAmI rAzi 3 dvArA bhAjita kI jAtI hai| isa prakAra prApta bhajanaphala samatribhuja kI kisI eka bhujA ke mAna ke varga kA varga hotA hai // 1541 // ___udAharaNArtha prazna kisI samatribAhu tribhuja ke saMbaMdha meM diyA gayA kSetraphala kevala 3 hai| usakI bhujA kA mApa gaNanA kara batalAo // 155 // kisI diye gaye kSetraphala ke zuddha saMkhyAtmaka mApa ko jJAta kara, usI zuddha kSetraphala kI tribhujAkAra AkRti kI bhujAoM, AdhAra aura laMba ko nikAlane ke liye niyama isa prakAra se racita hone vAle samadvibAhu tribhuja ke saMbaMdha meM, diye gaye kSetraphala ko mana se cunI huI rAzi dvArA bhAjita karane se prApta bhajanaphala ke varga meM, mana se cunI huI rAzi ke varga ko jor3ate haiN| yoga kA jaba vargamUla nikAlA jAtA hai, taba bhujA kA mAna utpanna hotA hai; cunI huI rAzi kI duganI rAzi AdhAra kA mApa detI hai, aura mana se cunI huI rAzi dvArA bhAjita kSetraphala laMba kA mApa utpanna karatA hai // 1563 // (1543) samatribhuja ke kSetraphala ke liye sUtra yaha hai : kSetraphala = aV, jahA~ bhujA kA mApa a hai / isake dvArA yahA~ diyA gayA niyama prApta kiyA jA sakatA hai| (1563) isa prakAra ke diye gaye praznoM meM samadvibAhu tribhuja ke kSetraphala kI arhA (mAna) aura mana se cune hue AdhAra kI AdhI rAzi dI gaI rahatI haiN| ina jJAta rAziyoM se laMca aura bhujA ke mApa saralatApUrvaka prApta kiye jA sakate haiN|

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228] gaNitasArasaMgrahaH [7.1571atroddezakaH kasyApi kSetrasya dvisamatribhujasya sUkSmagaNitaminAH / trINIcchA kathaya sakhe bhujabhUmyavalambakAnAzu // 1573 / / sUkSmagaNitaphalasaMkhyA jJAtvA tatsUkSmagaNitaphalavadviSamatribhujAnayanasya sUtramaSTaguNiteSTakRtiyutadhanamiSTapadahRdiSTArdham / bhUH syAdbhUnaM dvipadAhRteSTavarga bhuje ca saMkramaNam // 1583 / / udAharaNArtha prazna kisI samadvibAhu tribhuja ke saMbaMdha meM kSetraphala kA zuddha mApa 12 hai| mana se cunI huI rAzi 3 hai| he mitra, bhujAoM, AdhAra aura laMba ke mAnoM ko zIghra batalAo // 1573 // viSama bhujAoM vAle tathA datta zuddha mApa ke kSetraphala vAle tribhuja kSetra ko prApta karane ke liye niyama diyA gayA kSetraphala 8 dvArA guNita kiyA jAtA hai, aura pariNAmI guNanaphala meM mana se cunI huI rAzi kI vargita rAzi jor3I jAtI hai| isa prakAra prApta pariNAmI yoga ke vargamUla ko prApta karate haiM / isa vargamUla kA ghana, mana se cunI huI saMkhyA tathA Upara prApta vargamUla dvArA bhAjita kiyA jAtA hai / mana se cunI huI rAzi kI AdhI rAzi iSTa tribhuja ke AdhAra kA mApa hotI hai / pichalI kriyA meM prApta bhajanaphala isa AdhAra ke mApa dvArA hAsita kiyA jAtA hai| pariNAmI rAzi ko, uparyukta vargamUla, tathA 2 dvArA tathA bhAjita (mana se cunI huI rAzi ke) varga ke saMbaMdha meM, saMkramaNa kriyA karane ke upayoga meM lAte haiN| isa prakAra bhujAoM ke mAna prApta hote haiM // 158 // (1581) yadi tribhujakA kSetraphala kSa ho, aura da mana se cunI huI saMkhyA ho, to isa niyama ke anusAra iSTa mAnoM ko nimna prakAra prApta karate haiMda = AdhAra; aura (28kSa + da2) da da/kSa + dara 3 = 2 (bhujaaeN)| jaba kisI tribhuja kA kSetraphala aura AdhAra diye gaye rahate haiM, taba zIrSa kA bindupatha AdhAra ke samAnAntara rekhA hotI hai, aura mujAoM ke mAnoM ke aneka kulaka (sets ) ho sakate haiN| bhujAoM ke kisI viziSTa kulaka ke mAnoM ko prApta karane ke lie, yahA~ spaSTataH kalpanA kara lI gaI hai ki do bhujAoM kA yoga AdhAra aura dugunI U~cAI ke yoga ke tulya hotA hai, arthAt da+2 -... hotA hai / isa kalpanA se isa adhyAya kI 50 vIM gAthA meM diye gaye sAdhAraNa sUtra, da:4 { kisI tribhuja kA kSetraphala =V ya(ya-a) (ya-ba) (ya - sa)}, se bhujAoM ke mApa ke liye Upara diyA gayA sUtra prApta kiyA jA sakatA hai|

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-7. 1633 ] kSetragaNitavyavahAraH [229 atroddezakaH kasyApi viSamabAhosyazrakSetrasya sUkSmagaNitamidam / dve rUpe nirdiSTe trINISTaM bhamibAhavaH ke syuH // 1593 // punarapi sUkSmagaNitaphalasaMkhyA jJAtvA tatphalavadviSamatribhujAnayanasUtramsvASTahatAtseSTakRteH kRtimUlaM ceSTamitaraditarahRtam / jyeSThaM svAlpA?naM spalpAdhaM tatpadena ceSTena // 1603 // kramazo hatvA ca tayoH saMkramaNe bhUbhujau bhvtH| iSTAmitaradoH syAdviSamatrakoNake kSetre / / 1613 // ___ atroddezakaH dve rUpe sUkSmaphalaM viSamatribhujasya rUpANi / trINISTaM bhUdoSau kathaya sakhe gaNitatattvajJa // 1623 / / sUkSmagaNitaphalaM jJAtvA tatsUkSmagaNitaphalavatsamavRttakSetrAnayanasUtram - gaNitaM caturabhyastaM dazapadabhakta pade bhveddyaasH|| sUkSmaM samavRttasya kSetrasya ca pUrvavatphalaM paridhiH // 1633 / / udAharaNArtha prazna kisI asamAna bhujAoM vAlI tribhujAkAra AkRti ke saMbaMdha meM yaha batalAyA gayA hai ki zuddha kSetraphala kA mApa 2 hai, aura mana se cunI huI rAzi 3 hai| AdhAra kA mAna tathA bhujAmoM kA mAna kyA hai ? // 159 // punaH, viSama bhujAoM vAle tathA datta zuddha mApa kSetraphala vAle tribhuja kSetra ko prApta karane ke liye dUsarA niyama diye gaye kSetraphala ke mApa meM 8 kA guNA kara, aura taba usameM mana se cunI huI rAzi ke varga ko jor3akara, prApta yogaphala kA vargamUla prApta kiyA jAtA hai| yaha aura mana se cunI huI rAzi eka dUsare ke dvArA bhAjita kI jAtI haiN| ina bhajanaphaloM meM se bar3A, choTe bhajanaphala kI arddharAzi dvArA hAsita kiyA jAtA hai| isa prakAra prApta zeSa rAzi aura yaha choTe bhajanaphala kI arddharAzi kramazaH Upara likhita vargamUla aura mana se cunI huI saMkhyA dvArA guNita kI jAtI haiN| isa prakAra prApta guNanaphaloM ke saMbaMdha meM saMkramaNa kriyA karane para AdhAra aura bhujAoM meM se kisI eka kA mAna prApta hotA hai| mana se cunI huI rAzi kI AdhI rAzi viSama tribhuja kI dUsarI bhujA kI ahIM hotI hai // 160-1611 // udAharaNArtha prazna viSama tribhuja ke saMbaMdha meM kSetraphala kA zuddha mApa 3 hai / he gaNitajJa sakhe, AdhAra tathA bhujAoM ke mApa batalAo // 162 // datta sUkSma kSetraphala vAle, kisI samavRtta kSetra ko prApta karane ke liye niyama sUkSma kSetraphala kA mApa 4 dvArA guNita kara, 10 ke vargamUla dvArA bhAjita kiyA jAtA hai| isa prakAra pariNAmI bhajanaphala ke vargamUla ko prApta karane se vyAsa kA mAna prApta hotA hai| samavRtta kSetra ke saMbaMdha meM, Upara samajhAye anusAra, kSetraphala aura paridhi kA mApa prApta kiyA jAtA hai // 1633 // (1633) isa gAthA meM diyA gayA niyama sUtra, kSetraphala = E4/10 , jahA~ da vRtta kA vyAsa hai, se prApta kiyA gayA hai|

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230] gaNitasArasaMgraha [7. 1643atroddezakaH samavRttakSetrasya ca sUkSmaphalaM paJca nirdiSTam / viSkambhaH ko vAsya pragaNayya mamAzu taM kathaya // 1643 // vyAvahArikagaNitaphalaM ca sUkSmaphalaM ca jJAtvA tavyAvahArikaphalavattatsUkSmagaNitaphalavadvi samacaturazrakSetrAnayanasya trisamacaturazrakSetrAnayanasya ca sUtramdhanavargAntarapadayutiviyutISTaM bhUmukhe bhuje sthUlam / dvisame sapadasthUlAtpadayutiviyutISTapadahRtaM trisame // 1653 // udAharaNArtha prazna samavRtta kSetra ke saMbaMdha meM kSetraphala kA zuddha mApa 5 hai| vRtta kA vyAsa gaNanA kara zIghra btlaao||1641|| kisI kSetraphala ke vyAvahArika tathA sUkSma mApa jJAta hone para. do samAna bhujAoM vAle tathA tIna samAna bhujAoM vAle una kSetraphaloM ke mApa ke caturbhuja kSetroM ko prApta karane ke liye niyama do samAna bhujAoMvAle kSetraphala ke saMbaMdha meM, kSetraphala ke sannikaTa aura sUkSma mApoM ke vargoM ke antara ke vargamUla ko prApta karate haiM / isa vargamUla ko mana se cunI huI rAzi meM jor3ate haiM, tathA usI mana se cunI huI rAzi meM se vahI vargamUla ghaTAte haiM / AdhAra aura UparI bhujA ko prApta karane ke liye isa prakAra prApta rAziyoM ko mana se cunI huI rAzi ke vargamUla se bhAjita karanA par3atA hai| isI prakAra, sannikaTa kSetraphala meM mana se cunI huI rAzi kA bhAga dene para samAna bhujAoM kA mAna prApta hotA hai // 1653 // (1651) yadi 'rA' kisI do barAbara bhujAoM vAle caturbhuja kSetra ke sannikaTa kSetraphala ko, aura 'ra' sUkSma mAna ko prarUpita karate hoM, aura pa mana se cunI huI saMkhyA ho, to _pa- rA2-2 Vpa V AdhAra-V rA2-2.. aura pratyeka barAbara bhujAoM kA mAna = VP yadi do barAbara bhujAoM vAle caturbhuja kSetra kI bhujAoM ke mApa kramazaH a, ba, sa, da hoM, to rA = a ( va+da); pa= (da) . . ba + da aura ra= 1 a2-(ba-da)2 2 AdhAra aura UparI bhujA ke liye Upara diye gaye sUtra rA, ra / aura pa ke ina mAnoM kA pratisthApana karane para saralatApUrvaka / satyApita kiye jA sakate haiN| isI prakAra tIna barAbara . bhujAoM vAle caturbhuja ke saMbaMdha meM bhI yaha niyama ThIka siddha hotA hai|

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[231 -7. 1683] kSetragaNitavyavahAraH atroddezakaH gaNitaM sUkSmaM paJca trayodaza vyAvahArikaM gaNitam / dvisamacaturazrabhUmukhadoSaH ke SoDazecchA ca // 1663 / / trisamacaturazrasyodAharaNam / gaNitaM sUkSma pazca trayodaza vyAvahArikaM gaNitam / trisamacaturazravAhUna saMcintya sakhe mamAcakSva // 1673 // vyAvahArikasthUlaphalaM sUkSmaphalaM ca jJAtvA tavyAvahArikasthUlaphalavat sUkSmagaNitaphalavatsamatribhujAnayanasya ca samavRttakSetravyAsAnayanasya ca sUtramdhanavargAntaramUlaM yattanmUlAdvisaMguNitam / bAhustrisamatribhuje samasya vRttasya viSkambhaH // 1683 // oM vAle caturbhuja kSetrako sannikaTa kSetraphala kA mApa, mana se cunI huI rAzi dvArA bhAjita hokara, bhujAoM ke mAna ko utpanna karatA hai| tIna barAbara bhujAoM vAle caturbhaja kSetra kI dazA meM, Upara batalAye hae do kSetraphaloM ke vargoM ke aMtara ke vargamUla ko kSetraphala ke sannikaTa mApa meM jor3ate haiN| isa pariNAmI yoga ko vikalpita rAzi mAnakara usameM Upara batalAye hue vargamUla ko jor3ate haiM / punaH, usI vikalpita rAzi meM se ukta vargamUla ko ghaTAte haiM / isa prakAra prApta rAziyoM meM vargamUla kA bhAga alaga-alaga dekara, AdhAra aura UparI bhujA prApta karate haiN| yahA~ bhI kSetraphala ke vyAvahArika mApa ko isa vikalpita rAzi ke vargamUla dvArA bhAjita karane para anya bhujAoM ke mApa prApta hote haiN| udAharaNArtha prazna sUkSma kSetraphala kA mApa 5 hai, kSetraphala kA sannikaTa mApa 13 hai, aura mana se cunI huI rAzi 16 hai| do barAbara bhujAoM vAle caturbhuja kSetra ke saMbaMdha meM AdhAra, UparI bhujA aura anya bhujA ke mAna kyA-kyA haiM ? // 1663 // tIna barAbara bhujAoM vAle caturbhuja kSetra saMbaMdhI eka udAharaNa kSetraphala kA sUkSma rUpa se zuddha mApa 5 hai, aura kSetraphala kA vyAvahArika mApa 13 hai / he mitra, socakara mujhe batalAo ki tIna barAbara bhujAoM vAle caturbhuja kSetra kI bhujAoM ke mApa kyA-kyA haiM ? // 1673 // ____ samatribAhu tribhuja aura samavRtta ke vyAsa ko prApta karane ke liye niyama, jaba ki unake vyAvahArika aura sUkSma kSetraphala ke mApa jJAta hoM kSetraphala ke sannikaTa aura sUkSma rUpa se ThIka mApoM ke vargoM ke aMtara ke vargamUla ke vargamUla ko 2 dvArA guNita kiyA jAtA hai| pariNAma, iSTa samatribhuja kI bhujA kA mApa hotA hai| vaha, iSTa vRtta ke vyAsa kA mApa bhI hotA hai // 1683 // (1683) kisI samabAhutribhuja ke vyAvahArika aura sUkSma kSetraphala ke mAnoM ke liye isa adhyAya kI gAthA 7 aura 50 ke niyamoM ko dekhiye /

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232] gaNitasArasaMgrahaH [7. 1693 atroddezakaH sthUlaM dhanamaSTAdaza sUkSma trighano navAhataH karaNiH / vigaNayya sakhe kathaya trisamatribhujapramANaM me // 1693 // paJcakRtervargo dazaguNitaH karaNirbhavedidaM sUkSmam / / sthUlamapi paJcasaptatiretatko vRttaviSkambhaH // 1703 // vyAvahArikasthUlaphalaM ca sUkSmagaNitaphalaM ca jJAtvA tavyAvahArikaphalavattatsUkSmaphalavadvisamatribhujakSetrasya bhabhujApramANasaMkhyayorAnayanasya sUtram - phalavargAntaramUlaM dvirguNaM bhUrvyAvahArikaM baahuH|| bhUmyardhamUlabhakte dvisamatribhujasya karaNamidam // 1713 / / atroddezaka: sUkSmadhanaM SaSTiriha sthUladhanaM paJcaSaSTiruddiSTam / gaNayitvA brUhi sakhe dvisamatribhujasya bhujasaMkhyAm // 1723 // iSTasaMkhyAvadvisamacaturazrakSetraM jJAtvA tadvisamacaturazrakSetrasya sUkSmagaNitaphalasamAnasUkSmaphalavadanyadvisamacaturazrakSetrasya bhUbhujamukhasaMkhyAnayanasUtram - ___ udAharaNArtha prazna vyAvahArika kSetraphala 18 hai| kSetraphala kA sUkSma rUpa se zuddha mApa ( 3 ) ko 9 se guNita karane se prApta rAzi kA vargamUla hai| he sakhe, mujhe gaNanA ke pazcAt batalAo ki iSTa samatribhuja kI bhujA kA mApa kyA hai? // 169 // kSetraphala kA sUkSma mApa 6250 kA vargamUla hai / kSetraphala kA sannikaTa mApa 75 hai / aise kSetraphaloM vAle samavRtta ke vyAsa kA mApa batalAo // 1701 // ___ jaba kisI kSetraphala ke vyAvahArika aura sUkSma mApa jJAta hoM, taba aise kSetraphala ke mApoMvAle samadvibAha tribhuja ke AdhAra aura bhujA ke saMkhyAtmaka mAnoM ko nikAlane ke liye niyama kSetraphala ke vyAvahArika aura sUkSma mApoM ke vargoM ke aMtara ke vargamUla kI dugunI rAzi ko kisI samadvibAhu tribhuja kA AdhAra mAna lete haiN| datta vyAvahArika kSetraphala kA mApa barAbara bhujAoM meM se kisI eka kA mApa mAna liyA jAtA hai| AdhAra tathA bhujA ke ina mAnoM ko AdhAra ke prApta mAna kI arddharAzi ke vargamUla dvArA bhAjita karate haiN| taba iSTa samadvibAha tribhuja kA AdhAra aura bhujA ke iSTa mApa prApta hote haiN| yaha niyama samadvibAhu tribhuja ke saMbaMdha meM hai // 1713 // udAharaNArtha prazna yahA~ kSetraphala kA sUkSma rUpa se ThIka mApa 60 hai, aura vyAvahArika mApa 65 hai / he mitra, gaNanA ke pazcAt batalAo ki iSTa samadvibAhu tribhuja kI bhujAoM ke saMkhyAtmaka mApa kyA-kyA haiM // 1723 // ____ jaba cunI huI saMkhyA aura do barAbara bhujAoM vAlA caturbhuja kSetra diyA gayA ho, taba kisI aise dUsare do barAbara bhujAoM vAle caturbhuja kSetra kA AdhAra, UparI bhujA aura anya bhujAoM ko nikAlane ke liye niyama, jisakA sUkSma kSetraphala diye gaye do barAbara bhujAoM vAle caturbhuja ke sUkSma kSetraphala ke tulya ho //

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-7. 1743] kSetragaNitavyavahAraH [233 lambakRtAviSTenAsamasaMkramaNIkRte bhujA jyeSThA / hasvayutiviyuti mukhabhUyutidalitaM talamukhe dvisamacaturazre / / 1733 / / ___ atroddezakaH bhUrindrA dovizve vakraM gatayo'valambako ravayaH / iSTaM dik sUkSmaM tatphalavadvisamacaturazramanyat kim / / 1743 // yadi diye gaye do barAbara bhujAoM vAle caturbhuja kSetra ke laMba kA varga datta vikalpita saMkhyA ke sAtha viSama saMkramaNa kriyA karane ke upayoga meM lAyA jAtA hai, to prApta do phaloM meM se bar3A mAna do barAbara bhujAoMvAle iSTa caturbhuja kSetra kI barAbara bhujAoM meM se kisI eka kA mAna hotA hai| do barAbara bhujAoM vAle diye gaye caturbhuja kI UparI bhujA aura AdhAra ke mAnoM ke yoga kI arddharAzi ko, kramazaH, uparyukta viSama saMkramaNa meM prApta do phaloM meM se choTe phala dvArA bar3hAkara aura hAsita karane para do barAbara bhujAoM vAle iSTa caturbhuja kSetra ke AdhAra aura UparI bhujA ke mApa utpanna hote haiM / / 1733 // udAharaNArtha prazna diye gaye caturbhuja kSetra kA AdhAra 14 hai, do barAbara bhujAoM meM se pratyeka kA mApa 13 hai, UparI bhujA 4 hai, lamba 12 hai, aura datta vikalpita saMkhyA 10 hai| do barAbara bhujAoM vAlA aisA kauna sA caturbhuja hai, jisake sUkSma kSetraphala kA mApa diye gaye caturbhuja ke kSetraphala ke barAbara hai ? // 1743 // (1733) isa niyama meM aise prazna para vicAra kiyA gayA hai, jisameM aise do barAbara bhujAoM vAle caturbhuja kSetra kI racanA karanA hai, jisakA kSetraphala kisI dUsare do barAbara bhujAoM vAle caturbhuja ke tulya ho, aura jisakI UparI bhujA se AdhAra taka kI lamba dUrI bhI usI ke samAna ho| mAna lo diye gaye caturbhuja kI barAbara bhujAe~ a aura sa haiM, aura UparI bhujA tathA AdhAra kramazaH ca aura da haiN| yaha bhI mAna lo ki laMba dUrI pa hai / yadi iSTa caturbhuja kI saMvAdI bhujAe~ a, ba, sa,, da, hoM, to kSetraphala aura lamba dUrI, donoM caturbhujoM ke saMbaMdha meM barAbara hone se hameM yaha prApta hotA hai da + ba, = da+ba .........(1); aura a, - (6.2.11) = 52.......( 2 ); arthAt (a + 1) (a, -8.335) = 12 / mAnalo a, - 85 81 = nA; taba a, + 85 835 mA, aura (a, 4 65 858) + (a, - da. 21) mA+nA ! ... nA + nA = a,, ...........(3) ga. sA. saM0-30

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234] gaNitasArasaMgrahaH [-7. 1753 dvisamacaturazrakSetravyAvahArikasthUlaphalasaMkhyAM jJAtvA tavyAvahArikasthUlaphale iSTasaMkhyAvibhAge kRte sati tadvisamacaturazrakSetramadhye tattadbhAgasya bhUmisaMkhyAnayane'pi tattatsthAnAvalambakasaMkhyAnayane'pi sUtramkhaNDayutibhaktatalamukhakRtyantaraguNitakhaNDamukhavargayutam / mUlamadhastalamukhayutadalahRtalabdhaM ca lambAkaH kramazaH // 1753 // - jaba koI datta vyAvahArika mApa vAlA kSetraphala kisI dI gaI saMkhyA ke bhAgoM meM vibhAjita kiyA jAya, taba do barAbara bhujAoM vAle caturbhuja kSetra ke una vibhinna bhAgoM se AdhAroM ke saMkhyAtmaka mAnoM tathA vibhinna vibhAjana binduoM se mApI gaI bhujAoM ke saMkhyAtmaka mApa ko nikAlane ke liye niyama, jaba ki do bhujAoM vAle caturbhuja kSetra ke vyAvahArika kSetraphala kA saMkhyAtmaka mApa diyA gayA ho do barAbara bhujAoM vAle diye gaye caturbhuja kSetra ke AdhAra aura UparI bhujA ke saMkhyAtmaka mAnoM ke vargoM ke aMtara ko iSTa anupAtI bhAgoM ke kula mAna dvArA bhAjita kiyA jAtA hai| isa prakAra prApta bhajanaphala ke dvArA vibhinna bhAgoM ke niSpattiyoM ke mAna kramazaH guNita kiye jAte haiN| prApta guNanaphaloM meM se pratyeka meM diye gaye caturbhuja kI UparI bhujA ke mApa kA varga jor3A jAtA hai| isa prakAra prApta yoga kA vargamUla, pratyeka bhAga ke AdhAra ke mAna ko utpanna karatA hai| pratyeka bhAga kA kSetraphala, AdhAra aura UparI bhujA ke yoga kI arddharAzi dvArA bhAjita hokara, iSTa krama meM laMba kA mApa utpanna karatA hai, jo sannikaTa mApa ke liye bhujA kI taraha vartA jAtA hai // 1053 // 2 (a+da - ba1) - (a, - 618 ) / da+banA - da.+ba + 2 = da, athavA ba,............(4) yahA~ 'nA' iSTa athavA datta vikalpita saMkhyA hai| tIsare aura cauthe sUtra ve haiM, jo prazna kA sAdhana karane ke niyama meM diye gaye haiN| (1753 ) yadi ca cha ja jha do barAbara bhujAoM vAlA caturbhuja ho, aura ipha, gaha aura kala caturbhuja ko isa taraha vibhAjita karate hoM ki vibhAjita bhAga kSetraphala ke saMbaMdha meM kramazaH ma, na, pa, kha ke anupAta meM hoM, to isa niyama ke anusAra, jaba bhujA ca cha =a, cha ja =da, ja jha = sa aura jhacaba hai, taba ipha =/ da-bare , ma+na+pa+kha - da-ba-_xma+ba2 ... ka ; - gaha EN ____x(ma+na)+bare ma+na+pa+kha / - - a kalaEN a -x(ma+na+pa)+bare; V ma+na+pa+kha ityAdi / isI prakAra, -

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-7. 1763 ] kSetragaNitavyavahAraH [ 235 atroddezakaH vadanaM saptoktamadhaH kSitistrayoviMzatiH punastriMzat / bAhU dvAbhyAM bhaktaM caikaikaM labdhamatra kA bhUmiH // 1763 // udAharaNArtha prazna UparI-bhujA kA mApa 7 hai, nIce AdhAra kA mApa 23 hai, aura zeSa bhujAoM meM se pratyeka kA mApa 30 hai| aise kSetra meM aMtarAviSTa kSetraphala aise do bhAgoM meM vibhAjita kiyA jAtA hai ki pratyeka ko eka ( hissA ) prApta hotA hai| yahA~ nikAle jAne vAle AdhAra kA mAna kyA hai ? / / 1763 / / da + 7 x cara (4x7) ma+na+pa+kha ; ca ma+na+pa+kha: ipha+cajha iga (a46+) ma+na+pa+kha , gaha + ipha + __(46+4)x ma+na+pa+kha. gaka ma+na+pa+kha kala+gaha ityaadi| yaha saralatApUrvaka dikhAyA jA sakatA hai ki cacha = chaja - cajha "caha ipha-cajha ' . cacha (chaja+cajha) (chaja)2-(ca jha)2 - cai ( ipha+ cajha) (i pha)2 - (ca jha )2 cacha (chaja+cajha) ma+na+pa+kha ' cai (ipha+ cajha) ma (chaja)2-(cajha) - ma+na++kha ; .. (ipha )2 - ( cajha )2 ma .:. (hapha)2 = ma (cha ja- ca jhare),. cajha)ma+na+pa+kha "ma+na+pa+kha xma+ba'; aura i pha /da2 - bare -xma+ba2 / isI prakAra anya sUtra satyApita kiye jA ma+na+pa+kha na sakate haiN| yadyapi isa pustaka meM graMthakAra ne kevala yaha kahA hai ki bhajanaphala ko bhAgoM ke mAnoM se gaNita karanA par3atA hai, tathApi vAstava meM bhajanaphala ko pratyeka dazA meM bhAgoM ke mAnoM se UparI bhujA taka kI prarUpaNa karane vAlI saMkhyA ke dvArA guNita karanA par3atA hai| udAharaNArtha, pichale pRSTha kI AkRti meM +(ca T +kha

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236]] gaNitasArasaMgrahaH bhUmirdviSaSTizatamatha cASTAdaza vadanamatra saMdRSTam / lambazcatuzzatIdaM kSetraM bhaktaM narezcaturbhizca // 1773 // ekadvikatrikacatuHkhaNDAnyekaikapuruSalabdhAni / prakSepatayA gaNitaM talamapyavalambakaM hi // 1783 / / bhUmirazItirvadanaM catvAriMzacaturguNA ssssttiH| avalambakapramANaM trINyaSTau paJca khaNDAni // 1793 // - stambhadvayapramANasaMkhyAM jJAtvA tatstambhadvayAgre sUtradvayaM baddhvA tatsUtradvayaM karNAkAreNa itaretarastambhamUlaM vA tatstambhamUlamatikramya vA saMspRzya tatkarNAkArasUtradvayasparzanasthAnAdArabhya adhaHsthitabhUmiparyantaM tanmadhye eka sUtraM prasArya tatsUtrapramANasaMkhyaiva antarAvalambakasaMjJA bhavati / antarAvalambakasparzanasthAnAdArabhya tasyAM bhUmyAmubhayapArzvayoH karNAkArasUtradvayasparzanaparyantamAbAdhAsaMjJA syAt / tadantarAvalambakasaMkhyAnayanasya AbAdhAsaMkhyAnayanasya ca sUtramstambhau rajjvantarabhUhRtau svayogAhRtau ca bhuugunnitau| AbAdhe te vAmaprakSepaguNo'ntaravalambaH // 1803 // do barAbara bhujAoM vAle caturbhuja ke AdhAra kA mApa 162 hai, aura UparI bhujA kA mApa 18 hai / do bhujAoM meM se pratyeka kA mAna 400 haiM / isa prakAra, isa AkRti se ghirA huA kSetraphala, 4 manuSyoM meM vibhAjita kiyA jAtA hai| manuSyoM ko prApta bhAga kramazaH 1.2.3, aura 4 ke anupAta meM haiN| isa anupAtI vibhAjana ke anusAra pratyeka dazA meM kSetraphala, AdhAra aura do barAbara bhujAoM meM se eka ke mAnoM ko batalAo / / 1773-783 // diye gaye caturbhuja kSetra ke AdhAra kA mApa 80 hai, UparI bhujA 40 hai, tathA do barAbara bhujAoM meM se pratyeka 4460 hai / hisse kramazaH 3,8 aura 5 ke anupAta meM haiN| iSTa bhAgoM ke kSetraphala, AdhAroM aura bhujAoM ke mAnoM ko nikAlo / / 179 // jJAta U~cAI vAle do staMbhoM meM se pratyeka ke UparI sire meM do dhAge ( sUtra ) baMdhe hue haiN| ina do bhAgoM meM se pratyeka isa taraha phailA huA hai ki vaha sammukha staMbha ke mUla bhAga ko karNa ke rUpa meM sparza karatA hai, athavA dUsare staMbha ke pAra jAkara bhUmi ko sparza karatA hai / usa bindu se, jahA~ do karNAkAra dhAge milate haiM, eka aura dUsarA dhAgA isa taraha laTakAyA jAtA hai, ki vaha laMba rUpa hokara bhUmi ko sparza karatA hai / isa aMtima dhAge ke mApa kA nAma aMtarAvalambaka yA bhItarI laMba hotA hai / jahA~ para yaha laMbarUpa dhAgA bhUmi ko sparza karatA hai, usa bindu se kisI bhI ora prasthAna karane vAlI rekhA una binduoM taka jAkara (jahA~ karNa dhAge bhUmi ko sparza karate haiM ) AbAdhA athavA AdhAra kA khaMDa kahalAtI hai| aise lamba tathA AvAdhoM ke mAnoM ko prApta karane ke niyama pratyeka stambha ke mApa ko stambha ke mUla se lekara karNa dhAge ke bhUmi sparza bindu taka ke bIca kI lambAI vAle AdhAra ko mApa dvArA bhAjita kiyA jAtA hai| isa prakAra prApta pratyeka bhajanaphala, bhajanaphaloM ke yoga dvArA bhAjita kiyA jAtA hai| pariNAmI bhajanaphaloM ko saMpUrNa AdhAra ke mApa dvArA guNita karane para krama se AbAdhAoM ke mApa prApta hote haiM / ye AbAdhAoM ke mApa, kramazaH viloma krama meM, Upara diye gaye prathama bAra meM prApta bhajanaphaloM dvArA guNita hone para, pratyeka dazA meM aMtarAvalambaka (bhItarI lamba) ko utpanna karate haiM // 1801 // gaha kA mAna nikAlane ke liye - ma+na+pa+kha . kevala 'na' se hI nahIM varan ma+na se bhI guNita karanA par3atA hai|

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-7. 1823] kSetragaNitavyavahAraH [237 atroddezakaH SoDazahastocchAyau stambhAvavanizca SoDazoddiSTau / AbAdhAntarasaMkhyAmatrApyavalambakaM brUhi // 1813 // stambhaikasyocchAyaH SaTtriMzadviMzatirdvitIyasya / bhUmiAdaza hastAH kAbAdhA ko'yamavalambaH // 1823 // udAharaNArtha prazna diye gaye staMbha kI U~cAI 6 hasta hai / usa AdhAra kI lambAI jo una do vinduoM ke bIca kI hotI hai, jahA~ dhAge bhUmi ko sparza karate haiM, 16 hasta dekhI gaI hai| isa dazA meM AdhAra ke khaMDoM (AbAdhAoM) aura aMtarAvalambaka ke saMkhyAtmaka mAnoM ko nikAlo // 11 // eka staMbha kI U~cAI 36 hasta hai, dUsare kI 20 hasta hai| AdhAra rekhA kI lambAI 12 hasta hai / AbAdhAoM aura aMtarAvalambaka ke mApa kyA-kyA haiM ? // 1.21 // do staMbha kramazaH 12 aura 15 hasta haiM, una do (1803) AkRti meM yadi a aura ba stambhoM kI U~cAIyoM hoM, sa staMbhoM ke bIca kA aMtara ho, aura ma aura na kramazaH eka stambha ke mUla se lekara, bhUmi ko sparza karane vAle, dUsare stambha ke agra se phaile hue dhAge ke bhUmisparza bindu taka kI lambAIyA~ hoM, to niyamAnusAra, ( a . a (sa+ma) + ba (sa+na)} (sa+ma+na); (sa+ma) (sa+na) , . a (sa+ma)+ba (sa+na) sa+ma+na); jahA~ sa, aura sara sa+ma (sa+ma) (sa+na) sampUrNa AdhAra ke khaNDa haiN| Ara pa= sa.X 1sa+ma' athavA 12 sa+na' jaha , athavA sarax. , jahA~ paantarAvalambaka hai| isa Akati meM sajAtIya tribhujoM para vicAra karane para yaha jJAta hogA ki a .. sa, a (ma+ma) prApta hotA hai; ina niSpattiyoM se hameM sa, a (ma +ma), hama sa ba ( sa+na) a (sa+ma) a (sa + ma) (sa + ma +na) .. sa, + sa2 a (sa+ma)+ba (sa+na)'' a (sa+ma)+ba (sa+na). kyoMki sa + sa2 = sa +ma+na; ___ ba (sa+na) (sa+ma+na) ..aura pasax-- x2 a (sa+ma)+ba (sa+na) ' "sa+na sa + ma

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238] gaNitasArasaMgrahaH [7. 1833 dvAdaza ca paJcadaza ca stambhAntarabhUmirapi ca ctvaarH| dvAdazakastambhAyAdrajjuH patitAnyato mUlAt // 1833 // Akramya caturhastAtparasya mUlaM tathaikahastAcca / patitApAtkAbAdhA ko'sminnavalambako bhavati / / 1843 // bAhUpratibAhU dvau trayodazAvaniriyaM caturdaza ca / vadane'pi caturhastAH kAbAdhA ko'ntarAvalambazca / / 1853 / kSetramidaM mukhabhUmyorekaikonaM parasparAmAcca / rajjuH patitA mUlAttvaM brahmavalambakAbAdhe / / 1863 // bAhustrayodazaikaH paJcadaza pratibhujA mukhaM sapta / bhUmiriyamekaviMzatirasminnavalambakAbAdhe / / 1873 / / staMbhoM ke bIca kA aMtarAla (aMtara) hasta hai| 12 hasta vAle staMbha ke UparI agra se eka dhAgA sUtra AdhAra rekhA para dUsare staMbha ke mUla se 4 hasta Age taka phailAyA jAtA hai| isa dUsare staMbha ( jo 15 hasta U~cA hai ) ke amra se eka dhAgA usI prakAra AdhAra rekhA para pahile staMbha ke mUla se 1 hasta Age taka phailAyA jAtA hai| yahA~ AbAdhAoM aura aMtarAvalambaka ke mApa ko batalAo // 1853 // do barAbara bhujAoM vAle caturbhuja kSetra ke saMbaMdha meM do bhujAoM meM se pratyeka 13 hasta hai| yahA~ AdhAra 14 hasta, aura UparI bhujA 4 hasta hai| aMtarAvalambaka dvArA banAye gaye AdhAra ke khaMDoM ( AbAdhAoM) ke mApa kyA haiM, aura aMtarAvalambaka kA mApa kyA ? hai // 1853 // uparyukta caturbhuja kSetra ke saMbaMdha meM UparI bhujA aura AdhAra pratyeka 1 hasta kama haiN| do laMboM meM se pratyeka ke UparI agra se eka dhAgA dUsare laMba ke mUla taka pahuMcane ke liye phailAyA jAtA hai / aMtarAvalambaka aura utpanna AbAdhAoM ke mApa kyA haiM ? // 1861 // asamAna bhujAoM vAle caturbhuja ke saMbaMdha meM eka bhujA 13 hasta, sammukha bhujA 15 hasta, UparI bhujA 7 hasta aura AdhAra 21 hasta hai / aMtarAvalambaka tathA usase utpanna hue AbAdhAoM ke mAna kyA-kyA hai? // 1871 // eka samabAhu (1853) yahA~ do barAbara bhujAoM vAlA caturbhuja kSetra diyA gayA hai| dUsarI gAthA meM tIna barAbara bhujAoM vAlA tathA aura agalI gAthA meM viSamabAhu caturbhuja diye gaye haiN| ina saba dazAoM meM caturbhuja ke karNa sabase pahile gAthA 54 adhyAya 7 ke niyamAnusAra prApta kiye jAte haiN| taba UparI bhujA ke aMtoM se AdhAra para girAye hue laMboM ke mApoM aura una laMboM dvArA utpanna AdhAra ke khaMDoM (AbAdhAoM) ko (adhyAya 7 kI 49 vI gAthA meM diye gaye niyama kA prayoga kara ) prApta karate haiN| taba boM ke mApoM ko hasta mAnakara, Upara 1801 vIM gAthA ke niyama ko prayukta kara, aMtarAvalambaka tathA usase utpanna AbAdhAoM ko prApta karate haiN| 1873 vI gAthA meM diyA gayA prazna kannar3I TIkA meM kucha bhinna vidhi se kiyA gayA hai| UparI bhujA AdhAra ke samAnAntara mAna lI jAtI hai, aura laMba tathA usase utpanna AbAdhAoM ke mApa aise tribhuja kI racanA karake prApta karate haiM, jisakI bhujAe~ ukta caturbhuja kI bhujAoM ke barAbara hotI haiM, aura bisakA AdhAra caturbhuja ke AdhAra aura UparI bhujA ke antara ke barAbara hotA hai|

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[239 -7. 1893] kSetragaNitavyavahAra samacaturazrakSetra viMzatihastAyataM tasya / koNebhyo'tha catubhyo vinirgatA rajavastatra // 1883 // bhujamadhyaM dviyugabhuje' rajjuH kA syaatsusNviitaa| ko vAvalambakaH syAdAbAdhe ke'ntare tasmin // 1893 // 1. hastalipi meM azuddha pATha bhujacatuSu ca hai| 2. ke'ntare meM saMdhi kA prayoga vyAkaraNa kI dRSTi se a.ddha hai; para 2043 veM zloka ke samAna yahA~ graMthakAra kA prayojana chaMda hetu svara sambandhI milAna hai / caturbhuja kI pratyeka bhujA 20 hasta hai| usa AkRti ke cAroM koNa binduoM se, dhAge sammukha bhujA ke madhya bindu taka le jAye jAte haiM, yaha cAroM bhujAoM ke liye kiyA jAtA hai / isa prakAra prasArita dhAgoM meM pratyeka kI lambAI kA mApa kyA hai ? aise caturbhuja kSetra ke bhItara aMtarAvalambaka aura usase utpanna AbAdhAoM ke mApa kyA ho sakate haiM ? // 1883-1893 // ___staMbha kI U~cAI kA mApa jJAta hai| kisI kAraNavaza staMbha bhagna ho jAtA hai, aura bhagna staMbha kA UparI bhAga bhUmi para giratA hai| (bhagna staMbha kA ) nimna bhAga unnata bhAga ke UparI bhAga para bhavalambita rahatA hai| taba staMbha ke mUla se gire hue UparI agra ( jo aba bhUmi ko sparza karatA hai ) kI paiThika (AdhArIya ) dUrI jJAta kI jAtI hai| staMbha ke mUla bhAga se lekara zeSa unnata bhAga ke mApa 1 ma ka/ ( 1883-1893) isa prazna ke anusAra dI gaI AkRti isa prakAra hai: yahA~ bhItarI lamba ga ha aura ka la haiN| inheM prApta karane ke liye pahile phai ko prApta karate haiN| TIkAnusAra pha i kA mApa = (sama) - {(dama) + (dai) + 3 dama)2} hai| aba, phai aura basa athavA ada ko staMbha mAnakara saMketa meM / kathita niyama prayoga meM lAyA jA sakatA hai| (1903 ) yadi a ba sa samakoNa tribhuja hai saura yadi masa kA mApa aura aba tathA basa ke yoga kA mApa diyA gayA ho taba, aba aura ba sa ke mApa isa samIkaraNa dvArA nikAle jA sakate haiM ki basa = (a ba) + (asa)2; niyama diyA gayA sUtra yaha hai :( a ba+basa)-( a sa )2 , yaha arhA uparyukta 2(aba+(basa) ' samIkaraNa se saralatApUrvaka siddha kiyA jA sakatA hai| aba:

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240 ] gaNitasArasaMgrahaH [ 7. 1905stambhasyonnatapramANasaMkhyAM jJAtvA tasmin stambhe yenakenacitkAraNena bhagne patite sati tatstambhAramUlayormadhye sthitau bhUsaMkhyAM jJAtvA tatstambhamUlAdArabhya sthitaparimANasaMkhyAnayanasya sUtramnirgamavargAntaramitivargavizeSasya yadbhavedardham / nirgamanena vibhaktaM tAvasthitvAtha bhagnaH syAt / / 1903 // atroddezakaH stambhasya paJcaviMzatirucchrAyaH kazcidantare bhagnaH / stambhAramUlamadhye pazca sa gatvA kriyAn bhagnaH // 1913 / / veNUcchAye hastAH saptakRtiH kazcidantare bhagnaH / bhUmizca saikaviMzatirasya sa gatvA kiyAna bhagnaH / / 1923 / / vRkSocchAyo viMzatiragrasthaH ko'pi tatphalaM puruSaH / karNAkRtyA vyakSipadatha tarumUlasthitaH puruSaH // 1933 // tasya phalasyAbhimukhaM pratibhujarUpeNa gatvA ca / phalamagrahIca tatphalanarayorgatiyogasaMkhyaiva // 1943 / / paJcAzadabhUttatphalagatirUpA karNasaMkhyA kA / tavRkSamUlagatanaragatirUpA pratibhujApi kiyatI syAt // 1953 // kA saMkhyAtmaka mAna nikAlane ke liye yaha niyama hai saMpUrNa U~cAI ke varga aura jJAta AdhArIya ( basal ) dUrI ke varga ke aMtara kI arddha rAzi jaba saMpUrNa U~cAI dvArA bhAjita hotI hai, taba zeSa unnata bhAga kA mApa utpanna hotA hai| jo aba saMpUrNa U~cAI kA zeSa bacatA hai vaha bhagna bhAga kA mApa hotA hai / / 1901 / / udAharaNArtha prazna staMbha kI U~cAI 25 hasta hai / vaha mUla aura ana ke bIca kahIM TUTA hai| pharza para gire hue ana ( UparI bhAga ) aura staMbha ke mUla ke bIca kI dUrI 5 hasta hai| batAo ki TUTane kA sthAna bindu mUla se kitanI dUra hai ? // 191 / / ( ugane vAle ) bA~sa kI U~cAI kA mApa 49 hasta hai / vaha mUla aura ana ke bIca kahIM bhagna huA hai| bhAdhArIya dUrI 21 hasta hai| vaha mUla se kitanI dUrI para TUTA hai / / 1921 // kisI vRkSa kI U~cAI 20 hasta hai| koI manuSya usake UparI bhAga (coTI) para baiThakara karNarUpa patha meM phala ko nIce pheMkatA hai (arthAt vaha phala sarala rekhA meM girakara, samakoNa tribhuja kA karNa banAtA hai ) / taba dUsarA manuSya jo vRkSa ke nIce baiThA huA hai, phala taka sarala rekhA meM pahu~catA hai (yaha patha tribhuja kI dUrI bhujA kA nirmANa karatA hai), aura usa phala ko le letA hai| phala tathA isa manuSya dvArA taya kI gaI dUriyoM kA yoga 50 hasta hai| phala dvArA taya kiye gaye patha dvArA nirUpita karNa kA saMkhyAtmaka mAna kyA hai ? manuSya dvArA taya kiye gaye patha dvArA nirUpita anya bhujA kA mApa kyA ho sakatA hai ? // 1931-1953 / /

