Mahaviracharya krut Ganitasar Sangraha

Author(s): Alexzander Volodraski
Publisher: Z_Deshbhushanji_Maharaj_Abhinandan_Granth_012045.pdf
Catalog link: https://jainqq.org/explore/211694/1

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mahAvIrAcArya kRta 'gaNitasAra-saMgraha' -DaoN0 alekjeMDara volodAkI madhyakAlIna bhAratIya gaNita ke vikAsa meM mahAvIrAcArya kRta 'gaNitasArasaMgraha' kA viziSTa sthAna hai jisakI ora vijJAna ke itihAsa viSayaka graMthoM meM paryApta dhyAna nahIM diyA gayA hai| (udAharaNa ke liye de0 sandarbha sAhitya saM0 [1]) / isa lekha meM mahAvIrAcArya kI viSaya-vastu kA vizleSaNa tathA mUlyAMkana prastuta kiyA gayA hai| mahAvIrAcArya ke jIvana kI bahuta kama jAnakArI upalabdha hai| svayam unhoMne apane janmakAla, janma-sthAna aura mAtA-pitA tathA guruoM ke viSaya meM kucha nahIM likhA hai / 'gaNitasArasaMgraha' ke pahale adhyAya meM lekhaka ne kisI bhAratIya zAsaka ko saMbodhana kiyA hai jisane san 814-815 se lekara san 877-878 taka zAsana kiyA thaa| cUMki mahAvIra ne bhaviSya meM bhI ukta zAsaka kI saphalatA kI kAmanA prakaTa kI hai isaliye aisA anumAna lagAyA jA sakatA hai ki isa graMtha kI racanA navIM zatAbdI ke madhya meM huI hogI (de0 sandarbha sAhitya saM0 [1], [2], [3], [6], [7], [8], [9] ) / yaha kahanA kaThina hai ki mahAvIra bhArata ke kisa bhAga meM rahate the| adhisaMkhya vidvAna unheM dakSiNa bhArata kA nivAsI mAnate haiN| isakA kAraNa yaha hai ki 'gaNitasArasaMgraha' kI saMskRta ke atirikta tIna anya pANDulipiyoM meM praznoM kI vyAkhyA tathA unake uttara kannar3a meM die gae haiM jisakA dakSiNa bhArata meM madhya yuga meM bahuta pracAra thaa| isa dhAraNA ke pakSa meM eka tarka yaha bhI hai ki mahAvIra jaina dharma ke anuyAyI the jo mukhyataH dakSiNa bhArata meM adhika pracalita hai| 'gaNitasArasaMgraha' meM aMkagaNita tathA rekhAgaNita pUrI taraha se die gae haiM, sAtha hI bIjagaNita tathA saMkhyA siddhAMta ke bhI bahuta-se praznoM para prakAza DAlA gayA hai| gaNitasArasaMgraha' kI vizeSatA yaha hai ki yaha pUrNatayA gaNita kA graMtha hai jabaki mahAvIra se pahale ke AcAryoM ne gaNita ko jyotiSa kI racanAoM meM milA diyA hai| mahAvIra se pahale kI racanAoM meM pramukha niyama to milate haiM parantu udAharaNa aura prazna nagaNya haiN| mahAvIrAcArya ne niyama, udAharaNa aura prazna saba die haiM parantu pramANa isameM bhI nahIM haiN| isa dRSTi se yaha grantha aneka madhyayugIna bhAratIya, arabI aura pAzcAtya anyoM se bhinna nahIM hai jinameM viSaya kA matAMdha nirUpaNa kiyA jAtA thaa| gaNita ke adhikAMza bhAratIya granthoM meM tIna bhAga hote haiM-mukhya bhAga jisameM niyama aura praznoM kI zarte dI rahatI haiN| vizeSa bhAga jisameM praznoM kI zartoM tathA udAharaNoM ko isa taraha diyA jAtA hai ki parikalana meM AsAnI ho; aura aMta meM paravartI AcAryoM kI TIkA dI jAtI hai| pratyeka bhAga kI apanI-apanI vizeSatAeM hotI haiN| grantha kA mukhya bhAga padya meM hotA hai jisameM laya nahIM hotI parantu chaMda kA dhyAna rakhA jAtA hai| gaNita ke cihna, rekhAcitra aura sUtra nahIM die jAte haiM, saMkhyAoM ko bhI zabdoM ke dvArA vyakta kiyA jAtA hai| dUsare bhAga meM praznoM ke pratibaMdhoM (zartoM) aura udAharaNoM ko sAraNiyoM yA paTTikAoM ke rUpa meM diyA jAtA hai| isa bhAga meM cihnoM kA vyApaka prayoga hotA hai, rekhAgaNita ke praznoM meM rekhAcitra bhI die rahate haiN| aMtima bhAga meM TIkA ke sAtha praznoM ke vistRta hala tathA udAharaNa die jAte haiM aura sAtha meM anya granthoM ke saMdarbha aura uddharaNa bhii| mahAvIrAcArya ke grantha meM nau adhyAya tathA 1131 zloka haiN| inameM se 452 zloka niyamoM ke haiM tathA 679 zlokoM meM udAharaNa tathA prazna die gae haiN| *isa saMkSipta anuvAda meM aMkagaNIta ke aMta ko chor3a diyA gaa| hai| jana prAcya vidhAeM

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'gaNitasArasaMgraha' madhyayugIna bhAratIya gaNita ke granthoM meM sabase bar3A hai| isakA eka kAraNa yaha hai ki isameM udAharaNoM kA aMza mukhya grantha kA 3/5vAM bhAga hai / dUsarA kAraNa yaha hai ki mahAvIra ne niyama adhika vistAra se die haiN| sAmAnya niyamoM ke atirikta mahAvIra ne viziSTa paristhitiyoM ke liye alaga-alaga niyama bhI die haiM jo anya granthoM meM nahIM milate / saMkhyAoM ke liye prayukta zabda-cihna isa prakAra haiM0-AkAza 1-caMdra 2-netra, hasta 3-agni, ziva ke netra 4-sAgara 5-jJAnendriyA~, bANa 6-Rtu 7-zikhara, azva 8-senA, hasti, dizAe~, zarIra 9-saMkhyAe~, graha, padArtha yaha zabda-praNAlI kevala saMkhyAoM ko vyakta karane ke liye thii| isake dvArA pUrA prazna hala karanA asaMbhava hai| isa praNAlI ko samajhane ke liye prAcIna bhAratIya sAhitya, dharma aura mithakoM ko acchI taraha jAnanA Avazyaka thaa| bhArata meM gaNita ko bahuta U~cA sthAna prApta thaa| apane isa grantha ke Arambha meM saMjJAdhikAra prakaraNa meM gaNitazAstra kI prazaMsA meM mahAvIrAcArya ne isa prakAra likhA hai laukike vaidike vApi tathA sAmAyike'pi yaH / vyApArastatra sarvatra saMkhyAnamupayujyate / / kAmatantre'rthazAstra ca gAndharve nATake'pi vaa| sUpazAstre tathA vaidye vAstuvidyAdivastuSu / chando'laMkArakAvyeSu tarkavyAkaraNAdiSu / kalAguNeSu sarveSu prastutaM gaNitaM param // sUryAdigrahacAreSu grahaNa grhsNyutau| triprazne candravRttau ca sarvatrAMgIkRtaM hi tat / / dvIpasAgarazailAnAM saMkhyAvyAsaparikSipaH / bhavanavyantarajyotirlokalpAdhivAsinAm // nArakANAM ca sarveSAM shrenniibndhendrkotkraaH| prakIrNakapramANAdyA budhyante gaNitena te|| bIja gaNita saMskRta meM bIja gaNita ke lie kaI nAma haiN| unameM se eka hai avyakta gaNita arthAt ajJAta rAzi kI gaNanA kI klaa| aMka gaNita meM, jise vyakta gaNita bhI kahate haiM, jJAta rAzi kI gaNanA kI jAtI hai| RNa saMkhyAoM ke kriyA niyama jo brahmagupta kI racanAoM meM bhI milate haiM, mahAvIra ne isa prakAra diye haiM :-"yadi RNa rAzi ko RNa rAzi se yA dhana rAzi ko dhana rAzi se guNA kiyA jAe yA unheM vibhAjita kiyA jAye to unakA phala dhana rAzi hI hogaa| AcAryaratna zrI dezabhaSaNa jI mahArAja abhinandana grantha

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yadi do meM se eka rAzi dhana ho aura dUsarI RNa to phala RNa aaegaa| yadi dhana rAzi aura RNa rAzi kA yoga kiyA jAe to phala unake aMtara ke barAbara hotA hai| [9,1,50] * "do RNa yA do dhana rAziyoM kA yogaphala kramaza: RNa yA dhana hogaa| dhana rAzi, jise kisI rAzi se ghaTAnA ho RNa bana jAtI hai jabaki kisI rAzi se ghaTAI jAne vAlI RNa rAzi dhana ho jAtI hai|" [9,I,51] dhana aura RNa rAziyoM kA varga dhana hotA hai| ina vargoM ke vargamUla kramazaH dhana aura RNa hote haiN| cUMki RNa rAzi kA varga nahIM hotA isalie isake vargamUla bhI nahIM banAe jA sakate / [9,I, 52] isI taraha ke kaI niyama mahAvIra ke bAda ke bhAratIya gaNitajJoM ne bhI diye haiN| vijJAna ke itihAsa meM RNa saMkhyAoM kA sarvaprathama ullekha cInI grantha "gaNita ke nI adhyAya" ke AThaveM khaNDa meM milatA hai| isa grantha meM RNa saMkhyAoM ke jor3ane aura ghaTAne ke niyama bhI die gae haiN| isameM RNa saMkhyAoM ke lie 'phU' zabda kA prayoga kiyA gayA hai jisakA artha hai-RNa, udhAra, kamI / isa dRSTi se donoM bhASAoM ke zabda samAna hI haiN| bhArata meM RNa saMkhyAoM kI zuruAta IsA kI AraMbhika zatAbdiyoM meM huii| paraMtu, yaha spaSTa rUpa se nahIM kahA jA sakatA hai ki RNa saMkhyAe~ bhAratIya gaNitajJoM kI hI dena haiM yA unhoMne inheM cIna se grahaNa kiyaa| raikhika samIkaraNa pratizata, gati, mUlya kI adAyago Adi ke praznoM kA hala karate samaya yA unake niyama banAte samaya aksara raikhika samIkaraNa kA upayoga kiyA jAtA hai| aneka prakAra ke praznoM aura samasyAoM kA hala ajJAta rAzi vAle raikhika samIkaraNoM kI madada se nikala sakatA hai| udAharaNa ke lie:- "yadi kisI rAzi ke 3152536 azA . aMzoM kA yogaphala hai to vaha rAzi kyA hai ?" [9,III,108] isa prazna ko kalpita niyama ke siddhAMta se hala kiyA jAtA hai| "ajJAta rAzi ko 1 mAnakara ina aMzoM kA yogaphala nikAlanA caahie| aba yadi bhAgaphala ko isa jJAta yogaphala se vibhAjita kiyA jAe to vaha ajJAta rAzi mAlUma kI jA sakatI hai| [9,III,107] eka kalpita niyama kA siddhAMta una praznoM ke lie upayukta hai jo ax= taraha ke samIkaraNoM meM badale jA sakate haiM; vizeSakara jabaki kucha bhinnoM kA yogaphala 'a' ho| isa sthiti meM x ke rUpa meM vaha saMkhyA cunI jA sakatI hai jo ki hara kA guNaja ho| yadi samIkaraNa ax =b, ho, to hala isa prakAra hogA : h x=3x1b uparokta niyama paravartI araba aura yUropIya gaNita sAhitya meM bhI milate haiM / sAtavIM-AThavIM zatAbdI meM bakSAlI hastalipi graMtha meM aisI samasyAoM ke hala diye gae haiM jinakA samIkaraNa ax+b=p hotA hai| yadi samIkaraNa assbp ho, to usakA hala x=x+PP hogaa| ___ [5, pRSTha 371] a AryabhaTTa prathama (10, II, 30), brahmagupta (11, XVIII, 43) zrIpati, bhAskara dvitIya aura nArAyaNa (6, adhyAya 2, pRSTha 40-41) ne nimnalikhita raikhika samIkaraNoM ko hala karane ke niyama diye haiM : ax+c=bx+d brahmagupta kA niyama isa prakAra hai :-"eka ajJAta rAzi vAle rakhika samIkaraNa meM viparIta krama se lie gae jJAta padoM ke aMtara ko yadi ajJAta padoM ke guNakoM ke aMtara se vibhAjita kiyA jAe to ajJAta rAzi mAlUma kI jA sakatI hai|" [6, adhyAya 2; pRSTha 40] m=x, isa taraha ke samIkaraNa se saMbaMdhita eka prazna isa prakAra hai : 1. zrI ema. raMgAcArya kI pustaka ke saMdarbha aMgrejI anuvAda ke aMza ke hai| anuvAdaka -anu. jaina prAcya vidyAeM. . ...

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staMbha kI lambAI kyA hogI ? 1 4 3 saMkhyA batAe jAtI hai "yadi eka staMbha kA 80 x= isa prazna kA hala mahAvIrAcArya ne isa prakAra diyA hai| 2 geo a m x= 1 8 bhAga jamIna ke aMdara hai, C " eka rAjA ne kula AmoM kA + +...+ 7) kATheM bhAga liyA, rAnI ne zeSa kA hai, tIna rAjakumAroM ne pratyeka ke zeSa bhAga kA kramazaH ? isa prazna ko nimnAMkita raikhika samIkaraNa dvArA hala kiyA jA sakatA hai : x-dyx-az (x-ax) - 4g [x - ax - 2 (x-ajx)] - ..=b, isI prazna ko hala karane ke lie mahAvIrAcArya ne nimnalikhita niyama diyA hai : isakA hala isa prakAra hai aura nanheM rAjakumAra ne bace hue 3 Ama lie| jise mizrita bhinna ke prazna hala karanA AtA ho vaha AmoM kI kula [9, TV, 29-30] b [9. IV. 44] ( 1 - 12 ) ( 1 - as ) ... (1--an ) nimna prakAra ke praznoM ko hala karane ke lie do ajJAta rAziyoM vAlI do raikhika samIkaraNoM kI paddhati upayoga meM lAI "yadi 9 nIMbU aura 7 seboM kA mUlya 107 (paise) hai 7 nIMbU aura 9 seboM kA mUlya hai 101 (paise), to batAo ki eka nIMbU aura eka seba kA mUlya kyA hogA ?" [9, V1,140-2-142 1 nIMbU ke mUlya ko yadi * mAnA jAe aura seba ke mUlya ko y to nimnalikhita samIkaraNa prApta hote haiM : { ina samIkaraNoM kA sAmAnya rUpa isa prakAra hogA :-- { 3 9x+7y=107 7x +9y=101 pAnI meM, kAI meM aura staMbha aura 7 hAtha dikhAI de rahA hai to [9. IV. 5] ax+by=c bx+ay-d mahAvIrAcArya kI paddhati para AdhArita eka aura prazna nIce diyA gayA hai| "kula phaloM kI adhikatama saMkhyA se guNA kiye gaye kula phaloM ke adhikatama mUlya meM se phaloM kI nyUnatama saMkhyA se guNA kiye ye phaloM ke nyUnatama mUlya ko ghaTAyA jAtA hai| zeSa ko adhikatama aura nyUnatama phaloM kI saMkhyA ke varga ke aMtara se vibhAjita karane para adhikatama phaloM kA mUlya jJAta hotA hai| anya phaloM kA mUlya kula phaloM kI saMkhyA ke mUlya ko viparIta krama se guNA karane para jJAta hotA hai|" 1 [9, V1, 139 - 1 x = ac-bd a2-b2 y= [9.1V. 4] ad-bc a2-b2 AcAryaratna zrI dezabhUSaNa jI mahArAja abhinandana grantha