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-7. 1983] kSetragaNitanyavahAraH [241 jyeSThastambhasaMkhyAM ca alpastambhasaMkhyAM ca jJAtvA ubhayastambhAntarabhUmisaMkhyAM jJAtvA tajjyeSThasaMkhye bhagne sati jyeSThastambhAgre alpastambhAgraM spRzati sati jyeSThastambhasya bhagnasaMkhyAnayanasya sthitazeSasaMkhyAnayanasya ca sUtramjyeSThastambhasya kRterhasvAvanivargayatimapohyAdhama / stambhavizeSeNa hRtaM labdhaM bhagnonnatirbhavati // 1963 // atroddezakaH stambhaH paJcocchAyaH parastrayoviMzatistathA jyeSThaH / madhyaM dvAdaza bhagnajyeSThAgraM patitamitarAgre // 1973 // AyatacaturazrakSetrakoTisaMkhyAyAstRtIyAMzadvayaM parvatotsedhaM parikalpya tatparvatotsedhasaMkhyAyAH sakAzAt tadAyatacaturazrakSetrasya bhujasaMkhyAnayanasya karNasaMkhyAnayanasya ca sUtramgiryutsedho dviguNo giripuramadhyakSitirgirerardham / / gagane tatrotpatitaM giyardhavyAsasaMyutiH karNaH / / 1983 / / U~cAI meM bar3e (jyeSTha ) staMbha kI U~cAI kA saMkhyAtmaka mAna tathA U~cAI meM choTe ( alpa ) staMbha kI U~cAI kA saMkhyAtmaka mAna jJAta hai| ina do staMbhoM ke bIca kI dUrI kA saMkhyAtmaka mAna bhI jJAta hai| jyeSTha staMbha bhagna hokara isa prakAra giratA hai, ki usakA UparI ana alpa staMbha ke UparI agra para avalambita hotA hai, aura bhagna bhAga kA nimna bhAga, zeSa bhAga ke UparI bhAga para sthita rahatA hai / isa dazA meM jyeSTha staMbha ke bhanna bhAga kI lambAI kA saMkhyAtmaka mAna tathA usI jyeSTha staMbha ke zeSa bhAga kI U~cAI ke saMkhyAtmaka mAna ko prApta karane ke liye niyama jyeSTha staMbha ke saMkhyAtmaka mApa ke varga meM se, alpa staMbha ke mApa ke varga aura AdhAra ke mApa ke varga ke yoga ko ghaTAte haiM / pariNAmI zeSa kI aI rAzi ko do staMbhoM ke mApoM ke aMtara dvArA bhAjita karate haiN| prApta bhajanaphala bhanna staMbha ke unnata bhAga kI U~cAI hotA hai| // 196 // udAharaNArthe prazna ___eka staMbha U~cAI meM 5 hasta hai, usI prakAra dUsare jyeSTha staMbha U~cAI meM 23 hasta hai| unake bIca kI dUrI 12 hasta hai| bhagna jyeSTha staMbha kA uparI agra alpa staMbha ke UparI ana para giratA hai| bhanna jyeSTha staMbha ke unnata bhAga kI U~cAI nikAlo // 1972 // Ayata kSetra kI UrdhvAdhara (laMba rUpa) bhujA ke saMkhyAtmaka mAna kI do tihAI rAzi ko parvata kI U~cAI mAnakara, usa parvata kI U~cAI kI sahAyatA se ukta Ayata ke karNa aura kSaitija bhujA (AdhAra) ke saMkhyAtmaka mAnoM ko nikAlane ke liye niyama parvata kI dugunI U~cAI, parvata ke mUla se vahA~ ke zahara ke bIca kI dUrI kA mApa hotI hai| parvata kI AdhI U~cAI gagana meM Upara kI ora kI ur3Ana kI dUrI ( uDDayana ) kA mApa hai| parvata kI AdhI U~cAI meM, (parvata ke mUla se ) zahara kI dUrI kA mApa jor3ane se karNa prApta hotA hai // 1946 // (1963) yadi jyeSTha stambha kI U~cAI a aura alpa stambha kI ba dvArA nirUpita ho; unake bIca kI dUrI sa ho, aura a, bhanna stambha ke unnata bhAga kI U~cAI ho, to niyamAnusAra, . a-(ba+sa), a.: (a-ba) ga0 sA0 saM0-31 a

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gaNita sArasaMgrahaH atroddezakaH SaDyojanordhvazikhariNi yatIzvarau tiSThatastatra / eko'ciryayAgAttatrApyAkAzacAryaparaH / / 1993 // zrutivazamutpatya puraM girizikharAnmUlamavaruhyAnyaH / samagatika saMjAtau nagaravyAsaH kimutpatitam || 2003 // 242 ] DolAkArakSetre stambhadvayasya vA giridvayasya vA utsedhaparimANasaMkhyAmeva Ayatacaturazra - bhujadvayaM kSetradvaye parikalpya taddviridvayAntarabhUmyAM vA tatstambhadvayAntarabhUmyAM vA AbAdhAdvayaM parikalpya tadAbAdhAdvayaM vyutkrameNa nikSipya tavyutkramaM nyastAbAdhAdvayameva Ayata caturazrakSetradvaye koTidvayaM parikalpya tatkarNadvayasya samAnasaMkhyAnayanasUtram - udAharaNArtha prazna 6 yojana U~cAI vAle kisI parvata para 2 yatIzvara tiSThe the / unameM se eka ne paidala gamana kiyA / dUsare AkAza meM gamana kara sakate the| ye dUsare yatIzvara Upara kI ora ur3e, aura taba zahara meM karNa mArga se utare / prathama yatIzvara zikhara se parvata ke mUla taka sIdhe nIce kI ora udagra dizA meM utare, aura paidala zahara kI ora cale / yaha jJAta huA ki donoM ne samAna dUriyA~ taya kIM / parvata ke mUla se zahara taka kI dUrI kyA hai, aura UparI ur3Ana kI U~cAI kitanI hai ? // 1993 - 2003 // [ 7. 1992 laTakana ( Dola ) aura usake do bhUmi para AdhArita laMbarUpa avalaMboM dvArA nirUpita kSetra meM, do staMbhoM athavA do parvata zikharoM kI U~cAiyoM ke mApa do Ayata caturazra kSetroM kI kSaitija ( kSitija ke samAnAntara ) bhujAoM ke mApa mAna liye jAte haiM / taba ina jJAta kSaitija bhujAoM kI sahAyatA se, aura ( dazAnusAra) do parvata athavA do staMbha ke bIca kI AdhAra rekhA ke saMbaMdha meM laMba ke milana bindu dvArA utpanna AbAdhAoM ( khaMDoM) ke mAnoM ko prApta karate haiM / ina do AbAdhAoM ko viloma krama meM likhate haiM / isa prakAra viloma krama meM likhe gaye ( do AbAdhAoM ke ) mAnoM kI do AyatAkAra caturbhuja kSetroM kI do laMba bhujAoM ke mApa mAna lete haiM / ( aisI dazA meM ) ina do AyatoM ke karNoM ke samAna saMkhyAtmaka mAna ko prApta karane ke liye niyama ( 1993 - 2003 ) AkRti meM yadi parvata kI U~cAI 'a' dvArA nirUpita hai, zahara se parvata ke mUla kI dUrI 'ba' hai, aura karNa mArga kI lambAI 'sa' hai, to gAthA 1982 ke niyama kI pRSTabhUmi meM kI gaI kalpanA ke anusAra 'a' bhujA A bA kI 2 / 3 hai / isaliye Urdhva dizA kI ur3Ana dA bA arthAt a hai. ..(1) cU~ki do sAdhuoM kI ur3AneM barAbara hai, . : sa + a =a+ baiM; . ( 2 ) .. sa = a + ba.. " sa = a + + a ba, parantu sa = 8 a + ba e; .'. a ba = 2 a e; a ... ba= 2a.. ..(3) diye gaye niyama meM ye hI tIna sUtra ( 1 ), ( 2 ) aura ( 3 ) varNita haiM / bA ba sa A

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-7. 2033 ] DolAkArakSetrastambhadvitayordhvasaMkhye vA / zikharidvayordhvasaMkhye parikalpya bhujadvayaM trikoNasya // / 2013 // taddordvitayAntaragata bhUsaMkhyAyAstadAbAdhe / AnIya prAgvatte vyutkramataH sthApya te koTI / / 2023 // syAtAMtasminnAyatacaturazrakSetrayozca taddorbhyAm / koTibhyAM karNau dvau prAgvatsyAtAM samAnasaMkhyau tau // / 2033 // kSetragaNitavyavahAraH Dhola tathA usake do laMbarUpa avalaMboM dvArA nirUpita AkRti ke saMbaMdha meM, do staMbhoM kI athavA do parvatoM kI U~cAiyoM ke mApoM ko tribhuja kI do bhujAoM ke mApa mAna lete haiM / taba, diye gaye staMbhoM athavA parvatoM kI bIca kI AdhAra rekhA ke mAna ke tulya una do bhujAoM ke bIca kI AdhAra rekhA ke saMbaMdha meM, zIrSa se AdhAra para girAye gaye laMba se utpanna AbAdhAoM ke mAna pahile diye gaye niyamAnusAra prApta karate haiM / yadi ina AbAdhAoM ( khaMDoM) ke mAnoM ko viloma krama meM likhA jAve, to ve iSTa kriyA meM do AyatoM kI do laMba bhujAoM ke mAna bana jAte haiM / aba, pahile diye gaye niyamAnusAra do AyatoM ke karNau ke mAnoM ko uparyukta tribhuja kI do bhujAoM ( jo yahA~ Ayata kI do kSaitija bhujAe~ lI gaI haiM ) tathA una do laMba bhujAoM kI sahAyatA se prApta karate haiM / ye karNa samAna saMkhyAtmaka mAna ke hote haiM // 2013 - 2033 // ( 2013 - 2033) isa niyama meM varNita caturbhujoM meM, mAnalo, laMba bhujAe~ a, ba dvArA nirUpita haiM, AdhAra sa hai; sa, sa usake khaMDa ( AbAdhAyeM ) haiM, aura rajju ( rasse) ke pratyeka samAna bhAga kI laMbAI hai / aba, a' + sa = ba e + sa / .'. ( sa 2 + sa, ) (sa = sa ) = a - ba e; aura sa+sasa; a are - bara + sa sa ka = sa - la sa a - bara .. sa 2 = sa 2 2 ora sa1 = ye mAna, a aura ba bhujAoMvAle tribhuja ke 'sa' mApa vAle AdhAra ke khaMDoM ke haiN| AdhAra ke khaMDa zIrSa se laMba girAne se utpanna hue haiN| niyama meM yahI kathita hai| gAthA 49 kA niyama bhI dekhiye / ( 2103 ) yahA~ batalAyA huA patha samakoNa tribhuja kI bhujAoM meM se hokara jAtA hai / isa niyama meM diye gaye sUtra kA bIjIya nirUpaNa yaha hai [ 243 la sa sa ba bara + ara aXda, jahA~ ka karNapatha se jAne para vyatIta hue dinoM kI saMkhyA hai, a aura ba kramazaH do manuSyoM kI gatiyA~ haiM, aura da uttara dizA se jAnepara vyatIta hue dinoM kI saMkhyA hai / isa meM 'datta vyAsa para AdhArita nimnalikhita samIkaraNa se yaha spaSTa hai prazna bare kare = dara ba+- + (pha+ da ) zXara

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244] gaNitasArasaMgrahaH [7.204 atroddezakaH stambhasrayodazaikaH pnycdshaanyshcturdshaantritH| rajjubaiddhA zikhare bhUmIpatitA ka' AbAdhe // 204 / / te rajjU samasaMkhye syAtAM tadrajjumAnamapi kathaya // 205 // dvAviMzatirutsedho' girestathASTAdazAnyazailasya / viMzatirubhayormadhye tayozca zikhayoHsthitau sAdhU / / 206 / / AkAzacAriNau tau samAgatau nagaramatra bhikSAyai / samagatiko saMjAtau tatrAbAdhe kiyatsaMkhye // samagatisaMkhyA kiyatI DolAkAre'tra gaNitajJa // 2073 // vizatirekasyonnatiradrezca jinAstathAnyasya / tanmadhyaM dvAviMzatiranayorayozca zRGgayoH sthitvA / / 2083 / / AkAzacAriNau dvau tanmadhyapuraM smaayaatau| bhikSAyai samagatiko syAtAM tanmadhyazikharimadhyaM kima // 2891 // viSamatrikoNakSetrarUpeNa hInAdhikagatimatonarayoH samAgamadinasaMkhyAnayanasUtram 1. ka AbAdhe vyAkaraNarUpeNa azuddha hai, kyoMki dvivAcaka saMkhyA 'ke' aura 'AbAdhe' ke madhya koI saMdhi nahIM ho sakatI hai| 189 veM zloka kI TippaNI se milAna kariye / udAharaNArtha prazna eka staMbha U~cAI meM 13 hasta hai| dUsarA U~cAI meM 15 hasta hai| inake bIca kI dUrI 14 hasta hai| ina do staMbhoM ke UparI siroM para ba~dhA huA eka rassA ( rajju ) isa taraha nIce laTakatA hai, ki vaha ina do staMbhoM ke bIca kI dUrI ko sparza karatA hai| staMbhoM ke bIca kI AdhAra rekhA ke isa prakAra utpanna khaMDoM ke mAna kyA-kyA haiM ? rajju ke do laTakate hue bhAga lambAI meM samAna saMkhyAtmaka mAna ke haiN| rajju kA mApa bhI batalAo // 2041-2053 // kisI eka parvata kI U~cAI 22 yojana hai| dUsare parvata kI 10 yojana hai| una do parvatoM ke bIca kI dUrI 20 yojana hai| parvata ke zikhara para tiSThe hue do sAdhu AkAza meM gamana kara sakate haiN| bhikSA ke liye ve AkAza mArga se nIce Ate haiM, aura una parvatoM ke bIca base hue nagara meM milate haiN| yaha jJAta hai ki ve AkAza mArga se samAna dariyA~ taya kara Aye haiM / ina dazAoM meM do parvatoM ke bIca kI AdhArIya rekhA ke khaMDoM ke saMkhyAtmaka mAna kyA-kyA haiM ? he gaNitajJa, isa DolAkAra kSetra meM taya kI gaI samAna rAziyoM kA saMkhyAtmaka mAna kyA hai // 206-2071 // eka parvata kI U~cAI 20 yojana hai, aura isI prakAra dUsare parvata kI U~cAI 24 yojana hai| unake bIca kI dUrI 22 yojana hai| do sAdhu, jo alaga alaga parvata ke zRr para sthita the aura AkAza meM gamana kara sakate the, una do parvatoM ke bIca meM base hue nagara meM bhikSA ke liye utre| ve AkAza meM barAbara dUriyA~ taya karate hue dekhe gye| usa madhya meM base hue nagara aura parvatoM ke bIca kI dUrI kA mApa kyA hai ? // 2001-209 // viSama tribhuja kI sImAdvArA nirUpita mArga para asamAna gati se calane vAle do manuSyoM kA samAgama hone ke liye iSTa dinoM kI saMkhyA kA mAna nikAlane ke lie niyama

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___245 -7. 2133 ] kSetragaNitavyavahAra [245 dinagatikRtisaMyogaM dinagatikRtyantareNa hRtvAtha / hatvodaggatidivasaistallabdhadine samAgamaH syAntroH // 2103 / / atroddezakaH dve yojane prayAti hi pUrvagatistrINi yojanAnyaparaH / uttarato gacchati yo gatvAsau taddinAni paJcAtha / / 2113 / / gacchan karNAkRtyA katibhirdivasainaraM samApnoti / ubhayoyugapadgamanaM prasthAnadinAni sadRzAni // 2123 // paJcavidhacaturazrakSetrANAM ca trividhatrikoNakSetrANAM cetyaSTavidhabAhyavRttavyAsasaMkhyAnayanasUtramzrutiravalambakabhaktA pArzvabhujannA caturbhuje tribhuje / bhujaghAto lambahRto bhavedvahivRttaviSkambhaH // 2133 // ___ do manuSyoM kI dainika gatiyoM ke saMkhyAtmaka mAnoM ke vargoM ke yoga ko unhIM dainika gatiyoM ke mAnoM ke vargoM ke aMtara dvArA bhAjita kiyA jAtA hai| isa prakAra prApta bhajanaphala ko unameM se kisI eka ke dvArA uttara meM yAtrA karate hue (anya manuSya se milane hetu dakSiNa pUrva meM jAne ke pahile) vyatIta hue dinoM kI saMkhyA dvArA guNita karate haiM, ina do manuSyoM kA samAgama isa guNanaphala dvArA mApe gaye dinoM kI saMkhyA ke aMta meM hotA hai // 2103 // udAharaNArtha prazna pUrva kI ora yAtrA karanevAlA manuSya 2 yojana pratidina kI gati se calatA hai, aura uttara kI ora yAtrA karane vAlA dUsarA manuSya 3 yojana pratidina kI gati se calatA hai| yaha dUsarA manuSya 5 dinoM taka ( isa prakAra ) calane ke pazcAt karNa para calane ke liye mur3atA hai| vaha pahile manuSya se kitane dina pazcAt milegA ? donoM eka hI samaya prasthAna karate haiM, aura yAtrA meM donoM ko samAna samaya lagatA hai // 21-2113 // pA~ca prakAra ke caturbhuja kSetroM tathA tIna prakAra ke tribhuja kSetroMvAlI ATha prakAra kI AkRtiyoM ke parigata vRttoM ke vyAsoM ke saMkhyAtmaka mAna ko nikAlane ke liye niyama caturbhuja kSetra ke saMbaMdha meM, karNa ke mAna ko laMba ke mAna dvArA bhAjita kara, aura taba bAjU kI bhujA ke mAna dvArA guNita karane para, parigata vRtta ke vyAsa kA mAna utpanna hotA hai| tribhuja kSetra ke saMbaMdha meM AdhAra ko chor3akara, zeSa do bhujAoM ke mAnoM ke guNanaphala ko laMba ke mAna dvArA bhAjita karane para, parigata vRtta kA iSTa vyAsa utpanna hotA hai // 2133 // (2133 ) mAnalo ki tribhuja abasa kisI vRtta meM aMtalikhita hai / ada vyAsa hai aura bai, asa para laMba hai| bada ko jodd'o| aba tribhuja a ba da aura ba i sa ke koNa kramazaH Apasa meM barAbara haiM (arthAt ye tribhuja sajAtIya [ similar ] haiM) :: aba : ada=bai : basa, : ada = aba X basa / - yaha sUtra niyama meM caturbhuja tribhuja ke parigata vRtta ke vyAsa ko prApta karane ke liye diyA gayA hai|

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[7. 2143 246] gaNitasArasaMgrahaH atroddezakaH samacaturazrasya triMkabAhupratibAhukasya cAnyasya / koTiH paJca dvAdaza bhujAsya kiM vA bahivRttam / / 2143 // bAhU trayodaza mukhaM catvAri dharA caturdaza proktA / dvisamacaturazrabAhiraviSkambhaH ko bhavedatra // 2153 // paJcakRtirvadanabhujAzcatvAriMzacca bhuumirekonaa| trisamacaturazrabAhiravRttavyAsaM mamAcakSva // 2163 / / vyekA catvAriMzadvAhuH pratibAhuko dvipaJcAzat / SaSTibhUmirvadanaM paJcakRtiH ko'tra viSkambhaH / / 2173 // trisamasya ca SaD bAhustrayodaza dvisamabAhukasyApi / bhUmirdaza viSkambhAvanayoH ko bAhyavRttayoH kathaya / / 2183 / / bAhU paJcavyuttaradazakau bhUmizcaturdazo viSame / tribhujakSetre bAhiravRttavyAsaM mamAcakSva / / 2193 // dvikabAhuSaDazrasya kSetrasya bhavedvicintya kathaya tvam / bAhiraviSkambhaM me paizAcikamatra yadi vetsi / / 2201 // udAharaNArtha prazna ( samabAhu caturbhuja ) vargAkRti ke saMbaMdha meM, jisakI pratyeka bhujA 3 hai, aura anya caturbhuja kSetra ke saMbaMdha meM, jisakI laMba bhujA 5 aura kSaitija bhujA 12 hai, batalAo ki parigata vRtta ke vyAsa ke mApa kyA-kyA haiM? // 2141 // do pAzrva bhujAoM meM se pratyeka mApa meM 13 hai. UparI bhujA 4 hai. aura AdhAra mApa meM 14 hai| isa dazA meM aise do samAna bhujAoM vAle caturbhuja kSetra ke parigata vRtta ke vyAsa kA mApa btlaao||2151|| UparI bhujA aura do bAjU kI bhujAoM meM se pratyeka mApa meM 25 hai| AdhAra mApa meM 39 hai| yahA~ batalAo kI aise tIna barAbara bhujAoM vAle caturbhuja ke parigata vRtta ke vyAsa kA mApa kyA hai ? // 2163 // pArzva bhujAoM meM se kisI eka kA mApa 39 hai; dUsarI kA mApa 52 hai: AdhAra kA mApa 60 aura UparI bhujA kA mApa 25 hai| isa caturbhuja kSetra ke saMbaMdha meM parigata vatta kA vyAsa kyA hai ? // 2171 // kisI samabhuja tribhuja kI bhujA kA mApa 6 hai. aura samadvibAha tribhuja kI bhujA kA mApa 13 hai / isa dazA meM AdhAra kA mApa 10 hai| ina tribhujoM ke parigata vattoM ke vyAsoM ke mAna nikAlo // 28 // viSama tribhuja ke saMbaMdha meM do bhujAe~ mApa meM 15 aura 13 haiM: AdhAra kA mApa 14 hai| usake parigata vRtta ke vyAsa kA mAna mujhe batalAo // 219 ||ydi tuma gaNita kI paizAcika vidhiyA~ jAnate ho, to ThIka taraha socakara batalAo ki jisakI pratyeka bhujA kA mApa 2 hai aise niyamita SaTbhujAkAra AkRtivAle kSetra ke parigata vRtta ke vyAsa kA mAna kyA hogA ? // 2201 // (220%) isa gAthA para likhI gaI kannar3I TIkA meM prazna ko yaha sUcita kara hala kiyA hai ki niyamita SaTbhuja kA vikarNa parigata vRtta ke vyAsa ke tulya hotA hai| .

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-7. 2233] kSetragaNitavyavahAraH [247 iSTasaMkhyAvyAsavatsamavRttakSetramadhye samacaturazrAdyaSTakSetrANAM mukhabhUbhujasaMkhyAnayanasUtramlabdhavyAseneSTavyAso vRttasya tasya bhaktazca / labdhena bhujA guNayedbhavecca jAtasya bhujasaMkhyA // 2213 // atroddezakaH vRttakSetravyAsastrayodazAbhyantare'tra saMcinya / samacaturazrAdyaSTakSetrANi sakhe mamAcakSva / / 2223 / / ___ AyatacaturazraM vinA pUrvakalpitacaturazrAdikSetrANAM sUkSmagaNitaM ca rajjusaMkhyAM ca jJAtvA tattatkSetrAbhyantarAvasthitavRttakSetraviSkambhAnayanasUtramparidheH pAdena bhajedanAyatakSetrasUkSmagaNitaM tat / kSetrAbhyantaravRtte viSkambho'yaM vinirdiSTaH / / 2233 // vyAsa ke jJAta saMkhyAtmaka mAna vAle samavRtta kSetra meM aMtalikhita varga se prAraMbha hone vAlI ATha prakAra kI AkRtiyoM ke AdhAra, UparI bhujA aura anya bhujAoM ke saMkhyAtmaka mAnoM ko nikAlane ke liye niyama diye gaye vRtta ke vyAsa ke mAna ko nyAsa se prApta aise vRtta ke vyAsa dvArA bhAjita kiyA jAtA hai, jo nirdiSTa prakAra kI vikalpa se cunI haI AkRti ke paritaH khIMcA jAtA hai| isa mana se cunI huI AkRti ke bhujAoM ke mAnoM ko uparyukta pariNAmI bhajanaphaloM dvArA guNita karanA caahie| isa prakAra, diye gaye vRtta meM utpanna AkRti kI bhujAoM ke saMkhyAtmaka mAnoM ko prApta karate haiM // 2213 // udAharaNArtha prazna samavRtta AkRti kA vyAsa 13 hai| he mitra, ThIka taraha vicAra kara mujhe batalAo ki isa vRtta meM aMtalikhita vargAdi ATha prakAra kI vibhinna AkRtiyoM ke saMbaMdha meM vibhinna mApa kyA-kyA haiM // 2221 // kevala Ayata kSetra ko chor3akara pUrvakathita vibhinna prakAra ke caturbhuja aura tribhuja kSetroM ke aMtargata vRttoM ke vyAsa kA mAna nikAlane ke liye niyama, jabaki inhIM caturbhuja aura anya AkRtiyoM ke saMbaMdha meM kSetraphala kA sUkSma mApa aura parimiti kA saMkhyAtmaka mAna jJAta ho (Ayata kSetra ko chor3akara anya kisI bhI ) AkRti ke sUkSma jJAta kSetraphala ko ( usa AkRti kI) parimiti kI eka cauthAI rAzi dvArA bhAjita karanA cAhiye / vaha pariNAma usa AkRti ke aMtargata vRtta ke vyAsa kA mApa hotA hai // 2233 // (2213) iSTa aura mana se cunI huI AkRtiyoM kI sajAtIyatA ( similiarity ) se yaha niyama svameva prApta ho jAtA hai| (2233) yadi saba bhujAoM kA yoga 'ya' ho, aMtargata vRtta kA vyAsa 'va' ho, aura saMbaMdhita caturbhuja yA tribhujakSetra kA kSetraphala 'kSa' ho, to -x-=kSa hotA hai| isaliye niyama meM diyA gayA sUtra, va = kSaya, hai|

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248] gaNitasArasaMgrahaH [7. 2243 atroddezakaH samacaturazrAdInAM kSetrANAM pUrvakalpitAnAM ca / kRtvAbhyantaravRttaM brahmadhunA gaNitatattvajJa // 2243 // samavRttavyAsasaMkhyAyAmiSTasaMkhyAM bANaM parikalpya tadvANaparimANasya jyAsaMkhyAnayanasUtramvyAsAdhigamonassa ca caturguNitAdhigamena sNgunnitH| - yattasya vargamUlaM jyArUpaM nirdizetprAjJaH / / 2253 / / atroddezakaH vyAso daza vRttasya dvAbhyAM chinno hi rUpAbhyAm / chinnasya jyA kA syAtpragaNayyAcakSva tAM gaNaka / / 2263 / / samavRttakSetravyAsasya ca mauyAzca saMkhyA jJAtvA bANasaMkhyAnayanasUtramvyAsajyArUpakayogavizeSasya bhavati yanmUlam / / tadviSkambhAcchodhyaM zeSAmiSu vijAnIyAt // 2273 // udAharaNArtha prazna vargAdi pUrvollekhita AkRtiyoM ke saMbaMdha meM aMtargata vRtta khoMcakara, he gaNita tattvajJa, pratyeka aise aMtargata vRtta ke vyAsa kA mAna batalAo // 2241 / / kisI samavRtta ke vyAsa ke jJAta saMkhyAtmaka mAna ke bhItara (sImAntaH) bANa ke mApa kI jJAta saMkhyA lekara, aise dhanuSa ke dhAge ke saMkhyAtmaka mAna ko prApta karane ke liye niyama jisakA bANa usI diye gaye mApa ke tulya hai diye gaye vyAsa ke mAna aura bANa ke jJAta mAna ke aMtara ko bANa ke mAna kI caugunI rAzi dvArA guNita kiyA jAtA hai| pariNAmI guNanaphala kA jitanA bhI vargamUla AtA hai, use vidvAna puruSa ko dhanuSa kI DorI kA iSTa mApa batalAnA cAhiye // 2251 // udAharaNArtha prazna vRtta kA byAsa 10 hai| usakA 2dvArA apakartana kiyA jAtA hai| he gaNitajJa, ThIka gaNanA ke pazcAt diye gaye vyAsa ke kaTe hue bhAga ke saMbaMdha meM dhanuSa kI DorI kA mApa batalAo // 2263 // jaba kisI diye gaye vRtta ke vyAsa kA saMkhyAtmaka mAna aura usa vRtta saMbaMdhI dhanuSa DorI (jIvA) kA mAna jJAta ho, taba bANa kA saMkhyAtmaka mAna nikAlane ke liye niyama diye gaye vRtta ke saMbaMdha meM nyAsa aura jovA (dhanuSa-DorI rekhA) ke jJAta mAnoM ke vargoM ke aMtara kA jo vargamUla hotA hai use vyAsa ke mAna meM se ghaTAyA jAtA hai| pariNAmI zeSa kI arddharAzi bANa (rekhA) kA iSTa mAna hotI hai // 2273 // ( 2253 ) gAthA 2253, 2273, 2293 aura 2313 meM diye gaye sabhI niyama isa yathArthatA para Adharita hai ki kisI vRtta meM praticchedana karane vAle ( intersecting) cApa koM kI AbAdhAoM (khaMDoM) ke guNanaphala samAna hote haiM /

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-7. 2303] kSetragaNitavyavahAraH atrodezakaH daza vRttasya viSkambhaH ziJjinyabhyantare sakhe / dRSTASTau hi punastasyAH kaH syAdadhigamo vada / / 2283 // jyAsaMkhyAM ca bANasaMkhyAM ca jJAtvA samavRttakSetrasya madhyavyAsasaMkhyAnayanasUtram - bhaktazcaturguNena ca zareNa guNavargarAziriSusahitaH / samavRttamadhyamasthitaviSkambho'yaM vinirdiSTaH / / 2293 / / [ 249 atroddezakaH kasyApi ca samavRttakSetrasyAbhyantarAdhigamanaM dve / jyA dRSTASTau daNDA madhyavyAso bhavetko'tra / / 2303 // samavRttadvayasaMyoge ekA matsyAkRtirbhavati / tanmatsyasya mukhapRcchavinirgata rekhA kartavyA / tayA rekhayA anyonyAbhimukhadhanurdvayAkRtirbhavati / tanmukhapucchavinirgata rekhaiva taddhanurdvayasyApi jyAkRtirbhavati / taddhanurdvayasya zaradvayameva vRttaparasparasaMpAtazarau jJeyau / samavRttadvayasaMyoge tayoH saMpAtazarayorAnayanasya sUtram - udAharaNArtha prazna kisI diye gaye vRtta ke vyAsa kA mApa 10 hai / sAtha hI jJAta hai ki bhItarI dhanuSa-DorI kA mApa 8 hai / he mitra, usa dhanuSa DorI ke saMbaMdha meM bANa rekhA kA mAna nikAlo || 2283 // saMkhyAtmaka mAna jJAta hoM, taba diye gaye vRtta ke vyAsa niyama- jaba dhanuSa-DorI aura bANa ke saMkhyAtmaka mAna ko nikAlane ke liye dhanuSa - DorI ke mAna ke varga kA nirUpaNa karane vAlI saMkhyA, 4 dvArA guNita bANa ke mAna ke dvArA bhAjita kI jAtI hai / taba pariNAmI bhajanaphala meM bANa kA mAna jor3A jAtA hai / isa prakAra prApta rAzi niyamita vRtta kI, kendra se hokara mApI gaI, caur3AI kA mApa hotI hai // 2293 // udAharaNArtha prazna kisI samavRtta kSetra ke saMbaMdha meM, bANa rekhA 2 daMDa, aura dhanuSa DorI 8 daMDa hai / isa vRtta ke saMbaMdha meM vyAsa kA mAna kyA ho sakatA hai ? || 2303 // / mukha se puccha ko milAne jaba do vRtta paraspara eka dUsare ko kATate haiM, taba machalI ke hai / isa matsyAkRti ke saMbaMdha meM mukha se puccha ko milAnevAlI rekhA rekhA kI sahAyatA se eka dUsare ke sammukha do dhanuSoM kI utpatti hotI hai| vAlI sarala rekhA ina donoM dhanuSoM kI dhanuSa-DorI hotI hai / ina do dhanuSoM ke saMbaMdha meM do bANa rekhAe~ pArasparika atichAr3I ( overlapping ) vRttoM se saMbaMdhita do bANa rekhAoM ko banAne dUsare ko kATate haiM, taba ativAdI mAnoM ko nikAlane ke liye niyama vA samajhI jAtI haiM / jaba do samavRtta paraspara eka ( overlapping ) bhAga se saMbaMdhita bANa rekhAoM ke ga0 sA0 saM0-32 AkAra kI AkRti utpanna hotI khIMcI jAtI hai| isa

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250] gaNitasArasaMgrahaH grAsonavyAsAbhyAM grAse prakSepakaH prakartavyaH / vRtte ca parasparataH saMpAtazarau vinirdiSTau // 2313 // atroddezakaH samavRttayoyohi dvaatriNshdshiitihstvistRtyoH| grAse'STau ko bANAvanyonyabhavau samAcakSva // 2323 // iti paizAcikavyavahAraH samAptaH // iti sArasaMgrahe gaNitazAstre mahAvIrAcAryasya kRtau kSetragaNitaM nAma SaSThavyavahAraH samAptaH / praticchedita hone vAle vRttoM ke aise do vyAsoM ke do mAnoM kI sahAyatA se, jinheM vRttoM ke atichAdI ( overlapping ) bhAga kI sabase adhika caur3AI ke mAna dvArA hAsita karate haiM vRttoM ke atichAdI bhAga kI mahattama caur3AI ke isa jJAta mAna ke saMbaMdha meM prakSepaka kriyA karanA cAhiye / aise vrattoM ke saMbaMdha meM isa prakAra prApta do pariNAmoM meM se, pratyeka dUsare kA, atichAdI vRttoM saMbaMdhI do bANoM kA mApa hotA hai // 2313 // udAharaNArtha prazna do vRttoM ke saMbaMdha meM, jinake vistAra-vyAsa kramazaH 32 aura 60 hasta haiM / sAdhAraNa atichAdI bhAga kI mahattama caur3AI 8 hasta hai| yahA~ una do vRttoM ke saMbaMdha meM bANa rekhAoM ke mAnoM ko batalAo // 2323 // isa prakAra, kSetra gaNita vyavahAra meM paizAcika vyavahAra nAmaka prakaraNa samApta huaa| isa prakAra, mahAvIrAcArya kI kRti sAra saMgraha nAmaka gaNita zAstra meM kSetragaNita nAmaka SaSTam vyavahAra samApta huaa| (2313 ) isa niyama meM anudhyAnita prazna AryabhaTTa dvArA bhI sAdhita kiyA gayA hai| unake dvArA diyA gayA niyama isa niyama ke samAna hai|

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8. khAtavyavahAraH sarvAmarendra mukuTArcitapAdapIThaM sarvajJamavyayamacintyamanantarUpam / bhavyaprajAsarasijAkarabAlabhAnuM bhaktyA namAmi zirasA jinavardhamAnam // 1 // kSetrANi yAni vividhAni puroditAni teSAM phalAni guNitAnyavagAhanAni ( nena ) / karmAntikauNDraphalasUkSma vikalpitAni vakSyAmi saptamamidaM vyavahArakhAtam // 2 // sUkSmagaNitam atra paribhASAzloka: hastaghane pAMsUnAM dvAtriMzatpalazatAni pUryANi / utkIryante tasmAt SaTtriMzatpalazatAnIha // 3 // 8. khAta vyavahAra ( khoha athavA gar3hA saMbaMdhI gaNanAe~ ) maiM sira jhukAkara una vardhamAna jinendra ko bhaktipUrvaka namaskAra karatA hU~, jinakA pAdapITha (paira rakhane kI caukI) sabhI amarendroM ke mukuToM dvArA arcita hotA hai, jo sarvajJa haiM, avyaya haiM, acintya aura anantarUpa haiM, tathA jo bhavya jIvoM rUpI kamala samUha ko vikasita karane ke liye bAlabhAnu ( abhinava sUrya ) haiM // 1 // aba maiM khAta ke saMbaMdha meM ( vibhinna prakAra ke ) kamAMtika, auNDrapha au sUkSma phala kA varNana karU~gA / ye samasta prakAra, una uparyukta vibhinna prakAra kI raikhikIya AkRtiyoM se gaharAI mApane vAlI rAziyoM dvArA ghaTita guNana kriyA ke pariNAma svarUpa prApta kiye jAte haiM / yaha sAtavA~ vyavahAra, khAta vyavahAra hai // 2 // sUkSma gaNita paribhASA ke liye eka zloka ( vyAvahArika kalpanA ke liye eka gAthA ) - kisI eka ghana hasta mApa kI khoha ko bharane ke liye 3,200 pala mAtrA kI miTTI lagatI hai / usI ghana Ayatana vAlI khoha meM 3,600 pala mAtrA kI miTTI nikAlI jA sakatI hai // 3 // ( 2 ) auNDraphala zabda meM 'auNDra" pada vicitra saMskRta zabda mAlUma par3atA hai, aura kadAcit vaha hindI zabda auNDa se saMbaMdhita hai, jisakA artha " gaharA " hotA hai / ( 3 ) isa dhAraNA kA abhiprAya spaSTa 3,600 pala hotA hai, aura itanI jagaha ko paryApta hotI hai / rUpa se yaha hai ki eka ghana hasta dabI huI miTTI kA bhAra zithilatA se bharane ke liye 3,200 pala bhAra kI miTTI

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252 ] gaNitasArasaMgrahaH khAtagaNitaphalAnayanasUtramkSetraphalaM vedhaguNaM samakhAte vyAvahArika gaNitam / mukhatalayutidalamatha satsaMkhyAptaM syAtsamIkaraNam // 4 // atroddezakaH samacaturazrasyASTau bAhuH pratibAhukazca vedhazca / kSetrasya khAtagaNitaM samakhAte kiM bhavedatra // 5 // tribhujasya kSetrasya dvAtriMzadvAhukasya vedhe tu / SaTtriMzaddRSTAste SaDaGgulAnyasya kiM gaNitam // 6 // sASTazatavyAsasya kSetrasya hi paJcaSaSTisahitazatam / vedho vRttasya tvaM samakhAte kiM phalaM kathaya / / 7 / / Ayatacaturazrasya vyAsaH paJcAyaviMzatirbAhuH / SaSTirvedho'STazataM kathayAzu samasya khAtasya / / 8 // asmin khAtagaNite karmAntikasaMjJaphalaM ca auNDasaMjJaphalaM ca jJAtvA tAbhyAM karmAntikauNDUsaMjJaphalAbhyAm sUkSmakhAtaphalAnayanasUtram gar3hoM kI ghanAkAra samAI ( aMtarvastu) ko nikAlane ke liye niyama gaharAI dvArA guNita kSetraphala, niyamita ( regular ) khAta (gar3e)kI ghanAkAra samAI kA vyAvahArika mAna utpanna karatA hai| sabhI vibhinna mukha (UparI) vistAroM ke tathA unake saMvAdI nitala ( bottom ) vistAroM ke yogoM ko AdhA kiyA jAtA hai| taba ( unhIM arddhita rAziyoM ke) yoga ko kathita ardita rAziyoM kI saMkhyA dvArA bhAjita kiyA jAtA hai / ausata samAI ko prApta karane ke liye yaha kriyA hai // 4 // udAharaNArtha prazna niyamita khAta ke cheda ke pratirUpaka, samAna bhujAoMvAle caturbhuja kSetra, ke saMbaMdha meM bhujAe~ tathA gaharAI pratyeka mApa meM 8 hasta hai| isa niyamita gar3he (khAta ) meM ghanAkAra samAI kA mAna kyA hai ? // 5 // kisI niyamita khAta ke cheda kA nirUpaNa karanevAle samatribhuja kSetra ke saMbaMdha meM pratyeka bhujA 32 hasta hai, aura gaharAI 36 hasta 6 aMgula hai| yahA~ samAI kitanI hai ? // 6 // kisI niyamita khAta ke cheda (section ) kA nirUpaNa karanevAle samavRtta kSetra ke saMbaMdha meM vyAsa 108 hasta hai, aura khAta kI gaharAI 165 hasta hai| batalAo ki isa dazA meM ghanaphala kyA hai ? // 7 // kisI niyamita khAta ( gaDhDhe ) ke cheda kA nirUpaNa karanevAle Ayata caturbhuja kSetra kI caur3AI 25 hasta hai, laMbAI 60 hasta hai aura khAta kI gaharAI 108 hasta hai / isa niyamita khAta kI ghanAkAra samAI zIghra batalAo // 8 // pariNAma ke rUpa meM prApta karmAntika tathA auNDra ko jJAta kara unakI sahAyatA se, khAta saMbaMdhI gaNanA meM ghanAkAra samAI kA sUkSma rUpa se ThIka mAna nikAlane ke liye niyama (4) isa zloka kA uttarArddha spaSTataH usa vidhi kA varNana karatA hai, jisake dvArA hama kisI diye gaye aniyamita khAta ke samucita rUpa se tulya niyamita khAta ke vistAroM ko prApta kara sakate haiN|

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[253 -.13] khAtavyavahAra baahyaabhyntrsNsthitttttkssetrsthbaahukottibhuvH| svapratibAhusametA bhaktAstatkSetragaNanayAnyonyam // 9 // guNitAzca vedhaguNitAH karmAntikasaMjJagaNitaM syAt / tadbAhyAntarasaMsthitatattatkSetre phalaM samAnIya // 10 // saMyojya saMkhyayAptaM kSetrANAM vedhaguNitaM ca / auNDraphalaM tatphalayovizeSakasya tribhAgena / saMyuktaM karmAntikaphalameva hi bhavati sUkSmaphalam / / 113 // UparI chedIya ( sectional ) kSetra kA nirUpaNa karanevAlI AkRti ke AdhAra aura anya bhujAoM ke mAnoM ko kramazaH talo ke chedIya kSetra kA nirUpaNa karanevAlo AkRti ke AdhAra aura saMvAdI bhujAoM ke mAnoM meM jor3ate haiM / isa prakAra prApta kaI yoga prazna meM vicArAdhIna chedIya kSetroM kI saMkhyA dvArA bhAjita kiye jAte haiN| taba bhujAe~ jJAta rahane para, kSetraphala nikAlane ke niyamAnusAra, pariNAmI rAziyA~ eka dUsare ke sAtha guNita kI jAtI haiN| taba karmAntika kA ghanaphala utpanna hotA hai| Uparo chedIya kSetra aura nitala chedIya kSetra dvArA nirUpita unhIM AkRtiyoM ke saMbaMdha meM, inameM se pratyeka kSetra kA kSetraphaLa alaga-alaga prApta kiyA jAtA hai| isa prakAra prApta kSetraphaloM ko Apasa meM jor3A jAtA hai, aura taba yogaphala vicArAdhIna chedIya kSetroM ko saMkhyA dvArA bhAjita kiyA jAtA hai // 9-113 // isa prakAra prApta bhajanaphala gaharAI ke mAna dvArA guNita kiyA jAtA hai| yaha bhauNDra nAmaka ghanaphala mApa ko utpanna karatA hai| yadi ina do phaloM ke antara kI eka tihAI rAzi kamontika phala meM jor3a dI jAya to iSTa ghanaphala kA sUkSma rUpa meM ThIka mAna nizcaya rUpa se prApta hotA hai| (9-113 ) dI gaI AkRti meM aba sa da niyamita khAta (gade) kA UparI chedIya kSetra (mukha) hai, aura ha pha ga ha nitala chedIya kSetra hai| isa niyama meM vyavahAra meM lAI gaI AkRtiyA~ yA to vipATita ( kATe gaye ) stUpa (pyramids) haiM, jinake AdhAra Ayata athavA tribhuja hote haiM, athavA vipATita zaMkvAkAra ( zaMku ke AkAra kI) vastue~ haiN| isa niyama meM khAtoM kI ghanAkAra samAI ke tIna prakAra ke mApoM kA varNana hai / isameM se do, jaise karmAtika aura auNDra mAya, samAiyoM ke nyAvahArika mAnoM ko dete haiM / ina mAnoM kI sahAyatA se sUkSma mApa kI gaNanA kI jAtI hai| yadi kA kautika phala aura A auNDra phala kA nirUpaNa karate hoM, to sUkSma rUpa se ThIka mApa (A- kA+kA) arthAt (3 kA+ A) hotA hai| yadi kATe gaye tathA varga AdhAravAle stUpa ke UparI tathA nimna - tala kI bhujAoM kA mApa kramazaH 'a' aura 'ba'' ho to ghanAkAra samAI kA sakSma rUpa se ThIka mApaU (a+ba'2+2 aba') ke barAbara batalAyA jA sakatA hai, jahA~