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chaThe adhyAya ke zloka saMkhyA 270-272 1/2 meM eka rocaka prazna diyA gayA hai : "murgoM kI lar3AI ke samaya eka darzaka ne donoM murgoM ke mAlikoM se eka samajhautA kiyA pahale se usane kahA ki yadi tumhArA murgA jItegA to tuma mujhe jItI huI rAzi doge aura 2 kahA ki yadi tamhArA margA jItegA to tama mujhe jItI 3 duuNgaa| donoM hI sthitiyoM meM darzaka ko 12 svarNa mudrAeM / usake hArane para maiM tumheM jItI huI rAzi kA duuNgaa| dUsare mAlika se usane huI rAzi doge aura usake hArane para maiM tumheM tumhArI jotI huI rAzi kA 3 4 mileMgI / pratyeka mAlika ko kitanA-kitanA puraskAra milegA ?" donoM mAlikoM kI rAziyoM ko x aura 3 mAnate hue nimnalikhita samIkaraNa banate haiM: yA sAmAnyataH X= y = x d a b mahAvIrAcArya ke anusAra isa paddhati kA hala isa prakAra hai jaina prAcya vidyAeM - 3 4 2 3 3 y=12 x=12, 6(0+d) (c+d) b- (a+b)'c 5 d (a+b) -.m (a+b).d-(c+d).a y = 3z * = 6z y = m isI prakAra kA prazna bhAskara dvitIya ke graMtha meM bhI diyA gayA hai / " eka vyakti ne kahA ki yadi tuma mujhe 100 rupaye do to maiM tumase dugunA amIra ho jaauuNgaa| dUsare ne kahA ki yadi tuma mujhe 10 rupaye do to maiM tumase chaH gunA amIra ho jAU~gA / pratyeka ke pAsa kitanI pU~jI thI ?" [1, q 137-138] prazna tIna ajJAta mahAvIrAcArya ke graMtha ke 6-veM adhyAya meM zloka saMkhyA 90/- - 12 kA yaha nimnalikhita 91 2 rAziyoM vAlI tIna samIkaraNoM kI paddhati se hala hotA hai / xm. "anAra, Ama aura seba, pratyeka ke 3 nagoM kA mUlya 2 pana, 5 nagoM kA 3 pana aura 7 nagoM kA 5 pana hai| gaNita jAnane vAle mere mitra jaldI se yaha batAo ki 76 pana meM kitane phala kharIdoge jisameM Ama seba se 3 gunA aura anAra se 6 gunA adhika hoN|" prazna ke hala ke lie samIkaraNa isa prakAra hai : [ 2 x + 3 z=76 y + 'm 5 7 [9, V1, 268 --- 269 -- 1. 2 ( x, y, z - kramaza: anAra, Ama aura seba kI saMkhyA batAte haiM / yaha paddhati bar3I AsAnI se eka ajJAta rAzi vAle samIkaraNa meM badalI jA sakatI hai / 2282660 2 1ceung isa prazna kA uttara hai :- kula kharIde gaye anAra, Ama aura seboM kI saMkhyA kramaza: 70, 35 aura 11 hai| 81

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dvighAta samIkaraNa mahAvIrAcArya ke grantha meM dvighAta samIkaraNa para alaga se koI adhyAya nahIM hai| phira bhI kaI praznoM kA hala kevala dvidhAta samIkaraNoM ke mUla jJAta karane se nikala sakatA hai| isa taraha kA eka prazna hai : "UMToM ke jhuMDa kA - bhAga jaMgala meM hai, 15 U~Ta nadI ke kinAre aura zeSa U~Ta jo kula saMkhyA ke vargamUla kA dugunA haiM, pahAr3I para haiM / U~ToM kI saMkhyA kyA hai ?" [9, IV, 34]. jhuMDa meM U~ToM kI saMkhyA x mAnane para nimnalikhita samIkaraNa prApta hogA : x+20 +15=x. athavA +cv x + p=x yA phira, (1-2)x-ef x =p mahAvIrAcArya isa dvighAta samIkaraNa ko nimnalikhita niyama se hala karate haiM : "vargamUla ke guNAMka ke Adhe bhAga aura mukta pada ko bhinna rahita ikAI meM vibhAjita karanA caahie| isa prakAra prApta mukta pada ke varga ke kula yoga ke vargamUla ko prApta guNAMka meM jor3anA cAhie / isa rAzi kA varga hI ajJAta rAzi hai| mUla saMbaMdhI praznoM ko hala karane kI rIti yahI hai| [9, IV, 33] isa niyama ke anusAra hala isa prakAra nikalegA : 2 (2 +N ) +_P + P aisA pratIta hotA hai ki brahmagupta ko bhI jJAta thA ki dvighAta samIkaraNa ke do mUla hote haiN| TIkAkAra pRthudakasvAmI (san 860) ke anusAra isa prazna para nirbhara karatA hai ki mUla ko jor3A jAe yA ghaTAyA jaae| [6, khaMDa 2, pRSTha 75). paraMtu brahmagupta ke grantha meM mUloM ke isa dohare artha kA ullekha nahIM hai / jaisA ki pahale kahA jA cukA hai, mahAvIrAcArya ko vargamUloM ke dohare artha mAlUma the| isakA upayoga nimnalikhita prazna ko hala karane ke niyama meM kiyA gayA hai : "moroM ke jhuMDa kA - vAM bhAga, jo apanI hI saMkhyA se guNA kiyA huA hai, Ama ke per3a para baiThA hai| zeSa kA - vA~ bhAga, svayaM kI saMkhyA se guNA kiyA huA anya 14 moroM ke sAtha 'tamAla' ke per3a para hai| moroM kI kula saMkhyA kyA hai ? [9, IV, 59] moroM kI kula saMkhyA yadi hama x mAna leM to nimnalikhita samIkaraNa prApta hogA : x x + 15x15x + 14=x. yA sAmAnya rUpa meM. ax - x + p= 0. AcAryaratna zrI dezabhUSaNa jI mahArAja abhinandana grantha

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isa taraha ke samIkaraNa ko hala karane kA niyama hai :- "apane hI aMza se vibhAjita hara tathA mukta pada ke caugune ke aMtara ko isa hara se, jo ki aMza se vibhAjita ho, guNA kiyA jAtA hai| isake vargamUla ko aMza se vibhAjita isa hara se jor3A aura ghaTAyA jAtA hai| isakA AdhA hI ajJAta rAzi hai|" [9, IV,57] isa taraha, ___b //b -4p) H 2 kucha paristhitiyoM meM jabaki dvighAta samIkaraNa ke mUloM meM se koI eka mUla prazna ke upayukta nahIM hotA hai, mahAvIrAcArya kevala vahI mUla cunate haiM jisake dvArA sahI hala prApta kiyA jA sakatA hai| uccatama krama ke samIkaraNa kucha aise prazna haiM jinakA hala eka ajJAta rAzi vAle dvighAta samIkaraNoM se uccatara samIkaraNoM ke dvArA nikalatA hai| jaise jyAmiti zrer3hI ke hara 'q' ko jJAta karane ke lie samIkaraNa ko hala karanA hogaa| S = aq" zrer3hI kA hara , V ke barAbara hai| q=VE [9, II, 97] N-ghAta ke mUla nikAlane ke niyama mahAvIrAcArya ne nahIM diye haiN| spaSTataH aise mUloM kI eka cunI huI sUcI dI jAtI thii| "jyAmiti zreDhI kA pahalA pada 3 hai, kula padoM kI saMkhyA 6 hai aura yogaphala hai 4095 / jyAmiti dher3hI kA hara kyA hai ?" [9, 11, 102] yaha prazna paMcama ghAta ke samIkaraNa se hala hotA hai| xi =4095 3 (x + x + + x + x + 1)= 4095. yaha samIkaraNa nimnalikhita niyama se hala kiyA jAtA hai| "yogaphala ko pahale pada se vibhAjita kro| prApta bhAgaphala meM se pratyeka bAra eka ikAI ghttaao| isa saMkhyA meM jitane kA bhAga diyA jAegA vahI saMkhyA jyAmiti zrer3hI kA hara hogii|" [9, 11, 101j. vAstava meM yadi gher3hI ke hara ko x mAneM ton-1 ghAta kA samIkaraNa isa prakAra hogA: "-1 x-1-S. donoM bhAgoM ko pahale pada se vibhAjita karane para aura usameM ghaTAne para nimnalikhita samIkaraNa prApta hotA hai : x se kATane para aura 1 ghaTAne para jo samIkaraNa banA vaha isa prakAra hai : jaina prAcya vidyAeM

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zrar3hI kA ajAta hara jisase anukrama rAzi S, S, S, ......S...., ko vibhAjita kiyA jAtA hai, varaNa siddhAMta ke dvArA jJAta ho sakatA hai| isa udAharaNa meM x24. cauthe adhyAya ke zloka saMkhyA 54-55 meM eka bahuta rocaka prazna diyA gayA hai / "jaMgala meM kAma kara rahe hAthiyoM kI saMkhyA hai : kula hAthiyoM kI saMkhyA ke 2 bhAga ke vargamUla ke 9 guNe aura zeSa hAthiyoM kI saMkhyA ke 1 ke vargamUla ke 6 guNe kA yoga / aba yadi isa saMkhyA meM 24 aura jor3A jAye to hAthiyoM kI kula saMkhyA jJAta ho sakatI hai| vaha saMkhyA kyA hai ? yadi mAna leM ki hAthiyoM kI kula saMkhyA : ho to cauthe ghAta kA nimnalikhita samIkaraNa prApta hotA hai : 2+6 V3 (x--913) + 24=x. mahAvIrAcArya ke anusAra isakA hala nikAlane ke lie do dvighAta samIkaraNoM kA Azraya lenA par3atA hai| yadi _y = x-9 V3 x, ho to dvighAta samIkaraNa hogA y-6/3y =24. 1 = 60; y. =3 ke mUlya ko pahale samIkaraNa meM rakhane para nimnalikhita samIkaraNa prApta hotA hai : x = 150; X = 24. dvighAta samIkaraNa, 0 ke pUrNa mUla nahIM haiM / kevala x = 150 hI upayukta hai| cauthe adhyAya ke 56 veM zloka meM diyA gayA prazna 4 ghAta ke samIkaraNa se hala hotA hai| "suaroM kI eka nizcita saMkhyAjhuMDa ke - bhAga ke vargamUla kI caugunI-jaMgala meM hai| jhuMDa kA eka hissA-zeSa saMkhyA ke -- bhAga ke vargamUla ke dugune kA 4 gunA-pahAr3I para hai| dUsare hisse ke suara nadI kI tarapha jA rahe haiM jinakI saMkhyA hai zeSa ke Adhe ke vargamUla kA 9 gunnaa| isake alAvA jhuMDa meM 56 suara aura haiN| kula kitane suara haiM ?" suaroM kI kula saMkhyA ko . mAnate hue samIkaraNa banegA : +Vs+8 Vi(r-V) +9 VH[:-4 V -8 VI(x-4 Vi)] + 56=x. mahAvIrAcArya ke anusAra, isa samIkaraNa kA kramika hala tIna dvighAta samIkaraNoM se nikalatA hai| yadi yox-4V, SY AcAryaratna zrI devabhUvana jI mahArAja abhinandana anya

Page #9
to, 7 -8V - -8 10 yadi 2 to 2 9 56. aMta meM x kA mAna nikalA 200. a1= a1 =y-8 bhedI bhAratIya gaNita sAhitya meM aMkagaNita zrer3hI aura jyAmiti zrer3hI kA pramukha sthAna rahA hai| kucha taraha ke prazna asAdhAraNa taura para lokapriya hue jaise zataraMja ke AviSkAra se saMbaMdhita prazna, jisase ki jyAmiti zrer3hI ke yogaphala nikAle gaye jinameM hara kA mAna saMkhyA 2 thaa| yahI nahIM, isa taraha ke jyAmiti zrer3hI ke yogaphala nikAlane saMbaMdhI praznoM kA ullekha prAcIna cInI grantha "gaNita ke nau adhyAya" meM bhI hai| a1 = bher3I kA ullekha bahuta sI gaNita kI pustakoM tathA navavidyA ke granthoM ke gaNita saMbaMdhI adhyAyoM meM milatA hai| ina pratthoM meM kabhI-kabhI zrer3hI ke niyama aura prazna itanI adhika mAtrA meM ho jAte the ki unake lie "zrer3hI vyavahAra" kA eka vizeSa khaMDa alaga se diyA jAtA thaa| d= aMkagaNita zrer3hI ke praznoM ko hala karane ke niyama mahAvIrAcArya ke anusAra isa prakAra the : - d.n jaina prAcya vidyAeM S S n 2.s n S n 1 V 7-1 2 2 n - a - (n-1). d, 2 = 10 S= S = 9 V = (-8 V) 10 d S= 70 25 n 1 2 aMkagaNita zrer3hI ke yogaphala aura padoM kI saMkhyA jJAta karane ke niyama, jo unase pahale ke gaNitajJoM ne banAe the, mahAvIrAcArya ne isa prakAra diye haiM: : [ -2a } [(n-1)d+2a ] n. 2 d+as a1tan 2 =56. n, 2ds+ d -a +11+1++-- d d 2 [9. II, 73] [9,11,74] [9.11.76] [9, 11, 75] [9, II, 61] [9.11.62] [9, II, 64] [9.111.33] 81.

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nimnalikhita niyama bahuta hI rocaka DhaMga se banAyA gayA hai| kisI bhI saMkhyA vAle aMkagaNita zrer3hI ke padoM ke pahale pada ke lie saMkhyA 1 lI jAtI hai| pahale pada se ghaTAI huI padoM kI saMkhyA ko padoM kI saMkhyA aura | ke aMtara ke Adhe se vibhAjita karane para jo saMkhyA prApta hotI hai use zrer3hI kA aMtara mAna sakate haiN| yogaphala padoM kI kula saMkhyA ke varga ke barAbara haa| yaha saMkhyA, jise padoM kI saMkhyA se gUNA kiyA jAtA hai, padoM kI saMkhyA ke dhana ke barAbara hotI hai| 19,31C, 33] spaSTataH yahA~ mahAvIrAcArya aMkagaNita zrer3hI kI bAta kara rahe haiN| S= "(2k-1)=n', k-11 S.n=n.nns. jyAmiti zrer3hI ke niyama aura prazna AryabhaTTa aura brahmagupta ke granthoM meM nahIM milate haiN| jyAmiti zrer3hI ke yogaphala aura pada nikAlane ke niyama sabase pahale mahAvIra ne diye / usake bAda zrIdhara aura bhAskara dvitIya ne inheM isa prakAra prastuta kiyA :-- an+1=a.g" [9, II. 93] S aq"-a -1 mahAbIrAcArya ke graMtha meM ina niyamoM aura unake vividha prakAroM ke udAharaNa diye gaye haiN| saMcaya vinyAsa chaThe adhyAya ke 218veM zloka meM mizrita saMkhyAoM ke saMcaya jJAta karane kA sUtra diyA gayA hai jo isa prakAra hai : _ n(n-1) (n-2)...[n-(m-1)] 1.23...m isI niyama ke 3 udAharaNa haiM jinameM se eka isa prakAra hai :-"hIrA, nIlama, pannA, maMgA aura motiyoM ke vividha prakAra ke kitane hAra baneMge?" [9, VI, 220] aisA hI sUtra aura aise hI udAharaNa zrIdhara aura nArAyaNa ne bhI diye haiN| saMkhyA zRkhalAmoM kA yogaphala chaThe adhyAya meM mahAvIra ne saMkhyA zRMkhalA ke yogaphala nikAlane ke kucha niyama diye haiN| prAkRtika saMkhyA zRMkhalA ke vargoM kA yoga phala isa prakAra huA : E = 2 (n+yz Cr102 [9, IV, 296] 9,1, 296] aMkagaNita zrer3hI ke padoM ke vargoM kA yogaphala hai : Eu+k-1) dly = { [(2n=14+ +ad ] (n-1) +a } [9, V1, 298] AcAryaratna zrI dezabhUSaNa jI mahArAja abhinandana grantha