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254] gaNitasArasaMgrahaH [8.123 atroddezakaH samacaturazrA vApI viMzatiruparIha SoDazaiva tle| vedho nava kiM gaNitaM gaNitavidAcakSva me zIghram // 123 / / vApI samatribAhurvizatiruparIha SoDazaiva tale / vedho nava kiM gaNitaM karmAntikamauNDUmapi ca sUkSmaphalam / / 133 / / samavRttAsau vApI viMzatiruparIha SoDazaiva tle| vedho dvAdaza daNDAH kiM syAtkarmAntikauNDrasUkSmaphalam / / 143 / / AyatacaturazrasyatvAyAmaHSaSTireva vistaarH| dvAdaza mukhe tale'dhaM vedho'STau kiM phalaM bhavati // 15 // navatirazItiH saptatirAyAmazcordhvamadhyamUleSu / vistAro dvAtriMzat SoDaza daza sapta vedho'yam / / 163 / / udAharaNArtha prazna eka aisA kUpa hai jisakA chedIya ( sectional ) kSetra samabhuja caturbhuja hai| UparI (mukha) chedIya kSetra kI bhujAoM meM se pratyeka kA mAna 20 hasta hai aura nitala ( bottom ) chedIya kSetra kI pratyeka bhujA 16 hasta kI hai| gaharAI (vedha) 9 hasta hai| he gaNitajJa, ghanaphala kA mApa zIghra batalAo // 12 // samabhuja tribhujIya anuprastha chedavAle kUpa ke UparI chedIya kSetra kI bhujAoM meM se pratyeka 20 hasta kI aura nitala chedIya kSetra kI bhujAoM meM se pratyeka 16 hasta kI hai; gaharAI 9 hasta hai / kAntika ghanaphala, auNDra ghanaphala aura sUkSma rUpa se ThIka ghanaphala kyA-kyA haiM ? // 133 // samavRtta AkAra ke chedIya kSetravAle kUpa ke UparI chedIya kSetra kA nyAsa 20 daMDa aura nimna chedIya kSetra kA vyAsa 16 daMDa hai| gaharAI 12 daMDa hai / kAMtika, auNDra aura sUkSma ghanaphala kyA ho sakate haiM ? // 13 // ___ AyatAkAra chedIya kSetra vAle khAta ke UparI chedIya kSetra kI laMbAI 60 hasta aura caur3AI 12 hasta hai, tathA nimna chedIya kSetra kI lambAI Upara ke chadIya kSetra kI AdhI hai. aura caur3AI bhI AdhI hai| gaharAI 9 hasta hai| yahA~ ghanaphala kyA hai ? // 153 // ___ isI prakAra ke eka aura dUsare kUpa ke UparI chedIya kSetra, bIca ke chedIya kSetra aura nimna chedIya kSetra kI lambAIyA~ krazamaH 90,80 aura 70 hasta haiM, tathA caur3AIyA~ kramazaH 32,16 aura 10 hasta haiM / yaha gaharAI meM 7 hasta hai / iSTa ghanaphala kA mApa do ? // 163 // 'U vipATita stUpa kI U~cAI hai / ghanAkAra samAI ke sUkSma mApa ke liye diye gaye isa sUtra kA satyApana karmAtika aura auNDU phaloM ke nimnalikhita mAnoM kI sahAyatA se kiyA jAtA hai| / + 2 kA " 2 ) A = (a) + (ba' )2 4U, isI prakAra, sama tribhujAkAra evaM AyatAkAra AdhAravAle tiryaka chinna ( truncated ) stUpa tathA sama vRttAkAra AdhAra vAle tiryak chinna zaMkuoM ke saMbaMdha meM bhI satyApana kiyA jA sakatA hai|

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-8. 193] khAtavyavahAraH [255 vyAsaH SaSTirvadane madhye triMzattale tu paJcadaza / samavRttasya ca vedhaH SoDaza kiM tasya gaNitaphalam // 17 // tribhujasya mukhe'zItiH SaSTimadhye tale ca paJcAzat / bAhutraye'pi vedho nava kiM tasyApi bhavati gaNitaphalam // 18 // khAtikAyAH khAtagaNita phalAnayanasya ca khAtikAyA madhye sUcImukhAkAravat utsedhe sati khAtagaNitaphalAnayanasya ca sUtramparikhAmukhena sahito viSkambhastribhujavRttayostriguNAt / AyAmazcaturazre caturguNo vyAsasaMguNitaH / / 193 // samavRtta AkAra ke chedIya kSetra vAle khAta ke saMbaMdha meM mukha vyAsa 60 hasta hai, madhya vyAsa 30 hasta aura tala vyAsa 15 hasta hai| gaharAI 16 hasta hai| ghana phala kA mApa dene vAlA gaNita phala kyA hai ? // 17 // tribhujAkAra ke chedIya kSetravAle khAta ke sambandha meM, pratyeka bhujA kA mApa Upara 80 hasta, madhya meM 60 hasta aura talI meM 50 hasta hai| gaharAI 9 hasta hai| (ghanAkAra samAI denevAlA) ghanaphala kyA hai ? // 17 // kisI khAta kI ghanAkAra samAI ke mAna, tathA madhya meM sUcI mukhAkAra ke samAna utsedha sahita (Thosa miTTo kA gopucchavat eka aMta kI ora ghaTane vAle prakSepa projetion) sahitakhAta kI ghanAkAra samAI ke mAna ko nikAlane ke liye niyama__kendrIya puMja kI caur3AI ko veSTita khAta kI UparI caur3AI dvArA bar3hAkara, aura taba tIna dvArA guNita karane para, tribhujAkAra aura vRtAkAra khAtoM kI iSTa parimiti kA mAna utpanna hotA hai| caturbhujAkAra khAta ke sambandha meM, iSTa parimiti ke usI mAna ko, pUrvokta vidhi ke anusAra, caur3AI ko cAra dvArA guNita karane se prApta karate haiM // 19 // (193-203 ) ye zloka kisI bhI AkAra ke kendrIya puMja ke cAroM ora khodI gaI khAIyoM yA khAtoM ke ghanAkAra samAI ke mApa viSayaka haiM / kendrIya puMja ke cheda kA AkAra varga, Ayata, samabhuja tribhuja athavA vRtta sadRza ho sakatA hai| khAta (talI meM aura Upara ) donoM jagaha samAna cauDAI kA ho sakatA hai, athavA ghaTanevAlI yA bar3hanevAlI caur3AI kA ho sakatA hai| yaha niyama, ina sabhI tIna dazAoM meM, khAta kI kucha lambAI nikAlane meM sahAyaka hotA hai| (1) jaba khAta kI caur3AI samAMga (Upara nIce eka sI) ho, taba khAta kI laMbAI (da+ba)x3 hotI hai, jaba ki sama tribhujAkAra athavA vRttAkAra cheda ho / yahA~ 'da' kendrIya puMja kI bhujA kA mApa athavA vyAsa kA mApa hai, aura 'ba' khAta kI caur3AI hai| parantu yaha laMbAI =(da+ba)44 hotI hai, jaba ki cheda vargAkAra tathA kendrIya puMjavAlA vargAkAra khAta hotA hai| (2) yadi khAta talI meM yA Upara jAkara bindu rUpa ho jAtA ho, to kautika phala nikAlane ke liye, laMbAI = ( da +5)43 athavA ( da +4)x4 hotI hai, jaba kendrIya puccha kA cheda ( section ) ( 1 ) tribhujAkAra yA vRttAkAra athavA ( 2 ) vargAkAra hotA hai / auMDra phala prApta karane ke lie khAta kI lambAI kramazaH (da+ba)43 aura (da+ba)X4 lete haiN| ghanaphaloM nikAlane ke lie, ina bIja vAkyoM ko khAta kI AdhI caur3AI aura gaharAI se guNA

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265 -8. 553] khAtavyavahAraH bhUmimukhe dviguNe mukhabhUmiyute'bhagnabhUdayayutone / daiyodayaSaSThAMzaghne sthitapatiteSTakAH krameNa syuH / / 543 / / atroddezakaH prAkAro'yaM malAnmadhyAvartena caikahastaM gatvA / karNAkRtyA bhagnaH katISTakAH syuH sthitAzca patitAH kaaH|| 563 / / talI kI caur3AI aura UparI caur3AI meM se pratyeka ko duganA kiyA jAtA hai| inameM kramazaH Upara kI caur3AI aura talI kI caur3AI jor3I jAtI hai / pariNAmI rAziyA~, kramazaH, apatita bhAga kI dIvAla ko jamIna se Upara kI U~cAI dvArA bar3hAI va ghaTAI jAtI hai; aura isa prakAra prApta rAziyA~ laMbAI dvArA tathA saMpUrNa U~cAI ke bhAga dvArA guNita kI jAtI haiN| isa prakAra zeSa apatita bhAga tathA patita bhAga meM krama se iMToM kI saMkhyAe~ prApta hotI haiM // 54 // udAharaNArtha prazna __ pUrvokta mApa vAlI yaha kile kI dIvAla cakravAta vAyu se TakarAI jAkara talI se tiryaka rUpa . se vikarNa cheda para TUTa jAtI hai| isake saMbaMdha meM, sthita aura patita bhAga kI iMToM kI saMkhyAe~ kyAkyA haiM ? // 55 // vahI UMcI dIvAla cakravAta vAyu dvArA talI se eka hasta Upara se tiryaka rUpa se TUTI hai / sthita aura patita bhAga kI IToM kI saMkhyAeM kauna-kauna haiM / / 56 // (543) yadi talI kI caur3AI 'a' ho, Upara kI caur3AI 'ba' ho, 'U' kula U~cAI ho aura dIvAla kI laMbAI 'la' ho, tathA 'da jamIna se nApI gaI apatita dIvAla kI UMcAI ho: to (2a + ba+da ) aura (2va + a - da ) rAziyA~ sthita bhAga aura patita bhAga meM IToM kI saMkhyAoM kA nirUpaNa karatI haiN| isa sUtra se milatA julatA pratipAdana cInI graMtha cyu-cAMga suAna-cu meM haiM, jisake viSaya meM kUlija kI abhyukti hai, "yaha vicitra rUpa se varNita Thosa (solid) tribhujAkAra laMba samapArzva ( traingular right prism ) kA samacchinnaka hai, aura hameM yaha sUtra prApta hotA hai ki yaha ghanaphala samapArzva ke AdhAra para sthita una stU poM ke yoga ke tulya hotA hai, jinake zikhara sammukha phalaka ( face ) meM hote haiN| yaha sabase adhika hRdaya bhaMjaka sAdhyoM meM se eka hai, jinheM hama prArambhika Thosa jyAmiti meM par3hAte haiN| isake AviSkAra kA zreya lejAnDU (Legendre) ko . 12 diyA gayA hai"-J. L. Coolidge, A History of Geometrical Methods, p. 22, Oxford, (1940 ). dI gaI AkRti gAthA (zloka) 561 meM kathita dIvAla ko darzAtI hai; aura ka kha ga gha vaha samatala hai jisa para se dIvAla TUTate samaya bhagna hotI hai / ga0 sA0 saM0-34

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-8. 253 ] khAtavyavahAraH [257 utsedhe bahuprakAravati sati khAtaphalAnayanasya ca, yasya kasyacit khAtaphalaM jJAtvA tatkhAtaphalAt anyakSetrasya khAtaphalAnayanasya ca sUtramvedhayutiH sthAnahRtA vedho mukhaphalaguNaH svakhAtaphalaM / tricaturbhujavRttAnAM phalamanyakSetraphalahRtaM vedhaH / / 233 / / atroddezakaH samacaturazrakSetre bhuumicturhstmaatrvistaare| tatraikadvitricaturhastanikhAte kiyAn hi samavedhaH / / 243 / / samacaturazrASTAdazahastabhujA vApikA cturvedhaa| vApI tajjalapUrNAnyA navabAhAtra ko vedhaH / / 253 / / yasya kasyacitkhAtasya UrdhvasthitabhujAsaMkhyAM ca 'adhaHsthitabhujAsaMkhyAM ca utsedhapramANaM ca jJAtvA, tatkhAte iSTotsedhasaMkhyAyAH bhujAsaMkhyAnayanasya, adhaHsUcivedhasya ca saMkhyAnayanasya sUtram kisI khAta kI ghanAkAra samAI nikAlane ke liye niyama, jabaki vibhinna binduoM para khAta kI gaharAI badalatI hai, athavA jabaki ghanAkAra samAI samAna karane ke liye dUsare jJAta kSetraphala ke saMbaMdha meM Avazyaka khudAI kI gaharAI para khAta kI ghanAkAra samAI jJAta hai vibhinna sthAnoM meM mApI gaI gaharAiyoM ke yoga ko una sthAnoM kI saMkhyA dvArA bhAjita kiyA jAtA hai| isase ausata gaharAI prApta hotI hai| ise khAta ke UparI kSetraphala se guNita karane para tribhujAkAra, caturbhujAkAra athavA vRttAkAra cheda vAle kSetraphala sambandhI khAta kI ghanAkAra samAI utpanna hotI hai| diye gaye khAta kI ghanAkAra samAI, jaba dUsare jJAta kSetraphala ke mAna dvArA bhAjita kI jAtI hai, taba vaha gaharAI prApta hotI hai, jahA~ taka khudAI hone para pariNAmI ghanAkAra samAI eka-sI ho jAtI ho // 23 // udAharaNArtha prazna kisI samabhuja caturbhuja kSetra meM, jisake dvArA veSTita maidAna vistAra meM (laMbAI aura caur3AI meM) 4 hasta mApa kA hai, khAteM cAra bhinna dazAoM meM kramazaH 1, 2, 3 aura 4 hasta gaharI haiM / khAtoM kI ausata gaharAI kA mApa kyA hai ? // 24 // samabhuja caturbhuja kSetra jisakA cheda hai, aise kUpa kI bhujAe~ mApa meM 18 hasta haiN| usakI gaharAI 4 hasta hai / isa kUpa ke pAnI se dUsarA kUpa, jisake cheda kI pratyeka bhujA 9 hasta kI hai, pUrI taraha bharA jAtA hai / isa dUsare kUpa kI gaharAI kyA hai ? // 25 // jaba kisI diye gaye khAta ke saMbaMdha meM UparI chedIya kSetra kI bhujAoM ke mApa tathA nimna chedIya kSetra kI bhujAoM ke mApa jJAta hoM, aura jaba gaharAI kA mApa bhI jJAta ho, taba kisI cunI huI gaharAI para pariNAmI nimna cheda kI bhujAoM ke mAna ko prApta karane ke liye, tathA yadi talI kevala eka bindu meM ghaTakara raha jAtI ho, taba khAta kI pariNAmI gaharAI ko prApta karane ke liye niyama ga0 sA0 saM0-33

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258 ] gaNitasArasaMgrahaH mukhaguNavedho mukhatalazeSahRto'traiva sUcivedhaH syAt / viparIta vedhaguNamukhatalayutyavalambahRdvayAsaH || 263 / / atrodezakaH samacaturazrA vApI viMzatirUrdhve caturdazAdhAzca / vedho mukhe navAdhastrayo bhujAH ke'tra sUcivedhaH kaH / / 273 / / golAkAra kSetrasya phalAnayanasUtram [ 8. 26 Upara kI bhujA ke diye gaye mApa ke sAtha dI gaI gaharAI kA guNA karane para pariNAmasvarUpa prApta hone vAlA guNanaphala jaba UparI bhujA aura talI kI bhujA ke mApoM ke aMtara dvArA bhAjita kiyA jAtA hai, taba taka bindu ( arthAt jaba talI aMta se bindu rUpa raha jAtI ho ) kI dazA meM iSTa gaharAI utpanna hotI hai / bindurUpa talI se Upara kI ora iSTa sthiti taka mApI gaI gaharAI ko Upara kI bhujA ke mApa dvArA guNita karate haiM / taba prAptaphala ko bindurUpa talI kI ( yadi ho to ) bhujA ke mApa tathA Upara se lekara bindurUpa talI taka kI ) kula gaharAI ke yoga dvArA bhAjita karane se khAta kI iSTa gaharAI para bhujA kA mApa utpanna hotA hai / / 265 // udAharaNArtha eka prazna I samabhuja caturbhujAkAra AkRti ke chedavAlI eka vApikA hai / UparI bhujA kA mApa 20 hai, aura talI meM bhujA kA mApa 14 hai / AraMbha meM gaharAI 9 hai / yaha gaharAI nIce kI ora 3 aura bar3hAI jAne para talI kI bhujA kA mApa kyA hogA? yadi talI aMta meM bindu rUpa ho jAtI ho, to gaharAI kA mApa kyA hogA ? // 273 // golAkAra kSetra se veSTita jagaha kI ghanAkAra samAI kA mAna nikAlane ke liye niyama ( 263 ) isa zloka meM varNita kiye gaye prazna ye haiM (a) ulTAye gaye stUpa yA zaMku (cone) kI kula U~cAI nikAlanA, (ba) jaba kisI kATe gaye stUpa yA zaMku kI U~cAI aura UparI tathA nIce ke taloM kA vistAra diyA gayA hotA hai, taba kisI iSTa gaharAI para cheda ( section ) ke vistAra ko nikAlanA / tulanAtmaka adhyayana ke liye triloka prajJapti ( 1 / 194, 4 / 1794 ) tathA jambUdvIpa prazati ( 1, 27, 29 ) dekhiye yadi vargAkAra AdhArakhAle ruMDita ( kATe gaye ) stUpa meM AdhAra kI bhujA kA mApa 'a' UparI tala kI bhujA kA mApa 'ba' U~cAI 'u' ho to yahA~ diye gaye niyamAnusAra, kucha stUpa aura kisI dI gaI U~cAI u, para stUpa ke cheda kI bhujA kA aX u a - ba kI U~cAI U lekara U = .a (U- u mApa = U hotA hai / ye sUtrazaMku ke liye bhI prayojya hote haiM / stUpa ke bindurUpI bhAga ko banAnevAlI cheda kI bhujA kA mApa niyamAnusAra, dUsare sUtra ke hara U meM jor3A jAtA hai, kyoMki kucha dazAoM meM stUpa nizcaya rUpa se bindu meM prahAsita nahIM hotaa| jahA~ vaha bindu meM prahAsita nahIM hotA vahI~ isa bhujA kA mApa zUnya lenA par3atA hai /

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259 -8. 303] khAtavyavahAraH vyAsArdhaghanArdhaguNA nava golavyAvahArikaM gaNitam / taddazamAMzaM navaguNamazeSasUkSmaM phalaM bhavati // 28 // atroddezakaH . SoDazaviSkambhasya ca golakavRttasya vigaNayya / kiM vyAvahArikaphalaM sUkSmaphalaM cApi me kathaya // 293 / / zRMgATakakSetrasya khAtavyAvahArikaphalasya khAtasUkSmaphalasya ca sUtrambhujakRtidalaghanaguNadazapada navahRvyAvahArikaM gaNitam / triguNaM dazapadabhaktaM zRGgATakasUkSmaghanagaNitam / / 303 / / udAharaNArtha prazna arddha vyAsa ke dhana kI arddharAzi, 9 dvArA guNita hokara, golAkAra kSetra se veSTita jagaha kI ghanAkAra samAI kA sannikaTa mAna utpanna karatI hai| yaha sannikaTa mAna 9 dvArA guNita hokara aura 10 dvArA bhAjita hokara, zeSaphala kI upekSA karane para, ghanaphala kA sUkSma mApa utpanna karatA hai // 28 // kisI 16 vyAsa vAle gola ke saMbaMdha meM usake ghanaphala kA sannikaTa mAna tathA sUkSma mAna gaNanA kara batalAo // 29 // zraGgATaka kSetra (tribhujAkAra stUpa ) ke AkAra ke khAta kI ghanAkAra samAI ke vyAvahArika evaM sUkSma mAna ko nikAlane ke liye niyama, jabaki stUpa kI U~cAI AdhAra nirmita karane vAle samatribhuja ko bhujAoM meM se eka kI laMbAI ke samAna hotI hai ___ AdhArIya samabhuja tribhuja kI bhajA ke varga kI bharkharAzi ke ghana ko 10 dvArA gaNita kiyA jAtA hai / pariNAmI guNanaphala ke vargamUla ko 9 dvArA bhAjita kiyA jAtA hai| yaha sannikaTa iSTa mAna ko utpanna karatA hai / yaha sannikaTa mAna, jaba 3 dvArA guNita hokara 10 ke vargamUla dvArA bhAjita kiyA jAtA hai, taba stUpa khAta kI ghanAkAra samAI kA sUkSma rUpa se ThIka mApa utpanna hotA hai // 30 // ( 283 ) yahA~ diye gaye niyamAnusAra gola kA Ayatana (1) sannikaTa rUpa se (6) hotA hai aura (2) sUkSma rUpa se (6)xx hotA hai| kisI gola ke Ayatana ke ghanaphala kA zuddha sUtra ga ( trijyA ) hai / yaha Upara diye gaye mAna se tulanAyogya taba banatA hai, jabaki ga arthAt pArAdha kA anupAta / 10 liyA jAve / donoM hastalipiyoM meM 'tannavamAMza darza guNaM likhA hai, vyAsa jisase spaSTa hotA hai ki sUkSma mAna, sannikaTa mAna kA guNA hotA hai| parantu yahA~ graMtha meM taddazamAMzaM nava guNaM liyA gayA hai, jo sukSma mAna ko, sannikaTa kA batalAtA hai| yaha saralatApUrvaka dekhA jA sakatA hai ki yaha gola kI ghanAkAra samAI ke mApa ke saMbaMdha meM sUkSmatara mApa detA hai, jitanA kI aura koI bhI mApa nahIM detaa| (303) isa niyamAnusAra tribhujAkAra stUpa kI ghanAkAra samAI ke vyAvahArika mAna ko bIjIya rUpa se nirUpita karane para a4/5 arthAt 15/20 prApta hotA hai, aura sUkSma mAna

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260 ] gaNitasArasaMgrahaH [ 8.313 atroddezakaH vyazrasya ca zRGgATakaSar3abAhughanasya gaNayitvA / kiM vyAvahArikaphalaM gaNitaM sUkSmaM bhavetkathaya // 313 // vApIpraNAlikAnAM vimocane tattadiSTapraNAlikAsaMyoge tajjalena vApyAM pUrNAyAM satyAM tattatkAlAnayamasUtram - vApIpraNAlikAH svasvakAlabhaktAH svrnnvicchedaaH| - tadyutibhaktaM rUpaM dinAMzakaH syAtpraNAlikayutyA // tadinabhAgahatAste tajjalagatayo bhavanti tadvApyAm // 33 / / atroddezaka: catasraH praNAlikAH syustatraikaikA prapUrayati vApIm / dvitricatuHpaJcAMzairdinasya katibhirdinAMzaistAH // 34 // ____ trairAzikAkhyacaturthagaNitavyavahAre sUcanAmAtrodAharaNameva; atra samyagvistArya pravakSyate ___ udAharaNArtha prazna jisako laMbAI hai aise AdhArIya tribhuja ke tribhujAkAra stUpa ke ghanaphala kA vyAvahArika aura sUkSma mAna gaNanA kara batalAo // 31 // jaba kisI kUpa meM jAne vAle sabhI nala khule hue hoM, taba kUpa ko pAnI se pUrI taraha bhara jAne kA samaya prApta karane ke liye niyama, jabaki koI mana se cunI huI saMkhyA kI praNAlikAe~ vApikA ko bharane ke liye lagAI gaI hoM pratyeka nala ko nirUpita karane vAlI saMkhyA 'eka', alaga-alaga, naloM se pratyeka ke saMvAdI samaya dvArA bhAjita kI jAtI hai / bhinnoM dvArA nirUpita pariNAmI bhajana phaloM ko samAna hara vAle bhitroM meM pariNata kara liyA jAtA hai| eka ko samAna hara vAle bhinnoM ke yoga dvArA bhAjita karane para, eka dina kA vaha bhinIya bhAga utpanna hotA hai, jisameM ki saba nalikAoM ke khule rahane para vApikA pUrI bhara jAtI hai| una samAna hara vAle bhinnoM ko dina ke isa pariNAmI bhinnIya bhAga dvArA guNita karane para usa vApikA meM lage hae vibhinna naloM meM se pratyeka ke pAnI ke bahAva kA alaga-alaga mApa utpana hotA hai // 32-33 // udAharaNArtha prazna kisI vApikA ke bhItara jAnevAlI 4 nalikAe~ haiN| unameM se pratyeka, vApikA ko kramazaH dina ke bhAga meM pUrI taraha bhara detI hai| kitane dinAMza meM ve saba nalikAe~ eka sAtha khulakara pUrI vApikA ko bhara sakeMgI, aura pratyeka kitanA-kitanA bhAga bhareMgI ? // 34 // isa prakAra kA eka prazna pahile ho sUcanArtha trairAzika nAmaka cauthe vyavahAra meM diyA gayA hai: usa prazna kA viSaya yahA~ vistAra pUrvaka diyA gayA hai| 12 x/2 prApta hotA hai / yahA~ stUpa kI U~cAI tathA AdhArIya samatribhuja kI eka bhujA kA mApa a hai / yaha saralatA pUrvaka dekhA jA sakatA hai ki ye donoM mAna zuddha mAna nahIM haiN| yahA~ diyA gayA vyAvahArika mAna, sUkSma mAna kI apekSA vizuddha mAna ke nikaTatara hai|

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khAtavyavahAra 361 - samacaturazrA vApI navahastaghanA nagasya tle| tacchikharAjaladhArA caturazrAGgalasamAnaviSkambhA // 35 // patitAgre vicchinnA tayA ghanA sAntarAlajalapUNoM / zailotsedhaM vApyAM jalapramANaM ca me hi // 36 // vApI samacaturazrA navahastaghanA nagasya tale / aGgulasamavRttaghanA jaladhArA nipatitA ca tacchikharAt / / 37 / / agre vicchinnAbhUttasyA vApyA mukhaM praviSTA hi / sA pUrNAntaragatajaladhArotsedhena zailasya / utsedhaM kathaya sakhe jalapramANaM ca vigaNayya // 383 / / samacaturazrA vApI navahastaghanA nagasya tle| tacchikharAjaladhArA patitAGgalaghanatrikoNA sA // 39 // vApImukhapraviSThA sAgre chinnAntarAlajalapUrNA / kathaya sakhe vigaNayya ca giryutsedhaM jalapramANaM ca / / 403 / / kisI parvata ke tala meM eka vApikA, samabhuja caturbhuja cheda vAlI hai, jisakA pratyeka vimiti (dimension) meM mApa 9 hasta hai| parvata ke zikhara se samAMga samabhuja bhujAvAle , aMgala caturbhuja chedavAlI eka jaladhArA bahatI hai| jyoMhI jaladhArA vApikA meM giratI hai, tyoMhI zikhara se jaladhArA TUTa jAtI hai / tisa para bhI, usake dvArA vaha vApikA pAnI se pUrI taraha bhara jAtI hai / parvata kI U~cAI tathA vApikA meM pAnI kA mApa batalAo // 35-36 // parvata kI talI meM samacaturazra chedavAlI vApikA hai, jisakA (tIna meM se ) pratyeka vimiti meM vistAra 9 hasta hai / parvata ke zikhara se, . aMgula vyAsa vAle samavRtta cheda vAlI jaladhArA bahatI hai| jyoMhI jaladhArA vApikA meM giranA prAraMbha karatI hai, tyoMhI zikhara se jaladhArA TUTa jAtI hai| utanI jaladhArA se vaha vApikA pUrI bhara jAtI hai| he mitra, mujhe batalAo ki parvata kI U~cAI kyA hai, aura pAnI kA mApa kyA hai ? // 37-383 // kisI parvata kI talI meM samacaturazra chedavAlI vApikA hai jisakA (tInoM meM se) pratyeka vimiti meM vistAra 9 hasta hai / parvata ke zikhara se, pratyeka bhujA 1 aMgula hai jisakI aise samatribhujAkAra chedavAlI jaladhArA bahatI hai| jyoMhI jaladhArA vApikA meM giranA prAraMbha karatI hai, syoMhI zikhara se jaladhArA TUTa jAtI hai| utanI jaladhArA se vaha vApikA pUrI bhara jAtI hai / he mitra, gaNanA kara mujhe batalAo ki parvata kI U~cAI kyA hai aura pAnI kA mApa kyA hai ? // 391-40 // (35-421) yahA~ adhyAya 5 ke 15-16 zloka meM diyA gayA prazna tathA usake noTa kA prasaMga diyA gayA hai| pAnI kA Ayatana kadAcit vAhoM meM vyakta kiyA gayA hai / (prathama adhyAya ke 36 se lekara 38 taka ke zlokoM meM diye gaye isa prakAra ke Ayatana mApa ke saMbaMdha meM sUcI dekhiye)| kannar3I TIkA meM yaha diyA gayA hai ki 1 ghana aMgula pAnI, 1 karSa ke tulya hotA hai| prathama adhyAya ke 41 veM zloka meM dI gaI sUcI ke anusAra, 4 karSa milakara eka pala hotA hai| usI adhyAya ke 44veM zloka ke anusAra 123 pala milakara eka prastha hotA hai, aura usI ke 36-37 zloka ke anusAra prastha aura vAha kA saMbaMdha jJAta hotA hai|

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262 gaNitasArasaMgrahaH samacaturazrA vApA navahastaghanA nagasya tale / aGgulavistArAGgulakhAtAGgulayugaladIrghajaladhArA // 413 / / patitAgre vicchinnA vaapiimukhsNsthitaantraaljlaiH|| sampUrNA syAdvApI giryutsedho jalapramANaM kim / / 423 / / iti khAtavyavahAre sUkSmagaNitam saMpUrNam / citigaNitam itaH paraM khAtavyavahAre citigaNitamudAhariSyAmaH / atra paribhASAhasto dIrgho vyAsastadardhamaGgula catuSkamutsedhaH / dRSTastatheSTakAyAstAbhiH karmANi kAryANi // 433 / / iSTakSetrasya khAtaphalAnayane ca tasya khAtaphalasya iSTakAnayane ca sUtrammukhaphalamudayena guNaM tadiSTa kAgaNitabhaktalabdhaM yat / citigaNitaM tadvidyAttadeva bhavatISTakAsaMkhyA // 443 / / kisI parvata kI talI meM samabhuja caturbhuja chedavAlA eka aisA kuA~ hai jisakA tInoM vimitiyoM meM vistAra 9 hasta hai| parvata ke zikhara se eka aisI jaladhArA bahatI hai, jo samAMga rUpa se talI meM , aMgula caur3I, 1 aMgula DhAlU khAta taloM para, aura do aMgula laMbAI meM zikhara para rahatI hai / jyoMhI jaladhArA kueM meM giranA prAraMbha karatI hai, tyoMhI zikhara para jaladhArA TUTa jAtI hai| utanI jaladhAra se vaha kuA~ pUrI taraha bhara jAtA hai| parvata kI U~cAI kyA hai ? aura pAnI kA pramANa kyA hai? // 411-423 // isa prakAra khAta vyavahAra meM sUkSma gaNita nAmaka prakaraNa samApta huaa| citi gaNita ( IMToM ke Dhera saMbaMdhI gaNita ) isake pazcAt hama khAta vyavahAra meM citi gaNita kA varNana kreNge| yahA~ iSTakA (iMTa ) ke ekaka (ikAI) saMbaMdhI paribhASA yaha hai (ekaka) iMTa, laMbAI meM eka hasta, caur3AI meM usakI AdhI, aura muTAI meM 4 aMgula hotI hai| aisI IMToM ke sAtha samasta kriyAe~ kI jAtI haiM / / 433 // kisI kSetra meM diye gaye khAta ko ghanAkAra samAI, tathA ukta ghanAkAra samAI kI saMvAdI IToM kI saMkhyA nikAlane ke liye niyama khAta ke mukha kA kSetraphala, gaharAI dvArA guNita kiyA jAtA hai / pariNAmI guNanaphala ko ikAI iMTa ke ghanaphala dvArA bhAjita kiyA jAtA hai| isa prakAra prApta bhajanaphala, iMTa ke Dhera kA (ghanaphala) mApa samajhA jAtA hai / vahI bhajanaphala iMToM kI saMkhyA kA mApa hotA hai // 443 / / (441) yahA~ ITa ke Dhera kA ghanaphala mApa spaSTataH ikAI ITa ke padoM meM diyA gayA hai|

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khAtavyavahAraH atrodezakaH vedaH samacaturazrA sASTabhujA hastanavakamutsedhaH / ghaTitA tadiSTakAbhiH katISTakAH kathaya gaNitajJa // 453 // aSTakarasamatrikoNanavahastotsedha vedikA racitA / pUrveSTakAbhirasyAM katISTakAH kathaya vigaNayya // 463 // samavRttAkRtivedirnavahastova karASTrakavyAsA ghaTiteSTakAbhirasyAM katISTakAH kathaya gaNitajJa // 47 // Ayatacaturazrasya tvAyAmaH SaSTireva vistAraH / paJcakRtiH SaD vedhastadiSTakAcitimihAcakSva // 483 // prAkArasya vyAsaH sapta caturviMzatistadAyAmaH / ghaTiteSTakAH kati syuzcacchrAyo viMzatistasya / / 493 // vyAsaH prAkArasyordhve SaDagho'thASTa tIrthakA dIrghaH / ghaTiteSTakAH kati syuzcacchAyo viMzatistasya / / 503 // dvAdaza SoDaza viMzatirutsedhAH sapta SaT ca paJcAdhaH / vyAsA mukhe catustridvikAJcaturviMzatidIrghaH / / 513 // udAharaNArtha prazna 8. 513] 263 samacaturazra chedavAlI eka uThI huI vedI hai, jisakI bhujA kA mApa 8 hasta aura U~cAI 9 hasta hai / vaha vedI IMToM kI banI huI hai| he gaNitajJa, batalAo ki usameM kitanI iSTakAe~ haiM ? / / 45 / / samabhuja tribhuja chedavAlI kisI vedI kI bhujA kA mApa 8 hasta aura U~cAI 9 hasta hai / yaha upayukta IMToM dvArA banAI gaI hai / gaNanAkara batalAo ki isa saMracanA meM kitanI iSTakAe~ haiM ? / / 463 // vRttAkAra chedavAlI eka vedI jisakA vyAsa 8 ista aura U~cAI 9 hasta hai, unhIM IMToM kI banI hai / he gaNitajJa, batalAo ki usameM kitanI IMTeM haiM ? / / 47 / / AyatAkAra chedavAlI kisI vedI ke saMbaMdha meM laMbAI 60 hasta, caur3AI 25 hasta aura U~cAI 6 hasta hai / usa IMTa ke Dhera kA mApa batalAo / / 48 / eka sImArUpa dIvAla moTAI (vyAsa) meM 7 hasta, laMbAI ( AyAma ) meM 24 hasta, U~cAI ucchrAya ) meM 20 hasta hai / use banAne meM kitanI iSTakAoM kI AvazyakatA hogI ? / / 493 / / * kisI sImArUpa dIvAla kI muTAI zikhara para 6 hasta aura talI meM hasta hai / usakI laMbAI 24 hasta aura U~cAI 20 hasta hai / use banAne meM kitanI iSTakAoM kI AvazyakatA hogI ? // 503 // saMbaMdha meM U~cAiyA~ tIna sthAnoM meM kramazaH 12, 16 kramaza: 7, 6 aura 5 tathA Upara 4, 3 aura 2 hasta hai; kisI pravaNa ( utAravAlI ) vedI ke aura 20 hasta haiM; talI meM caur3AI ke mApa laMbAI 24 hasta hai / Dhera meM iSTakAoM kI saMkhyA batalAo // 513 // (503 - 513) dIvAla kI ghanAkAra samAI prApta karane ke liye uparyukta 4 the zloka ke uttarArddha meM diye gaye citrAnusAra parigaNita ausata caur3AI ko upayoga meM lAte haiM, isaliye yahA~ karmAntika phala kA mAna vicArAdhIna ho jAtA hai / (513) yaha pravaNa vedI do aMtoM ( ends ) meM do UrdhvAdhara (laMbarUpa) samataloM dvArA sImita hai /

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264] gaNitasArasaMgrahaH [ 8.523iSTavedikAyAM patitAyAM satyAM sthitasthAne iSTakAsaMkhyAnayanasya ca patitasthAne iSTakAsaMkhyAnayanasya ca sUtram - mukhatalazeSaH patitotsedhaguNaH sklvedhhRtsmukhH|| mukhabhUmyobhUmimukhe pUrvoktaM karaNamavaziSTam // 523 // __ atroddezakaH dvAdaza dairghya vyAsaH paJcAdhazcordhvamekamutsedhaH / daza tasmin pazca karA bhagnAstatreSTakAH kati syustAH / / 533 // prAkAre karNAkAreNa bhagne sati sthiteSTakAnayanasya ca patiteSTakAnayanasya ca sUtram kisI patita ( bhanna hokara girI huI ) vedI ke saMbaMdha meM sthita bhAga meM (zeSa apatita bhAga meM) tathA patita-bhAga meM IToM kI saMkhyA alaga alaga nikAlane ke liye niyama UparI caur3AI aura talI kI caur3AI ke aMtara ko patita bhAga kI U~cAI dvArA guNita karate haiM, aura pUrNa U~cAI dvArA bhAjita karate haiN| isa pariNAmI bhajanaphala meM UparI caur3AI kA mAna jor3a diyA tA hai| yaha patita bhAga ke saMbaMdha meM AdhArIya caur3AI kA mApa tathA apatita bhAga ke saMbaMdha meM UparI caur3AI kA mApa utpanna karatA hai| zeSa kriyA pahale varNita kara dI gaI hai / / 523 / / udAharaNArtha prazna vedI ke saMbaMdha meM laMbAI 12 hasta hai, talI meM caur3AI 5 hasta hai; UparI caur3AI 1 hasta hai, UparI caur3AI 1 hasta hai, aura U~cAI sarvatra 10 hasta hai| 5 hasta U~cAI kA bhAga TUTa kara gira jAtA hai| usa patita aura apatita bhAga meM alaga-alaga kitanI aikika iSTakAe~ haiM ? / / 533 / / jaba kile kI dIvAla tiryaka rUpa se TUTI ho, taba sthita bhAga meM tathA patita bhAga meM iSTakAoM kI saMkhyA nikAlane ke liye niyama zikhara aura pArzva tala pravaNa ( DhAlU ) haiM / UparI abhinata tala ke uThe hue aMta para caur3AI 2 hasta hai, aura dUsare aMta para caur3AI 4 hasta hai (citra dekhiye ) / (523) sthita apatita bhAga kI UparI caur3AI kA mApa jo vedI ke patita bhAga kI nitala caur3AI ke samAna hai, bIjIya rUpa se (a-3) da + ba hai, jahA~ talI kI caur3AI 'a' aura UparI caur3AI 'ba' hai, saMpUrNa U~cAI 24 'u hai, aura 'da' vedI ke patita bhAga kI U~cAI hai| yaha sUtra samarUpa tribhujoM ke guNoM dvArA bhI saralatApUrvaka zuddha siddha kiyA jA sakatA hai| niyama meM kathita :kriyA Upara gAthA 4 meM pahile hI varNita kI jA cukI hai|

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khAtavyavahAraH 265 -8.553] bhUmimukhe dviguNe mukhbhuumiyute'bhgnbhuudyyutone| dairyodayaSaSThAMzaghne sthitapatiteSTakAH krameNa syuH // 543 / / atroddezakaH prAkAro'yaM mUlAnmadhyAvartena caikahastaM gatvA / kaNoMkRtyA bhagnaH katISTakAH syuH sthitAzca patitAH kaaH||563 // talI kI caur3AI aura UparI caur3AI meM se pratyeka ko duganA kiyA jAtA hai| inameM kramazaH Upara kI caur3AI aura talI kI caur3AI jor3I jAtI hai / pariNAmI rAziyA~, kramazaH, apatita bhAga kI dIvAla kI jamIna se Upara kI U~cAI dvArA bar3hAI va ghaTAI jAtI hai| aura isa prakAra prApta rAziyA~ laMbAI dvArA tathA saMpUrNa U~cAI ke bhAga dvArA guNita kI jAtI haiM / isa prakAra zeSa apatita bhAga tathA patita bhAga meM krama se iMToM kI saMkhyAe~ prApta hotI haiM // 543 / / udAharaNArtha prazna pUrvokta mApa vAlI yaha kile kI dIvAla cakravAta vAyu se TakarAI jAkara talI se tiryak rUpa , se vikarNa cheda para TUTa jAtI hai| isake saMbaMdha meM, sthita aura patita bhAga kI IMToM kI saMkhyAe~ kyAkyA haiM ? // 55 // vahI UMcI dIvAla cakravAta vAyu dvArA talI se eka hasta Upara se tiryaka rUpa se TUTI hai / sthita aura patita bhAga kI IMToM kI saMkhyAeM kauna-kauna haiM / / 563 // 6 (542) yadi talI kI caur3AI 'a' ho, Upara kI caur3AI 'ba' ho, 'U' kula U~cAI ho aura dIvAla kI laMbAI 'la' ho, tathA 'da' jamIna se nApI gaI apatita dIvAla kI U~cAI ho; to U ( 2a+va+da ) aura laU (2va + a - da ) rAziyA~ sthita bhAga aura patita bhAga meM IToM kI saMkhyAoM kA nirUpaNa karatI haiN| isa sUtra se milatA julatA pratipAdana cInI graMtha cyu-cAMga suAna-cu meM haiM, jisake viSaya meM kUlija ko abhyukti hai, "yaha vicitra rUpa se varNita Thosa (solid) tribhujAkAra laMba samapArzva ( traingular right prism ) kA samacchinnaka hai, aura hameM yaha sUtra prApta hotA hai ki yaha ghanaphala samapArzva ke AdhAra para sthita una stU poM ke yoga ke tulya hotA hai, jinake zikhara sammukha phalaka (face ) meM hote haiN| yaha sabase adhika hRdaya bhaMjaka sAdhyoM meM se eka hai, jinheM ga hama prArambhika Thosa jyAmiti meM par3hAte haiN| isake AviSkAra kA zreya lejAnDU ( Legendre) ko 12 diyA gayA hai"-J. L. Coolidge, A History of Geometrical Methods, p. 22, Oxford, (1940 ). dI gaI AkRti gAthA (zloka ) 565 meM kathita dIvAla ko darzAtI hai; aura ka kha ga gha vaha samatala hai jisa para se dIvAla TUTate samaya bhagna hotI hai| ga0 sA0 saM0-34

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266 ] gaNitasArasaMgrahaH [ 8.57 prAkAramadhyapradezotsedhe taravRddhayAnayanasya prAkArasya ubhayapArzvayoH tarahAnerAnayanasya ca sUtram egged veva tarapramANamekonam / mukhatalazeSeNa hRtaM phalameva hi bhavati tarahAniH // 573 // atrodezakaH prAkArasya vyAsaH sapta tale viMzatistadutsedhaH / ekenA ghaTitastaravRddhya ne karodayeSTakayA || 583 // samavRttAryAM vAyAM vyAsacatuSke'rdhayuktakara bhUmiH / ghaTiteSTakAbhirabhitastasyAM vedhastrayaH kAH syuH / ghaTiteSTakAH sakhe me vigaNayya brUhi yadi vetsi // 60 // iSTakAghaTitasthale adhastalavyAse sati UrdhvatalavyAse sati ca gaNitanyAyasUtramdviguNanivezo vyAsAyAmayuto dviguNitastadAyAmaH / Ayatacaturazre syAdutsedhavyAsasaMguNitaH // 61 // kile kI dIvAla kI kendrIya U~cAI ke saMbaMdha meM ( IMToM ke ) taloM kI bar3hatI huI saMkhyA ko nikAlane ke lie niyama, aura nIce se Upara kI ora jAte samaya dIvAla kI donoM pArzvoM kI caur3AI meM kamI hone se tahoM kI ghaTatI ( kI dara) nikAlane ke lie niyama - kendrIya cheda kI U~cAI, dI gaI iSTakA ( IMTa) kI U~cAI dvArA bhAjita hokara, iSTakAoM kI tI kA iSTa mApa utpanna karatI hai / yaha saMkhyA, eka dvArA hAsita hokara aura taba UparI caur3AI tathA nIce kI caur3AI ke aMtara dvArA bhAjita hokara, taloM ke mAna meM ( in terms of layers ) mApI gaI caur3AI kI ghaTatI kI dara ( rate ) ke mAna ko utpanna karatI hai // 573 // udAharaNArtha prazna kisI U~cI kile kI dIvAla kI talI meM caur3AI 7 hasta hai / usakI U~cAI 20 hasta hai / vaha isa taraha se banI huI hai ki Upara caur3AI 1 hasta rahe / 1 hasta U~cI iSTakAoM kI sahAyatA se kendrIya ( taloM ) kI vRddhi tathA caur3AI kI ghaTatI ( kI dara ) kA mApa batalAo // 583 // kisI samavRttAkAra 4 hasta vyAsa vAlI vApikA ke cAroM ora 13 hasta moTI dIvAla pUrvokta IMToM dvArA banAI jAtI hai / vApikA kI gaharAI 3 hasta hai / yadi tuma jAnate ho, to he mitra, batalAo ki banAne meM kitanI IMTeM lageMgI ? // 593 - 60 // kisI sthAna ke cAroM ora banI huI saMracanA kI ghanAkAra samAI kA mAna nikAlane ke lie niyama, jaba ki saMracanA kA adhastala vyAsa aura Urdhvatala vyAsa diyA gayA ho saMracanA kI ausata muTAI kI duganI rAzi meM datta vyAsAyAma ( laMbAI evaM caur3AI ) kA mApa jor3A jAtA hai / isa prakAra prApta yoga duganA kiyA jAtA hai / pariNAmI rAzi saMracanA kI kula laMbAI hotI haiM, jabaki vaha AyatAkAra rUpa meM hotI hai / yaha pariNAmI rAzi, dI gaI U~cAI aura pUrvokta ausata muTAI se guNita hokara, iSTa ghanaphala kA mApa utpanna karatI hai // 61 // (593 - 60 ) yahA~ pUrvokta zloka 433 meM kathita ekaka iSTakA mAnI gaI hai / yaha prazna zloka 573 meM diye gaye niyama ko nidarzita nahIM karatA hai / use isa adhyAya ke 193 - 203 aura 443 va zlokoM ke niyamAnusAra sAdhita kiyA jAtA hai /

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-8. 64 ] khAtavyavahAraH atroddezakaH vidyAdhara nagarasya vyAso'STau dvAdazaiva cAyAmaH / paJca prAkAratale mukhe tadekaM dazotsedhaH // 62 // iti khAtavyavahAre citigaNitaM samAptam / kacikAvyavahAraH itaH paraM RkacikAvyavahAramudAhariSyAmaH / tatra paribhASA - hastadvayaM SaDaGgulahInaM kiSkAhvayaM bhavati / iSTAdyantacchedanasaMkhyaiva hi mArgasaMjJA syAt // 63 // atha zAkAkhyadvyAdidrumasamudAyeSu vakSyamANeSu / vyAsodaya mArgANAmaGgula saMkhyA parasparannAptA / / 64 // udAharaNArtha prazna [ 267 vidyAdhara nagara ke nAma se jJAta sthAna ke saMbaMdha meM caur3AI 8 hai, aura laMbAI 12 hai / prAkAra dIvAla kI tI kI muTAI 5 aura mukha meM ( Upara kI ) muTAI 1 hai / usakI U~cAI 10 hai / isa dIvAla kA ghanaphala kyA hai ? // 62 // isa prakAra khAta vyavahAra meM citi gaNita nAmaka prakaraNa samApta huA / +++ kacikA vyavahAra isake pazcAt hama krakacikA vyavahAra ( lakar3I corane vAle Are se kie gaye karma saMbaMdhI kriyAoM) kA varNana kreNge| pAribhASika zabdoM kI paribhASAH 6 aMgula se hIna do hasta, kiSku kahalAtA / kisI dI gaI lakar3I ko Arambha se lekara chedana ( kATane ke rAstoM ke mApa ) kI saMkhyA ko mArga saMjJA dI gaI hai // 63 // taba kama se kama do prakAra kI zAka ( teak ) Adi ( prakAroM vAlI ) lakar3iyoM ke Dhera ke saMbaMdha meM caur3AI nApane vAlI aMguloM kI saMkhyA aura laMbAI nApane vAlI saMkhyA, tathA mArgoM ko nApane vAlI saMkhyA, ina tInoM ko Apasa meM guNita kiyA jAtA hai| pariNAmI guNanaphala hasta aMguloM kI saMkhyA ke varga dvArA bhAjita kiyA jAtA hai / krakacikA vyavahAra meM yaha paTTikA nAmaka kArya ke mApa ko utpanna karatA hai / zAka ( teak-wood ) Adi ( prakAravAlI ) lakar3iyoM ke saMbaMdha meM caur3AI tathA laMbAI nApanevAlI hasto kI saMkhyAe~ Apasa meM guNita kI jAtI haiM / pariNAmI guNanaphala rAzi mArgoM kI saMkhyA dvArA guNita kI jAtI hai, aura taba Upara nikAlI gaI paTTikAoM kI saMkhyA dvArA bhAjita kI jAtI hai| yaha Are ke dvArA kiye gaye karma kA saMkhyAtmaka mApa hotA hai // 64-66 // ( 63 - 673 ) 1 kiSku = 13 hasta / kisI lakar3I ke Tukar3e ko cIrane meM kisI iSTa rAste athavA rekhA kA nAma mArga diyA gayA hai| kisI lakar3I ke Tukar3e meM kATe gaye tala kA vistAra, sAmAnyataH use cIrane meM kiye gaye kAma kA mApa hotA hai, jaba ki kisI viziSTa kaThoratAvAlI (jise kaThoratA kA ekaka mAna liyA ho aisI ) lakar3I dI gaI ho / kATe gaye taka kA yaha vistAra kSetraphala ke

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[ 8.65 268] gaNitasArasaMgrahaH hastAGgulavargeNa kAkacike paTTikApramANa syAt / zAkAhayadrumAdidrumeSu pariNAhadairghyahastAnAm // 65 / / saMkhyA parasparAMnA mArgANAM saMkhyayA guNitA / tatpaTTikAsamAptA krakacakRtA karmasaMkhyA syAt / / 66 / / zAkArjunAmlavetasasaralAsitasarjaDuNDukAkhyeSu / zrIparNIplakSAkhyadrumeSvamISvekamArgasya / SaSNavatiraGgulAnAmAyAmaH kiSkureva vistAraH // 673 / / atroddezakaH zAkAkhyatarau dIrghaH SoDaza hastAzca vistAraH / sArdhatrayazca mArgAzcASTau kAnyatra karmANi / / 683 / / ____ iti khAtavyavahAre krakacikAvyavahAraH smaaptH| iti sArasaMgrahe gaNitazAstre mahAvIrAcAryasya kRtau saptamaH khAtavyahAraH smaaptH|| paTTikA ke mApa ko prApta karane ke lie, nimnalikhita nAma vAle vRkSoM se prApta lakar3iyoM ke saMbaMdha meM pratyeka dazA meM mArga 1 hotA hai, laMbAI 96 aMgula hotI hai, aura caur3AI 1 kiSku hotI hai; una vRkSoM ke nAma ye haiM-zAka, arjuna, amlavetasa, sarala, asita, sarja aura DuNDako, tathA zrIparNI aura lakSa // 67-671 // udAharaNArtha prazna kisI zAka lakar3I ke Tukar3e ke saMbaMdha meM laMbAI 16 hasta hai, caur3AI 33 hasta hai aura mArga ( arthAt cIrane vAle Are ke rAstoM kI) saMkhyA 8 hai| yahA~ Are ke kAma ke kitane ekaka (ikAiyA~) karma (kArya) pUrNa huA hai ? // 6 // isa prakAra khAta vyavahAra meM kacikA vyavahAra nAmaka prakaraNa samApta haa| isa prakAra mahAvIrAcArya kI kRti sArasaMgraha nAmaka gaNitazAstra meM khAtamyavahAra nAmaka saptama vyavahAra samApta huaa| vizeSa ekaka (ikAI) dvArA mApA jAtA hai| yaha ekaka paTTikA kahalAtA hai / paTTikA laMbAI meM 96 aMgula aura caur3AI meM 1 kiSku athavA 42 aMgula hotI hai| yaha saralatA pUrvaka dekhA jA sakatA hai ki isa prakAra paTTikA 7 varga hAtha ke barAbara hotI hai| + 4

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9. chAyAvyavahAraH zAntirjinaH zAntikaraH prajAnAM jagatprabhutisamastabhAvaH / yaH prAtihAryASTavivardhamAno namAmi taM nirjita zatrusaMgham // 1 // ____ AdI prAcyAdyaSTadiksAdhanaM pravakSyAmaHsaliloparitalavasthitasamabhUmitale likhedvattam / bimbaM svecchAzaGkadviguNitapariNAhasUtreNa / / 2 / / tadvattamadhyasthatadiSTaMzaGkozchAyA dinAdau ca dinAntakAle / tadvRttarekhAM spRzati krameNa pazcAtpurastAcca kakup pradiSTA / / 3 // tadigdvayAntargatatantunA likhenmatsyAkRti yAmyakuberadikasthAm / tatkoNamadhye vidizaH prasAdhyAzchAyaiva yAmyottaradigdazArdhajAH // 4 // 1. M meM tatvaH pATha hai| 9. chAyA vyavahAra ( chAyA saMbaMdhI gaNita ) jo prajA ko zAMti kAraka haiM (zAMti dene vAle haiM ), jagatprabhu haiM, samasta padArthoM ko jAnanevAle haiM, aura apane ATha prAtihAryoM dvArA (sadA) vardhamAna (mahanIya) avasthA ko prApta haiM-aise (karma) zatru saMgha ke vijetA zrI zAMtinAtha jinendra ko maiM namaskAra karatA huuN||1|| Adi meM, hama prAcI (pUrva ) dizA ko Adi lekara, ATha dizAoM ke sAdhana karane ke lie upAya batalAte haiM pAnI ke UparI sataha kI bhA~ti, kSaitija samatala vAlI samatala bhUmi para kendra meM sthita svecchA se cunI huI laMbAI vAlI zaMku lekara, usakI laMbAI ko dviguNita rAzi kI laMbAI vAle dhAge ke phande (loop) kI sahAyatA se eka vRtta khIMcanA cAhiye // 2 // isa kendra meM sthita iSTa zaMku kI chAyA dina ke Adi meM tathA dina ke anta samaya meM usa vRtta kI paridhi ko sparza karatI hai / isake dvArA, krama se, pazcima dizA aura pUrva dizA sUcita hotI hai // 3 // ina do nizcita kI gaI dizAoM kI rekhA meM dhAge ko rakhakara, usake dvArA uttara se dakSiNa taka vistRta matsyAkAra (saMtare kI kalI ke samAna ) AkRti khIMcanA caahie| isa matsyAkRti ke koNoM ke madhya se jAne vAlI sarala rekhA uttara aura dakSiNa dizAoM ko sUcita karatI hai / ina dizAoM ke madhya meM (sthita jagaha meM ) vidizAyeM prasAdhita kI jAtI haiM // 4 // (4) vaha dhAgA jisakI sahAyatA se matsyAkAra AkRti khIMcI jAtI hai, gAthA 2 meM diye

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27. gaNitasArasaMgrahaH ajadhaTaravisaMkramaNadyadalajabhaikyArdhameva vissuvdbhaa||43|| laGkAyAM yavakoTyAM siddhapurIromakApuryoH / viSuvadbhA nAstyeva triMzaddhaTikaM dinaM bhavettasmAt // 53 // dezeSvitareSu dinaM triMzannADyAdhikonaM syAt / meSadhaTAyanadinayostriMzaddhaTikaM dinaM hi sarvatra // 6 // dinamAnaM dinadalabhAM jyotizzAstroktamArgeNa / jJAtvA chAyAgaNitaM vidyAdiha vakSyamANasUtraudhaiH / / 73 // viSuvacchAyA yatrayatra deze nAsti tatratatra deze iSTazaGkoriSTakAlacchAyAM jJAtvA tatkAlAnayanasUtramchAyA saikA dviguNA tayA hRtaM dinamitaM ca pUrvAhe / aparAhne taccheSaM vijJeyaM sArasaMgrahe gaNite / / 83 // viSuvadbhA ( arthAt jaba dina aura rAta donoM barAbara hote haiM, usa samaya par3ane vAlI chAyA) vAstava meM una dinoM ke madhyAhna ( dopahara ) samaya prApta chAyA ke mApoM ke yoga kI AdhI hotI hai, jaba ki sUrya meSa rAzi meM praveza karatA hai, tathA jaba vaha tulA rAzi meM bhI praveza karatA hai // 43 // laMkA, yavakoTi, siddhapurI aura romakapurI meM aisI viSuvadA (equinoctial shadow) bilakula hotI hI nahIM hai aura isalie dina 30 ghaTI kA hotA hai // 51 // anya pradezoM meM dina mAna 30 ghaTI se adhika yA kama rahatA hai| jaba sUrya meSa rAzi aura tulA ( ghaTAyana ) rAzi meM praveza karatA hai, taba sabhI jagaha dina mAna 30 ghaTI kA hotA hai // 6 // jyotiSa zAstra meM varNita vidhi ke anusAra dina kA mApa tathA dina kI madhyAhna chAyA kA mApa samajha lene ke pazcAt, chAyA saMbaMdhI gaNita nimnalikhita niyamoM dvArA sIkhanA cAhie // 73 // aise sthAna ke saMbaMdha meM dina kA vaha samaya nikAlane ke lie niyama, jahA~ viSuvacchAyA nahIM hotI ho, tathA kisI diye gaye samaya para ( dopahara ke pahile athavA pazcAt ) kisI diye gaye zaMku kI chAyA kA mApa jJAta ho kisI vastu ( zaMku) kI U~cAI ke padoM meM vyakta chAyA ke mApa meM eka jor3A jAtA hai, aura isa prakAra pariNAmI yoga dugunA kiyA jAtA hai| pariNAmI rAzi dvArA pUrNa dinamAna bhAjita kiyA jAtA hai| yaha samajhanA cAhiye ki sArasaMgraha nAmaka gaNita zAstra ke anusAra, yaha prApta phala pUrvAhna aura aparAha ke zeSa bhAgoM (athavA dopahara ke pahile dina ke bIte hue bhAga aura dopahara ke pazcAt dina ke zeSa rahane vAle bhAga) ko utpanna karatA hai // 8 // gaye trijyA kI mApa meM kucha adhika laMbAI vAlA honA cAhiye / yadi 'ka pU aura 'ka pa' pArzva AkRti meM kramazaH pUrva aura pazcima dizA prarUpita karate hoM, to AkRti u kha da ga, kramazaH pU aura pa ko kendra mAna kara aura pU ga, tathA pakha trijyAe~ lekara cApa khIMcane se prApta hotI haiM, para gakAkha jaba ki pU ga aura pa kha Apasa meM barAbara hoM / bhujA uda jo pUrvokta AkRti ke koga kA ardhana karatI hai, kramazaH uttara aura dakSiNa dizA kA prarUpaNa karatI hai| (8) yadi vastu kI U~cAI u hai, aura usakI chAyA kI laMbAI cha hai, to dina kA bItA huA

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-9. 123] chAyAvyavahAraH 27. atrodezakaH pUrvAhne pauruSI chAyA triguNA vada kiM gatam / aparAhe'vazeSaM ca dinasyAMzaM vada priya // 9 // dinAMze jAte sati ghaTikAnayanasUtramaMzahataM dinamAnaM chedavibhaktaM dinAMzake jAte / pUrvAhne gatanADyastvaparAhe zeSanADyastu // 10 // atroddezakaH viSuvacchAyAvirahitadeze'STAMzo dinasya gataH / zeSazcASTAMzaH kA ghaTikAH syuH khAgminADyo'hnaH // 113 / / mallayuddhakAlAnayanasUtramkAlAnayanAddinagatazeSasamAsonitaH kAlaH / stambhacchAyA stambhapramANabhaktaiva pauruSI chAyA // 123 // ___ udAharaNArtha prazna kisI manuSya kI chAyA usakI U~cAI se 3 gunI hai / he priya mitra, .batalAo ki pUrvAhna meM bIte hue dina kA bhAga evaM aparAha meM zeSa rahane vAlA dina kA bhAga kyA hai ? // 9 // dina kA bhAga (jo bIta cukA hai, yA bItane vAlA hai) prApta ho cukane para ghaTikAoM kI saMvAdI saMkhyA ko nikAlane ke liye niyama dina mAna ke jJAta mApa ko. (pahile hI prApta ) dina ke bIte hue athavA bItane vAle bhAga kA nirUpaNa karane vAle bhinna ke aMza dvArA guNita karane aura hara dvArA bhAjita karane se, pUrvAhna ke saMbaMdha meM bItI huI ghaTikAe~ aura aparAha ke saMbaMdha meM bItane vAlI ghaTikAe~ utpanna hotI haiM // 10 // udAharaNArtha prazna aise pradeza meM jahA~ viSuvacchAyA nahIM hotI, dina ? bhAga bIta gayA hai, athavA aparAba ke saMbaMdha meM zeSa rahane vAlA dina kA bhAga hai| isa bhAga kI saMvAdI ghaTikAe~ kyA haiM ? dina meM 30 ghaTikAe~ mAna lI gaI haiM // 11 // mallayuddha kAla nikAlane ke lie niyama jaba dina ke bIte hue bhAga tathA bItane vAle bhAga ke yoga dvArA dina kI avadhi hAsita kara, use ghaTikAoM meM parivartita kiyA jAtA hai, taba iSTa samaya utpanna hotA hai| athavA bItanevAlA samaya ( niyamAnusAra ) yaha hai (cha) athavA 2 (kospA + 1) ' u jahA~ koNa A usa samaya para sUrya kA U~cAI nirUpaka koNa hai| yaha sUtra kevala A = 450, chor3akara A ke zeSa mAnoM ke liye sannikaTa dina kA samaya detA hai / jaba yaha koNa 90deg ke nikaTatara pahu~catA hai, taba sannikaTa dina kA samaya aura bhI galata hotA jAtA hai / yaha sUtra isa tathya para AdhArita hai ki kisI samakoNa tribhuja meM choTe mAnoM ke lie koNa sannikaTataH sammukha bhujAoM ke samAnupAtI hote haiN| sannikaTa x

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272] gaNitasArasaMgrahaH [9. 133atroddezakaH pUrvAhne zaGkasamacchAyAyAM mallayuddhamArabdham / aparAhe dviguNAyAM samAptirAsIca yuddhakAlaH kH|| 133 // ___ aparAdhasyodAharaNam dvAdazahastastambhacchAyA caturuttaraiva viNshtikaa|| tatkAle pauruSikacchAyA kiyatI bhavedgaNaka // 143 // viSuvacchAyAyukte deze iSTacchAyAM jJAtvA kAlAnayanasya sUtramzaGkayuteSTacchAyA madhyacchAyonitA dviguNA / tadavAptA zaGkamitiH pUrvAparayordinAMzaH syAt // 153 // atroddezakaH dvaadshaanggulshngkodydlcchaayaangguldvyii| iSTacchAyASTAGgulikA dinAMzaH ko gataH sthitaH / vyaMzo dinAMzo ghaTikAH kAstriMzannADikaM dinam / / 17 / / 1. kisI bhI hastalipi meM prApya nahIM hai / kisI stambha kI chAyA ke mApa ko staMbha kI U~cAI dvArA bhAjita karane para pauruSI chAyA mApa (usa manuSya kI chAyA kA mApa usakI nija kI U~cAI ke padoM meM ) prApta hotA hai| 121 // ____ udAharaNArtha prazna koI mallayuddha pUrvAhna meM Arambha huA, jaba ki kisI zaMku kI chAyA usI zaMku ke mApa ke tulya thii| usa yuddha kA nirNaya aparAhna meM huA, jabaki usI zaMku kI chAyA kA mApa zaMku ke mApa se dugunA thaa| batalAo ki yaha yuddha kitane samaya taka calA ? // 13 // zloka ke uttarArdha niyama ke liye udAharaNArtha prazna kisI 12 hasta U~cAI vAle staMbha kI chAyA mApa meM 24 hasta hai| usa samaya, he aMkagaNitajJa, manuSya kI chAyA kA mApa kyA hogA ? // 14 // jaba kisI bhI samaya para chAyA kA mApa jJAta ho, taba viSuvacchAyA vAle sthAnoM meM bIte hue athavA bItane vAle dina ke bhAga ko prApta karane ke liye niyama zaMku kI jJAta chAyA ke mApa meM zaMku kA mApa jor3A jAtA hai| yaha yoga viSuvacchAyA ke mApa dvArA hAsita kiyA jAtA hai, aura pariNAmI aMtara ko dugunA kara diyA jAtA hai| jaba zaMku kA mApa isa pariNAmI rAzi dvArA bhAjita kiyA jAtA hai, taba dazAnusAra pUrvAhna meM dina meM bIte hue athavA aparAha meM dina meM bItane vAle dinAMza kA mAna utpanna hotA hai // 15 // udAharaNArtha prazna 12 aMgula ke zaMku ke saMbaMdha meM viSuvacchAyA dopahara ke samaya (dina ke madhyAhna meM)2 aMgula hai, aura avalokana ke samaya iSTa ( jJAta ) chAyA 8 aMgula hai| dina kA kaunasA bhAga bIta gayA hai, aura kaunasA bhAga zeSa rahA hai ? yadi dina kA bItA huA bhAga athavA bItane vAlA bhAga hai, to usako saMvAdI ghaTikAe~ kyA haiM, jabaki dina 30 ghaTiyoM kA hotA hai // 16-17 // (11) yahA~ dina ke samaya ke mApa ke liye diyA gayA sUtra bIjIya rUpa 2 (cha+u-va)

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-9. 20] chAyAvyavahAra [273 iSTanADikAnAM chAyAnayanasUtramdviguNitadinabhAgahRtA zaGkumitiH zaGkhamAnonA / dyadalacchAyAyuktA chAyA tatsveSTakAlikA bhavati / / 18 // __ atroddezakaH dvAdazAGgulazaGkodyu dlcchaayaangguldvyo| dazAnAM ghaTikAnAM mA kA chizannADikaM dinam / / 19 / / pAdacchAyAlakSaNe puruSasya pAdapramANasya paribhASAsUtrampuruSonnatisaptAMzastatpuruSA'stu daiyaM syAt / yadyevaM cetpuruSaH sa bhAgyavAna ghribhA spaSTA // 20 // ArUDhacchAyAyAH saMkhyAnayanasUtram ghaTiyoM meM die gaye dina ke samaya ko saMvAdI chAyA kA mApa nikAlane ke niyama zaMku ( style ) kA mApa dina ke diye gaye bhAga ke mApa ko dugunI rAzi dvArA bhAjita kiyA jAtA hai| pariNAmI bhajanaphala meM se zaMku kA mApa ghaTAyA jAtA hai, aura usameM viSuvacchAyA ( dopahara ke samaya kI aise sthAna kI chAyA, jahA~ dina rAta tulya hote haiM) kA mApa jor3a diyA jAtA hai| yaha dina ke iSTa samaya para chAyA kA mApa utpanna karatA hai // 18 // udAharaNArtha prazna yadi kisI 12 aMgula vAle zaMku ke saMbaMdha meM, dhudalacchAyA (viSuvacchAyA)2 aMgula ho. to jaba 10 ghaTI dina bIta cukA ho athavA bItane vAlA ho usa samaya zaMku kI chAyA kA mApa kyA hai? dina kA mAna 30 ghaTiyA~ hotA hai // 19 // chAyA ke pAda pramANa mApa ke dvArA lie gaye mApoM saMbaMdhI manuSya ke pAda mApa kI paribhASA kisI manuSya kI U~cAI ke 1/7 bhAga ke tulya usake pAda kI laMbAI hotI hai| yadi aisA ho. to vaha manuSya bhAgyazAlI hogaa| isa prakAra pAda pramANa se nApI gaI chAyA kA mApa spaSTa hai||20|| UrdhvAdhara dIvAla para ArUr3ha chAyA kA saMkhyAtmaka mApa nikAlane ke liye niyama hai, jahA~ 'ka' zaMku kI viSuvacchAyA kI laMbAI hai| yaha sUtra Upara kI gAthA 81 meM diye gaye sUtra kI pAda TippaNI para AdhArita hai| (18) bIjIya rUpa se, 2gha cha = -- u+va, jahA~ gha, dina ke samaya kA mApa ghaTI meM diyA gayA hai| yaha sUtra zloka 153 veM kI pAda TippaNo meM diye gaye sUtra se prApta hotA hai| ga0 sA0 saM0-35

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274] gaNitasArasaMgrahaH [9.21 nRcchAyAhatazaGkurbhittistambhAntaronito bhaktaH / nRcchAyayaiva labdhaM zaGkobhittyAzritacchAyA // 21 // ___ atroddezakaH viMzatihastaH stambho bhittistambhAntaraM karA aSTau / puruSacchAyA dvighnA bhittigatA stambhamA kiM syAt // 22 / / stambhapramANaM ca bhittyArUDhastambhacchAyAsaMkhyAM ca jJAtvA bhittistambhAntarasaMkhyAnayanasUtrampuruSacchAyAnighnaM stambhArUDhAntaraM tayormadhyam / stambhArUDhAntarahRtatadantaraM pauruSI chAyA / / 23 / / zaMku kI U~cAI ( manuSya kI U~cAI ke padoM meM vyakta ) manuSya kI chAyA dvArA guNita kI jAtI hai| pariNAmI guNanaphala dIvAla aura zaMku ke bIca kI dUrI ke mApa dvArA hAsita kiyA jAtA hai| isa prakAra prApta aMtara manuSya kI uparyukta chAyA ke mApa dvArA bhAjita kiyA jAtA hai| isa prakAra prApta bhajanaphala zaMku kI chAyA ke usa bhAga kA mApa hotA hai jo dIvAla para ArUr3ha hai // 21 // udAharaNArtha prazna koI staMbha 20 hasta U~cA hai / isa staMbha aura dIvAla ke bIca kI dUrI (jo chAyA rekhAnusAra nApI jAtI hai) 8 hasta hai / usa samaya manuSya kI chAyA manuSya kI U~cAI se dugunI hai| staMbha kI chAyA kA vaha kauna-sA bhAga hai jo dIvAla para ArUr3ha hai ? // 22 // jaba dIvAla para ArUr3ha (par3o huI ) chAyA kA saMkhyAtmaka mAna tathA staMbha kI U~cAI. donoM jJAta hoM, taba dIvAla aura staMbha ke aMtara ( bIca kI dUrI) ke mApa ke saMkhyAtmaka mAna ko nikAlane ke liye niyama staMbha kI U~cAI aura dIvAla para ArUr3ha (par3I huI ) chAyA ke mApa kA aMtara ( manuSya kI U~cAI ke padoM meM vyakta ) puruSa kI chAyA ke mApa dvArA guNita hokara, ukta staMbha aura dIvAla ke aMtara kI mApa ko utpanna karatA hai / isa aMtara kA mAna, staMbha kI U~cAI aura dIvAla para ArUr3ha (par3I huI) chAyAMza mApa ke aMtara dvArA bhAjita kiyA jAne para, (manuSya ko U~cAI ke padoM meM vyakta) mAnavI chAyA kA mApa utpanna karatA hai // 23 // (21) bIjIya rUpa se, , jahA~ u zaMku kI U~cAI hai, a dIvAla para ArUr3ha chAyA kI U~cAI ke padoM meM vyakta manuSya kI chAyA kA mApa hai, aura sa staMbha (zaMku) aura dIvAla ke bIca kI dUrI hai| niyama kA spaSTIkaraNa pArzva meM ___ diye gaye citra dvArA ho jAtA hai| yaha bAta dhyAna meM rakhane yogya hai ki yahA~ staMbha aura dIvAla ke bIca kI dUrI chAyA rekhA para hI nApI jAnA caahie| (23 aura 26) isa niyama tathA 26 vI gAthA ke niyama meM 21 vIM gAthA meM diye gaye udAharaNoM kI viloma dazA kA ullekha hai| a- uba-sa - - - - - - -- ---- -----

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-9. 20] chAyAvyavahAraH 275 atroddezakaH viMzatihastaH stambhaH SoDaza bhittyAzritacchAyA / dviguNA puruSacchAyA bhittistambhAntaraM kiM syAt / / 24 / / aparArdhassodAharaNam viMzatihastaH stambhaH SoDaza bhittyaashritcchaayaa| kiyatI puruSacchAyA bhittistambhAntaraM cASTau // 25 // ArUDhacchAyAyAH saMkhyAM ca bhittistambhAntarabhUmisaMkhyAM ca puruSacchAyAyAH saMkhyAM ca jJAtvA stambhapramANasaMkhyAnayanasUtramnRcchAyAnArUDhA bhittistambhAntareNa saMyuktA / pauruSabhAhRtalabdhaM viduH pramANa budhAH stambhe // 26 // atroddezakaH SoDaza bhittyArUDhacchAyA dviguNaiva pauruSo chAyA / stambhotsedhaH kaH syAdbhittistambhAntaraM cASTau // 27 // udAharaNArtha prazna . eka staMbha 20 hasta U~cA hai, aura dIvAla para par3ane vAlI chAyA ke aMza kA mApa (UMcAI) 16 hasta hai| usa samaya puruSa kI chAyA pauruSI U~cAI se dugunI hai| staMbha aura dIvAla ke aMtara kA mApa kyA ho sakatA hai ? // 24 // niyama ke uttarArddha bhAga ke lie udAharaNArtha prazna koI staMbha U~cAI meM 20 hasta hai, aura dIvAla para par3ane vAlI usakI chAyA kI U~cAI 16 hai / dIvAla aura staMbha kA aMtara 8 hasta hai| pauruSo U~cAI ke pramANa dvArA vyakta mAnavI chAyA kA mApa kyA hai ? // 25 // jaba dIvAla para par3ane vAlI chAyA ke bhAga kI UMcAI kA saMkhyAtmaka mAna, usa staMbha tathA dIvAra kA aMtara, aura mAnuSI U~cAI ke padoM meM vyakta mAnuSI chAyA kA mApa bhI jJAta ho, taba staMbha kI U~cAI kA saMkhyAtmaka mAna nikAlane ke liye niyama dIvAla para par3ane vAlI chAyA ke bhAga kA mApa, mAnavI U~cAI ke padoM meM vyakta mAnavI chAyA ke mApa dvArA guNita kiyA jAtA hai| isa guNanaphala meM staMbha aura dIvAla ke aMtara ( bIca kI darI) kA mApa jor3A jAtA hai| isa prakAra prApta yoga ko mAnavI U~cAI ke padoM meM vyakta mAnavI chAyA ke mApa dvArA bhAjita karane se jo bhajanaphala prApta hotA hai vaha buddhimAnoM ke dvArA staMbha kI u~cAI kA mApa kahA jAtA hai // 26 // udAharaNArtha prazna dIvAla para staMbha kI chAyA par3ane vAlA bhAga 16 ista hai| usa samaya mAnavo chAyA kA mAna mAnavI U~cAI se dugunA hai| dIvAla aura staMbha kA aMtara 8 hasta hai| staMbha kI U~cAI kyA hai? // 27 //

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276] gaNitasArasaMgrahaH [9, 28 zaGkapramANazaGkucchAyAmizravibhaktasUtramzaGkapramANazaGkucchAyAmizraM tu saikpaurussyaa| bhaktaM zaGkumitiH syAcchaGkucchAyA tadUnamizraM hi / / 28 / / atroddezakaH zaGkapramANazaGkucchAyAmizraM tu paJcAzat / zaGkatsedhaH kaH syAccatuguNA pauruSI chAyA // 29 // 'zaGkucchAyApuruSacchAyAmizravibhaktasUtramzaGkanaracchAyayutirvibhAjitA zaGkusaikamAnena / labdhaM puruSacchAyA zaGkucchAyA tadUnamizra syAt // 30 // atroddezakaH zaGkorutsedho daza nRcchAyAzaGkubhAmizram / / pazcottarapaJcAzannRcchAyA bhavati kiyatI ca / / 31 / / __ zaMku kI U~cAI tathA zaMku kI chAyA kI laMbAI ke mApoM ke datta mizrita yoga meM se unheM alaga-alaga nikAlane ke lie niyama- zaMka ke mApa aura usakI chAyA ke mApa ke mizrita yoga ko jaba dvArA bar3hAye gaye ( mAnavI U~cAI ke padoM meM vyakta) mAnavI chAyA ke mApa dvArA bhAjita karate haiM, taba zaMku kI U~cAI kA mApa prApta hotA hai / diye gaye yoga ko zaMku ke isa mApa dvArA hAsita karane para zaMku kI chAyA kA mApa prApta hotA hai // 28 // udAharaNArtha prazna zaMku ke U~cAI mApa aura usakI chAyA ke laMbAI mApa kA yoga 50 hai| zaMku kI U~cAI kyA hogI, jabaki mAnavI chAyA usa samaya mAnavI U~cAI kI caumunI hai ? // 29 // zaMku kI chAyA kI lambAI ke mApa aura (mAnavI U~cAI ke padoM meM vyakta ) mAnavI chAyA ke mApake mizrita yoga meM se unheM alaga-alaga prApta karane ke lie niyama zaMku kI chAyA tathA manuSya kI chAyA ke mApoM ke mizrita yoga ko eka dvArA bar3hAI gaI zaMku kI jJAta U~cAI dvArA bhAjita karate haiN| isa prakAra prApta bhajanaphala (mAnavI U~cAI ke padoM meM vyakta) mAnavI chAyA kA mApa hotA hai| uparyukta mizrita yoga jaba mAnavI chAyA ke isa mApa dvArA hAsita kiyA jAtA hai, taba zaMku kI chAyA kI laMbAI kA mApa utpanna hotA hai // 30 // udAharaNArtha prazna kisI zaMku kI U~cAI 10 hai| ( mAnavI U~cAI ke padoM meM vyakta ) mAnavI chAyA aura zaMku kI chAyA ke mApoM kA yoga 55 hai| mAnavI chAyA tathA zaMku kI chAyA kI laMbAI kyA-kyA haiM ? // 3 // (28aura 30) yahA~ diye gaye niyama gAthA 121 ke uttarArddha meM kathita niyama para AdhArita haiN|

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-9.34 ] stambhasya avanatisaMkhyAnayanasUtramchAyAvargAcchodhyA narabhAkRtiguNita zaGkukRtiH / saikanaracchAyAkRtiguNitA chAyAkRteH zodhyA // 32 // tanmUlaM chAyAyAM zodhyaM narabhAnavargarUpeNa' / bhAgaM hRtvA labdhaM stambhasyAvanatireva syAt // 33 // atrodezakaH chAyAvyavahAraH dviguNA puruSacchAyAyuttaradazahastazaGkorbhA / ekonatriMzatsA stambhAvanatizca kA tatra / // 34 // 1. hastalipi meM naramAna ke lie nRbhAvarga pATha hai; parantu vaha chaMda kI dRSTi se azuddha hai / kisI staMbha athavA UrdhvAdhara zaMku kI avanati ( jhukAva ) ke mApa ko nikAlane ke lie niyama -- mAnavI chAyA ke varga aura zaMku kI U~cAI ke varga ke guNanaphala ko dI gaI chAyA ke varga meM ghaTAyA jAtA hai / yaha zeSa, mAnavI chAyA kI varga rAzi meM eka jor3ane se prApta yogaphala dvArA guNi kiyA jAtA hai / isa prakAra prApta rAzi dI gaI chAyA ke varga meM se ghaTAyI jAtI hai / pariNAmI zeSa ke vargamUla ko chAyA ke diye gaye mApa meM se ghaTAyA jAtA hai / isa prakAra prApta rAzi ko jaba mAnavI chAyA kI varga rAzi meM eka jor3ane se prApta yogaphala dvArA bhAjita kiyA jAtA hai, taba staMbha kI zuddha avanati ( jhukAva ) kA mApa prApta hotA hai // 32-33 // udAharaNArtha prazna isa samaya mAnavI chAyA mAnavI U~cAI se dugunI hai| staMbha kI chAyA 29 hasta hai, aura staMbha kI U~cAI 13 hasta hai / yahA~ staMbha kI avanati kA mApa kyA hai ? // 34 // prAsAda ke bhItara 32-33 ) mAnalo avanata ( jhuke hue ) staMbha kI sthiti aba dvArA nirUpita hai / mAnalo vahI staMbha UrdhvAdhara (laMbarUpa ) sthiti meM a da dvArA nirUpita hai / kramazaH a sa tathA a i unakI chAyA haiM / taba usa samaya mAnava kI chAyA aura usakI ai a U~cAI kA anupAta hogI / mAnalo yaha anupAta ra ke barAbara ada hai / ba se ada para girAyA gayA laMba ba ga avanata staMbha aba kI avanati nirUpita karatA hai| yaha saralatA pUrvaka dikhAyA jA sakatA hai ki V ( a ba ) 2 - ( ba ga ) 2 a sa - ba ga ada 1 = a i ra asa - V ( a sa ) 2 - { = pha / isase yaha dekhA jA sakatA hai ki [ 277 ( a sa ) - ( a ba ) 2 x ra } ( ra+- + 1, ra +1 1 ba ga= yahA~ diyA gayA niyama isI sUtra ke rUpa meM prarUpita hotA hai /

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gaNitasArasaMgrahaH 278 ] kazcidrAjakumAraH prAsAdAbhyantarasthaH san / pUrvAhne jijJAsurdinagatakAlaM naracchAyAm // 35 // dvAtriMzaddhasto jAle prAgbhittimadhya AyAtA / ravibhA pazcAdbhittau vyekatriMzatka rordhva dezasthA // 36 // tadbhittidvayamadhyaM caturuttaraviMzatiH karAstasmin / kAle dinagatakAlaM nRcchAyAM gaNaka vigaNayya / kathayacchAyAgaNite yadyasti parizramastava cet // 373 // samacaturazrAyAM dazahastaghanAyAM naracchAyA | puruSotsedhadviguNA pUrvA prAktaTacchAyA // 383 // tasmin kAle pazcAttAzritA kA bhavedgaNaka | ArUDhacchAyAyA AnayanaM vetsi cetkathaya // 393 // zaGkordIpacchAyAnayanasUtram - zaGkanitadIponnatirAptA zaGkapramANena / tallabdhahRtaM zaGkoH pradIpazaGkantaraM chAyA / / 403 / / [ 9.35 ThaharA huA koI rAjakumAra pUrvAhna dina meM bIte hue samaya ko jJAta karane kA, tathA ( mAnavI U~cAI ke padoM meM vyakta ) mAnavI chAyA ke mApa ko jJAta karane kA icchuka thA / taba sUrya kI razmi pUrva kI ora kI dIvAla ke madhya meM 32 hasta U~cAI para sthita khir3akI meM se Akara, pazcima ora kI dIvAla para 29 hasta kI U~cAI taka pdd'ii| una do dIvAloM kA aMtara 24 hasta hai / he chAyA praznoM se bhijJa gaNitajJa, yadi tumane chAyA-praznoM ( se paricita hone ) meM parizrama kiyA ho, to ( usa dina ) bIte hue dina ke samaya kA mApa aura usa samaya ( mAnavI U~cAI ke padoM meM vyakta ) mAnavI chAyA kA mApa batalAo / / 35-372 // pUrvAhna samaya mAnavI chAyA mAnavI U~cAI se dugunI hai / pratyeka vimiti meM ( dimension) 10 hasta vAle vargAkAra cheda ke UrdhvAdhara khAta ke saMbaMdha meM pUrvI dIvAla se utpanna, pazcimI dIvAla para par3ane vAlI ko U~cAI kyA hogI ? he gaNitajJa, yadi jAnate ho, to batalAo kI laMbarUpa dIvAla para ArUr3ha chAyA chAyA kA mApa kitanA hogA ? // 382-393 // kisI dIvAla ke prakAza ke kAraNa utpanna honevAlI zaMku kI chAyA ko nikAlane ke liye niyama: zaMku kI U~cAI dvArA hAsita dIpaka kI U~cAI ko zaMku kI U~cAI dvArA bhAjita karanA cAhiye / yadi isa prakAra prApta bhajanaphala ke dvArA dIpaka aura zaMku ke bIca ko kSaitija dUrI kI bhAjita kiyA jAya to zaMku kI chAyA kA mApa utpanna hotA hai // 402 // ( 35-372 ) yaha prazna zlokoM 83 aura 23 meM diye gaye niyamoM ke viSaya meM hai / ( 383 - 393 ) yaha prazna zloka 21 meM diye gaye niyamAnusAra hala kiyA jAtA hai / (403) bIjIya rUpa se kathita niyama yaha hai:-cha-sa ba - a " a jahA~ 'cha' zaMku kI chAyA kA

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-9. 44] chAyAvyavahAraH [279 atroddezakaH zaGkapradIpayormadhyaM SaNNavatyaGgulAni hi / dvAdazAGgulazaGkostu dIpacchAyAM vadAzu me SaSTirdIpazikhotsedho gaNitArNavapAraga // 42 // dIpazakuntarAnayanasUtramzaGkunitadIponnatirAptA zaGkuprAmANena / tallabdhahatA zaGkucchAyA zaGkapradIpamadhyaM syAt / / 43 // atroddezakaH zaGkucchAyAGgulAnyaSTau SaSTirdIpazikhodayaH / zaGkhadIpAntaraM brUhi gaNitArNavapAraga // 44 // dIponnatisaMkhyAnayanasUtram udAharaNArtha prazna kisI zaMku aura dIpaka kI kSaitija dUrI vAstava meM 96 aMgula hai| dIpaka kI lau kI U~cAI jamIna se 60 aMgula hai| he gaNitArNava (gaNita samadra) ke pAragAmI. mujhe zIghra hI 12 aMgula U~ce zaMku ke saMbaMdha meM dIpaka kI lau ke kAraNa utpanna hone vAlI chAyA kA mApa batalAo // 41-42 // dIpaka aura zaMku ke kSaitija aMtara ko prApta karane ke lie niyama ( jamIna se ) dIpaka kI U~cAI ko zaMku kI U~cAI dvArA hAsita kiyA jAtA hai| pariNAmI rAzi ko zaMku kI U~cAI dvArA bhAjita karate haiM / zaMku kI chAyA ke mApa ko, isa prakAra prApta bhajanaphala dvArA guNita karane para, dIpaka aura zaMku kA kSaitija aMtara prApta hotA hai // 43 // udAharaNArtha prazna zaMku kI chAyA kI laMbAI 8 aMgula hai| dIpa zikhA (dIpaka kI lau) kI (jamIna se) U~cAI 60 aMgula hai| he gaNitArNava ke pAragAmI, dIpaka aura zaMku ke kSaitija aMtara ke mApa ko btlaao||44|| dIpaka kI ( jamIna se Upara kI ) U~cAI ke saMkhyAtmaka mApa ko prApta karane ke liye niyama-- mApa hai, 'a' zaMku kI U~cAI kA mApa hai, ba dIpaka kI U~cAI kA mApa hai, aura 'sa' dopaka tathA zaMka ke bIca kA kSaitija aMtara hai| yaha sUtra pArzva meM dI gaI AkRti se spaSTa rUpa se siddha kiyA jA sakatA hai| (43) pichalI TippaNI meM upayoga meM lAye gaye pratIkoM ko hI upayoga meM lAkara, isa niyamAnusAra sa= chax hotA hai / (44) agale 46-47 veM zlokoM ke anusAra zaMku kI U~cAI kA diyA gayA mApa 12 aMgula hai|