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prAkRtika saMkhyA zRMkhalA ke ghanoM kA yogaphala isa prakAra hai : Ta = (") (n+1). [9, VI, 301] aMkagaNita zrer3hI ke padoM ke ghanoM kA yogaphala hai : [a+(k-1)d] =Sata-d)+Sd, [9, VI, 303] isameM S kA mAna isI zrer3hI ke padoM kA yogaphala hai| pahalI / prAkRtika saMkhyA zRMkhalA ke vaga aura dhanoM ko nikAlane kI vidhi kA ullekha AryabhaTTa prathama se lekara nArAyaNa Adi sabhI bhAratIya AcAryoM ke graMthoM meM milatA hai| yaha vidhiyA~ bAvIlona aura mitra ke nivAsiyoM, nAniyoM aura cIna ke logoM ko bhI jJAta thiiN| bAda meM ina vidhiyoM kA ullekha araba aura pazcima yUropa ke gaNita sAhitya meM bhI milatA hai| yahI niyama bAda meM zrIdhara aura nArAyaNa ke granthoM meM bhI milate haiN| [4, pR0 233, 255] saMkhyA siddhAMta bhAratIya gaNitajJoM ne saMpUrNa dhana saMkhyAoM kI elgoSmi vidhi banAI jisakA uddezya pahale aura dUsare ghAta ke anizcita samIkaraNoM kA hala nikAlanA thaa| mahAvIra ke anusAra saMpUrNa dhana saMkhyAoM ke anizvita samIkaraNoM ko hala karane kA niyama isa prakAra hai :axtC=by [9, VII, 1152 , 13671 hala nikAlane kI yaha vidhi AryabhaTTa prathama, brahmagupta aura bhAskara dvitIya ke niyamoM para AdhArita hai| yaha vidhiyA~ vistArapUrvaka yuzkyevica kI pustaka meM dI gaI haiN| (1, pR0 144-147) sAmAnya niyamoM ke alAvA mahAvIra ne kucha viziSTa paristhitiyoM meM hala nikAlane kI vidhi bhI btaaii| "do sone kI char3oM meM, jinakA bhAra kramazaH 16 aura 10 hai, sone kI mAtrA ajJAta hai| lekina donoM ko milA dene para sone kI mAtrA 4 hai / pratyeka char3a meM sone kI mAtrA kyA hai ?" [9, VI, 188] yaha prazna nimnalikhita anizcita samIkaraNa meM badalA jA sakatA hai :16x+10y-4 (16+10) yahA~ x aura ' char3oM meM sone kI mAtrA hai| sAmAnya samIkaraNa isa prakAra huA, ax+by=c (a+b) yA, a(x-c)=bc-) inakA hala hai, * =c+ y=c : isa samIkaraNa ko hala karane kA niyama isa prakAra hai : "sone ko do alaga-alaga sthAnoM para rakheM / char3oM meM sone ke jJAta bhAra ko eka se vibhAjita karake bArI-bArI se eka ghaTAne aura eka jor3ane para sone kI mAtrA jJAta kI jA sakatI hai|" isase Age mahAvIra likhate haiM ki yadi sveccha maMkhyA ko pahalI char3a meM sone kI mAtrA mAneM to dUsarI char3a meM sone kI mAtrA pahale kI taraha mAlUma kI jA sakatI hai| [9, VI, 189] jaina prAcya vidyAe~

Page #12
pratizata, kapa, vikrama aura kucha dUsarI prakAra ke praznoM ke lie ajJAta padoM vAle raikhika samIkaraNa prayoga meM lAye jAte haiN| chaThe adhyAya ke 160 se 162veM zlokoM meM diye gaye prazna se nimnalikhita samIkaraNa banatA hai : Xx+*g+*g+xq=a+b<< yahA~ a, b, c, d - jJAta rAziyA~ haiN| mahAvIra ke anusAra isa prazna kA hala isa prakAra hai 85 a, a, a2 Apt yahA~ sveccha saMkhyA hai| P - p2, _a+b+c+d 3 Xg a+b+c+d X1= m2n2 ma+n2* _a+b+c+d 3 c, Xg= AryabhaTTa prathama aura nArAyagaM dvArA diye gaye hala bhI aise hI haiM / IsA pUrva prathama sahasrAbdi ke madhya meM likhe gaye "rajjU niyamoM meM samIkaraNa +2 ke parimeya hala diye gaye haiN| saMpUrNa saMkhyAoM ke hala sabase pahale brahmagupta aura phira mahAvIra ne nikAle, jo isa prakAra hai : p2q2, 2pg, p+-+q2. yahA~ pg sveccha saMkhyAe~ haiM jo ki prAcIna yUnAniyoM ke bhI pahale jJAta thiiN| do aura tIna tattvoM se eka AkRti banAo !" a+b+c+d 3 samIkaraNa x2 +a+-=z ke parimeya hala mahAvIra ke anusAra isa prakAra haiM : (S) (5+0) p2 a+b+c+d 3 x4= a2 Api + pe a .b 2 C d samIkaraNa x 2 + y = c2 ke parimeya hala isa prakAra hue : p-p4, c P.Vc2-p2, c. cUMki saMkhyA kA cunanA kaThina na thA isalie mahAvIra ne eka aura hala DhUMDha nikaalaa| 2mn ma+ne c, c. sAtaveM adhyAya ke 112 veM zloka meM mahAvIra ne samIkaraNa praNAlI 1121 { [9, VII 159] [9, V11. 9221 OVERM 95 VII. [9, VII, 122421 mx+ny+prxy ko hala karane kI vidhi btaaii| yahA~ m. p. (0) sveccha saMkhyAeM haiN| AcArya ratna zrI dezabhUSaNa jI mahArAja abhinandana grantha