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gaNitasArasaMgrahaH 280 ] zaGkucchAyAbhaktaM pradIpazaGkantaraM saikam / zaGkhapramANaguNitaM labdhaM dIponnatirbhavati / / 45 / / atroddezakaH zaGkucchAyAdvinighneva dvizataM zaGkadIpayoH / antaraM hyaGgulAnyatra kA dopasya samunnatiH // 46 // zaMku pramANamatrApi dvAdazAGgulakaM gate / jJAtvadAharaNe samyagvidyAtsUtrArthapaddhatim / / 47 / puruSasya pAdacchAyAM ca tatpAdapramANena vRkSacchAyAM ca jJAtvA vRkSonnateH saMkhyAnayanasya ca, vRkSonnatisaMkhyAM ca puruSasya pAdacchAyAyAH saGkhyAnayanasya ca sUtramsvacchAyayA bhaktAMnajeSTavRkSacchAyA punassaptabhirAhatA sA / vRkSonnatiH sAdrihRtA svapAdacchAyAhatA syAddrumabhaiva nUnam // 48 // [ 9. 45 dIpaka aura zaMku ke kSaitija aMtara ke mApa ko, zaMku kI chAyA dvArA bhAjita kiyA jAtA hai| taba isa pariNAmI bhajanaphala meM eka jor3A jAtA hai / isa prakAra prApta rAzi jaba zaMku kI U~cAI ke mApa dvArA guNita kI jAtI hai, taba dopaka kI ( jamIna se Upara kI ) U~cAI kA mApa utpanna hotA hai // 45 // udAharaNArtha prazna zaMku kI chAyA kI laMbAI usakI U~cAI se dugunI hai| dopaka aura zaMku kI kSaitija dUrI kA mApa 200 aMgula hai / isa dazA meM dIpaka kI jamIna se U~cAI kitanI hai ? isI tathA gata prazna meM zaMku kI U~cAI 12 aMgula lekara niyama ke sAdhana kA artha bhalIbhA~ti sIkha lenA cAhiye // 46-47 // meM dI gaI ) vRkSa kI chAyA kI laMbAI kA mApa jJAta hoM, mApa nikAlane ke lie niyama; sAtha ho jaba ( usI pAda mApa tathA manuSya kI chAyA ko laMbAI kA saMkhyAtmaka mApa kI chAyA kI laMbAI kA saMkhyAtmaka mApa nikAlane ke liye jaba manuSya kI ( pAda pramANa meM dI gaI ) chAyA kI laMbAI kA mApa tathA ( usI pAda pramANa taba usa vRkSa kI U~cAI kA saMkhyAtmaka pramANa meM ) vRkSa kI U~cAI kA saMkhyAtmaka jJAta ho, taba ( usI pAda pramANa meM ) vRkSa niyama kisI vyakti dvArA cune gaye vRkSa kI chAyA kI laMbAI ke mApa ko nija pAda pramANa meM nApI gaI usakI nija kI chAyA ke mApa dvArA bhAjita kiyA jAtA hai / isase vRkSa ko U~cAI prApta hotI hai / yaha vRkSa kI U~cAI 7 dvArA bhAjita hokara aura nija pAda pramANa meM nApI gaI nija kI chAyA dvArA guNita hokara, niHsandeha, vRkSa kI chAyA kI zuddha laMbAI ke mApa ko utpanna karatI hai // 48 // sa (45) isI prakAra, = ( + 1 )a (48) yaha niyama uparyukta 123 veM zloka ke uttarArddha meM diye gaye niyama kI yahA~ diye gaye niyama meM manuSya kI U~cAI aura usake pAda mApa ke bIca kA saMbaMdha gayA hai / viloma dazA hai / upayoga meM lAyA

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chAyAvyavahAraH [281 atroddezakaH AtmacchAyA catuHpAdA vRkSacchAyA zataM padAm / vRkSocchrAyaH ko bhavetsvapAdamAnena taM vada / / 49 // vRkSacchAyAyAH saMkhyAnayanodAharaNamAtmacchAyA catuHpAdA pazcasaptatibhiryutam / zataM vRkSonnativRkSacchAyA syAtkiyatI tadA // 50 // purato yojanAnyaSTau gatvA zailo dazodayaH / sthitaH pure ca gatvAnyo yojnaashiititsttH||51|| tadagrasthAH pradRzyante dIpA rAtrau pure sthitaiH / puramadhyasthazailasyacchAyA pUrvAgamUlayuk / asya zailasya vedhaH ko gaNakAzu prakathyatAm // 523 / / iti sArasaMgrahe gaNitazAsne mahAvIrAcAryasya kRtau chAyAvyavahAro nAma aSTamaH smaaptH|| // samApto'yaM saarsNgrhH|| udAharaNArtha eka prazna pAda mApa meM nija kI chAyA kI lambAI 4 hai| ( usI pAda mApa meM ) vRkSa kI chAyA kI lambAI 100 hai| batalAo ki ( usI pAda mApa meM ) vRkSa kI U~cAI kyA hai ? // 49 // kisI vRkSa kI chAyA ke saMkhyAtmaka mApa ko nikAlane ke saMbaMdha meM udAharaNa kisI samaya nija kI chAyA kI lambAI kA mApa nija ke pAda se caugunA hai| kisI vRkSa kI U~cAI ( aise pAda-mApa meM) 175 hai| usa vRkSa kI chAyA kA mApa kyA hai? // 50 // kisI nagara ke pUrva kI ora 8 yojana (dUrI) cala cukane ke pazcAt, 10 yojana U~cA zaila (parvata) milatA hai| nagara meM bhI 10 yojana U~cAI kA parvata hai / pUrvI parvata se pazcima kI ora 80 yojana cala cukane ke pazcAt , eka aura dUsarA parvata milatA hai / isa aMtima parvata ke zikhara para rakhe hue dIpa nagara nivAsiyoM ko dikhAI dete haiN| nagara ke madhya meM sthita parvata kI chAyA pUrvI parvata ke mUla ko sparza karatI hai| he gaNaka, isa (pazcimI ) parvata kI U~cAI kyA hai ? zIghra batalAo // 51-523 / / isa prakAra, mahAvIrAcArya kI kRti sAra saMgrahanAmaka gaNita zAstra meM chAyA nAmaka aSTama vyavahAra samApta huaa| isa prakAra yaha sArasaMgraha samApta huaa| (51-523 ) yaha udAharaNa uparyukta 45 veM zloka meM diye gaye niyama ko nidarzita karane ke liye hai|

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pariziSTa 1 saMkhyAoM kA abhidhAna karanevAle sAmAnya aura saMkhyAtmaka arthabodhaka saMskRta zabda zabda sAmAnya artha saMkhyA abhidhAna udgama akSi agni site The eye Aga Fire manuSya kI do A~kheM hotI haiN| 3 homAniyoM kI saMkhyA 3 hai, arthAt , gArhapatya, AhavanIya aura dakSiNa / zUnya ko chor3akara kevala 9 aGka hote haiN| vedoM ke adhyayana ke saMbaMdha meM 6 vibhAga hote haiM, arthAta . zikSA, kalpa, vyAkaraNa, nirukta, chandas , jyotiSa / aGka saMkhyA Number vijJAna kA eka vibhAga An auxiliary division or department of science parvata A mountain aGga acala paurANika bhUgola meM mAne gaye 7 mukhya parvata jo kulAcala kahalAte haiM; arthAt , mahendra, malaya, sahya, zaktimat , RkSa, viMdhya, paariyaatr| | acala dekhie| adri parvata A mountain ananta / AkAza The sky | AkAza ko zUnya samajhA jAtA hai| anala Aga Fire agni dekhie| anIka | senA An army saMskRta meM 8 prakAra kI senAoM kA ullekha hai, arthAt patti, senAmukha, gulma, gaNa, vAhinI, pRtanA, camU, aniikinii| (jinAgama meM gaNa kI jagaha akSauhiNI kA ullekha hai|) ananta dekhie| antarikSa AkAza The sky . andhi ambaka ambara mahAsAgara The ocean 4 cAra mahAsAgara mAne jAte haiM, arthAt , pUrvI, dakSiNI, pazcimI aura uttrii| AMkha The eye 2 | akSi dekhie| | AkAza The sky | 0 | ananta dekhie /

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gaNitasArasaMgraha zabda sAmAnya artha saMkhyA abhidhAna udgama ambudhi ambhodhi azva azvin AkAza ina indu indriya | mahAsAgara The ocean| 4 | abdhi dekhie / mahAsAgara The ocean 4 | andhi dekhie / ghor3A A horse 7. sUrya ke ratha meM 7 ghor3e mAne jAte haiN| ghor3e sahita Consi- 7 azva dekhie| ting of horse AkAza The sky ananta dekhie| sUrya The sun varSa ke bAraha mAhoM ke saMvAdI sUryoM kI saMkhyA 12 hotI hai; arthAt , dhAtR, mitra, aryaman , rudra, varuNa, sUrya, bhaga, vivasvata, pUSan , savitR, tvaSThU aura viSNu / ye bAraha Aditya kahalAte haiN| candramA The moon pRthvI ke liye kevala eka candramA hai| indra devatA The god caudaha manvantaroM meM se pratyeka ke liye 1 indra kI dara se Indra caudaha indra hote haiN| indriya An organ 5 | indriyAM pAMca prakAra kI hotI haiM, A~kha, nAka, jIbha, kAna of sense aura zarIra ( sparzan ) / greft An elephant saMsAra kI ATha dizA vidizAoM kI rakSA ATha hAthI karate hue kahe jAte haiN| ve airAvata, puNDarIka, vAmana, kumuda, aJjana, puSpadanta, sArvabhauma aura supratIka haiN| | dhanuSa An arrow manmatha ke pA~ca bANa mAne jAte haiM, arthAt , aravinda, azoka, cUta, navamalikA aura nIlotpala / A~kha The eye akSi dekhie| andhi dekhie| mahAsAgara The ocean bhagavAn viSNu viSNu ke 9 avatAra mAne jAte haiM / God Visnu Rtu A season saMskRta sAhitya ke anusAra varSA meM 6 Rtue~ hotI haiM, arthAt , vasanta, grISma, varSa, zarad , hemanta, zizira / hAtha The hand mAnava ke do hAtha hote haiN| jo kiye jAte haiM, vrata 5 | jaina dharma ke anusAra pA~ca prakAra ke vrata hote haiM, arthAt , That which has ahiMsA, anRta, asteya, brahmacarya aura aparigraha / to be done : an act of devotion or austerity iSu udadhi Rtu kara karaNIya

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gaNitasArasaMgraha zabda sAmAnya artha saMkhyA abhidhAna udgama karin karman hAthI Anelephant | 8 karma athavA kArya karane / 8 kA prabhAva Action: the effect of action as its karma candramA The moon 1 ibha dekhie| jaina dharma ke anusAra ATha prakAra ke karma (prakRtibaMdha) hote haiM, arthAt , jJAnAvaraNIya, darzanAvaraNIya, mohanIya, antarAya, vedanIya, nAmika, gotrika aura AyuSka / kalAdhara indu dekhie / kaSAya kumAravadana saMsArI vastuoM meM Asakti 4 / jaina dharma ke anusAra karmoM ke Asrava kA eka bheda kaSAya Attachment to hai, jisake cAra prakAra haiM, arthAt , krodha, mAna, mAyA worldly objects aura lobha / kumAra athavA hiMdU yuddha- yaha yuddhadeva chaH mukhovAlA mAnA jAtA hai| deva ke mukha The SaNmukha dekhiye| faces or Kumara of the Hindu war-god viSNu kA eka nAma A| 9 | upendra dekhie / name of Visnu candramA The moon indu dekhie| AkAza Sky ananta dekhie| kezava kSapAkara khara gagana gaja gati giri AkAza Sky | ananta dekhie| hAthI Elephant | ibha dekhie| punarjanma kA mArga | jaina dharma ke anusAra saMsArI jIva cAra gatiyoM meM janma lete Passage into haiM, arthAt , deva, tiryaJca, manuSya, naraka / pithegorasa kA rebirth Tetractys isase tulanIya hai| parvata Mountain - acala dekhie| guNa Quality Adi padArtha meM tIna guNa mAne jAte haiM, arthAt , satva, rajas , tamas / graha A planet | hindU jyotiSa meM 9 prakAra ke graha mAne jAte haiM, arthAt , maMgala, budha, bRhaspati, zukra, zani, rAhu, ketu, sUrya aura cndrmaa| / | A~kha The eye mA | 2 | akSi dekhie| praha cakSus

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gaNitasArasaMgraha zabda sAmAnya artha saMkhyA abhidhAna udgama 1 candra candramas jaladhara patha jaladhi candramA The moon candramA The moon AkAza Sky mahAsAgara Ocean 1 | indu dekhie| indu dekhie| ananta dekhie| 4 abdhi dekhie| jalanidhi mahAsAgara Ocean | abdhi dekhie| jina vaha nAma jisameM arihaMta | 24 | jina Agama ke anusAra bharata karmakSetra meM avasarpiNI kAla siddha, AcArya, upAdhyAya meM 24 tIrthaMkara hote haiM; prathama tIrthaMkara RSabhadeva aura aura sarva sAdhuoM kA aMtima tIrthakara varddhamAna mahAvIra mAne jAte haiN| nAma garbhita rahatA hai| The name which implies Arhat, | Siddhas, Achryas, Upadhyayas & all Saints. jvalana tatva tatva tanu | Aga Fire agni dekhie| jaina dharma meM sAta tatvoM kI mAnyatA isa prakAra hai: jIva Elementary Pri- (cetana), ajIva ( acetana), Asrava (karmoM ke Ane nciples. ke dvAra), baMdha ( karmoM kA AtmA ke sAtha sambandha ), saMvara (Asrava kA nirodha), nirjarA ( karmoM kA eka deza nAza) aura mokSa (AtmA kA pUrNa rUpa se karmoM se chuuttnaa)| kAya Body ziva kA tanu ATha vastuoM se banA huA mAnA jAtA hai : | pRthvI, apa , tejas , vAyu, AkAza, sUrya, candra, yajamAna / Evidence tarka ke chaH prakAra haiM : pratyakSa, anumAna, upamAna, zabda, aMpatti aura anupalabdhi / viSNu Visnu upendra dekhie| Tirthankar or 24 | jina dekhie| Jina. hAthI An elephant | 8| ibha dekhie / sAMsArika karma 8. karman dekhie| Worldly action! tAya'dhvaja tIrthaka dantin durita

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gaNitasArasaMgraha zanda sAmAnya artha saMkhyA abhidhAna udgama dik dika dika hak 2 / dRSTi pArvatI kA avatAra durgA ke 9 avatAra mAne jAte haiN| Name of Manifestation of Parvati or Durga. dizA bindu Quarter | 8 | loka meM ATha dizAbindu mAne jAte haiN| or a cardinal point of the universe. dizAe~ Directions| 10 | dasa dizAoM kI mAnyatA isa prakAra hai ki cAra dizAe~, cAra vidizAe~ tathA adho aura Urdhva dizAe~ milakara dasa dizAe~ hotI haiN| 371919 Sky ananta dekhie| A~kha The eye akSi dekhie| " " " dravya kA lakSaNa sat hai jinAgama ke anusAra 6 dravya haiM: aura jo utpatti, vinAza jIva, dharma, adharma, pudgala, kAla aura AkAza / aura dhrauvyatA sahita hai vaha sat hai| Elementary substance whose characteristic is existence implying manifestation, disappearance & permanence. hAthI 8 ima dekhie| An Elephant dravya pRthvI meM sthita paurANika / 7 inake sAta vibhAga haiM: jambU, plakSa, zAlmalI, kuza, dvIpa vibhAga | krauJca, zAka, pausskr| A puranic insular division of the terrestrial world.

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gaNitasArasaMgraha zabda sAmAnya artha saMkhyA abhidhAna udgama dhAtu zarIra ke saraMcaka sapta dhAtue~ ye I-rasa ( Chyle ), rakta, mAMsa, avayava Constituent carvI, asthi, majA, vIrya / principles of the body. chaMda ke eka vibheda | 18 | isa chaMda meM zloka ke pratyeka pada meM 18 akSara kA nAma Name of rahate haiN| a kind of metre. dhRti naga nabhasa naya parvata 7 | acala dekhie| Mountain rAjAoM ke vaMza kA nAma | 9| kahA jAtA hai ki magadha meM 9 nanda rAjAoM ne rAjya Name of adyna-1 kiyaa| sty of kings AkAza Sky ananta dekhiye| vastu ke eka aMza grahaNa | 2 | jinAgama meM mukhyataH do nayoM kA nirUpaNa hai: dravyArthika karane vAlA jJAna | naya aura paryAyArthika naya / Method of Comprehending things from particular standpoints. nayana nAga nidhi A~kha The eye 2 akSi dekhie / hAthI An elephant_ 8 ibha dekhie / khajAnA Treasure kubera ke pAsa nava prasiddha nidhiyA~ mAnI jAtI haiM: padma, mahApadma, zaGkha, makara, kacchapa, mukunda, kunda, nIla, khaveM / jinAgama meM cakravartI ke bhI inase bhinna nava nidhiyoM kA ullekha hai| A~kha The eye akSi dekhie| vastuoM ke vibheda jinAgama meM sAta tatva tathA puNya aura pApa ye do Category of milakara nava padArtha hote haiN| tatva dekhie / things netra padArtha

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gaNitasArasaMgraha zabda sAmAnya artha udgama saMkhyA ANGabhiyAna pannaga sarpa The serpent hindU purANoM meM kabhI kabhI ATha aura kabhI kabhI sAta prakAra ke sau kA varNana milatA hai| payodhi | samudra Ocean andhi dekhie| payonidhi pAvaka | agni Fire agni dekhie| pura nagara City hindU purANoM ke anusAra tIna asuroM ke prarUpaka tIna puroM ne devoM ke prati atyAcAra kiyA aura ziva ne unheM vinaSTa kiyA / tripurAntaka se tulanA karie / puSkarin / hAthI Elephant ibha dekhie| prAleyAMzu caMdramA The Moon indu dekhie| bandha karma baMdha Karmic jinAgama meM baMdha ke mukhyataH cAra bheda batalAe gaye bondage haiM: prakRti baMdha, sthiti baMdha, anubhAga baMdha aura pradeza baMdha / bANa bANa Arrow iSu dekhie| nakSatra hindU jyotiSa meM sUrya patha para mukhyataH 27 nakSatroM A constellation kI gaNanA kI gaI hai| Dara Fear bhAva tatva Elements | pAMca tatva yA paMca bhUta ye haiM : pRthavI, ap , tejas , vAyu, aakaash| bhAskara sUrya The Sun 12 / ina dekhie| bhuvana loka The World Urvaloka, madhyaloka, aura adholoka, kI mAnyatA hai| bhUta tatva Element bhAva dekhie| parvata Mountain acala dekhie| mada ghamaNDa Pride aSTa mada ke bheda isa prakAra hai: jJAna, rUpa, kula, jAti, bala, Rddhi, tapa, zarIra kA mada / mahIdhra parvata Mountain acala dekhie| mAtRkA | devI A goddess sAdhAraNataH sAta prakAra kI deviyoM mAnI jAtI haiN| muni sAdhu Sage 7 mukhyataH sAta prakAra ke RSiyoM kA ullekha milatA hai : kazyapa, atri, bharadvAja, vizvAmitra, gautama, jamadagni, vsisstth| indu dekhie| mRgAGka caMdramA The Moon - 1 rudroM kI saMkhyA 11 mAnI gaI hai| mRDa ziva yA rudra kA nAma A name of Siva or Rudra 11

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gaNitasArasaMgraha - zabda sAmAnya artha saMkhyA abhidhAna udgama 10. yati muni Sage 7 | muni dekhie| rajanIkara | caMdramA The Moon | 1 | indu dekhie| trayanidhi Trinity | jinAgama meM mokSa kA mArga samyagdarzana, samyagjJAna, aura samyagcAritra kA eka honA batalAyA gayA hai, jinheM tIna ratna bhI nirUpita kiyA gayA hai| mUlyavAna patthara A pre- | 9| nava prakAra ke ratna mAne gaye haiM : vajra, vaiDUrya, gomeda, cious gem puSparAga, padmarAga, marakata, nIla, muktA, prvaal| chidra Opening mAnava zarIra meM nava mukhya randhra hote haiN| svAda Taste mukhya rasa chaH haiM : madhura, amla, lavaNa, kaTuka, tikta, kaSAya / ziva kA nAma Name 11 mRDa dekhie / of a Deity AkAra Form or | 1 pratyeka vastu kA kevala eka rUpa hotA hai| shape nava zaktiyoM kI prApti | 9 | nava labdhiyoM nimnalikhita haiM : ananta darzana, anantaAttainment of jJAna, kSAyika samyaktava, kSAyika cAritra, kSAyika dAna, nine powers zAyika lAbha, kSAyika bhoga, kSAyika upabhoga, kSAyika viiry| ye karmoM ke kSaya se kSAyika bhAva ke rUpa prApta hote haiN| landhi Attainment labdha dekhie| lekhya World bhuvana dekhie| locana A~kha The eye akSi dekhie| varNa 6 | jinAgama meM varNa ke pAMca prakAra haiM : kRSNa, nIla, pIta, | rakta aura zveta / . vaidika devatAoM kI eka 8 ye devatA saMkhyA meM ATha hote haiN| aifa A class of Vedio deities vahni agni Fire 3 | agni dekhie| vAraNa hAthI Elephant ibha dekhie| vArSi samudra Ocean andhi dekhie| caMdramA The moon indu dekhie| viSadhi samudra Ocean . 4 andhi dekhie| viSanidhi loka w now vidhu

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* gaNitasArasaMgraha zabda sAmAnya artha saMkhyA abhidhAna udgama viSaya vizva veda vaizvAnara iMdriyoM ke viSaya Ob- | 5 | paMcendriyoM ke viSaya pAMca haiM : gandha, rasa, rUpa; sparza, ject of sense shbd| viyat AkAza Sky ananta dekhie| vaidika devatAoM kA | 13 | isa samUha meM 13 sadasya hote haiN| eka samUha Agroup of Vedic deities viSNupAda AkAza Sky ananta dekhie| The Vedas cAra veda ye haiM : Rk, yajus , sAma, atharva / agni Fire | agni dekhie| vyasana burI Adata. An jinAgama meM jIva kA ahita karane vAle sapta vyasana unwholesome nimnalikhita rUpa meM ullikhita haiM: dyUta, mAMsa bhakSaNa, addiction madirApAna, vezyAgamana, parastrI sevana, asteya, AkheTa / vyoma AkAza Sky ananta dekhie| vrata aNu vrata yA mahAvrata jinAgama meM aNu vrata aura mahAvrata 5 haiN| hiMsA, Partial or whole jhUTha, kuzIla, parigraha aura steya (corI) nAmaka paMca act of devotion pApoM se eka deza virakta honA aNuvrata hai| hiMsAdi pAMca or austerity pApoM kA sarvathA tyAga karanA mahAvrata hai| karaNIya bhI dekhie| zaGkara rudra kA nAma Name mRDa dekhie| of Rudra zara bANa Arrow iSu dekhie| zazadhara iz The Moon indu dekhie| zazalAJchana " " muy'aakt " " zazin " " zastra bANa Arrow iSu dekhie| zikhin agni Fire agni dekhie| zilImukhapada SaTpada The legs madhumakkhI yA bhauMre ke chaH paira mAne jAte haiN| of & bee zaila parvata Mountain 7 | acala dekhie| zveta 4 | andhi dekhie| salilAkara | samudra Ocean sAgara / "

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10 zabda sAyaka sindhura sUrya soma stambrema svara haya hara hara netra hutavaha hutAzana himakara himagu himAMzu sAmAnya artha bAga Arrow erit Elephant The Sun The moon hAthI Elephant saMgIta kA note of musical scale svara A the ghor3A Horse rudra kA nAma Name of Rudra Siva's eyes agni Fire "" "" caMdramA The Moon "" 3 39 59 gaNitasArasaMgraha saMkhyA abhidhAna 5 iSu dekhie / 8 ibha dekhie / ina dekhie / 12 4 8 7 11 indu dekhie / ibha dekhie / sAta zabda svara hai SaDaja, RSabha, gAMdhAra, madhyama, paJcama, dhaivata, viSAda / saMgIta ke prArambha meM inhIM sapta svaroM ke Adi akSaroM ko grahaNa kara sa, ri, ga, ma, pa, dha, ni kA jJAna karAyA jAtA hai / atha dekhie / mRDa dekhie / 3 ziva kI do A~khoM ke sivAya eka aura AMkha mastaka ke madhya meM rahatI hai| 3 ani dekhie / 39 udgama 35 35 1 indu dekhie / , "" "" "" 39 33

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pariziSTa 2 anuvAda meM avatarita saMskRta zabdoM kA spaSTIkaraNa AbAdhA Segment of a straight line forming the base of a Abadha triangle or a quadrilateral. ADhaka A measure of grain. Adhak pariziSTa-4 kI sAriNI 3 dekhie / adhvAna The vertical space required for presenting the long Adhyan and short syllables of all the possible varieties of metre with any given number of syllables, the space required for the symbol of a short or a long syllable being one agunla and the intervening space between each variety being also an angula. adhyAya 6-3331 se 336 kA TippaNa dekhie / Adidhana Each term of a series in arithmetical progression is Adidhana conceived to consist of the sum of the first term and a multiple of the common difference. The sum of all the first terms is called the Adidhan. adhyAya 2---63 aura 64 kA TippaNa dekhie / Adimizradhana The sum of a series in arithmetical progression Adimisradhana combined with the first term thereof. adhyAya 2--80 se 82 kA TippaNa dekhie / agara A kind of fragrant wood; Agaru Amyris agallocha. amla vetasa A kind of sorrel; Rumex vesicarius. Amla-vetasa amoghavarSa Name of a king; lit : one who showers down truly Amoghvarsa ___useful rain. aMza A measure of weight in relation to metals.. Amsa pariziSTa 4 kI sAriNI 6 dekhie / aMzamUla Square root of a fractional part. Amsamula adhyAya 4-3 kA TippaNa dekhie /

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12 aMgula Angula aMtArAvalambaka Antaravalam baka aMtyadhana Antyadhana aNu Anu ariSTanemi Aristanemi arbuda Arbud arjuna Arjuna asita Asita azoka Asoka - phaLa AundraAundraphala Avali Avali ayana Ayana bIja Bija gaNita sArasaMgraha A measure of length; finger measure. adhyAya 1 - 25 se 29 tathA pariziSTa 4 kI sAriNI 1 dekhie / Inner perpendicular; the measure of a string suspended from the point of intersection of two strings streched from the top of two pillars to a point in the line passing through the bottom of both the pillars. The last term of a series in arithmetical or geometrical progression. Atom or particle. adhyAya 1-25 se 27 tathA pariziSTa 4, sAriNI 1 dekhie / The twenty second Tirthnkar. Name of the eleventh place in notation. Name of a tree; Terminalia, Arjuna, W. & A. Name of a tree; Grislea Tomentosa. Name of a tree; Jonesia Asoka Roxb. A kind of approximate measure of the cubical contents of an excavation or of a solid. This kind of approximate measure is called Auttra by Brahmagupta. adhyAya 8-2 kA TippaNa dekhie / A measure of time pariziSTa 4, sAriNI 2 dekhie / "" 39 "" Literally seed; here it is used to denote a set of two positive integers with the aid of the product and the squares whereof, as forming the measure of the sides, a right angled triangle may be constructed. adhyAya 7 - 203 kA TippaNa dekhie /

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gaNitasArasaMgraha bhAgAnubaMdha bhAga A measure of baser metals. Bhaga pariziSTa 4, sAriNI 6 dekhie| A measure fraction. A variety of miscellaneous problems on fractions, adhyAya 4-3 kA TippaNa dekhie| bhAgabhAga A complex fraction, Bhagabhaga bhAgAbhyAsa A variety of miscellaneous problems on fractions. Bhagabhyasa adhyAya 4-3 kA TippaNa dekhie / bhAgahAra Division. Bhagahara bhAgamAtra Fractions consisting of two or more of the varieties of Bhagamatr Bhaga, Prabhaga, Bhugabhaga, Bhagunubandha and Bhagapavaha fractions. adhyAya 3-138 kA TippaNa dekhie / Fractions in association, Bhaganubandha adhyAya 3-113 kA TippaNa dekhie / bhAgApavAha Dissociated fractions, Bhagapavaha adhyAya 3-123 kA TippaNa dekhiye / bhAgasamvarga A variety of miscellaneous problems on fractions. Bhagasamvarga adhyAya 4-3 kA TippaNa dekhie / bhAjya The middlo one of the three places forming the cube Bhajya root group ; that which has to be divided. adhyAya 2-53 aura 54 kA TippaNa dekhie| bhAra A measure of baser metals. pariziSTa 4, sAriNI 6 dekhie / Bhara bhimadRzya A variety of miscellaneous problems on fraction, Bhinnadrgya adhyAya 4-3 kA TippaNa dekhie / bhinnakuTTIkAra Proportionate distribution involving fractional Bhinnakutti- quantities. pRSTha 123 kI pAda-TippaNI dekhie / kara cakrikAbhaJjana The destroyer of the cyle of recurring rebirths; also Cakrikabhan the name of a king of the Rastrakuta dynasty. jana campaka Name of a tree bearing a yellow fragrant flower; Campaka MicheliaChampaka. chanda A syllabic metre. Chandas citi Summation of series, Citi

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gaNita sArasaMgraha citra-kuTTIkAra Curious and interesting problems involving proCitra-kuttikara portionate division, citra-kuTTIkAra mizra Mixed problems of a curious and interesting nature Citra-kuttikara involving the application of the operation of pro misra portionate division, A measure of distance, pariziSTa 4 kI sAriNI 1 dekhie / Tenth place. 14 daMDa Danda daza Dasa dazakoTi Dasa-koti dazalakSa Dasa-Laksa daza sahasra Dasa-sahasra dharaNa Dharana dInAra Dinara drakSUNa Draksuna eka Eka gaNDaka Gandaka Ten Crore. ghana Ghana Ten Lakhs or one million, Ten thousand, A weight measure of gold or silver; pariziSTa 4 kI sAriNiyA~ 4 aura 5 dekhie / A weight measure of baser metals. Also used as the name of a coin. pariziSTa 4 kI sAriNI 6 dekhie / droNa Drona DuNDuka Dunduka dviragrazeSamUla Dviragrasesamula A weight measure of baser metals. pariziSTa 4 kI sAriNI 6 dekhie / A measure of capacity in relation to grain. pariziSTa 4 kI sAriNI 3 dekhie / Name of a tree. A Variety of miscellaneous problems on fractions. Unit place. A weight measure of gold. pariziSTa 4 kI sAriNI 4 dekhie / Cubing; the first figure on the right, among the three digits forming a group of figures into which a numerical quantity whose cube root is to be found out has to be divided. adhyAya 2-53, 54 kA TippaNa dekhie /

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ghanamUla Ghanamula ghaTI Ghati guNakAra Gunakara guNadhana Gunadhana guA Gunja hasta Hasta hitAla Hintala icchA Iccha indranIla Indranila jambU Jambu janya Janya jina Jinas jinapati Jinapati jina - zAnti Cube root. gaNita sArasaMgraha A measure of time pariziSTa 4 kI sAriNI 2 dekhie / Multiplication. The product of the common ratio taken as many times as the number of terms in a geometrically progressive series multiplied by the first term 12-93 kA TippaNa dekhie / A weight measure of gold or silver. pariziSTa 4 kI sAriNiyAM 4 aura 1 dekhie / A measure of length pariziSTa 4 kI sAriNI 1 dekhie / Name of a tree; Phaenix or Elate Paludosa. 15 That quantity in a problem on Rule-of-Three in relation to which something is required to be found out according to the given rate. Sapphire. Name of a tree; Eugenia Jambalona. Trilateral and quadrilateral figures that may by derived out of certain given data called bijas. Those who have attained partial or whole success in getting themselves absorbed in the unification of their souls right faith, right knowledge and right character may be called Jinas. The chief of the Jinas, generally, Tirthankara. The sixteenth Tirthankara. Jina-Santi jina - varddhamAna Jina-Vardhamana The last or twenty-fourth Tirthankara.

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gaNitasArasaMgraha Name of a tree; Nauclea Cadamba. . kadamba Kadamba kalA Kala kalAsavarNa Kalasavarna karma Karmas A weight measure of baser metals, pariziSTa 4, sAriNI 6 dekhie / Fraction. adhyAya 3 ke prathama zloka meM pRSTha 36 para kalAsavarNa kI pAda TippaNI dekhie| The mundane soul has got vibrations through mind, body or speech. The molecules and atoms, which assumo the form of mind, body or speech, engender vibrations in the soul, whereby an infinite number of subtle atoms and ultimate particles are attracted and assimilated by the soul. This assimilated group of atoms is termed as Karma, Its effect is visible in the multifarious conditions of the soul. There are eight main classifications of the nature of Karmas, pariziSTa 1 meM karma dekhie| A kind of approximate measure of the cubical contents of an excavation or of a solid. adhyAya 8-9 kA TippaNa dekhie| A weight measure of gold or silver. pariziSTa 4 kI sAriNiyA~ 4 aura 5 dekhie / A Karsa. karmAntika Karmantika karSa Name of a treo; Pandanus Odoratissimus. Karsa kArSApaNa Karsapana ketakI Ketaki khArI Khari kharva Kharva kiSku Kisku A measure of capacity in relation to grain. The thirteenth place in notation, A measure of length in relation to the sawing of wood. Crore, the 8th place in notation. koTI Koti koTikA Kotika kroza Krasa A numerical measure of cloths, jewels and canes. pariziSTa 4 kI sAriNI 7 dekhie / A measure of length. pariziSTa 4 kI sAriNI 1 dekhie /

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kRSNAgaru Krasnagaru kRti Krti kSepapada Ksepapada kSityA Ksitya kSobha Ksobha artoit Ksoni kuDadda yA kuDaba Kudaha or Kudaba kumbha Kumbha kuGkama Kunkuma kurvaka Kurvaka kuTaja Kutaja kuTTIkAra Kuttikara lAbha Labha lakSa Laks laGkA Lanka lava Lava madhuka Madhuka gaNita sArasaMgraha A kind of fragrant wood; a black variety of Agallochum. Squaring. Half of the difference between twice the first term and the common difference in a series in arithmetical progression. The 21st place in notation. The 23rd place in notation. The 17th place in notation. A measure of capacity in relation to grain. Y kI sAriNI 3 dekhie / 35 17 39 Quotient or share. "" The pollen and filaments of the flowers of saffron, Croeus sativus. Name of a tree; the Amaranth or the Barleria. Name of a tree; Wrightia Antidysenterica. Proportionate division, adhyAya 6 - 793 dekhie / Lakh, the 6th place in notation. The place where the meridian passing through Ujjain meets the equator. A measure of time pariziSTa 4 kI sAriNI 2 dekhie / Name of a tree, Bassia Latifolia.

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18 gaNitasArasaMgraha The middle term of a series in arithmetical progression. adhyAya 2-63 kA TippaNa dekhie / The 14th place in notation. The 22nd place in notation. The 24th place in notation, madhyadhana - Madhya dhana mahAkharva Mahakharva mahAkSityA Mahaksitya mahAkSobha Mahaksobha mahAkSoNI Mahaksoni mahApadma Mahapadma mahAzaGkha Vahasankha mahAvIra Mahavira The 18th place in notation. The 16th place in notation. The 20th place in notation. A name of Vardhamana, mAnI A measure of capacity in relation to grain. pariziSTa 4, sAriNI 3 dekhie| A kind of drum ; for a longitudinal section, see note to chapter 7th, 32nd stanza. Section ; the line along which a piece of wood is cut by a saw. A weight measure of silver. pariziSTa 4, sAriNI 5 dekhie / Mani mardala Mardala mArga Marga mASa Masa meru Meru mizradhana Misradhana mRdaGga Mrdaniga Name of a tapering mountain forming the centre of Jambu dvipa, all planets revolving around it. Mixed sum, adhyAya 2-80 se 82 kA TippaNa dekhie| A kind of drum ; for a longitudinal section see note to chapter 8th, 32nd stanza. A measure of time. pariziSTa 4, sAriNI 2 dekhie / muhUrta Muhurta mukha Mukha The topside of a qudrilateral, Square root; a variety of miscellaneous problems on fractions. adhyAya 4-3 kA TippaNa dekhie / Mula

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gaNitasArasaMgraha Involving square root; a variety of miscellaneous problems on fractions. adhyAya 4-3 kA TippaNa dekhie| A kind of drum; same as Mradanga, mUlamizra Mulamisra maraja Muraja nandyAvarta Nandyavarta narapAla Narapala nIlotpala Nilot pala niruddha Niruddha Name of a palace built in a particular form. adhyAya 6-3321 kA TippaNa dekhie| King; probably name of a king. Blue water-lily. Least common multiple. niSka A golden coin. Niska nyarbuda Nyarbuda The 12th place in notation. pAda A measure of length. pariziSTa 4, sAriNI 1 dekhie / Pada The 15th place in notation, A kind of gem or precious stone, padma Padma padmarAga Padmaraga paizAcika Paigacika Relating to the devil; honce very difficult or complex. A measure of time. pariziSTa 4, sAriNI 2 dekhie / Paksa pala Pala paNa Pana paNava Panava paramANu parikarman Parikarman pAva Parsva A weight measure of gold, silver and other metals. pariziSTa 4 kI sAriNiyA~ 4, 5, 6 dekhie| A weight measure of gold; also a golden coin. pariziSTa 4 kI sAriNI 4 dekhie / A kind of drum; for longitudinal section see note to Chapter 7th, 32nd stanza. Ultimate particle. pariziSTa 4, sAriNI 1 dekhie / Arithmetical operation, The 23rd Tirthankara,

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20 pATalI Patali paTTikA Pattika phala Phala lakSa Plaksa prabhAga pramANa Pramana Prabhaga prakIrNaka Prakirnaka prakSepaka Praksepaka prakSepaka karaNa Praksepaka-karana prapUrNikA Prapuranika prastha Prastha pratyutpanna Pratyutpanna pravartikA Pravartika punnAga Punnaga purANa Purana puSyarAga Pusyaraga gaNitasArasaMgraha A tree with sweet-scented blossoms; Bignonia Suaveolens. A measure of saw-work. pariziSTa 4, sAriNI 10 tathA adhyAya 8- 63 se 673 kA TippaNa dekhie / A given quantity corresponding to what has to be found out in a problem on the Rule-of-Three, adhyAya 5 - 2 kA TippaNa dekhie / Name of a tree; the waved-leaf fig-tree, Ficus In - fectoria or Religiosa, Fraction of a fraction, Miscellaneous problems. Proportionate distribution, An operation of proportionate distribution, A measure of length pariziSTa 4, sAriNI 1 dekhie / The given quantity corresponding to Iccha, in a problem on Rule-of- Three. adhyAya 5 -- 2 kA TippaNa dekhie / Literally, that which completes or fills; here, baser metals mixed with gold; dross. A measure of capacity in relation to grain pariziSTa 4 kI sAriNiyA~ 3 aura 6 dekhie / Multiplication. A measure of capacity in relation to grain, Name of a tree; Rottleria Tinctoria. A weight measure of silver; probably also a coin, pariziSTa 4, sAriNI 5 de khie / A kind of gem or precious stone.

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rathareNu Ratharenu romakApurI Romkapuri Rtu Rtu sahasra Sahasra zaka " Saka sakala kuTTIkAra Sakala Kutti kara sAla Sala salakI Sallaki samaya Samaya saGkalita Sankalita zaGkha Sankha saGkramaNa Sankramana saGkrAnti Sankranti zAnti Santi sarala Sarala sArasa Sarasa gaNita sArasaMgraha A particle. pariziSTa 4 sAriNI 1 dekhie / A place 90deg to the west of Lanka. Season, here used as a measure of time pariziSTa 4, sAriNI 2 dekhie / Thousand. The teak tree. Proportionate distribution, in which fractions are not involved. The Sala tree; Shorea Robusta or Valeria Robusta. 21 Name of a tree; Boswellia Thurifera. The ultimate part of time measure pariziSTa 4, sAriNI 2 dekhie / Summation of series. The 19th place in notation. An operation involving the halves of the sum and the difference of any two quantities. adhyAya 6-2 kA TippaNa dekhie / The passage of the sun from one zodiacal sign to another. See Jina-Santi Name of a tree; Pinus Longifolia. A kind of bird; the Indian crane.