Page #13
yadi tInoM rAziyA~, jo ki x +yi- samIkaraNa ke upayukta hoM, taba samIkaraNa isa prakAra hogA : mxz+ny, +pz=R isa sthiti meM praNAlI kA hala isa prakAra hai : xxl_R - R R rxv1 y=Y1 rx1y1 ZlR xiy isI vidhi se mahAvIra nimnalikhita prazna hala karate haiN| "eka Ayata kA kSetraphala usake parimApa ke barAbara hai| usakI bhajAoM kA mApa btaao|" [9, VII, 115] "eka Ayata kA kSetraphala usake vikarNoM ke mApa ke barAbara hai| usakI bhujAe~ kisake barAbara haiM ?" [9, VII, 11511 pahale prazna meM prApta samIkaraNa praNAlI isa prakAra hai : Sx+y== / 2x+2y=xy, dUsare meM, S xi+yl=z z=xy a-b2, 2ab, t+bdeg ko pAithegorasa saMkhyAe~ mAnate hue pahalI samIkaraNa praNAlI kA hala isa prakAra hogA : 2 (a-b)+4ab 2(a-b2)+4ab 2ab - 2 (a-b)+4ab . 2ab (d-b3) (2-2), aura dUsarI praNAlI kA hala, a+be d +bp (a+b) 2ab , - b 2ab (a-b2) mahAvIra, bhAskara dvitIya aura nArAyaNa ne kaI udAharaNa diye haiM jo ki tIsare ghAta ke anizcita samIkaraNa banAte haiN| udAharaNa ke lie, mahAvIra ke anusAra aMkagaNita zrer3hI ke yogaphala se pahale pada, padoM kI saMkhyA aura zrer3hI kA aMtara jJAta kiyA jA sakatA hai / isa prazna kA hala 3 ajJAta rAziyoM vAle anizcita samIkaraNoM se prApta hogA / _s= [+ dy-1)]... hala karane kA niyama isa prakAra hai : yogaphala ko usake kisI bhI bhAjaka se, jo ki padoM kI saMkhyA hogA, vibhAjita kro| sveccha saMkhyA ko bhAgaphala se ghaTAo, ghaTAne para jo saMkhyA AegI vaha pahalA pada hogii| prApta aMtara kula padoM kI saMkhyA ke Adhe se vibhAjita, jo ki 1 se ghaTAyA gayA , zrer3hI kA aMtara kahalAtA hai| [9, VII,78] jaina prAcya vidyAeM

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kSetraphala kA mApa jyAmiti ke adhyAya ke AraMbha meM mahAvIra likhate haiM ki kSetraphala kA mApa do prakAra kA honA cAhie-vyAvahArika AvazyakatAoM ke lie sannikaTa pApa aura yathArtha mApa / gaNita meM pAraMgata vidvAna kaI prakAra kI AkRtiyoM se paricita haiM jinameM trikoNa, caturbhuja aura vakra dekhAoM se banI AkRtiyA~ zAmila haiN| [9, VII, 2-3] isake bAda AkRtiyoM ke prakAra kA vivaraNa diyA gayA hai jaise, trikoNa tIna prakAra ke hote haiM, caturbhuja 5 prakAra ke aura vakra rekhAoM se banI AkRtiyA~ 8 prakAra kI hotI haiM / bAkI sabhI AkRtiyA~ inhIM AkRtiyoM se banatI haiN| gaNitajJoM ke anusAra trikoNa tIna prakAra ke hote haiM-samabAhu, samadvibAhu aura viSamabAhu / caturbhuja samabAhu, do barAbara bhujAoM vAle, do viparIta barAbara bhujAoM vAle, tIna barAbara bhujAoM vAle aura viSamabAhu hote haiN| vRtta, ardhavRtta, AyatavRtta, kambukAvRtta, nimnavRtta, unnatavRtta, bAhya valaya aura bhItarI vanaya-yaha vakra rekhAoM se banI AkRtiyoM ke prakAra haiN| [9, VII, 4-6 | isake bAda mahAvIra ne pratyeka sannikaTa aura yathArtha AkRtiyoM ke lie sUtra banAe / trikoNa aura caturbhuja ke sannikaTa kSetraphala jJAta karane kA niyama isa prakAra hai-"viparIta bhujAoM ke yogaphala ke Adhe kA guNanaphala, trikoNa aura caturbhuja ke kSetraphala ke barAbara hotA hai| [9, VIL, 7] brahmagupta ne trikoNa aura caturbhuja ke kSetraphala jJAta karane ke lie sannikaTa sUtra banAye jo kramazaH isa prakAra haiM : s=2 aura, s= at bd caturbhuja kA sannikaTa kSetraphala jJAta karane kA sUtra misra ke vidvAnoM ko bhI jJAta thaa| isI sUtra ke lie mahAvIra ne 11 udAharaNa diye haiM jinameM se kucha isa prakAra haiM :"eka tribhuja kI pArzva bhujA, viparIta bhujA aura AdhAra kA mApa hai 8 daMDa / batAo usakA sannikaTa kSetraphala kyA hai ?" [9, VII, 8] "do samAna bhujAoM vAle eka tribhuja kI samAna bhujAoM kI laMbAI hai 77 daMDa / AdhAra kI laMbAI hai 22 daMDa aura 2 hasta / tribhuja kA kSetraphala kyA hai ?" [9, VII, 9] "3 samAna bhujAoM vAle eka caturbhuja kI pratyeka samAna bhujA kA mApa 100 daMDa hai. AdhAra kA mApa hai 8 daMDa aura 3 hst| caturbhuja kA kSetraphala btaao|" [9. VII, 15] caturbhuja kA yathArtha kSetraphala hai. S== p-a) (p-b)(p-C) (p-d). [9, VII, 50] Sa+c citra : 1 AcAryaratna zrI dezabhUSaNa jI mahArAja abhinandana anya

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mahAvIra kahate haiM ki yadi caturbhuja viSamabAhu hai taba dUsare sUtra kA upayoga nahIM kiyA jA sakatA / pahalA sUtra brahmagupta aura zrIdhara ne diyaa| [4, pR0 239] chaThe adhyAya ke 84veM zloka meM caturbhuja ke vikarNa nikAlane ke sUtra diye gaye haiN| vikarNa == tac + bd) kab+cd) ad + bc vikarNa- /fac-+-bd iad+bc) [9, VII, 54] ab+cd yaha sabhI sUtra cakrIya caturbhujoM ke lie upayukta haiM / ina sUtroM ko samajhane ke lie nimnalikhita udAharaNa diye gaye haiM : "eka samAna bhujAoM vAle caturbhuja kI bhujAoM kA mApa 5 hai| batAo ki vikarNa kA mApa aura yathArtha kSetraphala kyA hai ?" [9, VII, 55] "tIna samAna bhujAoM vAle eka caturbhuja kI pratyeka bhujA kA mApa hai 13 kA varga, aura AdhAra 407 hai| vikarNa, U~cAI aura kSetraphala btaao|" [9, VII, 58] "eka vRtta kI paridhi kA mApa usake vyAsa kA 3 gunA hai| usake ardhavyAsa ke varga kA tigunA vRtta kA kSetraphala hai| gaNitajJoM ke anusAra ardhavRtta kA kSetraphala aura ardhaparidhi kA mApa upayukta pariNAmoM kA AdhA hotA hai|" [9, VIL, 19] isa taraha, 1=3d, S = ...d.. citra : 2 yahAM T 2 3 hai| yadi 12/10 ho to mahAvIra sahI sUtra isa taraha batAte haiM :1 = + lode, S = /10 (1) [9, VII, 60] bahuta-se udAharaNa inhIM sUtroM se hala kiye jAte haiM / AyatavRtta kA parimApa aura kSetraphala nikAlane kA niyama isa prakAra hai :-laghuvyAsa ke Adhe se bar3hAyA huA aura 2 se guNA kiyA huA dIrghavyAsa hI AyatavRtta kA parimApa hotA hai| parimApa meM guNA kiyA huA laghuvyAsa kA cauthA bhAga AyatavRtta kA kSetraphala hotA hai| [9, VIL,21] citra : 3 jana prAcya vidyAeM 31