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22 sArasaMgraha Sarasangraha sarja Sarja sarvadhana Sarvadhana zata . Sata zatakoTi Satakoti satera Satera zeSa Sesa zeSamUla Sesamula siddhapurI Siddhapuri siddha Siddhas zoDazikA Sodasika zodhya " Sodhya gaNita sArasaMgraha Literally, a brief exposition of the essentials or principles of a subject; here, the name of this work on arithmetic. Name of a tree; Same as the Sala tree. The sum of a series in arithmetical progression. adhyAya 2-63 aura 64 kA TippaNa dekhie / A hundred. A hundred crores. A weight measure of baser metals. pariziSTa 4 kI sAriNI 6 dekhiye / The terms that remain in a series after a portion of it from the beginning is taken away. adhyAya 2 ke pRSTha 32 para vyutkalita kA TippaNa dekhie / A variety of miscellaneous problems on fractions. adhyAya 4-3 kA TippaNa dekhie / A variety of miscellaneous problems on fractions. adhyAya 4-3 kA TippaNa dekhie / The antipodes of Lanka, The emancipated souls. These souls, due to complete freedom from karmic bondage attain all attributes of soul, viz, infinite perception, power, knowledge, bliss etc. karmamala se rahita, sarvajJa, paramapada meM sthita siddha bhagavAn ATha guNoM se sampanna haiM- jJAnaguNa, darzanaguNa, samyaktvaguNa, zakti guNa, avyAbAdhaguNa, avagAhanAguNa, sUkSmatvaguNa, agurulaghuguNa / A measure of capacity in relation to grain pariziSTa 4, sAriNI 3 dekhie / One of the three figures of a cubic root group. adhyAya 2-53 aura 54 kA TippaNa dekhie /

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gaNitasArasaMgraha zrAvaka Sravaka A lay follower of Jainism, having the following eight chief vows : abstenance from wine, flesh, boney; partial nonviolence, truth and chastity; partial non-thievery and partial setting of limits to possession. zroparNI Name of a tree ; Premna Spinosa. Sriparni A measure of time, fifTe , afrit afati stoka Stoka sUkSmaphala Suksmaphala suvarNa kuTTIkAra Suvarnakuttikara Accurate measure of the area or of the "cubical contents. Proportionate distribution as applied to problems relating to gold. The 20th Tirthankara, Munisurata, suvrata Suprata Farol A gold coin. Svarna syAdvAda Syadavada The doctrine of Syadvada, known as saptabha. riginaya, is represented as being based on the Naya (that which reveals only partial truth ) method, This is set forth as follows: May be, it is ; may be, it is not ; may be, it is and it is not ; may be, it is indescribable ; may be, it is and yet indescribable; may be, it is not and it is also indescribable; may be it is and it is not and it is also indescribable. adhyAya 1-8 meM pRSTha 2 para pAdaTippaNI dekhie / Name of a tree ; Xanthoch ymus Pictorius. tamAla Tamala Name of a tree with beautiful flowers, tilaka Tilaka

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gaNitasArasaMgraha tIrtha Tirtha is interpreted to mean a ford intended to Tirtha cross the river of mundane existence which is subject to karma and cycle of births and rebirths, The Jina, Tirthankara, may be conceived to be a cause of enabling the souls of the living beings to get out of the stream of samsara or the recurring cycle of embodied existence. 276777 - 798 88 92 fergoteradi tIrthakara Patriarchs endowed with superhuman qualities; those Tirthankara who have attained infinite perception, knowledge power and bliss through supreme concentration and promulgate the truth matchlessly. According to Jainism Tirthankaras are always present in Videha Ksetra, but in the Bharata and Airavata Ksetras they are present in the fourth era of the two aeons (i) causing increase and (ii) causing decrease. Twenty-four Tirthankaras have been in the past fourth era of the aeon, causing decrease. Out of them Lord Rsabha was the first and Lord Vardhamana was the last Tirthankara. trasareNu A particle. affae , apoft e dragi Trasarenu triprazna Name of a chapter in Sanskrit astronomical works. Tripragna adhyAya 1-12 meM pRSTha 2 para pAdaTippaNa dekhie / tulA A weight measure of baser motals. Tula ubhayaniSedha A di-deficient quadrilateral, Ubhayanisedha 37714 V-349 fecqu a faci 308991a A measure of time. Uccbvasa pariziSTa 4, sAriNI 2 dekhie / utpala The water-lily flower. Utpala uttaradhana The sum of all the multiples of the common diffeUttaradhana rence found in a series in arithmetical progression, adhyAya 2-63 aura 64 kA TippaNa dekhie /

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gaNitasArasaMgraha varNa uttaramizradhana A mixed sum obtained by adding together the Uttaramisra- common difference of a series in arithmetical dhana progression and the sum thereof. adhyAya 2-80 se 82 kA TippaNa dekhie| vAha A measure of capacity in relation to grain. Vaha vajra A weapon of Indra ; for longitudinal section see Vajra note to Chapter 7th, stanza 32. vajrApavartana Cross reduction in multiplication of fractions. Vajrapavartana adhyAbha 3-2 kA TippaNa dekhie / vakula Name of a tree ; Mimusops Elengi. Vakula vallikA Proportionate distribution based on a creeper-like Vallika chain of figures. adhyAya 6--1153 kA TippaNa dekhie / varddhamAna See Jina-Vardhamana, Vardhamana vargamUla Square root. Vargamula Literally colour; here denotes the proportion of Varna pure gold in any given piece of gold, pure gold being taken to be of 16 Varnas. vicitra-kuTTIkAra Curious and interesting problems involving proporVicitra tionate division. adhyAya 6 meM pRSTha 145 para TippaNa dekhiye| kuttikara vidyAdhara-nagara A rectangular town is what seems to be intended Vidyadhara- here. nagara viSama kuTTIkAra Proportionate distribution involving fractional Visama quantities. adhyAya 6 meM pRSTha 123 para viSama kuTTIkAra kI pAda TippaNI kuttikara dekhie| viSama saGkramaNa An operation involving the halves of the sum and Visama- the difference of the two quantities represented by sankramana the divisor and the quotient of any two given quantities. adhyAya 6-2 kA TippaNa dekhie| vitarita A measure of length. pariziSTa 4 kI sAriNI 1 dekhie / The first Tirthankara. See Tirthankara. Vrsabha vRSabha

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gaNita sAra saMgraha A measure of length. byavahArAGgula Vyavahararigula pariziSTa 4, sAriNI 1 dekhie / 26 vyutkalita Vyutkalita yava Yava yavakoTi Yavakoti yoga Yoga yojana Yojana Subtraction of part of a series from the whole series in arithmetical progression. adhyAya 2 meM vyutkalita kI pAda TippaNI pRSTha 32 para dekhie / A kind of grain; a measure of length pariziSTa 4, sAriNI 1 dekhie | Longitudinal section of & grain AkRti ke liye adhyAya 7-32 kA TippaNa dekhie / A place 90deg to the East of Lanka. Penance; practice of meditation and mental concentration. A measure of length. pariziSTa 4, sAriNI 1 dekhie /

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pariziSTa-3 uttaramAlA adhyAya-2 (2) 1152 kamala (3) 2592 padmarAga (4) 15151 puSyarAga (5) 53946 kamala (6) 9255327948 kamala (7) 12345654321 (8) 43046721 (9) 1419147 (10) 111111111 (11) 11000011000011 (12) 100010001 (13) 1000000001 (14) 111111111, 222222222, 333333333, 444444444, 555555555; 666666666, 777777777, 888888888, 999999999 (15) 11111111 (16) 16777216 (17) 1002002001 (20) 128 dInAra (21) 73 suvarNa khaMDa (22) 131 dInAra (23) 179 suvarNa khaMDa (24) 803 jambU phala (25) 173 jambU phala (26) 4029 ratna (27) 27994681 suvarNa khaMDa (28) 2191 ratna (32) 1, 4, 9, 16, 25, 36; 49; 64; 81, 225, 256, 625; 1296, 5625 (33) 114244; 21724921, 65536 (34) 4294967296; 152399025 11108889 (35) 40793769; 50908225; 1044484 (37) 1, 2, 3, 4, 5, 6, 7, 8, 9, 16; 24 (38) 81; 256 (39) 65536, 789 (40) 7979, 1331 (41) 36,25 (42) 333, 111, 919 (48) 1,8;27; 64125, 216; 343,512, 729, 3375,15625, 46656, 456533, 884736 (49) 1030301,5088448% 137388096,368601813, 2427715584 (50)9663597, 77308776; 260917119; 628470208 .1207 149625 (51) 4741632 37933056, 128024064; 303464448, 592704000 1024192512; 1626379776; 2427715584 (52) 859011369945948864 (55) 1, 2, 3, 4, 5 6, 7, 8, 9, 17, 123 (56) 24; 333; 852 (57) 6464; 4242 (58) 426; 639 (59) 1344; 1176 (60) 950604 (65) 55; 110; 165; 220 275, 330,385; 440, 495; 550 (66) 40 (67) 564; 754, 980; 1245; 1552; 1904, 2304 (68) 4000000 (71) 5, 8; 15 (72) 9, 10; (77) 2; 2 (79) 2; 520; 10; jaba ki cunI huI saMkhyAe~ 2 aura 10 rahatI haiM / (83) 2, 3, 5, 2, 3,5 / / (85) 120; 24: jaba ki iSTa zredi kA yoga jJAtayoga se dviguNita hotA hai| tathAH 30:60 jaba ki iSTa zredi kA yoga jJAtayoga se AdhA hotA hai| (87) 46, 4; jaba ki yoga samAna hote haiN| tathA; 36; 24; jaba ki ekayoga dUsare se dviguNita hotA hai / tathA; 44; 26; jaba ki ekayoga dUsare se triguNita hotA hai / (88) 100:216; jaba ki yoga samAna hoN| tathA: 232, 192; jaba ki eka yoga anya se dviguNita hotA hai| tathA; 34: 228; jaba ki eka yoga anya se AdhA hai| (90) 21; 17, 13, 9, 5, 1, 25; 17, 9, 1 (92) 6; 5, 4, 3,2; 1 (96) 4374 svarNa sikke (99) 1275 dInAra (100) 68887, 22888183593 (102) 42

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gaNitasArasaMgraha (104) 4 (105 ) 8; 9; 15 (111 ) 224; 201; 175 4200; 75250 (113) 182938 5846 (114) 180 2044; 1020 ; 508 252; 124 60 / 28 adhyAya - 3 (3) he paNa (4) 120 paNa (2) 260 paNa (6) 24 pala (7) 6 143; 22; 133 (9) paNa (10) 173 paNa (11) 1454 pala (12) 62468 / 244; 261 (112) 4836; 4656; 11260 40 ( 115) 4092; (2x) 2; 2; 22; 245; 400; 22000; (24) ; ; ; (**) ; ; ; ; (17) isa adhyAya ke prazna 14 aura 15 dekhie; 9339 23 (?<) 2; 20; 88; (?) 39; 28; -133'; 12; 1600; 482; (Ro); 2; 42875 1100 " 8535 29; 298; 383; 992; 32 12167 1968 2008; 3432; (R) ; ; ; ; ; 3; 2; 4; 1; 1; 2; 2^; 18; 73; 78; 41; 42; (RR) 22; 13 (2x); 28; 22;2368; 2008; 3840; E (26) pratyeka zreDhi meM prathama pada 1 hai aura pracaya 2 hai / yogoM ke varga hai, 16, 27, 3, 4, f*%, 72, 733 | aimia a zs, 28, 2%, 277, 333, 442, 027, 100%, 1771, 1738 / 25 2 512 1250 125 12) (28) ghana yoga za7, ve4, 25, 2 haiM / prathama pada he, 1, 5, 24, 14 haiM / pracaya 3, 2, haiN| padoM kI saMkhyA, 3, 6, 3, 3 haiM / (30) ; 26 (3) 43; 93 (32) hai; 2 ( 39 ) jaba yoga samAna ho to 1552, 476 paraspara meM samAna yoga hotA hai| jaba yoga tathA 1 275 prathama pada aura pracaya hote haiM; tathA dviguNita yoga ke anupAta meM hoM to prathama pada aura pracaya 43 aura ; 30; 44; 27; 24; ***; **4; 738; 17* 389 755248 hotA hai / (42) 2048 2048 (50) pa (53) prathama pada -15; 353 3 283; (57 aura 58) 1 (59) 1 (61 aura 62) 1; 1; 1; 1 (67 se 71) 4 (35) pa badalane yogya (63) 0 (37); prathama pada aura pracaya hote haiM : 2 ke anupAta meM hoM to 75 aura 123676 hotA hai / jaba yoga 1 : 3 63 hote haiM; aura Arddhita yoga (44) 4, 821 52 (48) 8 25 6 3 467 (51) 1440; 23520 haiN| yoga (60) 1; 1; 1 (64) (74) 2; 3; 4 (ba) 2; 3; 9; 27; 81; 162 (sa) 2; 3 ; 9 ; 27; 81; 243 486 340; 260 (ba) 44; 220; 460; 299 ( sa ) 78 286 550; 325 420; jaba ki mana se cunI huI rAzi sarvatra 1 ho; (ba) 3; 11; 232, 53592 jaba ki mana se cunI huI rAziyA~ 2, 1, 1 hoM / 37136.22880. 133 (49) pa (52) 4; 21;; haiN| padoM kI saMkhyA 1;4; 4 (65 aura 66 ) ; Te (76) (a) 2; 3; 9; 27; 54 (78) (a) 8; 136; (81) (a) 5; 21;

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gaNita sArasaMgraha (83) 2; ; ; jaba ki cunI huI rAziyA~ 6, 8, 9 hoM / (84) 8; 12; 16; jaba ki cunI huI rAziyA~ 6, 4, 3 hoM / (86) (a) 18; 9; jaba ki cunI huI saMkhyA 3 ho / (ba) 30; 15; jaba cunI huI saMkhyA punaH 3 ho / (88) (a) 6; 12 jahA~ 2 cunI huI saMkhyA hai / " 5 1 " "" / (ba) 3; 15 (sa) 46; 92 (da) 22; 110 11 2 " " 5 " " (90) (a) 4; 28 (91) 16; 240 "" 37 39 (42 se 45 ) 100 muni (53) aMgula 48 (54 (59) 144 yA 112 mayUra (63) 100 yA 40 hAthI 1 / (ba) 25; 175 (92) 151; 3020 / o (94) (a) 22, 44, 33, 66, 58, 116, jaba ki yoga hai, re aura 8 meM vipATita kiyA jAtA hai aura cunI huI saMkhyA 2 rahatI hai / (ba) 11, 22, 59 236; 199; 38; 20; jaba ki yoga meM vipATita kiyA jAtA hai / ( 96 ) 52 (97) 21 (98 ) 6 (100 se 102) 1 (103 aura 104) 1 (105 aura 106) 1 (108) 3 (110) ; 40 ; ; yadi hai; para aura mana se cunI huI rAziyA~ haiM / (111) 76 (112) ( 115) 14Tai niSka (116) ( 117) 2 droNa aura 3 mAzA ( 118) 13 niSka (120) 1 (121) 13 (123) ; ; ; yadi ; ; re mana se vipATita kiye gaye bhAga haiM / (124) hai ( 127) 24 karSa (128) se (129) 1 (130) 1 (131) 1 (133) 3, 4, ; jaba ki hai, para aura mana se vipATita kiye gaye bhAga haiM / (134) (137) hai jaba ki deM, che, che, Te, he Adi ke sthAna ko chor3akara anya sthAnoM meM mana se cune hue bhinna haiM / jaba ki hai, pe, che, che, Te aise hI sajAtIya bhinna haiM / ( 139 aura 140) 817 / (114) 0 (119) 2 29 adhyAya- 4 (5) 24 hasta (6) 20 madhumakkhiyA~ (bhRMga) (7) 108 kamala (8 se 11) 288 sAdhu (12 se 16) 2520 zuka (17 se 22) 3456 muktA ( 23 se 27) 7560 SaTpada (28) 8192 gAe~ ( 29 aura 30) 18 Ama (31) 42 hAthI (32) 108 purANa (34) 36 U~Ta (35) 144 mayUra (36) 576 pakSI (37) 64 bandara (38) 36 koyaleM 100 haMsa 196 siMha ( 41 ) 24 hAthI (50) 324 hiraNa (58) 96 yA 32 vAha (62), 64 yA 16 mahiSa (67) 100 kapota (39) (46) 144 hAthI (48) 16 madhukara (49) aura 55) 150 hAthI (56) 200 barAha (60) 240 yA 120 hasta (64) 120 yA 45 mayUra (66) 16 kapota (68) 256 rAjahaMsa (70) 72 (71) 324 hAthI ( 72 ) 1728 sAdhu / adhyAya - 5 (3) 638 yojana (4) 536 yojana (5) 105600000 (6) 1040 dina (7) 31103 varSa 0262 (8) 94uTha e vAha (9) 323 pala (10) 573 pala (11) 1963 bhAra (12) 66533 dInAra

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30 gaNitasArasaMgraha (13) 23803 pala (14) 163 yugala (15 aura 16) 11166 yojana; 2758 vAha (17) 112 droNa mudga; 504 kuDaba ghI; 336 doNa taNDula; 448 yugala vastra; 336 gAe~; 168 suvarNa (18) 160; 11233 dharaNa (19) 120 khaMDa (20) 525 khaMDa (21) 24 tIrthakara (22) 216 zilA (24 aura 25) 5 varSa aura 117 dina (26) 2133 dina (27) 10 varSa aura 24 dina (28 se 30) 35115 dina (31) 765 dina (33) 10 purANa; 18 purANa; 28 purANa (34) 296120 suvarNa (35) 36 godhUma (36) 4000 paNa (37) 250 karSa (38) 960 anAra (39) 560000 suvarNa (40) 750 suvarNa (41) 54 (42) 252 suvarNa (43) 945 vAha / adhyAya-6 (3) 7; 5 : 4, 5 (5) 9; 18 aura 256 purANa (6) 1732 karSApaNa (7) 51 purANa aura 14 paNa (8) 200 (9) 336 karSApaNa (11) 1333 purANa (12) 14 (13) 50, 60, 70 (15) 10 mAsa (16) 6 mAsa (17) 10 mAsa (19 aura 20) 357 pala (22) 30; 18 (24) 30 (26) 5 mAsa (27) 5 mAsa; 75 (28) 46 mAsa; 313 (30) 313 (31) 60, 6 mAsa (32) 24 mAsa; 36 (34) 10; 23 mAsa (36) 48; 10 mAsa; 24 (38) 10, 6, 3, 15 (40) 40, 30, 20, 50 (41) 5, 10, 15, 20, 30; (43)5mAsa; 4 mAsa; 3 mAsa; 6mAsa; (45) 8 (46) 6; 16 (48) 20; 28; 36 (49 aura 50) 25 (52) 18 (53) 30 (55) 900 (56) 800 (58) 28 mAsa (59) 18 mAsa (61) 2400, 800; 1200; 96; (62) 1000; 420, 480; 90 (64) 60 (65) 50 (67) 2400; 2720, 3400 (68) 1050; 1400; 1800 (69) 5100, 4590, 4050 (70) 1300, 1198; 1150; (72 aura 733) 2070-4, 8103, mAsa (735 se 76) 440, 11, 5 mAsa (783) 23 mAsa; haiM (803) 48; 32, 24, 16 (813) 3; 9; 27, 81; 243 (823 se 853) 120; 80, 40; 160; 60; 20; (863) 48; 72; 96; 120; 144 (903 se 916) 70 anAra; 35 Ama; kapittha (923 se 943) dugdha prathama ghaTa 13 dvitIya ghaTa 13 tRtIya ghaTa 6 (953 aura 963) 15 manuSya; 50 manuSya (983) 4, 9, 18, 36 (993) 8; 13, 21, 36 (1003) 2, 4, 7, 13, 256 (1013) 16, 39, 96; 234 (1033) 220; 37 (1043) 2073 (1053) 6; 4; 3 ( aMtima do mana se cunI huI rAziyA~ haiM / ) (1063) 8 (1083) 8031600; 1860; 2231 (1103) 148; 35328; 184 (1123 aura 1133) 13 kusuma (1143) 1104 kusuma (1173) 5 (1183) 17 (1193) 26 (1203) 9 (1213) 55 (1221) 61 (1233) 59 (1243) 39 (1253) 16 (1263) 15 (1973) 537 (1283) 138 (1293) 194 (1313) 11 (1323 aura 1333) 25 (1353) 3 (1373) 10, 57 (1381) dhanAtmaka saMyavita saMkhyAoM kI dazA meM-21, 16, 13, 11, 21, 19; 37,7; 37; 6,16, 135, 12, 1, 25 / RNAtmaka saMyavita saMkhyAoM kI dazA meM dadhi MN VA

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gaNita sArasaMgraha 11; 18; 23; 27; 19; 23; 7; 39; 11, 44, 41; 51; 46; 59; 37 (140 se 1423). 8; 5 / (1443 aura 1453 ) - prathama DherI dvitIya " 16 tRtIya " 18 nUlya 2 (1473 se 149 ) : mayUra 7 saMkhyA paNa meM mUlya (150) mAtuluMga 14 parimANa paNoM meM mUlya zuNThi 20 12 kadalI 3 3 3 kapota 16 12 pippala 44 16 kapittha 3 2 1 haMsa 45 36 ( 152 aura 153) paNa 9; 205 6 ho to 6; 14; 2; 7 jaba cunI huI lambAI 10 yojana; pratyeka azvako 40 yojana vahana karanA par3atA hai / 35 36 saMkhyA 8 ho (a) dADima 1 1 marica 4 1 3 sArasa 4 32 (155 aura 156) to 5; 6; 164 31 jaba cunI huI saMkhyA (158) kSetra kI (165 aura 166 ) 2, 3, OM, u 8; 201 (1733) 1 (160 se 162) 10; 9 8 5 (164) 20; 15 aura 12 40 (168) 243 paNa; (170 se 1713 ) ; 103, 2, ke, 32; (1743) 87 hai; (1773 aura 178) 14 (179) 3; (181) 21; (184) udeg; ''; (186) 20; 4; 4; 4; 4; 24; (188) athavA ; (190); 8; 13; 10; ; (193 se 1963) ''; ' N'; ' u deg; (ba) (1983); 560; 448 (2003 se 201 ) +-3; 100; 18deg deg; ' N; 47; 1\7; 34; 68; 136 (207 aura 208) 2400; (213 se 215 ) (217) 11 (219 ) 6; 15 20; 15; 6; 1; 63 (220) 5; 10; (223 se 225) 10; 24; 32 ; 13; (191) ''; 5; 15'; (204 aura 205) 3, 2; 64; 10; 5; 1; 31 (221) 4; 6; 4; 1; 15 (227 ) 4 panasa ( Jack fruits) (229) 2 yojana ( 231 aura 232) 18, 57, 155, 490 dInAreM ( 236 aura 237) 15; 1; 3; 5 ( 239 aura 240 ) 261, 921 1416; 1801 2109, 110880 (242 aura 243) 11, 12, 30 (244 aura 2443) 3 4 5 (2453 aura 247 ) 5177. 103 169; 223; 268 (248 ) 14760. 356,585; 445; 624 (249 se 2503) 55 71; 66; 876 ( 2533 se 2553) 7, 8, 9 (2563 se 2583) 11; 17.20 (260 aura 2613) 7; 3; 2 (2623) 8; 12, 14, 15, 31 (2633) 54; 72; 78; 80; 121 (2643) 1875, 2625, 2925; 3045; 3093, 5187 (2663) 4; 7; 13 (2673) 12; 16; 22; 31 ( 270 se 2723) 42; 40 (2743) 5; 8

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gaNitasArasaMgraha (2763) 186 (2773) 151 (2783) 54315 (2801) 26 (2823 se 283) 1296,1225 (285) (a) (ba) - - (287) - (289) 37 (291) 40, 184 (293) 2, 3 (295) 5 striyA~; 40 phUla (297) 204; 2109; 2870, 73810; 180441, 16206 (300) 1095; 1624 (304) 2555; 126225 (3063) 27663 (3083) 504, 732, 1020; 1375, 5304, 150875; 272304 (3103) 1563100, 5038869; 9646, 12705; 114400 (3123-313) 133, 1 (315) 426 (316) 416348873 (318) 2, 3, 5; 40 (320)2 (321 se 3213) 24 dina (3233) 3 (3253) 6 (3273) 25 dina (3293) 13; 9 (3313) 55 (3323) 620 (3373) uttara ke lie anuvAda kI pAdaTippaNI dekhie / adhyAya-7 (8) 32 varga daNDa (9) 866 varga daNDa aura 4 varga hasta (10) 98 varga daNDa (11) 1200 varga daNDa (12) 3600 varga daNDa (13) 1952 varga daNDa (14) 23783 varga daNDa (15) 63043 varga daNDa (16) 1925 varga daNDa (17) 7425 varga daNDa (18) 50 varga hasta (20) a) 54, 243 (ba) 27; 1213 (22) 84, 252 (24) 48 hasta; 195 varga hasta (26) 378 (27) 135 (29) 189 varga hasta; 135 varga hasta (31) 100% 972, 36; (33) 1600 (34) 2,400 varga daNDa (35) 462 varga daNDa (36) 640 vargadaNDa (38) 324 vargadaNDa; 486 vargadaNDa (40) 13%; 180 (41) 18; 301 (42) 201, 31; (44) 2533, 39 (46) 13; 26 (48) 155 (51) / 768 vargadaNDa; V 48; 4; 4 daNDa (52) 60 varga daNDa; 12; 5; 5 daNDa (53) 84; 12, 5, 9 (55) V 50; 25 (56) 13; 60 (57) 65; 1500 (58) 312, 288; 119; 120, 34560 (59) 315; 280; 48; 252; 132; 168, 224; 189; 44100 (61) V 3240; V65610 / 36000 / 8100000; V4840; V 146410; (62) V360; / 3240; / 3240; V 262440 (64) V6048; V54432; (663) / 2560 daNDa; V 42250 varga daNDa; (683) / 39690 varga daNDa; / 20250 varga daNDa (693) /31360 varga daNDa (713) / 1440 varga daNDa (721) V5760 (753) V360; 12; 6 (773) 192+ / 23040 (783) 192 - V5760 (793) 192 -V 23040 (813) / 11360; V4860; V4840, (833) 16-/160 (853) V8-/10 (873) 16; 12; 48 (893) 20; 8 (913) 3, 4, 5 (923) 5, 12, 13 (943) 16, 30, 34 (963) 5; 3; tIna dazAoM ke liye / (981) a. 60; 61; ba. 11, 61; sa. 11; 60; (1003) 80; 102, 61, 60; 109, 11; 5460 (1023) 169; 407; 169; 120; 312; 119; 34560 (1043) 125, 300, 260; 195, 224; 189; 48; 252, 168; 132; 44100 (1093) 34; 60; 16; (1113) 13, 15, 14, 12 (1133) 4; 1 (1143) / 22 (1153) 6; 3 (1163) VT (1173) 32; (lamba 24 ) (1183) 4 (1193) para ( lambI ) (1213) 3, 8 (1233 aura 1243) 39; 52, 25; 60; 33, 56, 63, 16 (1263) 5, 12 (1283) 5; 12 (1303) 25, 60 (134) 8; 15, 3, 20 (135) 8, 7, 2, 28

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gaNitasArasaMgraha 33 (136) 32; 87; 6; 232 (138) 37; 24; 29; 40 (139) 17; 16; 13; 24 (140) 625; 672; 970; 1904 (141) 281; 320, 442; 880 (143 se 145) vRtta 25920 mahilAe~; 720 daNDa | sama caturazra ( varga ) 34560 mahilAe~; 720 daNDa / samabAhu tribhuja 38880 mahilAe~; 1080 daNDa / Ayatacaturazra : 38880 mahilAe~; 1080 daNDa, 540 daNDa / (147) (i) bhujA 8 (ii) AdhAra 12; lamba5 (149) ; ; ; ; 4 (151) 13; 13, 13, 3; 12 (153 se 1533) 3; 16; 11; 12 (1553) 48 (1573) 5; 6; 4 (1593) (1623) ; ; (1643) 40 (1663) 7; 1; (1673) ; ; 3 (1693) 6 (1703) 10 (1723) 10; 133 (1743) bhujAe~ -5; mukhabhujA ; talabhujA uu (176) 17 (1773 se 1783) (a) 3600; 7200; 10800; 14400; (ba) 54; 90; 126; 166; (sa) 100; 100; 100; 100 (1793) (a) 2700; 7200, 4500; (ba) 50; 70; 80; (sa) 60; 120 ; 60 (1813) 8 hasta; 8 hasta (1823) 7 hasta; hasta; - hasta (1833 aura 1843) 3 hasta; 6 hasta. 9 hasta (1853) 7 hasta; 7 hasta; hasta (1863) 3 hasta; - hasta; hasta (1873) 9 hasta; 12 hasta 9 hasta (1883 aura 1893) 8 hasta; 2 hasta 4 hasta (1993) 13 hasta (1923) 29 hasta (1933 se 1953) 29 hasta ; 21 hasta (1973) 10 hasta (1993 se 2003) 12 yojana; 3 yojana (2043 se 205 ) 9 hasta 5 hasta V 250 hasta (206 se 2073 ) 6 yojana; 14 yojana; V520 yojana (208 3 se 2093) 15 yojana; 7 yojana (2113 se 2123) 13 dina (2143) 18; 13 (2153) 45 (2163) 135 (2173) 65 (2283) 48; 13 (2193) 5 (2203) 4 (2223) varga 14 Ayata : 5; 12; do samAna bhujAoM vAlA caturbhuja bhujAe~ ; mukha bhujA - 6 tala 5 tIna samAna bhujAoM vAlA caturbhuja bhujAe~ ; tala - asamAna bhujAoM vAlA caturbhuja bhujAe~ ; ; mukhabhujA 5; tala 12 samabAhu tribhuja //g samadvibAhu tribhujaH -- bhujAe~ 12; AdhAra 3 viSama tribhuja : bhujAe~; 12, tala (2243) varga, 3 do samAna bhujAoM vAlA caturbhuja : paMpa tIna samAna bhujAoM vAlA caturbhuja : 512 viSama caturbhuja, samabAhu tribhuja : 12, samadvibAhu tribhuja : SaTakoNa : V u, yadi kSetraphala isa adhyAya ke 863 veM zloka meM data niyama ke anusAra jAtA hai / (2263) 8 (2283) 2 (2303) 10 (2323) 6; 2 / : viSama tribhuja : 8 48 kiyA adhyAya-8 (5) 512 ghana hasta (6) 18560 ghana hasta (7) 144320 ghana hasta (8) 162000 ghana hasta (12) 2928 ghana hasta (133) 1458 ghana hasta; 1476 ghana hasta; 1464 ghana hasta (143) 2916 ghana hasta; 2952 ghana hasta 2928 ghana hasta (153) 3360 ghana hasta (163) 18380 ghana hasta (173) 16100 ghana hasta (183) 182833 ghana hasta (213) (i) 3024 ghana daNDa, 2024 ghana daNDa; 4032 ghana daNDa (ii) kendrIya puJja eka ora ghaTatA huA hai 1488; 1488; 1984 ghana daNDa (223) 4032; 1984 ghanadaNDa (243) 40 ghana hasta ( 253) 16 hasta ( 273 ) 12 30 (293) 2304; 20733 (313) / 720; 648 (34) 14 dinAMza, 14, 14, 14, 14 kue~ .kA bhAga (35 aura 36) 13 yojana aura 976 daNDa, 39563 vAha (37 se 383) 17 yojana, 1 kroza

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34 gaNita sArasaMgraha aura 1968 daNDa (393 aura 403) 26 yojana aura 1952 daNDa (413 aura 423) 6 yojana, 2 kroza aura 488 daNDa (453) 6912 ikAI IMTeM (463) 3456 ikAI IMTeM (473) 2184 ikAI IMTeM (483) 108000 ikAI IMTeM (493) 40320 ikAI IMTeM (503) 40320 ikAI IMTeM (513) 20736 ikAI IMTeM (533) 1440 ikAI IMTeM aura 2880 ikAI IMTeM (553) 2640 ikAI IMTeM 1680 ikAI IMTeM (563) 2880 ikAI IMTeM aura 1440 ikAI IMTeM (583) 20; he (59-60) 891 ikAI IMTeM (62) 18720 ikAI IMTeM (683) 64 paTTikA | adhyAya - 9 ghaTI (133) 12 dinAMza (143) 2 (163 se 17) dinAMza; hasta (24) 8 hasta (25) 2 (27) 20 hasta (29) 10 373) paTe dinAMza 8 (383 aura 393) 5 hasta (413 se (49) 175 pAda (50) 1 0 pAda (93) dinAMza (113) 3 10 ghaTI (19) 8 aGgula (22) 16 (31) 5; 50 (34) 5 hasta (35 se 42) 24 aGgula (44) 32 aGgula (46 aura 47) 112 aGgula (51 se 523) 100 yojana / -

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pariziSTa-2 mApa-sAriNiyA~ 1. rekhA mApa * ananta paramANu 8 aNu 8 trasareNu 8 rathareNu 8 u. bho. bA. 8 ma. bho. bA. 8 ja. bho. bA. 8 karmabhUmi kA bAla-mApa 8 lIkSA mApa 8 tila-mApa 8 yava-mApa 500 vyavahArAGgula vartamAna narAGgula 6 AtmAGgula 2 pAda 2 vitasti 4 hasta 2000 daNDa 4 kroza = 1 aNu = 1 trasareNu = 1 rathareNu = 1 uttama bhogabhUmi bAla-mApa = 1 madhyama mogabhUmi kA bAla-mApa asaMkhyAta samaya saMkhyAta Avali 7 ucchvAsa 7 stoka = 1 jaghanya " 39 53 = 1 karmabhUmi kA bAla-mApa 1lIkSA-mApa = 1 tila mApa yA sarasoM-mApa = 1 yava-mApa = 1 aGgula yA vyavahArAGgula = 1 pramANa vA pramANAhula = 1 AtmAGgula = 1 pAda-mApa ( tiryak ) 1 vitarita = 1 hasta = 1 daNDa t = 1 kroza = 1 yojana 2. kAla mApa [] = 1 Avali = 1 ucchvAsa = 1 stoka = 1 lava * isa sambandha meM tiloyapaNNattI meM diyA gayA rekhA-mApa dRSTavya hai 1993 - 132 / + tiloyapaNNattI meM lIkSA ke pazcAt jUM mApa hai| 1 tikoNatI meM daNDa ko dhanuSa, mUsala yA nALI bhI batAyA hai| [] isa sambandha meM tilovapaNNattI meM diyA gayA kAla-mApa dRSTavya hai 1 4; 285-246

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36 gaNitasArasaMgraha 383 lava 2 ghaTI 30 muhUrta 15 dina 2 pakSa 2 mAsa 3 Rtu =1 ghaTI = 1 muhUrta = 1 dina = 1 pakSa =1 mAsa =1 Rtu =1 ayana = 1 varSa 2 ayana 3. dhAritA-mApa (dhAnya-mApa ) 4 SoDazikA = 1 kuDaha 4 kuDaha = 1 prastha 4 prastha =1 ADhaka 4 ADhaka = 1 droNa 4 droNa =1 mAnI 4 mAnI = 1 khArI 5 khArI =1 pravartikA 4 pravartikA =1 vAha 5 pravartikA 4. suvarNa bhAra-mApa 4 gaNDaka = 1 guJjA 5 guJjA =1 paNa 8 paNa =1 dharaNa 2 dharaNa = 1 karSa 4 karSa -1pala 5. rajata bhAra-mApa 2 dhAnya =1 guJjA 2 guJjA = 1 mASa 16 mASa =1 dharaNa 23 dharaNa = 1 karSa yA purANa 4 karSa yA purANa 1 pala 6. lohAdi bhAra-mApa 4pAda =1 kalA 61 kalA =1 yava

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gaNitasArasaMgraha 4 yava = 1 aMza 4 aMza =1 bhAga 6 bhAga = 1 drakSNa 2 drakSaNa -1dInAra 2 dInAra = 1 satera 123 pala =1 prastha 200 pala =1 tulA 10 tulA = 1 bhAra 7. vastra, AbharaNa aura vetramApa 20 yugala = 1 koTikA 8. bhUmi-pramANa 1 dhana hasta ghanIbhUta bhUmi =3600 pala 1 ghana hasta DhIlI (loose) = 3200 pala 9. ITa-pramANa 1 hasta 43hasta 44 aGgula IMTa = ikAI ITa 10. kASTha-pramANa 1 hasta aura 18 aGgula -1 kiSku 96 aGgula lambe aura 1 kiSku caur3e kASThakhaMDa ko Are se kATane meM kiyA gayA kArya = 1 paTTikA 11. chAyA-pramANa manuSya kI U~cAI = usakA pAda mApa

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pariziSTa-5 graMtha meM prayukta saMskRta pAribhASika zabdoM kA spaSTIkaraNa [hindI-varNamAlA krama meM ] zabda sUtra adhyAya pRSTha spaSTIkaraNa abhyukti agaru sugaMdhita kASTha / Amyris agallocha agra Age athavA Arambha kaa| aGga zratajJAna ke bhedoM meM se eka bheda kA nAma aMga hai / ye bAraha hote haiN| lambAI kA maap| akula 25-29 pariziSTa 4 kI sUcI 1 bhI dekhiye| aNu adhvAna 25-27 1 ... paramANu yA aMtyamahattA ko prApta pudgala kaNa / kisI datta saMkhyA ke akSaroMvAle chanda 3361 ke samasta sambhava prakAroM ke dIrgha aura laghu akSaroM ko upasthita karane ke lie udagra (vertical) antarAla / laghu athavA dIrgha akSara ke pratIka kA antarAla eka aMgula tathA pratyeka prakAra ke bIca kA antarAla bhI eka aMgula hotA hai| samAntara yA guNottara zredi meM aMtima pd| bhItarI lamba; do stambhoM ke zikhara se donoM stambhoM ke tala se jAne vAlI rekhA meM sthita bindu taka tata (stretched ) do dhAgoM ke mithazchedana bindu se laTakane vAle dhAge kA maap| antyadhana antarAvalambaka

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gaNitasArasaMgraha zabda / sUtra adhyAya pRSTha spaSTIkaraNa abhyukti antazcakravAla vRtta apara amogha varSa ::: kaGkaNa kI bhItarI paridhi / uttara, bAda kii| rAjA kA nAma; (sAhityaka) : vaha jo vAstava meM upayogI varSA karate haiN| khaTTI pattiyoM vAlI eka prakAra kI jdd'ii| kAla kA mApa / amlavetasa : Rumex Vesicarius. pariziSTa 4 kI sUcI 2 dekhiye| : ayana ariSTanemi arjuna :: bAIsa veM tiirthNkr| vRkSa kA naam| Ferminalia Arjuna W. & A. arbuda avanati avalamba avyakta azoka gyArahaveM sthAna kI saMketanA kA nAma / jhukAva / zIrSa se girAyA huA lamba / ajJAta / vRkSa kA nAma / asita Jonesia Aso ka Roxb. Grislea To mentosa. pariziSTa 4 kI sUcI 3 dekhiye| ADhaka dhAnya-mApa Adi Adidhana Adi mizradhana zreDhi kA prathama pada / samAntara zredi ke pratyeka pada ko prathama pada evaM pracaya ke apavartya ke yoga se saMyavita mAna lete haiM / samasta prathama padoM ke yoga ko Adidhana kahate haiN| prathama pada se saMyukta / samAntara zredi kA yog| kisI tribhuja yA caturbhuja ke AdhAra ko saMcarita karanevAlI sarala rekhA kA khaNDa / janendra (Ellipse) AbAdhA Ayata vRtta

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gaNitasArasaMgraha zabda sUtra adhyAya pRSTha spaSTIkaraNa abhyukti AyAma Avali :: lmbaaii| | kAla maap| pariziSTa 4 kI sUcI 2 dekhiye| icchA : trairAzika prazna sambandhI vaha rAzi jisake sambandha meM datta artha ( Rate) para kucha nikAlanA iSTa hotA hai| zanipriya, nIlamaNi hAthI ke dAMta (khIsa ) kA AkAra / kAla mApa / Sapphire : indranIla ibhadantAkAra ucchavAsa pariziSTa 4 kI sUcI 2 dekhiye| uttara dhana 63-64 uttara mizradhana samAntara zreDhi meM pAye jAne vAle pracaya ke samasta apavayoM kA yog| samAntara zreDhi ke pracayoM tathA zreDhi ke yoga ko jor3ane se prApta mizra yogaphala / jala meM Ugane vAlA nalinI puSpa / uchAya yA uuNcaaii| uThe hue sammitIya tala vAlI AkRti / eka prakAra kA caturbhuja / kAla mApa / utpala utsedha unnata vRtta ubhaya niSedha Rtu :: : pariziSTa 4 kI sUcI 2 dekhiye| eka auNDra-auNDraphala / ikAI kA sthAna / kisI sAMdra athavA khAta kI ghanAtmaka samAI kA vyAvahArika mApa jise brahmagupta ne autra kahA hai| dhAtuoM sambandhI bhAra kA maap| . aMza : aMzamUla pariziSTa 4 kI sUcI 6 dekhiye| pariziSTa 4 kI sUcI 3 dekhiye| : bhinnAMza kA vargamUla / aMzavarga : bhinnAMza kA vrg| kadamba : vRkSa kA naam| Nauclea Cadamba. kambukA vRtta 6 zaMkha ke AkAra kI AkRti /

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gaNitasArasaMgraha zabda sUtra adhyAya pRSTha spaSTIkaraNa abhyukti karNa karma karmAntikA karSa kalA kalA savarNa kArSApaNa kiSku sammukha koNa binduoM ko jor3ane vAlI sarala rekhA / jIva ke rAgadveSAdika pariNAmoM ke pariziSTa 1 meM bhI nimitta se kArmANa vargaNArUpa jo pudgala 'karma' dekhie| skaMdha jIva ke sAtha baMdhako prApta hote haiM, unako karma kahate haiN| kisI sAndra athavA khAta kI ghanAtmaka samAI kA vyAvahArika mApa / svarNa yA rajata kA bhAra mApa / pariziSTa 4 kI sUciau~ 4 aura 5 dekhiye| kupya (base) dhAtuoM kA bhAra maap| pariziSTa 4 kI sUcI 6 dekhiye| bhinna / adhyAya tIna ke prArambha meM pAda TippaNI dekhiye| krss| kASTha cIrane ke sambandha meM lambAI kA maap| kuMkuma phUloM ke parAga evaM aMzu / Croeus sativus anupAtI vibhAjana / dhAnya kA Ayatana sambandhI mApa / pariziSTa 4 kI sUcI 3 dekhiye| vRkSa kA nAma / Wrightia Antidysen terica. dhAnya kA Ayatana sambandhI mApa / pariziSTa 4 kI sUcI 3 dekhiye| vRkSa kA nAma / the Amaranath or the Barleria, Pandanus Odoratissimus, kuTTIkAra kuDaba kuddhaa| kutjA kumbha kurvaka ketakI

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gaNitasArasaMgraha zabda adhyAya pRSTha spaSTIkaraNa abhyukti koTi koTikA kroza kRti kRSNAgaru kharva khArI gaccha gaNDaka karor3a, saMketanA kA AThavA~ sthAna / vastra, AbhUSaNa tathA beta kA saMkhyAtmaka | pariziSTa 4 kI maap|.. -- - sUcI 7 dekhiye| lambAI ( dUrI) kA mApa / pariziSTa 3 kI sUcI 1 dekhiye| varga karaNa kriyaa| sugandhita kASTha kI kAlI vibhinnatA / saMketanA kA terahavA~ sthAna / dhAnya kA Ayatana sambandhI mApa / zreDhi ke padoM kI sNkhyaa| svarNa kA bhAra mApa / pariziSTa 4 kI sUcI 4 dekhiye| pUrvAhna meM bItA huA dinAMza / svarNa yA rajata kA bhAra mApa / pariziSTa 4 kI sUciyA~ 4 evaM 5 dekhiye| jiivaa| gatanA Dya guJjA guNa gunnaa| guNakAra guNadhana guNottara zredi ke padoM kI saMkhyA ke tulya sAdhAraNa niSpattiyoM ko lekara, unake paraspara guNanaphala meM prathama pada kA guNA karane se guNadhana prApta hotA hai| guNottara zreDhi (Geometrical progression). kAla mApa guNa saGkalita pariziSTa 4 kI sUcI 2 dekhiye| 53-54 kisI rAzi kA ghana karanA: jisa rAzi kA ghanamUla nikAlanA iSTa hotA hai, use ikAI ke sthAna se prArambha kara tIna-tIna ke samUha meM vibhAjita kara lete haiM / ina samUhoM meM se pratyeka kA dAhinI ora kA aMtika aMka ghana kahalAtA hai| ghanamUla nikAlane kI kriyaa| bana mUla

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cakrikAbhaJjana caturmaNDala kSetra campaka vaya chanda janya zabda jambU jina sUtra caramA citi citra kuTTIkAra citra kuTTIkAra mizra 273 jinapati jyeSTha dhana DuNDuka 6 823 6 68 1032 303 216 333/ 903 64 ? 833 102 67 adhyAya pRSTha 7 4 2 6 6 6 6 1 201 69 4 22 112 169 177 262 145 | anupAtI vibhAjana samanvita vicitra evaM manoraJjaka prazna | 6 160 anupAtI vibhAjana kriyA ke prayoga garbhita vicitra evaM manoraJjaka nizcita prazna | gaNita sArasaMgraha 80 spaSTIkaraNa 6 91 janmamaraNa ke cakra kA saMhAra karanevAle; rASTrakUTa rAjavaMza ke rAjA kA nAma / madhya sthiti pIle sugandhita puSpa vAlA vRkSa prcy| vaha rAzi jo samAntara zreDha ke uttarottara padoM meM samAna antara sthApita karatI hai / 7 | 204 'bIja' nAmaka datta nyAsa se vyutpAdita tribhuja aura caturbhuja AkRtiyA~ / vRkSa kA nAma / zeSa mUlya zreDhi saMkalana | Dhera / 6 108 | tIrthaMkara | 6 112 sabase bar3A dhana / 8 268 | vRkSa kA nAma / abhyukti jinhoMne ghAtiyA karmoM kA nAza kiyA hai ve sakala jina haiM inameM arahaMta aura siddhagarbhita haiM / AcArya, upAdhyAya tathA sAdhu eka deza jina kahe jAte haiN| kyoMki ve ratnatraya sahita hote haiN| saMta samyaka dRSTi se lekara ayogI paryanta sabhI jina hote haiM / 43 Michelia Champaka A syllabic metre Eujenia Jambalona. jinhoMne aneka viSama bhavoM ke gahana duHkha pradAna karane vAle karma zatruoM ko jItA hai - nirjarA kI hai, ve jina kahalAte hai /

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3838 44 tamAla tAlI tilaka tIrthaM tIrthekara tulA zabda trasareNu triprazna trisamacaturabha daNDa daza daza koMTi daza lakSa daza sadasa dviya zeSamUla dvisama tribhuja disama caturabha dvidvisama caturabha dInAra dRSTa dhana drakSUNa droNa dhanuSAkAra kSetra sUtra 39 1163 1 1 2 26 12 5 63 65 64 64 mr 5 " "" 43 84 43 37 43 adhyAya pRSTha 4 6 6 119 4 72 91 6 1 1 1 1 1 1 1 1 4 "" 2 19 1 1 74 | 9 91 gaNitasAra saMgraha VU U V tIrthoM ko utpanna karanevAlI, cAraghAtiyA karmoM kA nAzakara arhata pada se vibhUSita AtmA / 6 kupya ( Baser) dhAtuoM kA bhAra 8 mApa / 4 kaNa | kSetramApa | 2 saMskRta jyotiSa graMthoM ke kisI adhyAya kA nAma / 181 tIna samAna bhujAoM vAlA caturbhuja kSetra / 4 dUrI kI mApa / 8 2 26 1 spaSTIkaraNa vRkSa kA nAma / 8 vRkSa kA nAma sundara puSpoM vAlA vRkSa / uthalA sthAna jahA~ se nadI Adi ko pAra kara sakate haiN| 8 dasa karor3a / saMketanA kA dasavA~ sthAna | dasa hajAra / mitroM ke vividha praznoM kI eka jAti / 68 180 | do samAna bhujAoM vAlA (samadvibAhu ) tribhuja kSetra | 180 do samAna bhujAoM vAlA caturbhuja kSetra / 180 Ayata kSetra | 6 kupya dhAtuoM kA bhAra mApa / TaMka(sikke) kA nAma bhI dInAra hai| dasa lAkha ( One million ) | jJAta dhana 6 kupya dhAtuoM (Baser metals ) kA bhAra mApa / dhAnya sambandhI Ayatana mApa 190 vRtta ke cApa evaM cApakarNa se sImita kSetra abhyukti Xantho chymus Pictorius pariziSTa 4 kI sUcI 1 dekhiye / pariziSTa 4 kI sUcI 6 dekhiye | ," " pariziSTa 4 kI sUcI 3 dekhiye /

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gaNitasArasaMgraha zabda sUtra adhyAya pRSTha spaSTIkaraNa abhyukti dharaNa 39 / 1 5 | svarNa yA rajata kA bhAra mApa / pariziSTa 4 kI sUciyA~ 4 aura 5 dekhiye| nandyAvarta | 6 | 177 vizeSa prakAra ke bane hue rAjamahala kA nAma / narapAla rAjA; sambhavataH kisI rAjA kA nAma / niruddha laghuttama samApavartya / niSka svarNa TaMka ( sikkaa)| nIlotpala nemikSetra / nIla kamala (jala meM ugane vAlI nIlI nlinii)| 4 do saMkendra paridhiyoM kA madhyavartI | 200 kSetra ( Annulus) / 8 saMketanA kA bArahavA~ sthAna / nyarbuda paTTikA paNa | 267 krakaca karma ( Saw-work ) kA | pariziSTa 4 kI mApa / sUcI 10 dekhiye| svarNa kA bhAra mApa: svarNa TaMka | pArAzaSTa 4 ko (sikkaa)| sUcI 4 dekhiye| 8 DiMDama yA merI paNava 1 (anvAyAma cheda) padma 66 | 1 8 | saMketanA kA paMdrahavA~ sthAna | padmarAga | eka prakAra kA ratna / paramANu | 1 | 4 | pudgala kA avibhAgI kaNa | pariziSTa 4 kI sUcI 1 dekhiye|

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46 gaNitasArasaMgraha zabda adhyAya pRSTha spaSTIkaraNa abhyukti parikarma 3 khd pakSa da pATalI gaNitIya kriyaaeN| indranandi kRta zrutAvatAra (zloka 160 -161) ke anusAra kundakundapura ke padmanandi (arthAt kundakunda) ne apane guruoM se siddhAnta kA adhyayana kiyA aura SaTakhaMDAgama ke tIna khaMDoM para parikarma nAma kI TIkA likhii| yaha anupalabdha hai| (triloka prajJapti, bhAga 2, 1951 kI prastAvanA se uddhRt)| svarNa, rajata evaM anya dhAtuoM kA pariziSTa 4 kI bhAra maap| sUciyA~ 4, 5, 6 dekhiye| | kAla maap| pariziSTa 4 kI sUcI 2 dekhiye| madhura gaMdha vAle puSpoM Bignonia vAlA vRkSa / Suaveolens, lambAI kA maap| pariziSTa 4 kI sUcI 1 dekhiye| 108 pArzvanAtha, 23veM tIrthakara / bAjU meN| 73 vRkSa kA nAma / Rottleria Tinctoria 6 | rajata kA bhAra mApa, sambhavataH | pariziSTa 4 kI TaMka bhii| sUcI 5 dekhiye| eka prakAra kA ratna / 213/ pizAca sambandhI; isaliye atyanta kaThina athavA jttil| vividha prshnaabli| pArzva yA bAjU kI bhujA / guNana / | (sAhityika ) vaha jo pUrNa rUpa se bhara athavA tuSTa kara detI hai; yahA~ svarNa mizrita kupya dhAtue~; talachaTa . (dross ) / pAda Km. << pArzva punnAga purANa puSyarAga paizAcika GN prakIrNaka pratibAhu pratyutpanna prapUraNikA m al_G.