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kSetraphala hogA dIrghavyAsa ko aura laghuvyAsa ko 6 mAnate hue mahAbIra ke anusAra parimApa huA 20 +6, aura AyatavRtta kA b (2a+b) 4 parimApa aura kSetraphala nikAlane ke sahI sUta nimnalikhita niyama se prApta kiye jA sakate haiM "laghuvyAsa ke varga ke chaH gune aura dIrghavyAsa ke varga ke dugune ko jodd'o| isakA vargamUla vRtta ke parimApa ke barAbara huA / parimApa ko laghuvyAsa ke cauthe bhAga se guNA karane para AyatavRtta kA sahI kSetraphala nikAlA jA sakatA hai| [9, VII, 63] 1=V6b* +-4a2 s=N 6b2+4a2 yaha spaSTa hai ki AyatavRtta kA kSetraphala nikAlane kA sUta vatta ke kSetraphala nikAlane ke sUtra se hI banA hai / d 4 S=== 2 1, vRtta kI paridhi aura AyatavRtta kI paridhi nikAlane ke sUtroM meM bhI sAmya hai / 1= 10d2 = N6d2 +4ds. - mahAvIra nimnalikhita udAharaNa dete haiN| " eka AyatavRtta ke dIrghavyAsa kI laMbAI hai 36 aura laghuvyAsa kI laMbAI 12 hai| usakA parimApa aura kSetraphala batAo / " [9. VII. 64] ma0 raMgAcArya [9] aura unake bAda jI0 sAraThIna [8, khaMDa 1, pRSTha 570] ke anusAra eka AyatapurA dIrghavRta hI hotA hai| isa dRSTikoNa se sahamata nahIM huA jA sakatA hai / sIpa ke AkAra kI AkRti (kambukAvRta) kA, jo ki do jur3e hue vibhinna vyAsa vAle ardhavRttoM se banatI hai, sannikaTa parimApa aura kSetraphala vRtta ke lie bane niyamoM se nikAle jA sakate haiM / -: 8 citra: 4 3 " adhikatama caur3AI se sIpa ke muMha kI caur3AI kA AdhA ghaTAne para aura 3 se guNA karane para AkRti kA parimApa jJAta hotA hai / isa parimApa ke Adhe ke varga ke eka tihAI ko yadi sIpa ke muMha kI caur3AI ke Adhe ke varga ke se guNA kiyA jAya to sIpa kA kSetraphala jJAta hogA / " [9, VII, 23] 4 adhikatama caur3AI arthAt dIrghavRtta ke vyAsa ko va aura sIpa ke muMha kI caur3AI ko 6 mAnate hue parimApa hogA, AcArya ratna zrI dezabhUSaNa jI mahArAja abhinandana grantha

Page #17
1=3(a- th), aura kSetraphala, isa sUtra ke lie nimnalikhita udAharaNa diyA gayA hai : 'sIpa ke dIrghavyAsa kA mApa hai 18 hasta aura sIpa ke maMha kI caur3AI hai 4 hst| usakA parimApa aura kSetraphala btaao|" [9, VII, 24] yadi TRV10 ho to sahI sUtra isa prakAra hogA, ___= ( 4-1 ) 0 SE | 4/62 4) V 10 [9, VII, 65 nimna aura unnata vRtta kI sataha (jaise ki yajJa-kuNDa aura kachue kI pITha kI sataha hotI hai) kA kSetraphala nikAlane kA sUtra hai :-"paridhi ke eka cauthAI ko yadi vyAsa se guNA kiyA jAye to nimna aura unnata vRtta kI sataha kA kSetraphala jJAta hotA hai|" [9,VII,25] citra:5 yaha satra Ayata yA capaTe golArdha ke lie hai kyoMki sAmAnya golArdha kA kSetraphala hogA citra: 6 jaina prAcya vidyAe~

Page #18
bhItarI aura bAharI valaya ke kSetraphala isa prakAra hoMge :-"bhItarI vyAsa ko valaya kI caur3AI se jor3ane para aura phira 3 tathA valaya kI caur3AI se guNA karane para bAharI valaya kA kSetraphala jJAta hotA hai| yadi vyAsa se valaya kI caur3AI ko jor3ane kI bajAya ghaTAyA jAe to bhItarI valaya kA kSetraphala prApta hogaa|" [9, VIL, 28] SbAharI =3 (d + a) a bhItarI = 3 (d-a) a yahA~ d = vyAsa, a = valaya kI caur3AI aura 63 hai| yadi II10 ho to yathArtha kSetraphala jJAta kiyA jA sakatA hai| ___[9. VII, 671 jau, muraja, paNava aura vajra kI taraha kI AkRtiyoM kA kSetraphala prApta karane ke lie unake madhya bhAga kI caur3AI aura kinAroM se lI gaI caur3AI ke yoga ke Adhe ko laMbAI se guNA kiyA jAtA hai| [9. VII, 32] AkAra kSetra (yavAkAra kSetra) murajAkAra kSetra 'epHo muradzha paNvAkAra kSetra > bayAkAra kSetra vajrAkAra kSetra panava vadzhra citra:7 yadi a = AkRti ke madhya kI caur3AI, a = eka kinAre se lI gaI caur3AI aura b = laMbAI ho to s-4 + boy 2 arthAt sabhI AkRtiyA~ AyatAkAra rUpa meM badala dI jAtI haiM jinameM pratyeka kI ausata caur3AI aura AraMbhika laMbAI lI jAtI hai| yaha niyama aura caturbhuja kA kSetraphala jJAta karane ke niyama meM paraspara saMbaMdha hai| aisA pratIta hotA hai ki yaha donoM hI niyama samAna paristhitiyoM meM banAye gaye haiN| zrIdhara kRta "patigaNita" ke eka ajJAta TIkAkAra ne vajra ke AkAra kI AkRti ko do barAbara samalaMboM ke rUpa meM dikhAyA hai jo ki eka dUsare ke sAtha nimnatama AdhAroM ke dvArA jur3e haiN| [4, pRSTha 238]. cAra udAharaNa isI niyama ke lie diye gaye haiN| "jau ke AkAra kI AkRti kI laMbAI hai 80, aura madhya bhAga kI caur3AI 40 hai| jau kA kSetraphala kyA hogA ?" [9, VIL, 33] "muraja ke AkAra kI AkRti kA kSetraphala batAo yadi usakI laMbAI 80 daMDa, kinAroM se lI gaI caur3AI 20 daMDa aura madhya bhAga kI caur3AI 40 daMDa ho|" [9, VIL, 34]. "paNava ke AkAra kI AkRti kA kSetraphala kyA hogA yadi usakI laMbAI hai 77 daMDa, do kinAroM meM se pratyeka se lI gaI caur3AI ho 8-8 daMDa, aura madhya bhAga kI caur3AI ho 4 dNdd|" [9, VII, 35] "yadi vajra ke AkAra kI AkRti kI laMbAI hai 96 daMDa, madhya bhAga suI kI noka ke barAbara hai aura kinAroM se lI gaI AcAryaratna zrI dezabhUSaNa jI mahArAja abhinandana grantha

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caur3AI hai 13 daMDa to usakA kSetraphala batAo / " [9, VII, 36] 3 "dhanuSa ke samAna AkRti kA kSetraphala bAna aura pratyaMcA kI laMbAI ko jor3ane aura phira bANa kI laMbAI ke Adhe se guNA karane para prApta hotA hai bAga kI laMbAI ke vartamUla ke pAMca gune meM pratyaMcA kI laMbAI ke varga ko jor3ane se dhanuSa kI laMbAI patA calatI hai / " [9, VII, 43] isa sUtra meM vRtta 'khaMDa aura isI vRttakhaMDa se prApta jIvA kI laMbAI prApta karane ke sannikaTa sUta diye hue haiM jahAM dhanuSa, pratyaMcA, bANa kramazaH vRtta ke cApa, jIvA aura vyAsa ke khaMDa haiM / vyAsa kA yaha khaMDa vRttakhaMDa ke bhItara hotA hai aura jIvA para laMga loga hai| citra : 8 "dhanuSa aura pratyaMcA kI laMbAI ke vargoM kA aMtara pA~ca se vibhAjita karane para aura phira isakA vargamUla nikAlane para bANa kI laMbAI jJAta karane ke lie bANa kI laMbAI ke varga ko 5 se guNA karake, dhanuSa kI laMbAI ke varga se ghaTAo aura phira isa aMtara kA vargamUla nikaalo|" [9. VII. 45 reis = (a + h). ~/. S vRtta 1 = Sh2 + 2, 2' 12 a= - h=v a == 12 5h 2, 1, a, h kramaza: cApa, jIvA aura vyAsa kA khaMDa haiN| ina sUtroM se nimnalikhita prazna hala kiye jA sakate haiM, h a2 5 "dhanuSa ke samAna AkRti meM pratyaMcA kI laMbAI hai 26 aura bANa kI laMbAI 13 hai / kSetraphala aura dhanuSa kI laMbAI btaao|" [9. VII, 44 ]. "yadi isI dhanuSa ke bANa kI laMbAI athavA pratyaMcA kI laMbAI ajJAta ho to donoM kA mAna batAo / " [9, VII 46] sahI sUtra isa prakAra hoMge, 1 = V6h2 + a 2, h = V 12 a2 6 12 6h2, S vRtakhaMDa=2" 10 "pahie ke rima kI jaisI AkRti kA kSetraphala bhItarI aura bAharI paridhi ke jor3a ke Adhe ko pahie kI pIr3AI se guNA karane para jJAta hotA hai / isakA AdhA ardhacaMdra AkRtiyoM kA kSetraphala hogA. [9. VII. 721 jaina prAcya vidyAe~ 70/1/ [9, VII, 70. 73/1/ 74 - 1 65