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gaNitasArasaMgraha zabda sUtra adhyAya pRSTha spaSTIkaraNa abhyukti prabhAga pramANa 3 59 / bhinna kA bhinna (bhAga kA bhaag)| 1 4 lambAI kA mApa / pariziSTa 4 kI sUcI 1 dekhie| icchA kI saMvAdI datta rAzi jo trairAzika praznoM se sambandhita hai| dhAnya sambandhI Ayatana mApa / pravartikA prastha pariziSTa 4 kI sUciyA~ 3 aura 6 dekhiye| prakSepaka prakSepaka karaNa plakSa FNT ur ur v 108 anupAtI vitaraNa / 08 anupAtI vitaraNa sambandhI kriyA / | 268 vRkSa kA nAma; produmbara / Fious Infectoria, or Religiosar phala trairAzika prazna meM nikAlI jAne vAlI rAzi kI saMvAdI datta raashi| 7 kaGkaNa kI bAhirI paridhi / bahizcakravAla vRtta 197 bANa 111, bAlendu kSetra bIja dhanuSAkAra kSetra meM cApa aura cApakarNa kI mahattama udagra duurii| (height of a segment) 200 caMdramA kI kalA sadRza kSetra / / ( sAhityika ), boyA jAne vAlA dhAnya aadi| 204 | (yahA~) isakA upayoga dhanAtmaka do pUrNAGkoM ke abhidhAna hetu hotA hai jinake guNanaphala evaM vargoM kI sahAyatA se bhujAoM ke mApa ko nikAlane para samakoNa tribhuja saMracita hotA hai| | 7 bhAga kupya ( baser ) dhAtuoM kA mApa pariziSTa 4 kI sUcI 6 dekhiye| bhAgAnubaMdha 113 saMyava bhinna ( Fractions in association) viyuta bhinna (Dissociated fractions ) bhAgApavAha

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gaNitasArasaMgraha zabda sUtra adhyAya pRSTha spaSTIkaraNa abhyukti bhAgAbhyAsa bhAgabhAga bhAgamAtR sy bhAga samvarga bhAgahAra bhAjya 4 | 68 | prakIrNaka bhinnoM kA eka prakAra / | 360 jaTila bhinna (Complex frac --- - tion ) / bhAga, prabhAga, bhAgabhAga, bhAgAnubandha, aura bhAgApavAha bhinna jAtiyoM ke do yA do se adhika prakAroM ke saMyoga se saMracita / prakIrNaka bhinnoM kI eka jAti / vibhAjana kriyaa| ghanamUla samUha kI racanA karane vAle tIna sthAnoM meM se bIca kA sthAna / jisameM bhAga dete haiN| kupya ( baser ) dhAtuoM kA mApa / pariziSTa 4 kI sUcI 6 dekhiye| bhAra bhinna kuTTIkAra 123 | bhinnIya rAziyoM kA antardhAraka anupAtI vitaraNa / prakIrNaka bhinnoM kI eka jAti / 72 vRkSa kA nAma / bhinna dRzya madhuka Bassia Latifolia madhyadhana mardala (anvAyAma cheda) 2 | 21 / samAnAntara zredi kA madhya pada / | 188 DiDima yA bherii| mahAkharva 1 mahApadma mahAvIra mahAzaMkha mahAkSityA mahAkSobha mahAkSoNI rrrrrrr . saMketanA kA caudahavA~ sthAna | saMketanA kA solahavA~ sthAna / 1 24veM tIrthaMkara varddhamAna svAmI / saMketanA kA bIsavA~ sthAna / saMketanA kA bAIsauM sthAna / saMketanA kA caubIsavA~ sthAna / saMketanA kA aThArahavA~ sthAna / 167 cheda (section); vaha anurekhA jisa para se kASTha kA Tukar3A Are se cIrA jAtA hai| mArga 8

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mAnI mASa zabda mizradhana mukha muraja muhUrta mUla mUlamizra meDa mRdaMga (anvAyAma cheda) yava yada koTi yoga yojana rathareNu rUpa romakApurI sUtra 37 40 80-82 50 32 * w m 26 3 3 5 32 27 42 53 42 31 26 973 adhyAya pRSTha 1 1 2 7 9 1 2 4 4 5 4 5 1 5 gaNita sAra saMgraha 188 mRdaMga ke samAna DiMDima yA bherI / 5 kAla mApa 83 spaSTIkaraNa dhAnya sambandhI Ayatana mApa / rajata kA bhAra mApa TaMka (sikkA) / 24 saMyukta yA milA huA yoga / 193 caturbhuja kI UparI bhujA (top-side) zaGkhAkAra aura | mRdaGga AkAra vAle kSetroM meM bhI mukha kA upayoga huA hai| 15 vargamUla; prakIrNaka bhinnoM ko eka jAti 68 68 | jisameM vargamUla aMtarbhUta ho; prakIrNaka mitroM kI eka jAti / jambUdvIpa ke madhyabhAga meM sthita sumeru parvata / vizeSa vivaraNa ke liye triloka prajJapti bhAga 2 meM (4 / 1802 - 1811 ; 4 / 2812, 2823) dekhiye / 1 4 1 6 9 270 188 eka prakAra kI DiMDima yA bherI / 1 4 6 111 9 270 49 abhyukti pariziSTa 4 kI sUcI 2 dekhiye / pariziSTa 4 kI sUcI 5 dekhiye | tapasyA; dhyAna kA abhyAsa lambAI kA mApa eka prakAra kA dhAnya lambAI kA mApa pariziSTa 4 kI eka prakAra kA dhAtu mApa / sUcI 1 dekhiye / laMkA ke pUrva se 900 kI ora eka sthAna / 75 vacana kAya ke nimitta se AtmA ke ( jaina paribhASA ) pradezoM ke caMcala hone kI kriyA / pula kaNa pUrNAMka | / laMkA ke pazcima se 90deg kI ora eka sthAna / pariziSTa 4 kI sUcI 2 dekhiye / ( anya mata se ) pariziSTa 4 kI sUcI 1 dekhiye / 59 59

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50 laGkA lava lakSa lAbha vakula zabda vajra (anvAyAma cheda) vajravartana vargamUla varNa vardhamAna vallikA vallikA kuTTIkAra sUtra 33 64 5 25 32 2 w 36 169 1 } 1152 vAha 38 vicitra kuTTIkAra 216 vitasti vidyAdhara nagara viSama kuTTIkA viSama caturazra 30 62 134 5 adhyAya pRSTha spaSTIkaraNa 9 270 | vaha sthAna jahA~ ujjaina se nikalane vAlA dhruvavRtta ( meridian ) viSu vat rekhA se milatA hai / kAla mApa / 1 6 4 60 3 2 6 7 5 8 lAkha, saMketanA kA chaThavA~ sthAna / bhajanaphala yA hissA ( aMza ) / 92 72 vRkSa kA nAma / 5 83 1 gaNitasArasaMgraha 188 iMdra kA Ayudha / 36. | bhinnoM ke guNana meM tiryak prahrAsana / 15 vaha iSTa rAzi jisakA varga karane se vaha datta rAzi utpanna hotI hai jisakA vargamUla nikAlanA iSTa hotA hai / 6 135 ( sAhityika ) raMga zuddha svarNa 16 varNa kA mAnakara datta svarNa kI zuddhatA ke aMza kA abhidhAna varNa dvArA hotA hai / caubIsaveM tIrthaMkara | 115 1 5 6 145 latA sadRza aMkazRMkhalA para AdhArita anupAtI vitaraNa | dhAnya sambandhI Ayatana mApa / anupAtI vibhAjana samanvita vicitra evaM manoraJjaka praznAvali / 4 lambAI kA mApa / 8 267 yahA~ AyatAkAra nagara kA prayojana mAlUma par3atA hai / 6 123 bhinnIya rAziyoM kA aMtardhAraka anupAtI ( bhinna kuTTIkAra ) / 181 | sAmAnya caturbhuja / abhyukti pariziSTa 4 kI sUcI 2 dekhiye / Mimusops Elengi. pariziSTa 4 kI sUcI 1 dekhiye /

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gaNitasArasaMgraha zabda adhyAya pRSTha spaSTIkaraNa abhyukti viSama saMkramaNa koI bhI datta do rAziyoM ke bhAjaka aura bhajanaphala dvArA prarUpita do rAziyoM ke yoga evaM aMtara kI arddha rAziyoM sambandhI kriyaa| prathama tIrthaMkara kA nAma / lambAI kA mApa / vRSabha 108 vyavahArAMgula 27 1 4 pariziSTa 4 kI sUcI 1 dekhiye| vyutkalita zaGkha zata 8 zata koTi zAka zAnti zeSa 2 32 | samAnAntara zredi kI samasta zredi meM se zreDhi kA aMza ghaTAne kI kriyA / saMketanA kA unnIsavAM sthAna / sau saikdd'aa| sau krodd'| 267 vRkSa kA nAma ( Teak tree ) / 108 zAntinAtha tIrthaGkara / Arambha se zreDhi ke aMza ko nikAla dene para zeSa bacanevAle pada / aparAhna meM bItanevAlA dinAMza / prakIrNaka bhinnoM kI eka jAti / ghanamUla samUha ke tIna aMkoM meM se ek| zeSanADya zeSamUla zodhya 53-14 zrAvaka zrIparNI jainadharma kA pAlana karane vAlA gRhastha / vRkSa kA nAma / Premna Spinosa. zraGgATaka SoDazikA tribhujAkAra stUpa / dhAnya sambandhI Ayatana mApa / pariziSTa 4 ko sUcI 3 dekhiye| sakala kuTTIkAra saGkramaNa ---- -6 124 anupAtI vitaraNa jisameM bhinna aMta bhUta nahIM hote| | do rAziyoM ke yoga evaM antara kI arddha rAziyoM sambandhI kriyA / zredi kA yoga nikAlane kI kriyA / 3 saGkalita saGkrAnti 5 | 85 | sUrya kA eka rAzi se dUsarI rAzi meM praveza karane kA maarg|

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52 satera samacaturabha sama tribhuja samaya samavRtta sarala sarja zabda sarvadhana sallakI sahasra sArasa sAra saMgraha sAla siddha siddhapurI sumati suvarNakuTTIkAra suvrata sUkSmaphala stoka sUtra 43 1123 5 32 w 6 26 63 36 23 24 1 169 adhyAya pRSTha 1 nono 67 63-64 2 63 7 kono 4 1 8 | 268 21 80 1 4 6 spaSTIkaraNa 6 | kupya ( baser) dhAtuoM kA bhAramApa / 213 vargAkAra AkRti | 189 6 vaha tribhuja jisakI saba bhujAe~ samAna hoN| / kAlamApa eka paramANu kA dUsare paramANu ke vyatikrama karane meM jitanA kAla lagatA hai, use samaya kahate haiN| 181 vRtta ( Circle ) | 72 vRkSa kA nAma 67 8 gaNita sArasaMgraha 72 hajAra / 74 eka prakAra kA pakSI / 3 ( sAhityaka ) kisI viSaya ke 91 * 108 2 181 23 1 5 vRkSa kA nAma ( sAla vRkSa ke samAna ) / samAntara zredi kA yoga / vRkSa kA nAma / mukta aamaa| 9 | 270 | laGkA ke pratidhruvastha | siddhAntoM kA saMkSipta pratipAdana / ( yahA~ ) gaNita graMtha kA nAma / vRkSa kA nAma / ghAtiyA aura aghAtiyA karmoM kA nAza kara aSTaguNoM Adi ko prApta abhyukti pariziSTa 4 kI sUcI 6 dekhiye / pariziSTa 4 kI sUcI 2 dekhiye / Pinus Longifolia 4 pAMcaveM tIrthaGkara kA nAma / 70 6 135 svarNa sambandhI praznoM meM prayukta anu pAtI vitaraNa | bIsaveM tIrthaMkara kA nAma / kSetraphala athavA ghanaphala kA zuddha mApa / pariziSTa 4 kI sUcI 2 dekhiye / kAlamApa | Boswellias Thurifera Shorea Ro busta, or Valeria Robusta.

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gaNitasArasaMgraha zabda sUtra adhyAya pRSTha spaSTIkaraNa abhyukti syAdabAda "kathaMcit" kA paryAyavAcI zabda / (pAda TippaNI bhI dekhiye ) / sone kA TaMka ( sikkA ) / lambAI kA mApa / svarNa hasta 4 suvarNa bhii| pariziSTa 4 kI sUcI 1 dekhiye| Phaenix or Elate Paludosa. hintAla 6 119 vRkSa kA nAma / kSityA kSepapada 70 2 saMketanA kA ikkIsavAM sthAna | 22 samAntara zreDhi ke dugune prathama pada evaM pracaya ke aMtara kI arddharAzi / saMketanA kA satrahavAM sthAna / | saMketanA kA teIsavAM sthAna / kSoNI kSobha 6 8818 pAnA maga prtaapaan| noTa-uparyukta sAraNI meM sUtra adhyAya evaM pRSTha ke prArambha ke kucha stambha bhUla se rikta raha gaye haiN| unheM kramAnusAra nIce diyA jA rahA hai agru-9|3|37 agra-62 / angg-45|4|75| anggul-27|1|4| aNu-4 adhvaan-177| antydhn-63|2|21| antraavlmbk-18037/236| antazcakravAla vRtt-673|7|197) apr-272| amoghvrss-3|1|| amlvets-67/8|268| ayn-35|1|| arissttnemi-84116|108| arjun-67|8|268| arbud-65|1|8| avnti-277| avlmb-192| avykt-122|3|62| ashok-241472| asit-678.268| aaddhk-36|1|5 aadi-64||2|| aadidhn-21|| Adi mizradhana-24| aabaadhaa-49|7|192| aaytvRtt-181| aayaam-9/7/184| aavli-32|1|4| icchaa-25483| indrniil-220|6|147/ ibhdntaakaar-803200| ucchvaas-33|1|5|

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54 gaNitasArasaMgraha uttara dhn-2|| uttara mishrdhn-24|| utpnn-140|3|67| utsedh-19817241| unnata vRtt-181| ubhaya nissedh-189|| Rtu-35|1|5| ek-63|1|8| aunnddr-aunnddrphl-251| ... aNsh-42|1|6| aNshmuul-3|4|68 aNshvrg-3|4|68| kdmb-6|469| kmbukaavRtt-181|| krnn-194|| krm-60|17| krmaantikaa-253| karSa 39-40 / 15 / klaa-42|1|6| kalA svrnn-2|3|36| korssaapnn-11|5|84| kissku-63|8|267/ kungkm-63|3|10| kuttttiikaar-108| kuddb-kuddhaa-36|15| kuttj-23|4|72| kumbh-38|11| kurbk-26|472| ketkii-102|3|59| kotti-64|18| kottikaa-45|16| krosh-31|1|4| kRti-13|3|38| kRssnnaagru-6|5|84| khrv-66|18| khaarii-37|1|| gcch-61||20| gnnddk-39|115| gtnaaddy-271| gunyjaa-39|115| gunn-181|| gunnkaar-2|3|36| guNadhana-28 guNa sngklit-94|2|29| ghn-43|2|16| ghnmuul-53|2|18| ghttii-33|1|5|

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pariziSTa-5 DaoN0 hIrAlAla jaina ne jaba san 1923 - 24 meM kAraMjA ke jaina bhaNDAroM kI granthasUcI taiyAra kI thI tabhI se unheM vahA~ kI gaNitasAra saMgraha kI prAcIna pratiyoM kI jAnakArI thI / prastuta grantha ke punaH sampAdana kA vicAra utpanna hote hI unhoMne una pratiyoM ko prApta kara unake pAThAntara lene kA prayatna kiyaa| isa kArya meM unheM unake priya ziSya va vartamAna meM pAlI prAkRta ke prAdhyApaka zrI jagadIza killedAra se bahuta sahAyatA milii| ukta pratiyoM kA jo paricaya tathA unameM se upalabdha TippaNa yahA~ prastuta kiye jA rahe haiM ve ukta prayAsa kA hI phala hai / ataH sampAdaka ukta sajjanoM ke bahuta anugrahIta haiM / kAraMjA jaina bhaNDAra kI pratiyoM kA paricaya kramAMka - a0 naM0 63 ( 1 ) ( mukha pRSTha para ) chattIsI gaNita graMtha ( 1 ) - ( puSpikA meM ) sArasaMgraha gaNitazAstra / ( 2 ) patra 49 - prati patra 11 paMktiyA~- AkAra 11. 7545" (3) prathama vyavahAra patra 15, dvitIya 22 (1), dvitIya 32, tRtIya 37, caturtha 42 ( 4 ) prAraMbha - // 80 // OM namaH siddhebhyaH // alaMghyaM trijagatsAraM 30 (5) antima - ( patra 42 ) iti sArasaMgrahe nAma caturtho vyavahAraH samAptaH // zrIvItarAgAya namaH // cha // chattIsametena sakala 8 bhinna 8 bhinnajAti 6 prakIrNaka 10 trairAzika 4 iMttA 36 nU chattIsame budu vIrAcAryarU pelhagaNitavanu mAdhavacaMdratraividyAcAryaru zodhisidarA gi zodhya sArasaMgrahame nisikoMbudu | vargrasaMkalitAnayanasUtraM // gaNitazAstre mahAvIrAcAryasya kRtau trirAziko (6) antima - ( patra 49 ) ghanaM 35 aMkasaMdRSTiH chaH // iti chattIsIgaNitagraMthasamAptaH // cha // cha // zrIH // zubhaM bhUyAt sarveSAM // // saMvat 1702 varSe mAtra zira vadI 4 budhe saMvat 1702 varSe mAha zrudi 3 zukle zrImUlasaMghe sarasvatIgache balAtkAragaNe zrIkuMda kuMdAcAryAnvaye bha0 zrIsakala kIrtidevAstadanvaye bha0 zrIvAdibhUSaNa tatpaTTe bha0 zrIrAmakIrtitatpaTTe bha0 zrIpadmanaMdIvirAjamAne AcAryazrInareMdrakIrttistacchiSya bra0 zrIlAyakA tacchiSya bra0 kAmarAjasta cchiSya bra0 lAlaji tAbhyAM zrIrAyadeze zrIbhIloDAnagare zrIcaMdraprabhacaityAlaye dosI kuMhA bhAryA padamA tayoH sutau dosI kezara bhAryA lAchA dvitIya suta dosI vIrabhANa bhAryA jitAde tAbhyAM svajJAnAvarNikarmakSayArthaM nijadravyeNa likhApya chattIsIgaNitazAstraM dattaM zrIrastu // (7) prAptisthAna- balAtkAragaNamaMdira, kAraMjA, a0 naM0 63 (8) sthiti utkRSTa, akSara spaSTa, ( 9 ) vizeSatA - pRSThamAtrA, TippaNa - ( samAsa me )

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gaNitasArasaMgraha prati kramAMka-a0 naM064 (1) sArasaMgraha gnnitshaastr| (2) patrasaMkhyA 142 pratipatra 10 paMktiyA~-pratipaMkti 25 akSara AkAra 514411" / (3) prathamavyavahAra 37 dvitIya 78 tRtIya 95 caturtha 104 paJcama 111 SaSTha 131 saptama 140 aMtima 142 / (4) prArabha-80 // zrI jinAya nmH|| zrIgarubhyo namaH // praNipatya varddhamAnaM vidyAnaMdaM vizuddhaguNanilayaM / sUriM ca mahAvIraM kurve tadgaNitazAstrasadvati // 1 // alaMdhyaM ityAdi / aMtima-chattIsI TIkA graMthasaMkhyA 30005 zubhaM bhavatu / zrIrastu / / zubhaM / / svasti zrI saMvat 1616 varSe kArtika sudi 3 gurau zrIgaMdhArazubhasthAne zrImadAdijinacaityAlaye zrImUlasaMghe zrIsarasvatIgacche zrIbalAtkAragaNe zrIkaMdakaMdAcAryAnvaye bha0 padmanaMdidevAstatpaTTe bha0 zrIdeveMdrakIrtidevAstatpaTTe bha0 zrIvidyAnaMdidevAstatpaTTe bha. zrI mallibhUSaNadevAstatpaTTe bha. zrIlakSmIcaMdradevAstapaTTe bha0 zrIvIracaMdradevAstatpaTTe bha0 zrIjJAnabhUSaNadevAstadanvaye AcAryasumatikIrtarupadezAt zrIhaMba jJAtIya sonI sAMtu bhAryA bAI haraSAI tayoH putra sonI devara bhAryA maraghAI tayoH sutau sonI devajI kSImajI eteSAM madhye sonI dedharakena idaM zAstraM likhApya pradattaM kiMcat zrAvakaiH likhApitaM / / cha / / AvIrattabhUSaNAnAmidaM / / chattIsi gaNitani TikA saMvat 1842 miti vesAkha sudi 11 bhaTTAraka zrIvIdyAbhUSaNa idaM gaNata chattisI bhaTTAraka zrI devendrakIrtijIjyAM pradattaM subhaM bhUyAt / (6) balAtkAra maMdira kAraMjA ka0 64 / prati kramAMka-a0 naM065 (1) sArasaMgraha gaNitazAsa-prazasti me-SaTatriMzatikAgaNitazAstra / (2) patra 53; prati patra 10 paMktiyA~; AkAra 11"4475 / (3) prathama vyavahAra 16, dvitIya 34; tRtIya 40; caturtha 46; paMcama 53 / (4) praarNbh-80|| zrIvItarAgAya namaH // alaMdhyaM trijagatsAraM ityAdi / (5) antima-(patra 53) ghanaM // iti sArasaMgrahe gaNitazAstre mahAvIrAcAryasya kRtau vargasaMkalitAdivyavahAraH paMcamaH smaaptH|| saMvat 1725 varSe kArtika zudi 10 bhaume zrImUlasaMdhe sarasvatIgache balAtkAragaNe zrIkuMdakuMdAcAryAnvaye bha0 zrIsakalakIrtyanvaye bha0 zrIvAdibhUSaNadevAstatpaTTe bha0 zrIrAmakIrti devAstatpaTTe bha0 zrIpadmanaMdidevAstatpaTTe bha0 zrIdeveMdrakIrtigurUpadezAt muni zrIzrutakIrtistacchiSya muni zrIdevakIrtistacchiSya AcArya zrIkalyANakIrtistacchiSya muni zrItribhuvanacaMdreNedaM SaTatriMzatikA gaNitazAstraM karmakSayAthai likhitaM / / prAptisthAna-balAtkAragaNamaMdira, kAraMjA, a0 naM0 65 / (8) sthiti madhyama, akSara spaSTa / (9) vizeSatA-samAsa me TippaNa: kvacit pRSThamAtrA /

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gaNita sArasaMgraha noTa - aisA pratIta hotA hai mAno yaha mAdhavacaMdra traividyadeva kA vibhinna graMtha ho 1. varga saMkalitAnayanasUtraM / 296-97 / 2. ghana saMkalitAnayanasUtraM / 301-82 / 3. ekavArA disaMkalitadhanAnayanasUtraM / 4. sarvadhanAnayane sUtradvayaM / 5. uttarottaracayabhavasaMkalitadhanAnayanasUtraM / 6. ubhayAntAdAgata puruSadvaya saMyogAnayanasUtraM / 7. vaNikkara sthitaghanAnayanasUtraM / 8. samudramadhye - 1-2-3 / 9. chedozazeSa jAtau karaNasUtraM / 10. karaNasUtratrayam / 11. guNaguNyamizre sati guNaguNyAnayanasUtraM / 12. bAhukaraNAnayanasUtraM / 13. vyAsAdyAnayanasUtraM / iti sArasaMgrahe gaNitazAstre mahAvIrAcAryasya kRtau vargasaMkalitAdivyavahAraH paMcamaH samAptaH / prati kramAMka - a0 naM0 62 ( 1 ) uttarachattIsI TIkA / (2) patra 19; prati patra 13 paMktiyA~; AkAra 11" x 4-75 / ( 3 ) AraMbha - OM namaH siddhebhyaH // siddhebhyo niSThitArthebhyo i0 / ( 4 ) antima - ghanaH 2927715584 // cha // iti zrIuttarachattIsI TIkA samAptA // * AcArya zrIkalyANakIrtistacchiSya muni zrItribhuvanacaMdreNedaM gaNitazAstraM likhitaM // ujalo pASANa sutArI gaja 1 samacorasa maNa 48 pAlevo pASANa gaja 1 maNa 60 SAro pASANa gaja 1 maNa 40 / ( 5 ) prAptisthAna - a0 naM0 62 / (6) sthiti uttama, akSara spaSTa / ( 7 ) kvacit TippaNa | prati kramAMka - a0 naM0 66 ( 2 ) patra 15; pratipatra 14 paMktiyA~; AkAra 11-545" ( 3 ) * brahma jasavaMtAkhyena svaparapaThanArthe svahastena likhitaM / (5) a0 naM0 66 / 57 prati kramAMka - a0 naM0 60 ( 2 ) patra 20 pratipatra 11 paMktiyA~ AkAra 12" 45" 5 ! (5) a0 naM0 60 /

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gaNitasArasaMgraha prati kramAMka-a0 naM061 (2) patra 18; pratipatra 14 paMktiyoM; AkAra 105 46" / (5) a0 naM0 61 / gaNitasArasaMgraha pratikramAMka 63% a, pra0kra065 =ba, pra0kra064%sa arthabodhaka TippaNa zloka 1-1 aladhyam-a mithyAdRSTibhiH / ba mithyAdRSTibhiH lavayitum yazakyamityarthaH / sa AptAbhAsAgamyam atallabhyamasti / sa trijagatsAram-nirAvaraNatvAdananyasAdhAraNatvAcca lokatrayasAram , trijagadvyArAdhyamityarthaH / a anantacatuSTayam anantajJAna-darzana-sukha-vIryacatuSTayam / sa tasmai mahAvIrAya vardhamAnasvAmine / sa jinendrAya-ekadezena karmArAtIn jayantIti jinA asaMyatasamyagdRSTyAdayasteSAmindraH svAmI, tasmai nmH| atAyine-dharmopadezakatvena bhavyatrANAya / zloka 1-2 a ji [jainendreNa-jino devatA yeSAM te jainAH, teSAmindraH, tena / pakSejinendrasyAyaM sambandhI jainendraH tena vA / jina eva jainaH, sa eva indraH pradhAno yatra saMkhyAjJAnapradIpe saH, tena / sa jainendreNa-jinapraNItena / sa saMkhyAjJAnapradIpena-gaNitazAstrajyotiSA / sa mahAtviSAbahuprakAzena / sa sarvam - SaDbhavyasamudAyarUpam / a tam-mahAvIram , pakSe saMkhyAjJAnapradIpam / / zloka 1-3 sa prINitaH-tarpitaH / sa prANisasyauSaH vineyajanasya sNghaatH| a nirItiHnirgatA ItayaH ativRSTyanAvRSTimUSaka-zalabha-zuka-svacakra-paracakralakSaNAH yasmAt asau nirItiH / a niravagrahaH-nirgato'vagrahaH zatruH yasmAt yatra vA saH, vythaa-vrssaavidhaatrhitH| sa zrImatA-lakSmImatA / a amoghavarSeNa-saphalavRSTyA, pakSe satyasvarUpopadezavRSTyA / sa saphalasaddharmopadezAmRtavRSTyA / a sveSTahitaiSiNA-svastha iSTaM sveSTam , tacca taddhitaM ca sveSTahitam, tadicchatIti sveSTahitaiSI tena | vA svasya iSTAH sveSTAH, tAn prati hitam icchatIti sveSTa hitaiSI, tena / sa sveSTahitamicchatA / zloka 1-4 a cittavRttihavirbhujI [ji]-shukldhyaanaanau| sa bhasmasAt bhAvam-bhasmasvarUpam / 'aIyu:-gacchanti sma / a te-AgamaprasiddhAH kaam-krodhaadishtrvH| a avandhyakopAH [pa]saphalakopAH ityrthH| zloka 1-5 sa vazIkurvan-svAdhInaM vidadhat / sa nAnuvazaH-anyAdhIno na bhavati / sa praiHekaantvaadibhiH| abhibhUtaH-a parAbhUtaH / sa tiraskRtaH / sa prbhuH-jgdaaraadhyH| sa apuurvmkrdhvjH-abhinvmiinketnH| zloka 1-6 a vikrama-kramAkrAnta-cakrIcakra-kRtakriyaH-vikramakrameNa parAkramasaMtatyA AkrAntAH te ca te cakriNazca, teSAM cakraM samUhaH, tena kRtakriyA sevA yasyAsau tathoktaH / pakSe cakra senAsti yeSAM te cakriNaH, zeSaM pUrvavat / a cakrikAbhaJjanaH-saMsAracakrabhaJjanaH, pakSe-paracakrabhaJjanaH / a aJjasAparamArthena / zloka 1-7 a vidyAnadyadhiSThAna:-vidyA dvAdazAGgalakSaNAH pakSe-dvAsaptatikalAlakSaNAstA eva nadyaH tAsAm adhiSThAnam AzrayaH yaH sH| sa maryAdAvajravedikaH-maryAdaiva vajravedikA yasya saH / a ratnagarbhaH-ratnAni samyagdarzanAdIni, pakSe- svAdIni, garbhe te yasya so [yasyAsau] / va ratnAni samyagdarzanA. dIni, pakSe-hastyazvAdIni garbhe te yasyAsau tathoktaH / a yathAkhyAtacAritrya [tra] jaladhiH-kSAyikacAritrya [tra] jaladhiH, pakSe-yathAkhyAtaM pravRddhairyathoktam , taccataccAritryaM [] AcaraNaM ca /

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gaNitasArasaMgraha zloka 1-8 sa devasya - sa jinasya / sa zAsanam anekAntarUpaM vardhatAm / zloka 1-9 sa lokike - vRddhivyavahArAdau / a vaidike --Agame / sa sAmAyike - pratikramaNAdau / a yaH yaH kazcit vyApAraH pravRttiH tatra sarvatra saMkhyAnaM gaNitam upayujyate upayogI bhavati / zloka 1-10 a arthazAstre - jIvAdikapadArthe / zloka 1-11 a prastutam -- kathitam / apurA -- pUrvam / 59 zloka 1 - 12 a grahacAreSu - saMkramaNeSu / ba sUryAdisaMkramaNeSu / sa grahaNe - candra-sUryoparAge / a grahasaMyutau -- grahayuddhe / a triprazne -- trayaH praznAH naSTa - muSTi-cintArUpAH yatra tat tripraznam, horAzAstramityarthaH, tasmin / sa athavA trayo dhAtu-mUla-jIvaviSayAH praznAH yatra tat tripraznam / praznavyAkaraNAya sadbhAvakevalajJAna horAdizAstram / sa candravRttau - candracAre / ba omits budhyante ( zloka 14 ) / ba omits -- yAtrAdyAH ( zloka 15 ) / zloka 1-13 a parikSipaH - paridhiyaH / zloka 1-14 a utkarAH - samUhAH / a budhyante - jJAyante / zloka 1 - 15 a tatra -- zreNIbaddhAdiSu jIvAnAm / a saMsthAnam - samacaturasrAdi / a aSTaguNAdayaH - aNimAdayeH / a yAtrAdyAH -gati / a saMhitAdyAzca - saMdhipratiSThAgrantho vA / zloka 1-17 a guruparvataH - guruparipATIbhyaH / zloka 1-20-a kalA savarNa saMrUDha luThatpAThIna saMkule - kIdRgvidhe sArasaMgrahavAridhau / kalAsavarNAH bhinnapratyupannAdayaH te eva luThatpAThInAsteSAM saMkaTe saMkocasthAne / zloka 1-21 a prakIrNaka-a tRtIyavyavahAraH / a mahAgrAhe -- matsyavizeSaH / a mizraka - a vRddhivyavahArAdi / zloka 1-22 a kSetravistIrNa pAtAle - tribhuja - caturbhujAdikSetrANi eva vistIrNapAtAlAni yatra sa tasmin / a khAtAkhyasikatA kule -- khAtAkhyam eva sikatAH tAbhiH Akule | a karaNaskandhasaMbandhacchAyAbelA virAjite - karaNaskandhena karaNasUtrasamUhena saMbandho yasyAH sA karaNaskandhasaMbandhA, sA cAsau chAyAgaNitaM ( 1 ) karaNaskandhasaMbandhacchAyA, sA eva velA, tayA virAjitA tasmin / zloka 1-23 a guNasaMpUrNaiH - laghukaraNAdyaSTaguNasaMpUrNaiH / karaNopAyaiH - a karaNAnupayogopAyaiH sUtraiH / zloka 1-24 a yat -- yasmAt sarvazAstre / saMjJayA - a paribhASayA / zloka 1-25-a paramANuH / paramANusvarUpam - aNavaH kAryaliGgAH syudvisparzAH parimaNDalAH / ekavarNa- rasAH nityAH syuranityAzca paryayaiH // 34 ( 1 ) apradezinaH iti gomaTasAre / paramANupiNDarahitamiti bhAvArtha: / kAryAnumeyAH ghaTapaTAdiparyAyAsteSAm aNUnAm astitve cihnam / sUkSmAH vartulAkArAH / kau dvau snigdha-rUkSayoranyataraH zItoSNayoranyataraH / tathA hi-zIta- rUkSa, zItasnigdha, uSNa-snigdha, uSNa-rUkSa ekAevApekSayA ekayugmaM bhavati / guru-laghu-mRdu-kaThinAnAM paramANuSvabhAvAt teSAM skandhAzritatvAt / * a taiH - paramANubhiH / saH - aNuH syAt / atra so'NuH kSetraparibhASAyAm / ba paramANuH - yastu tIkSNenApi zastreNa chettuM bhettuM mocayituM na zakyate, jalAnalAdibhirnAzaM naiti ekaikarasa-varNa- gandha - dvisparzam / snigdha-rUcasparzadvayamityuktamAdipurANe / zabdakAraNamazabdaM skandhAntaritamAdi - madhyAvasAnarahitamapradezamindriyaira grAhyamavibhAgi tat dravyaM paramANuH /

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gaNitasArasaMgraha baloka 1-26 a atH-annutH| tasmAt-trasareNutaH / shiroruhH-(bhvnti)| zloka 1-27 alikSA-likSApramANaskandhaH / saH-sa tilH| aSTaguNAni-aSTaguNAni bhavanti prasareNvAdyakulAntAni / zloka 1-28 a pramANam-pramANAGgulam / zloka 1-29 a tiryakpAdaH-pAdasya aGguSThakaniSThAparyanta bhAga tirykpaadH| tiryakpAdadvayaM vitastiH / ba tiryagpAda:-omits. zloka 1-31 a paribhASA-aniyamena niyamakAriNI paribhASA / zloka 1-32 a aNuraNvantaram -mandagatimAzritaH san , zIghragatimAzritazcet caturdazarajjum atikrAmati / smyH-proktH| asNkhyaiH-jghnyyuktaasNkhyaiH| ba asaMkhyaiH-omits. lokeomits (?) zloka 1-33 a stoka iti mAnam / teSAm-lavAnAm / sArdhASTAtriMzatA-38 / zloka 1-34 a pakSaH-bhavet / zloka 1-35 ataiH-RtubhiH / vatsaro sNvtsrH| zloka 1-36 a ttr-dhaanymaane| catasraH-SoDazikaH / kuDavaH-sahasrazca tribhiH SabhiH zataizca vrohibhiH smaiH| yaH saMpUrNo bhavet so'yaM kuDavaH paribhASyate // loke pavAlu 8 / prastha:-loke pAlI 8 ba prastha:-omits. zloka 1-38 a seyaM prvrtikaa| tAH khAryAH [ryaH] / tasyAH prvrtikaayaaH| zloka 1-39 a gaNDakaiH-kastuMburUbhiH, loke dhAnA, dharaNe-dharaNadvayam / zloka 1-40 a dhAnyadvayena-loke dhAnAdvayena ba kustuMbaradayena / atra-rajataparikarmaNi / zloka 1-41 a purANAn-karSAn / rUpye-rajata-paribhASAyAM mAgadhadezavyavahAramAzritya / zloka 1-42 a kala-kaleti nAma bhavet / zloka 1-43 a asmAt-drakSuNAt / sateraM-saterAkhyaM mAnaM bhavati / ba lohe-lohaparibhASAyAm / zloka 1-44 a'pracakSate' antasya 'a' Adezo bhavati / zloka 1-45 a ba vastrAbharaNa-kaTAdInAm / zloka 1-46 ba atra-parikarmaNi / zloka 1-48 a bhinnAni-yathA guNAkArabhinnaH bhAgahArabhinnaH kRtibhinnaH pratyekabhinnaH iti paraM yojyam / ba tacca-vidyA kalAsavarNasya' iti vA paatthH| zloka 1-49 ba hRtaH zUnyena bhaktaH san / khavadhAdiH-zUnyasya bhjn-gunnn-vrgmuulaadiH| yogyarUpakam-yojyarAzisamAnam / sa zUnyena tADito guNito rAziH khaM zUnyaM syAt / sa rAziH zUnyena hataH [ hRtaH ] bhaktaH / zUnyena yutaH shitH| zUnyena hIno rahito'pi avikArI vikAravAn na bhavati tadavastha evakhavadhAdiH kha zUnyasya vadho guNanaM khaM zUnyaM syAt / Adizabdena bhajana-varga-ghana-tanmUlAni gRhyN| zloka 1-50 ba pAte guNane / vivara-mahArAzau svalparAzimapanIyAvaziSTazeSo vivrmityucyte|

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gaNitasArasaMgraha sa RNayo:-RNarUparAzyoH / dhanayoH-dhanarUparAzyoH / bhjne-bhaaghaare| phalam-guNitaphalam / tu-punH|-adds ceymNksNdRssttiH|-adds illustrations to explain rules on 50 (stanza ). zloka 1-51 sa yogaH-saMyojanam / zodhyam-apaneyam / zloka 1-52-ba mUle-vargamUle / svarNe-dhanaRNe syAtAm / Adds two stanzas after 52. Printed in text at No. 69-70. laghukaraNohApohAnAlasyagrahaNadhAraNopAyaiH / vyaktikarAGkaviziSTaiH gnnkossttaabhirgunnaijnyeyH||1|| iti saMjJA samAsena bhASitA munipuMgavaiH / vistareNAgamAd vedyaM vaktavyaM yaditaH param // 2 // tatpadam-RNarUpavargarAzermUlaM kathaM bhavet ityAzaGkAyAm idamAha-RNarAziH nijaRNavargo na bhavet , kiMtu dhanarUpeNa vargo bhavet / tasmAt RNarAzeH sakAzAt mUlaM na bhavet , kiMtu dhanarAzeH sakAzAt RNarAzermUlaM syAt / sa dhanarAzeH RNarAzezca vargo dhanaM bhavati / Adds illustrations to explain rules on 52 ( stanza ). zloka 1-58 a RturjIvo-SaD jiivaaH| kumAravadanam-kArtika [ keya ] vadanam / ba kumAravadanam-kArtikeyavadanam / zloka 1-69 ba zIghraguNana-bhajanAdilakSaNaM laghukaraNam / anena prakAreNa guNanAdau kRte satIpsitaM labdhaM syAditi pUrvameva parijJAnalakSaNaH ahaH / itthaM guNanAdau kRte satIpsitaM labdhaM na syAditi pUrvameva parizAnalakSaNaH apohH| guNanAdikriyAyAM mandabhAvarAhityalakSaNamanAlasyam / kathitArthalakSaNaM grahaNam / kathitArthasya kAlAntare'pyavismaraNalakSaNA dhaarnnaa| sUtroktaguNanAdikamAdhAraM kRtvA svabuddhayA prakArAntaraguNanAdivicAralakSaNaH upaayH| aMkaM vyaktaM sthApayitvA guNanAdikaraNalakSaNo vyaktikarAMkaH / ityaSTabhirguNai gaNitajJo bhavediti zeyaH / iti / zloka 2-1 a (1) yena rAzinA guNyasya bhAgo bhavet tena guNyaM bhaktvA guNakAraM guNayitvA sthApanAlakSaNo rAzikhaNDaH / yena rAzinA guNaguNakArasya bhAgo bhavet tena guNakAraM bhaktavA guNyaM guNayitvA sthApanAlakSaNo'rdhakhaNDaH / guNya-guNakAro [rau] abhedayitvA sthApanAlakSaNaH ttsthH| iti triprakAraiH sthitaguNya-guNakArarAziyugalaM kavATasaMdhANakrameNa vinyasya / (2) rAzerAditaH ArabhyAntaparyantaM guNanalakSaNena anulomamArgeNa / (3) rAzerantataH ArabhyAdiparyantaM guNanalakSaNena vilomamArgeNa ca guNyarAziM guNakArarAzinA guNayet / (4) 'guNayet guNena guNyaM kavATasaMdhikrameNa saMsthApya' iti pAThAntara-pAdayam / (5) guNyaguNakAraM yathA va 144 guNyaM = pratyeka padmAni guNakAra ili 38: 24 48 1152 rAzikhaNDa

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62 gaNitasAra saMgraha (6) guNakAraM 8 asya bhAga 4, anena guNyaM guNita cet 4 ( 8 ) tA = tAmarasaM / ( ( 7 ) va = vaza [ sa ] ti / 9 ) pa = padamAni / ( 10 ) vinaSTo ekaH yebhyasteSvikAm / ( 11 ) maNayaH / ( 12 ) khara iti SaD jIva / ( 13 ) rAzinA guNyalabdham bhAge sthApyamadhaH tenaiva guNakAraM guNayitvA sthApanA* / uparitana zloka 2- 7 a viSanidhiH = jalanidhiH / * zloka 2... a puruSaH - jIvo ityarthaH / 7 6 2 1/1 1/4/1/2 zloka 2-9 a [ kharaH - ] "satyasaMdhaH kharo jJeyaH kharo'pi puruSo mataH" ityabhidhAnAt / zloka 2-10 a tat rAzim / zloka 2-11 a paJcaSaTkaM ca- Adau 7 paJcaSaTkaM 66666 SaTtrikaM 333333 tat bhinnaM likhitam - 333333666667 / zloka 2-15 a trayaH - sAntaH trayaH zabdo'yam / zloka 2-17 a himAMzva - himAMzu agre [ ragre ] yeSAM tAni, himAMzvayAni ca tAni randhrANi ca tattathoktAna, / kaNThikA-- kaNThabhUSaNam / ba ekarUpam - ekasyAbhidhAnaM granthAntare / zloka 2 - 18 kI utthAnikA--ba paramAgamapratipAdita karaNAnuyoge graha-nakSatra-prakIrNaka- tArAdigaNanAbhidhAnaM karaNamityucyate, tasya sUtram, sUcayati saMkSepeNArthe sUcayati iti sUtraM tattathoktam / zloka 2- 19 a pratilomapathena - vilomamArgeNa bhAjyam - aMkAnAM vAmato gatiH, tena antataH Arabhya bhAjyam / vidhAya - apavartanavidhiM vidhAya / tayoH -- bhAjya bhAgahArarAzyoH / sa uparisthita bhAjyarAziM adhaH sthitena bhAgahAreNAnanta AramyAdiparyanta bhajanalakSaNena pratilomapathena bhajet / yadi tayorbhAjya-bhAgaddArayoH sadRzApavartanavidhiH samAnarAzinA bhAjya bhAgahArAva pavartanalakSaNavidhAnaM saMbhava tarhitaM kRtvA bhajet / zloka 2-20 a aMzo bhAgaH / nuH narasya / - bhAgahArasya bhAga (1) dvau vA catvAro vA teSu ekabhAgena bhAjyaM bhAjayet, dvitIyabhAgena bhAjyaM bhAjayet, tRtIyabhAgena bhAjyaM bhAjayet, caturthabhAgena bhAjyaM bhAjayet / apavartanavidhiH / ekazatayutam -- ekenAdhikaM zatam ekazatam / zloka 2-26 a tridazasahasrI - tribhiH guNitA daza tridaza, tridazAnAM sahasrANAM samAhAraH tridazasahasrI | hATakAni -- kanakAni / zloka 2-29 a ghAto varga 64 syAt / sveSTonayutadvayasya - samAnau dvau rAzI vinyasya 858 sveSTana-yuta 6 / 10 tayorghAtaH 60 sveSTa 2 kRtI 4 yuktaH 64 vargaH syAt / seSTakRtiH - iSTakRtisahitaH / ekAdi - ekAdi dviSTa gacchAnAM yutiH saMkalanaM rUpeNoNo [ no ] gacchaH dalitaH pracayatADito mizraH prabhaveNa padAbhyastaH iti sUtreNa vargo bhayet 64 / iti dhanaM 8 | 8 2 1 zloka 2-30 a dvisthAnaprabhRtInAm -- SaTpaMcAzat dvizata ( 256 ) iti tristhAnAntaM varge / * yaha jJAta nahIM hotA ki inakA sambandha kisa-kisa zloka se hai / + ( NAntataH 1 )

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gaNita sArasaMgraha SaDvargaH 36 / paMcAzatvarga : 2500 / dvizatavargaH 40000 / sarvavargasaMyogaH 42536 / dvizata-SaTpaMcASaD [ 0zad ] ghAtaH 11200 | paMcAzat SaDaSAtaH 300 / tadviguNaH 22400 / 600 | tena vimizritaH sarvavargasaMyogaH 65536 / teSAm -- dviprabhRtikalpitasthAnAnAm / kramaghAtena - dvisthAnaprabhRtirAzInAm antyasthAnaM zeSasthAnairguNayitvA punaH zeSAntyasthAnaM zeSasthAnairguNayitvA tena krameNa prathamasthAnaparyanta guNanalakSaNa kramaghAtaH / tena punaH dvisthAnaprabhRtInAM rAzInAm, ityabhiprAyeNa vargaracanAM sphuTayati / 4 dvivarga 4 trivarga 9 caturvarga 16 tatsaMyoga: 29 teSAM kramaghAtaH dvikatrikamizreNa catuSkaM 3 guNayet 20 / dvikena trikaM guNayitvA mizritaH san 26 / dviguNo 52 / anena mizritena vargaH 81 / 2 zloka 2 - 31 a kRtvAntyakRtim - kRtvA 75 antyakRtiM 4915 antyaM dviguNamutsArtha 495 70 4945 70 | 6 |4| 5 | 4 | 5 | x | 3 | 4 | 6 6 |6|4 | 3 |2|0|0| 6 | 6 6 2 | 5 | 3 | 6 | 6 | 9|3 | 5 |2| 5 |0 3 | 3 4925 70 5 pAt zeSAnutsArya kRtvA tasyakRtiM |7 || 5 | kartavyaH dvayaMkAnAM vargakoSThaH / paMcAMkAnAM vargakoSTharacanA 4|9|0|5 7 2 63 labdhavargAH 4294967296 // u0 10 4.15 14 labdhaH 5625 iti sarvatra zeSa sa ayamarthaH - antyarAzi varge kRtvA punarantyarAziM dviguNaM kRtvA puro gamayitvA zeSasthAnairguNayet / zeSasthAnAni puro gamayitvA pUrvakathitakriyA kartavyA /

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pariziSTa- 6 [Reprinted from the First Edition. ] PREFACE Soon after I was appointed Professor of Sanskrit and Comparative Philology in the Presidency College at Madras, and in that capacity took charge of the office of the Curator of the Goverment Oriental Manuscripts Library, the late Mr. G. H. Stuart, who was then the Director of Public Instruction, asked me to find out if in the Manuscripts Library in my charge there was any work of value capable of throwing new light on the history of Hindu mathematics, and to publish it, if found, with an English translation and with such notes as were necessary for the elucidation of its contents. Accordingly the mathematical manuscripts in the Library were examined with this object in view; and the examination revealed the existence of three incomplete manuscripts of Mahaviracarya's Ganita-sara-sangraha. A cursory persual of these manuscripts made the value of this work evident in relation to the history of Hindu Mathematics. The late Mr. G. H. Stuart's interest in working out this history was so great that, when the existence of the manuscripts and the historical value of the work were brought to his notice, he at once urged me to try to procure other manuscripts and to do all else that was necessary for its proper publication. He gave me much advice and encouragement in the early stages of my endeavour to publish it; and I can well guess how it would have gladdened his heart to see the work published in the form he desired. It has been to me a source of very keen regret that it did not please Providence to allow him to live long enough to enable me to enhance the value of the publication by means of his continued guidance and advice; and my consolation now is that it is something to have been able to carry out what he with scholarly delight imposed upon me as a duty. Of the three manuscripts found in the library one is written on paper in Grantha characters, and contains the first five chapters of the work with a running commentary in Sanskrit; it has been denoted here by the letter P. The remaining two are palm-leaf

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gaNitasArasaMgraha manuscripts in Kanarese characters, one of them containing, like P, the first five chapters, and the other the seventh chapter dealing with the geometrical measurement of areas. In both these manuscripts there is to be found, in addition to the Sanskrit text of the original work, a brief statement in the Kanarese language of the figures relating to the various illustrative problems as also of the answers to those same problems, Owing to the common characteristics of these manuscripts and also owing to their not overlapping one another in respect of their contents, it has been thought advisable to look upon them as one manuscript and denote them by K. Another manuscript, denoted by M, belongs to the Government Oriental Library at Mysore, and was received on loan from Mr. A Mahadeva Sastri, B, A,, the Curator of that institution. This manuscript is a transcription on paper in Kanarese characters of an original palmleaf manuscript belonging-to a Jaina Pandit, and contains the whole of the work with a short commentary in the Kanarege language by one Vallabha, .who claims to be the author of also a Telugu commentary on the same work, Althought incorreot in many places. it proved to be of great value on account of its being complete and containing the Kanarese commentary; and my thanks are specially due to Mr. A. Mahadeva Sastri for his leaving it sufficiently long at my disposal. A fifth manuscript, denoted by B, is a transcription on paper in Kanarese characters of a palm-leaf manuscript found in a Jaina monastery at Mudbidri in South Canara, and was obtained through the kind effort of Mr. R. Krishnamacharyar, M. A,, he Sub-assistant Inspector of Sanskrit Schools in Madras, and Mr. U. B. Venkataramanaiya of Mudbidri. This manuscript also contains the whole work, and gives, like K, in Kanarese a brief statement of the problems and their answers. The endeavour to secure more manuscripts having proved fruitless, the work has had to be brought out with the aid of these five manucripts; and owing to the technical character of the work and its elliptical and often riddle-like language and the inaccuracy of the manuscripts, the labour involved in bringing it out with the translation and the requisite notes has been heavy and trying. There is, however, the satisfaction that all this labour has been bestowed on a worthy work of considerable historical value.

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gaNitasArasaMgraha It is a fortunate circumstance about the Ganita-sara-sangraha that the time when its author Mahaviracarya lived may be made out with fair accuracy. In the very first chapter of the work, we have, immediately after the two introductory stanzas of salutation to Jina Mahavira, six stanzas describing the greatness of a king, whose name is said to have been Cakrika-bhanjana, and who appears to have been commonly known by the title of Amoghavarsa Nrpatunga; and in the last of these six stanzas there is a benediction wishing progressive prosperity to the rule of this king. The results of modern Indian epigraphical research show that this king Amoghavarsa Nrpatunga reigned from A. D. 814 or 815 to A. D. 877 or 878.* Since it appears probable that the author of the Ganita-sara-sangraha was in some way attached to the court of this Rastrakuta king Amoghavarsa Nrpatunga, we may consider the work to belong to the middle of the ninth century of the Christian era. It is now generally accepted that, among well-known early Indian mathematicians Aryabhata lived in the fifth, Varahamihira in the sixth, Brahmagupta in the seventh and Bhaskaracarya in the twelfth century of the Christian era ; and chronologically, therefore, Mahaviracarya comes between Brabmagupta and Bhaskaracarya. This in itself is a point of historical noteworthiness, and the further fact that the author of the Ganita-sara-san graha belonged to the Kanarese speaking portion of Souih India in his days and was a Jaina in religion is calculated to give an additional importance to the historical value of his work. Like the other mathematicians mentioned above, Mahaviracarya was not primarily an astronomer, although he knew well and has himself remarked about the usefulness of mathematics for the study of astronomy. The study of mathematics seems to have been popular among Jaina scholars; it forms, in fact, one of their four Anuyogas or auxiliary sciences indirectly serviceable for the attainment of the salvation of soul-liberation known as maksa. A comparison of the Ganita-sara-sangraha with the corresponding portions in the Brahmasphuta-siddhanta of Brahmagupta is * Vide Nilgund Inscription of the time of Amoghavarsa I, A. D. 866 ; edited by J. F. Fleet, PH.D., C. I. E., in Epigraphia Indica, Vol. VI, pp. 98--108.

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gaNitasArasaMgraha calculated to lead to the conclusion that, in all probability, Mahaviracarya was familiar with the work of Brahmagupta and endeavoured to improve upon it to the extent to which the scope of his Ganita-sara-sangraha permitted such improvement, Mahavira. charya's classification of arithmetical operations is simpler, his rules are fuller and he gives a large number of examples for illustration and exercise, Prthudaksvamin, the well-known commentator on the Brahmasphuta-siddhanta, could not have been chronologically far removed form Mahaviracarya, and the similarity of some of the examples given by the former with some of those of the latter naturally arrests attention. In any case it cannot be wrong to believe, that, at the time, when Mahaviracarya wrote his Gaaita-sara-sangraha, Brahmagupta must have been widely recognized as a writer of authority in the field of Hindu astronomy and mathematios. Whether Bhaskaracarya was at all acquainted with the Ganita-sara-sangraha of Mahaviracarya, it is not quite easy to say. Since neither Bhaskaracarya nor any of his known commentators seem to quote from him or mention him by name, the natural conclusion appears to be that Bhaskaracarya's Siddhanta-sirumani, including his Lilavati and Bijagamita, was intended to be an improvement in the main upon the Brahmasphuta-siddhanta of Brahmagupta. The fact that Mahaviracarya was a Jaina might have prevented Bhaskaracarya from taking note of him; or it may be that the Jaina mathematician's fame had not spread far to the north in the twelfth century of the Christian era. His work, however, seems to have been widely known and appreciated in Southern India, so early as in the course of the eleventh century and perhaps under the stimulating influence of the enlightened rule of Rajarajanarendra of Rajahmundry, it was translated into Telugu in verse by Pavulari Mallana; and some manuscripts of this Telugu translation are now to be found in the Government Oriental Manuscripts Library here at Madras. It appeared to me that to draw suitable attention to the historical value of Mahaviracarya's Ganita.sara-sangraha, I could not do better than seek the help of Dr. David Eugene Smith of the Columbia University of New York, whose knowledge of the history of mathematics in the West and in the East is known to be wide

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68 gaNitasArasaMgraha and comprehensive, and who on the occasion when he met me in person at Madras showed great interest in the contemplated publication of the Ganita-sara-sangraha and thereafter read a paper on that work at the Fourth International Congress of Mathematicians held at Rome in April 1908. Accordingly I requested him to write an introduction to this edition of the Ganita-sara-sangraha, given in brief outline what he considers to be its value in building up the history of Hindu mathematics. My thanks as well as the thanks of all those who may as scholars become interested in this publication are therefore due to him for his kindness in having readily complied with my request; and I feel no doubt that his introduction will be read with great appreciation. Since the origin of the decimal system of notation and of the conception and symbolic representation of zero are considered to be important questions connected with the history of Hindu mathematics, it is well to point out here that in the Ganita-sarasangraha twenty four rotational places are mentioned, commencing with the units place and ending with the place called mahaksobha, and that the value of each succeeding place is taken to be ten times the value of the immediately preceding place. Although certain words forming the names of certain things are utilized in this work to represent various numerical figures, still in the numeration of of numbers with the aid of such words the decimal system of notation is almost invariably followed If we took the words moon, eye, fire and sky to represent respectively 1, 2, 3 and 0, as their Sanskrit equivalents are understood in this work, then, for instance, fire-sky-moon-eye would denote the number 2103, and moon-eye-sky-fire would denote 3021, since these nominal numerals denoting numbers are generally repeated in order from the units place upwards. This combination of nominal numerals and the decimal system of notation has been adopted obviously for the sake of securing metrical convenience and avoiding at the same time cumbrous ways of mentioning numerical expressions; and it may well be taken for granted that for the use of such nominal numerals as well as the decimal system of notation Mahaviracarya was indebted to his predecessors. The decimal system of notation is

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gaNita sArasaMgraha 69 distinctly described by Aryabhata, and there is evidence in his writings to show that he was familiar with nominal numerals. Even in his brief mnemonic method of representing numbers by certain combinations of the consonants and vowels found in the Sanskrit language, the decimal system of notation is taken for granted; and ordinarily 19 notational places are provided for therein. Similarly in Brahmagupta's writings also there is evidence to show that he was acquainted with the use of nominal numerals and the decimal system of notation, Both Aryabhata and Brahmagupta claim that their astronomical works are related to the Brahma-siddhanta; and in a work of this name, which is said to form a part of what is called Sakalya-samhita and of which a manuscript copy is to be found in the Government Oriental Manuscripts Library here, numbers are expressed mainly by nominal numerals used in accordance with the decimal system of notation. It is not of course meant to convey that this work is necessarily the same as what was known to Arayabhata and Brahmagupta; and the fact of its using nominal numerals and the decimal system of notation is mentioned here for nothing more than what it may be worth. It is generally recognized that the origin of the conception of zero is primarily due to the invention and practical utilization of a system of notation wherein the several numerical figures used have place-values apart from what is called their intrinsic value. In writing out a number according to such a sytem of notation, any notational place may be left empty when no figure with an intrinsic value is wanted there. It is probable that owing to this very reason the Sanskrit word sunya, meaning 'empty', came to denote the zero; and when it is borne in mind that the English word 'cipher' is derived from an Arabic word having the same meaning as the Sanskrit sunya, we may safely arrive at the conclusion that in this country the conception of the zero came naturally in the wake of the decimal system of notation and so early as in the fifth century of the Christian era, Aryabhata is known to have been fully aware of this valuable mathematical conception. And in regard to the question of a symbol to represent this conception, it is well worth bearing in mind that operations with the zero cannot be

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gaNita sArasaMgraha carried on-not to say cannot be even thought of easily-without a symbol of some sort to represent it. Mahaviracarya gives, in the very first chapter of his Ganita-sara-sangraha, the results of the operations of addition, subtraction, multiplication and division carried on in relation to the zero quantity; and although he is wrong in saying that a quantity, when divided by zero, remains unaltered, and should have said, like Bhaskaracarya, that the quotient in such a case is infinity, still the very mention of operations in relation to zero is enough to show that Mahaviracarya must have been aware of some symbolic representation of the zero quantity. Since Brahmagupta, who must have lived at least 150 years before Mahaviracarya, mentions in his work the results of operations in relation to the zero quantity, it is not unreasonable to suppose that before his time the zero must have had a symbol to represent it in written calculations. That even Aryabhata knew such a symbol is not at all improbable. It is worthy of note in this connection that in enumerating the nominal numerals in the first chapter of his work, Mahaviracarya mentions the names denoting the nine figures from 1 to 9, and then gives in the end the names denoting zero, calling all the ten by the name of sankhya and from this fact also, the inference may well be drawn that the zero had a symbol, and that it was well known that with the aid of the ten digits and the decimal system of notation numerical quantites of all values may be definitely and accurately expressed. What this known zero-symbol was, is, however, a different question. 70 The labour and attention bestowed upon the study and translation and annotation of the Ganita-sara-sangraha have made it clear to me that I was justified in thinking that its publication might prove useful in elucidating the condition of mathematical studies as they flourished in South India among the Jainas in the ninth century of the Christian era; and it has been to me a source of no small satisfaction to feel that in bringing out this work in this form, I have not wasted my time and thought on an, unprofitable undertaking. The value of the work is undoubtedly more historical than mathematical, But it cannot be denied that the step by step construction of the history of Hindu culture is a worthy endeavour,

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gaNita sArasaMgraha 71 and that even the most insignificant labourer in the field of such an endeavour deserves to be looked upon as a useful worker. Although the editing of the Ganita-sara-sangraha has been to me a labour of love and duty, it has often been felt to be heavy and taxing; and I, therefore, consider that I am specially bound to acknowledge with gratitude the help which I have received in relation to it. In the early stage, when conning and collating and interpreting the manuscripts was the chief work to be done, Mr. M. B. Varadaraja Aiyangar, B. .A, B. L., who is an Advocate of the Chief Court at Bangalore, co-operated with me and gave me an amount of aid for which I now offer him my thanks. Mr. K. Krishnaswami Aiyangar, B. A.; of the Madras Christian College, has also rendered considerable assistance in this manner; and to him also I offer my thanks. Latterly I have had to consult on a few occasions Mr. P V. Seshu Aiyar, B. A, L. T., Professor of Mathematical Physics in the Presidency College here, in trying to explain the rationale of some of the rules given in the work; and I am much obliged to him for his ready willingness in allowing me thus to take advantage of his expert knowledge of mathematics. My thanks are, I have to say in conclusion, very particularly due to Mr. P. Varadacharya, B, A., Librarian of the Government Oriental Manuscripts Library at Madras, but for whose zealous and steady co-operation with me throughout and careful and continued attention to details, it would indeed have been much harder for me to bring out this edition of the Ganit-sara-sangraha. February 1912, Madras. } M. RANGACHARYA.

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INTRODUCTION BY DAVID EUGENE SMITH PROFESSOR OF MATHEMATICS IN TEACHERS' COLLEGE, COLUMBIA UNIVERSITY, New York. We have so long been acoustomed to think of Pataliputra on the Ganges and of Ujjain over towards the Western Coast of India as the ancient habitats of Hindu mathematics, that we experience a kind of surprise at the idea that other centres equally important existed among the multitude of cities of that great empire. In the same way we have known for a century, ohiefly through the labours of such scholars as Colebrooke and Taylor, the works of Aryabhata, Brahmagupta, and Bhaskara, and have come to feel that to these mon alone are due the noteworthy contributions to be found in native Hindu mathematics. Of course a little reflection shows this conolusion to be an incorrect one. Other great schools, particularly of astronomy, did exist, and other scholars taught and wrote and added their quota, small or large, to make up the sum total. It has, however, been a little discouraging that native scholars under the English supremacy have done so little to bring to light the ancient mathematical material known to exist and to make it known to the Western world. This neglect has not certainly been owing to the absence of material, for Sanskrit mathematical manuscripts are known, as are also Persian, Arabio, Chinese, and Japanese; and many of these are well worth translating from the historical standpoint. It has rather been owing to the fact that it is hard tof ind a man with the requisite scholarship, who can afford to give his time to what is necessarily a labour of love. It is a pleasure to know that such a man has at last appeared and that, thanks to his profound scholarship and great pereseverance,

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gaNita sArasaMgraha we are now receiving new light upon the subject of Oriental mathematics, as known in another part of India and at a time about midway between that of Aryabhata and Bhaskara, and two centuries later than Brahmagupta. The learned scholar, Professor M. Rangacarya of Madras, some years ago became interested in the work of Mahaviracarya, and has now completed its translation, thus making the mathematical world his perpetual debtor; and I esteem it a high honour to be requested to write an introduction to so noteworthy a work. 73 Mahaviracarya appears to have lived in the court of an old Rastrakuta monarch, who ruled probably over much of what is now the kingdom of Mysore and other Kanarese tracts, and whose name is given as Amoghavarsa Nrpatunga. He is known to have ascended the throne in the first half of the ninth century A. D., so that we may roughly fix the date of the treatise in question as about 850. The work itself consists, as will be seen, of nine chapters like the Bija-ganita of Bhaskara; it has one more chapter than the Kuttaka of Brahmagupta. There is, however, no significance in this number, for the chapters are not at all parallel, although certain of the otpics of Brahmagupta's Ganita and Bhaskara's Lilavati are included in the Ganita-Sara-Sangraha. In considering the work, the reader naturally repeats to himself the great questions that are so often raised:-How much of this Hindu treatment is original ? What evidences are there here of Greek influence ? What relation was there between the great mathematical centres of India? What is the distinctive feature, if any, of the Hindu algebraic theory? Such questions are not new. Davis and Strachey, Colebrooke and Taylor, all raised similar ones a century ago, and they are by no means satisfactorily answered even yet. Nevertheless, we are making good progress towards their satisfactory solution in the not too distant future. The past century has seen several Chinese and Japanese mathematical works made more or less familiar to the West; and the more important Arab treatises are now quite satisfactorily known, Various editions of Bhaskara have appeared in India; and in general the great treatises of the Orient

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gaNita sArasaMgraha have begun to be subjected to critical study. It would be strange, therefore, if we were not in a position to weigh up, with more certainty than before, the claims of the Hindu algebra, Certainly the persevering work of Professor Rangacarya has made this more possible than ever before. 74 As to the relation between the East and the West, we should now be in a position to say rather definitely that there is no evidence of any considerable influence of Greek algebra upon that of India. The two subjects were radically different. It is true that Diophantus lived about two centuries before the first Aryabhata, that the paths of trade were open from the West to the East, and that the itinerant scholar undoubtedly carried learning from place to place. But the spirit of Diophant us, showing itself in a dawning symbolism and in a peculiar type of equation, is not seen at all in the works of the East. None of his problems, not a trace of his symbolism, and not a bit of his phraseology appear in the works of any Indian writer on algebra, On the contrary, the Hindu works have a style and a range of topics peculiarly their own. Their problems lack the cold, clear, geometric precision of the West; they are clothed in that poetic language which distinguishes the East, and they relate to subjects that find no place in the scientific books of the Greeks. With perhaps the single exception of Metrodorus, it is only when we come to the puzzle problems doubtfully attributed to Alcuin that we find anything in the West which resembles, even in a slight degree, the work of Alcuin's Indian contemporary, the author of this treatise. It therefore seems only fair to say that, although some knowledge of the scientific work of any one nation would, even in those remote times, naturally have been carried to other peoples by some wandering savant, we have nothing in the writings of the Hindu algebraists to show any direct influence of the West upon their problems or their theories. When we come to the question of the relation between the different sections of the East, however, we meet with more difficulty. What were the relations, for example, between the school of Pataliputra, where Aryabhata wrote, and that of Ujjain, where both Brahmagupta and Bhaskara lived and taught? And what was the relation of each

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gaNitasArasaMgraha of these to the school down in South India, which produced this notable treatise of Mahaviracarya? And, a still more interesting question is, what can we say of the influence exerted on China by Hindu scholars, or vice versa? When we find one set of early inscriptions, those at Nana Ghat, using the first three Chinese numerals, and another of about the same period using the later forms of Mesopotamia, we feel that both China and the West may have influenced Hindu science. When, on the other hand, we consider the problems of the great trio of Chinese algebraists of the thirteenth century, Ch'in Chiushang, Li Yeh, and Chu Shih-chieh, we feel that Hindu algebra must have had no small influence upon the North of Asia, although it must be said that in point of theory the Chinese of that period naturally surpassed the earlier writers of India, The answer to the questions as to the relation between the schools of India cannot yet be easily given. At first it would seem a simple matter to compare the treatises of the three or four great algebraists and to note the similarities and differences. When this is done, however, the result seems to be that the works of Brahmagupta, Mahaviracarya, and Bhaskara may be described as similar in spirit but entirely different in detail, For example, all of these writers treat of the areas of polygones, but Mahaviracarya is the only one to make any point of those that are re-entrant, All of them touch upon the area of a segment of a circle, but all give different rules. The so-called janya operation (page 209) is akin to work found in Brahmagupta, and yet none of the problems is the same. The shadow problems, primitive cases of trigonometry and gnomonics, suggest a similarity among these three great writers, and yet those of Mahaviracarya are much better than the one to be found in either Brahmagupta or Bhaskara, and no questions are duplicated. In the way of similarity, both Brahmagupta and Mahaviracarya give the formula for the area of a quadrilateral, (-a) (8-b)(s-c)(s-d) -but neither one observes that it holds only for a cyclic figure. A few problems also show some similarity such as that of the broken tree, the one about the anchorites, and the

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gaNitasArasaMgraha common one relating to the lotus in the pond, but these prove only that all writers recognized certain stock problems in the East, as we generally do to-day in the West. But as already stated, the similarity is in general that of spirit rather than of detail, and there is no evidence of any close following of one writer by another. When it comes to geometry there is naturally more evidence of Western influence. India seems never to have independently developed anything that was specially worthy in this science, Brahmagupta and Mahaviracarya both use the same incorrect rules for the area of a triangle and quadrilateralt hat is found in the Egyptian treatise of Ahmes. So while they seem to have been influenced by Western learning, this learning as it reached India could have been only the simplest. These rules had long since been shown by Greek scholars to be incorrect, and it seems not unlikely that a primitive geometry of Mesopotamia reached out both to Egypt and to India with the result of perpetuating these errors. It has to be borne in mind, however, that Mahaviracarya gives correct rules also for the area of a triangle as well as of a quadrilateral without indicating that the quadrilateral has to be cyclic. As to the ratio of the circumference to the diameter, both Brahmagupta and Mahaviracarya used the old Semitic value 3, both giving also 10 as a closer approximation, and neither one was aware of the works of Archimedes or of Heron. That Aryabhata gave 3:1416 as the value of this ratio is well known, although it seems doubtful how far he used it himself. On the whole the geometry of India seems rather Babylonian than Greek. This, at any rate, is the inference that one would draw from the works of the writers thus far known. As to the relations between the Indian and the Chinese algebra, it is too early to speak with much certainty. In the matter of problems there is a similarity in spirit, but we have not yet enough translations from the Chinese to trace any close resemblance. In each case the questions proposed are radically different from those found commonly in the West, and we must conclude that the algebraio taste, the purpose, and the method were all distinot in the

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gaNitasArasaMgraha two great divisions of the world as then known. Rather than assert that the Oriental algebra was influenced by the Occidental we should say that the reverse was the case. Bagdad, subjeoted to the influence of both the East and the West, transmitted more to Europe than it did to India. Leonardo Fibonacci, for example, shows much more of the Oriental influence than Bhaskara, who was practically his contemporary, shows of the Occidental. Professor Rangacarya has, therefore, by his great contribution to the history of mathematics confirmed the view already taking rather concrete form, that India developed an algebra of her own; that this algebra was set forth by several writers all imbued with the same spirit, but all reasonably independent of one another; that India influenced Europe in the matter of algebra, more than it was influenced in return; that there was no native geometry really worthy of the namo; that trigonometry was practically non-existent save as imported from the Greek astronomers; and that whatever of geometry was developed came probably from Mesopotamia rather than from Greece, His labours have revealed to the world a writer almost unknown to European scholars, and a work that is in many respects the most scholarly of any to be found in Indian mathematical literature. They have given us further evidence of the fact that Oriental mathematios lacks the cold logio, the consecutive arrangement, and the abstract character of Greek mathematics, but that it possesses a richness of imagination, an interest in problem-setting, and poetry, all of which are lacking in the treatises of the West, although abounding in the works of China and Japan. If, now, his labours shall lead others to bring to light and set forth mor and more of the classics of the East, and in particular those of early and mediaeval China, the world will be to a still larger extent his debtor, se

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prastAvanA ko anukramaNikA aMkagaNita - 3, 4, 6, 7, 10, 15. aMka jyotiSa -- 4. ananta rAziyoM kA gaNita - 9. anukala kalana--( Integral Calculus ) 4, 5. anuyoga sUtra - 7. aparimeya - ( Irrational ) 4. amoghavarSa - 1, 10. arthamitikI - ( Arithmetica ) 4, 18. arthadRSTi - 9, 20. alaukika gaNita - 9. alpabahutva - ( Comparability ) 26, 34. avibhAjyoM kI rIti - ( Method of indivisibles ) 4. asadbhAsa - ( Paradoxes ) 4, 26. ahiMsA - 12, 13, 14, 17, 30. Amisa - ( Ahmes ) 3. ArkimiDIz2a -4, 5. AryabhaTa - 7. iTalI - 2, 4. udsthaitikI -- ( Hydrostatics ) 5, ( sthaitikI ) 6. karma siddhAnta - 16, 17. kAparanikasa - 5. kAlpanika rAzi - ( Imaginary quantity ) 11. kuntala - ( Spiral ) 5. kUphU - ( Khufu ) 13, 14, 16, 17. keMTara, jArja - 9, 15, 16. kUTa sthiti rIti - ( Rule of false position ) 3. gaNitasAra saMgraha - 1, 9, 16. gaNitIya vizleSaNa - ( Mathematical Analysis ) 2, 3, 4, 10. grIka - 4, 5, 7, ( yUnAnI ) - 7, 14, 15. gommaTasAra TIkA - 34. caturgati ( caducaMkramaNa ) - 16, 23. caturbhuja - 11, 15, 20.

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gaNita calana kalana - ( Differential calculus ) 5. cIna - 21, 30, 31, 32, 33, 34. z2Ino ( Zeno ) 4, 26, 27, 28, 29. ( tarka ) - 27, 28. jyotirvijJAna - 3, 6. jyotiSa - 8, 14, 15, 16, 18, 22, 25, ( paTala ) 12, ( bedAMga ) - 6, 7. TaoNlemI - 18,30. ToDaramala - 20, 26, 34. DAopheMTasa - 5, 11, 18. DeDI kaeNnDa - 4 tIrthaMkara- 12, ( varddhamAna mahAvIra ) 13, 14, 18, 19, 20, 23, 29, 30, 32, 34. tiloyapaNNattI - 17, 19, 21, 26, 30, 34, ( triloka prazati ) - 7, 15.. tribhuja - 2, 3, 4, 5, 11, 20, 22. trikoNamiti - ( Trigonometry ) - 7, 8. lIz2a - 4, 13, 18, 21, 22. dazamalava paddhati - ( Decimal system ) 2, 3, 7, ( dAzamika ) 18, 19, 20. nizzeSaNa vidhi - ( Method of exhaustion ) 4. nebyukaDanejara - 20. nemicandrArya - 15. paramANu - ( Indivisible ultimate particle ) 26, 27, 28, 29, 32. paridhi vyAsa anupAtaT)-2, 3, 15. peppasa - 5 fam-3, 4, 5, 12, 13, 16, 18, 19, 20, 21, 23, 24, 25, 26, 34, piremiDa - ( stUpa ) - 3, 4, 16, 17. pepAyarasa ( mAsko ) - 4, 15, (rinDa ) - 3. pradeza ( Point ) - 26, 28, 29. phalanIyatA-- ( Funotionality ) 2. bIjagaNita - ( Algebra ) 3, 6, 7, 10, 11, 12, 18, 20. bebilana - 2, 3, 12, 15, 17, 20, 21, 22, 30. brahmagupta - 8, 10, 11, 12. brAhmaNa sAhitya - 6. brAjhI-6. -5, 12, 13, 15, 19, 20, 26, 30, 32, 33. bhAskara - 9. mahAvIrAcArya - 1, 9, 10, 11, 12, 16. mAyA gaNanA - 7. fa-3, 4, 12, 13, 14, 15, 16, 17, 22, 23.

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gaNitasArasaMgraha mohenajodar3o-6. yUklira-4,b. yUDo-4. yUnAna-12, 13, 16, 17, 18, 19, 21, 22, 31, 34. rajja-(Rope)3,5,15,16. rUpaka saMkhyAye-( Figurate numbers) 4. rAzi siddhAnta-(Set theory) 13, 20. rekhAgaNita-(Geometry) 4,b. bakSAlI (bhojapatra)-7, 11. vIrasenAcArya-9, 15, 16, 21, 28. zAMkava gaNita-(Conics ) 2, 4, 5. zUnya-7, 10, 18, 34. SaTkhaMDAgama-9, 16, 19, 24, 28. SASThikA (Sexagesimal )2, 18, 19, 20, 21. samaya-( Instant ) 26, 28, 29. samIkaraNa-(Equation)2, 5, 6, 10, 11, 20. salAgA ( gaNana)-9, (artha) ( Logarithm)-19. sAkATI-27. sumera-2,5,18... sthAna mAna ( Place value)-3, 7, ( aA~)-10, 18, 19, 20. phiksa-(Sphinx ) 13, 14, hipArakasa-5. hiraoNDageTasa-14, 16. @eke

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prastAvanA pRSTha 1 2 2 3 3 3 3 4 4 4 4 4 4 5 5 5 5 5 5 5 5 BACK2AARPRL 8 9 11 15 22 24 24 25 25 25 26 26 paMkti 9 11 17 15 21 3 11 16 17 22 23 1 3 8 15 16 25 28 PE 23 33 22 8 29 13 20 11 15 zuddhi-patra 'azuddha bebIloniyA bebIlona: 99 39 " pepIriyoM pepirasa 39 ArkimiDIz2a paithegorasa "" 19 39 39 ArkimiDIz2a atiparavalaja ArkimiDIja hiparakasa DAyosa mairathAna bebIlona Peleian sam bakhzAlI Health Pythagorus 39 33 39 39 19 99 99 zuddha bebilana 39 " "" 39 pepAyariyoM pepAyarasa " ArkimIDIsa pithegorasa 299 39 33 39 ArkimIDIz2a atiparavalayaja ArkimIDIja hipArakasa DAopheMTasa mairAthAna bebilana Pellian san bakSAlI Heath Pythagoras "" " "" " 35 " 39

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82 graMtha pariziSTa 14 31 3 O 8 37 118 181 192 200 205 221 268 11 11 11 11 12 13 13 14. 15 15 15 20 38 39 39 paMkti 34 gAthA 14 gAthA 22 gAmA 27 gAthA 33 gAthA 33 gAthA 44 gAyA 54 gAthA 70: 22 14 9 1 16 4 6 15 27 12 18 19 10 24 30 gaNitasArasaMgraha 34 21 1 11 30. azuddha Civilization banvendra guNakai lIkSA saMkhyA tAvali dala phalazatadvayam yugalayugmaM saMjJA nimnakhita palazatadvayam yugalaMyugmaM saMjJAH nimnalikhita bhUlabhUta mUlabhUta viSaya kI chaH prakAra chaThaveM viSaya AbAdhA AvAghA atroddezakaH mizraka Adi se Duko Adhak Adhyan Adidhan Amoghvarsa Tirthnkar bhAgasamvarga Crore by zuddha Civilisation baghendra gaNakai likSA saMkhyAtAvali Tiirthankara Tirthankara phUla Amoghavarsa Tirthankara Bhagapavaha Bhagapavaha pUrNikA pariziSTa-5 Ferminalia saMcarita kSetra gaNita Adi lekara gaNanAnIta huNDuka Adhaka Adhvana Adidhana bhAgasaMvarga crore be Tirthankara Tirthankara prapUraNikA pariziSTa - 2 a Terminalia saMracita

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JIVARAJA JAINA GRANTHAMALA 1. Tiloyapannatti of Yativrsabha (Part I, Chapters 1-4): An Ancient Prakrit Text dealing with Jaina Cosmography, Dogmatics etc. Prakrit Text authentically edited for the first time with various Readings, Preface & Hindi Paraphrase of Pt. BALACHANDRA by Drs. A. N. UPADHYE and H. L, JAIN. Published by Jaina Samskrti Samraksaka Samgha, Sholapur (India). Double Crown pp. 6-38532. Sholapur, 1943. Price Rs. 12:00. Second Edition, Sholapur, 1956. Price Rs. 16.00. 1. Tiloyapannatti of Yativrsabha (Part II, Chapters 5-9). As above, with Introductions in English and Hindi, with an alphabetical Index of Gathas, with other Indices (of Names of works mentioned, of Geographical Terms, of proper Names, of Technical Terms, of Differences in Tradition, of Karanasutras and of Technical Terms compared) and Tables (of Naraka-jiva, Bhavana-vasi Deva, Kulakaras, Bhavana Indras, Six Kulaparvatas, Seven Ksetras, Twentyfour Tirthankaras, Age of the galakapursas, Twelve Cakravartins, Nine Narayanas, Nine Pratisatrus, Nine Baladevas, Eleven Rudras, Twentyeight Naksatras, Eleven Kalpatita, Twelve Indras, Twelve Kalpas and Twenty Prarupanas). Double Crown pp. 6-14-108-529 to 1032, Sholapur, 1951, Price Rs. 16.00. 2. Yasastilaka and Indian Culture, or Somadeva's Yasastilaka and Aspects of Jainism and Indian Thought and Culture in the Tenth Century, by Professor K. K. HANDIQUI, Vice-Chancellor, Gauhati University, Assam, with Four Appendices, Index of Geographical Names and General Index, Published by J. S. S. Sangha, Sholapur. Double Crown pp. 8-540. Sholapur, 1949. Price Rs. 16'00. 3. Pandavapuranam of subhacandra: A Sanskrit Text dealing with the Pandava Tale. Authentically edited with various Readings, Hindi Paraphrase, Introduction in Hindi etc. by Pt. JINADAS. Published by J. S. S. Sangha, Sholapur, Double Crown pp. 4-40-8-520, Sholapur, 1954, Price Rs. 12.00.

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gaNitasArasaMgraha 4. Prakrta-sabdanusasanam of Trivikrama with his own commentary: Critically Edited with Various Readings, an Introduction and Seven Appendices ( 1. Trivikrama's Sutras; 2. Alphabetical Index of the Sutras: 3. Metrical Version of the Sutrapatha: 4. Index of Apabhramsa Stanzas; 5. Index of Desya words; 6. Index of Dhatvadesas, Sanskrit to Prakrit and vice versa: 7, Bharata's Verses on Prakrit) by Dr. P. L. VAIDYA, Director, Mithila Institute, Darbhanga. Published by the J. S. S. Sangha, Sholapur. Demy pp. 44-478. Sholapur, 1954. Price Rs. 10.00. 5. Siddhanta-sarasamgraha of Narendrasena: A Sanskrit Text dealing with Seven Tattvas of Jainism. Authentically Edited for the first time with various Readings and Hindi Translation by Pt, JINADAS P, PHADKULE. Published by the J. S, S. Sangha, Sholapur. Double Crown pp. about 300. Sholapur 1957. Price Rs, 10 00. 6. Jainism in South India and Some Jain Epigraphs : A learned and well documented Dissertation on the career of Jainism in the South, especially in the areas in which Kannada, Tamil and Telugu Languages are spoken, by P.B. DESAI, M. A., Assistant Superintendent for Epigraphy, Ootacamund, Some Kannada Inscriptions from the areas of the former Hyderabad State and round about are edited here for the first time both in Roman and Devanagary characters, along with their critical study in English and Saranuyada in Hindi, Equipped with a List of Inscriptions edited, a General Index and a number of illustrations. Published by the J. S. S. Sangha, Sholapur, Sholapur 1957. Double Crown pp. 16-456. Price Rs. 16'00. 7. Jambudivapannatti-Samgaho of Padmanandi : A Prakrit Text dealing with Jajna Geography, Authentically edited for the first time by Drs. A. N. UPADHYE and H.L. JAINA, with the Hindi Anuvada of Pt. BALACHANDRA, The Introduction institutes a careful study of the Text and its allied works. There is an Essay in Hindi on the Mathematics of the Tiloyapannatti by Prof. L. C. JAIN, M. Sc., Jabalpur. Equipped with an Index of Gathas, of Geogra. phical Terms and of Technical Terms, and with additional Variants of Amera Ms. Published by the J. S. S. Sangha, Sholapur, Double Crown pp. about 500. Sholapur, 1957.

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gaNita sArasaMgraha 8. Bhattaraka-sampradaya: A History of the Bhattaraka Pithas especially of Western India, Gujarat, Rajasthan and Madhya Pradesh, based on Epigraphical, Literary and Traditional sources, extensively reproduced and suitably interpreted, by Prof. V. JORHAPURKAR, M. A., Nagpur. Demy pp. 14 +24+ 326, Sholapur, 1958, Price Rs. 8/-. 24 9. Prabhrtadisamgraha: This is a presentation of topic-wise discussions compiled from the works of Kundakunda, the Samayasara being fully given. Edited with Introduction and Translation in Hindi by: Pt. Kailashchandra Shastri, Varanasi. Published by the J. S. S. Sangha, Sholapur, Demy pp. 10-106-10-288, Sholapur 1960. Price Rs. 60. 10. Pancavimsati of Padmanandi: (c. 1136 A. D.). This is a collection of 26 prakaranas (24 in Sanskrit and 2 in Prakrit), small and big, dealing with various religious topics: religious, spiritual, ethical, didactic, hymnal and ritualistic. The text, along with an anonymous commentary, critically edited by Dr. A. N. Upadhye and Dr. H. L. Jain with the Hindi Anuvada of Pt. Balachandra Shastri, The edition is equipped with a detailed Introduction shedding light on the various aspects of the work and personality of the author both in English snd Hindi. There are useful Indices, Printed in the N. S. Press, Bombay. Double crown pp. 8-64-284. Sholapur, 1962, Price Rs. 10/-. 11. Atamanusasana of Gunabhadra (middle of the 9th century A. D.). This is a religio-didactic anthology in elegant Sanskrit verses composed by Gunabhadra, the pupil of Jinasena, the teacher of Rastrakuta Amoghavarsa, The Text 'critically edited along with the Sanskrit commentary of Prabhacandra and a new Hindi Anuvada by Dr. A. N. Upadhye, Dr. H. L. Jain and Pt. Balachandra Shastri, The edition is equipped with Introductions in English and Hindi and some useful Indices. Demy pp. 8-112-260, Sholapur, 1962. Price Rs. 5/-. 12. Ganitasara Samgraha of Mahaviracarya ( c.9th century A. D.): This is an important treatise in Sanskrit on early Indian mathematics composed in an elegant style with a practical

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gaNitasArasaMgraha approach, Edited with Hindi Translation by Prof. L. C. Jain, M. Sc., Jabalpur, Double Crown pp. 17 +34 + 282 +82, Sholapur, 1963. Price Rs. 121- 13. Lokavibhaga of Simhasuri : A Sanskrit digest of a missing ancient Prakrit text dealing with Jaina Cosmography. Edited for the first time with Hindi Translation by Pt. Balachandra Shastri. Double Crown pp. 8-52-256, Sholapur 1962. Price Rs. 10/-. 14. Pun yasrava-kathakoga of Ramachandra : It is a collection of religious stories in simple snd popular Sanskrit. The text authentically edited by Dr. A.N. Upadhye and Dr. H. L. Jain with the Hindi Anuvada of Pt. Balachandra Shastri. (To be out soon). 16. Jainism in Rajasthan: This is a dissertation on Jainas and Jainism in Rajasthan and round about area from early times to the present day, based on epigraphical, literary and traditional sources by Dr. Kailashchandra Jain, Ajmer. (To be out soon). 16. Visvatattva-prakasa of Bhavasena ( 14th century A. D.): It is & treatise on Nyaya. Edited with Hindi Summary and Introduction in which is given an authentic Review of Jaina Nyaya literature by Dr. V. P. Johrapurkar, Nagpur. (To be out soon). Works in preparation Subhasita-samdoha, Dharma-par ksa, Jnanarnava, Kathakosa of Sricandra, Dharmaratnakara, etc. For copies write to : Jaina Samskrti Samrakshaka Sangha, 'Santosh Bhavan, Phaltan Galli, Sholapur ( C. Rly): India

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jIvarAja jaina granthamAlA, solApUra (1) tiloyapaNNatti bhAga 1 lA (2) tiloyapaNNatti bhAga 2 rA (3) Yasastilaka and Indian Cultvre (4) pANDavapurANa ( zubhacandra ) (5) pAkRtazabdAnuzAsanam ( trivikrama ) (6) siddhAntasArasaMgraha (narendrasena ) 7o) Jainism in South India and Some Jaina Epigraphs (8) jaMbUdIvapaNNatti-saMgaho ( padmanandI) (9) bhaTTArakasaMpradAya (10) prAbhRtAdisaMgraha (11) padmanandipaJcaviMzati (12) AtmAnuzAsana ( guNabhadra ) (13) lokavibhAga paTkhaNDAgama ( dhavalasiddhAnta) bhAga zAstrAkAra pustakAkAra apApya aprApya 10-12 ru,12-0 * AgAmI prakAzana * vizvatattvaprakAza, subhASitasaMdoha, puNyAsravakathAkoza, rAjasthAna meM jainadharma, jJAnAvarNa, dharmaparIkSA, dharmaratnAkara inyAdi.