Page #20
citra :9 yadi 1, I, aura a kramaza: bhItarI paridhi, bAharI paridhi aura pahie kI caur3AI hoM to kSetraphala hogA, [9, VII, 803 mahAvIra sahI kSetraphala dUsarI taraha se prApta karate haiM / s = + a / 10. yadi 1=3d ho to Upara diyA gayA sUtra AsAnI se samajhA jA sakatA hai / "eka vRtta kA kSetraphala vyAsa ke varga se ghaTAne para usa AkRti kA kSetraphala prApta hotA hai jo ki cAra barAbara paraspara saTe hue vRttoM ke bhItarI bhAga meM banatI hai| [9. VII, 82 isa taraha, yadi d= vyAsa ho to vakra AkRti ABCD kA kSetraphala hogA, vAstava meM, d= varga EFGH kA kSetraphala hai, -4 4 barAbara vakra AkRtiyoM (AEB, BFC, CGD,DHA) kA kSetraphala hai| yaha AkRtiyA~ kramazaH AOB, BOC, COD aura DOA ke barAbara haiM arthAt yaha kSetraphala una cAra barAbara paridhiyoM vAlI bhItara banI AkRtiyoM kA hai jo eka dUsare ko chU rahI haiN| nimnalikhita udAharaNa isa sUtra se hala kiyA jAtA hai : 'yadi vRttoM kA byAsa 4 ho to cAra samAna paraspara saTe hue vRttoM ke bIca ke bhAga kI AkRti kA kSetraphala btaao|" 9. VII, 83 ] AcAryaratna zrI dezamUSaNa jI mahArAja abhinandana grantha

Page #21
citra : 10 mahAvIra ke grantha ke AThaveM khaMDa meM paramparA se calI A rahI bhAratIyoM kI gaNanA karane kI kalA kA vivaraNa hai jo ki kaI kAryoM se saMbaMdhita haiM, jaise kuA~ khodanA, lakar3I kI cirAI, zahatIroM ke Dhera meM unakI kula saMkhyA jJAta karanA, Adi / isI saMdarbha meM prijma aura gole ke AyatanoM kA bhI ullekha kiyA gayA hai| prijma ke AkAra meM khode gaye eka gaDDhe kA Ayatana usake AdhAra ke kSetraphala ko gaharAI se guNA karane para prApta hogaa| coTI se AdhAra taka kI U~cAI ko isa Ayatana meM jor3ane para aura use mApoM kI saMkhyA se vibhAjita karane para prijma ke Ayatana kA ausata mAna prApta hotA hai| [9, VIII, 4]. isI sUtra se hala hone vAle cAra praznoM meM se eka nimnalikhita hai| "eka gaDDhe ke AdhAra kA AkAra trikoNa hai| isa trikoNa kI pratyeka bhujA kA mApa 32 hasta aura gaharAI 36 hasta aura 6 aMgula hai / AkRti kA Ayatana btaao| [9, VIII, 6] gole kA Ayatana nimnalikhita sUtra se nikAlA jA sakatA hai| ardhavyAsa ke ghana ke Adhe ko se guNA karane para gole kA sannikaTa Ayatana prApta hotA hai| isa prApta saMkhyA ko 9 se guNA karane para aura 10 se vibhAjita karane para gole kA yathArtha Ayatana prApta hotA hai / [ 9, VIII 881] isa taraha gole kA sannikaTa Ayatana hogA, () aura yathArtha Ayatana : v=I (4) mahAvIra kA sUtra bhAskara dvArA likhe gaye sUtra kI apekSA isa sahI hala se adhika milatA hai. lekina zrIdhara ke sUtra se adhika sahI hala nikAlA jA sakatA hai___y = 4R (1 + hai) [4, pRSTha 154]. upasaMhAra bhAratIya gaNita meM mahAvIra kA kyA sthAna hai ? jaise ki pahale jJAta ho cukA hai ki mahAvIra kA grantha usase pahale kI nakSatra vidyA saMbaMdhI kRtiyoM meM likhe gae gaNita ke khaNDoM se bar3A hai / aisA saMbhava hai ki mahAvIra ke grantha meM dI gaI bahuta sI bAteM AryabhaTra prathama, brahmagupta aura bhAskara prathama ko jJAta thiiN| parantu bahuta se niyamoM kI racanA Ara unake udAharaNoM kI jAnakArI hameM mahAvIra dvArA prApta hotI hai / "gaNitasArasaMgraha" pahalA graMtha hai jisameM nimnalikhita niyama diye gae haiM :jaina prAcya vidyAeM

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vibhAjana ke niyama saMkhyA ko varga aura ghana meM badalane kI viziSTa paristhitiyA~, bhinna ke ghana aura ghanamUloM ko prApta karane kI vidhi, anupAta ke niyama, aura pratizata aura sone kI zuddhatA jJAta karane ke niyama / mahAvIra una AraMbhika gaNitajJoM meM se haiM jinhoMne do ajJAta rAzi vAlI do raikhika samIkaraNoM kI praNAlI anizcita raikhika samIkaraNoM kI praNAlI, aura dUsare ghAta kI anizcita samIkaraNa praNAlI ko hala karane ke niyama bnaae| isake atirikta unhoMne kaI ajJAta rAzi vAle raikhika samIkaraNoM ko hala karane kI maulika vidhiyoM, caube aura AThaveM ghAta ke samIkaraNoM ke mUla nikAlane kI vidhi, aMkagaNita zrer3hI ke pahale pada aura zrer3hI kA aMtara jJAta karane kI vidhi aura jyAmiti zrer3hI ke kisI bhI pada aura yogaphala ko prApta karane kI vidhi bhI banAI / bhAratIya gaNita ke itihAsa meM mahAvIra ne sabase pahale batAyA ki laghuttama samAna guNaja kyA hai| mahAvIra ne hI dhana saMkhyAoM ke vargamUloM ke dohare artha batAe aura yaha bhI batAyA ki RNa saMkhyAoM ke vargamUla nahIM prApta kie jA sakate haiM / mahAvIra aura unake bAda ke gaNitajJoM ke graMthoM meM zrIdhara ne "gaNitasArasaMgraha " se kaI niyama aura prazna lie haiN| nArAyaNa ke granthoM meM bhI milate haiN| sAtavIM-navIM zatAbdI meM ajJAta hai| gaharA saMbaMdha hai| vizeSakara zrIdhara para mahAvIra kA bahuta prabhAva hai| vaise hI prazna aura niyama AryabhaTTa prathama, zrIpati, bhAskara dvitIya aura brahmagupta ke bAda mahAvIra ke ziSyoM ne jo kAma kiyA vaha abhI taka 5. saMdarbha sAhitya 0 pa0 yuzkyevica istoriyA mAtemAvikI va sarayedaniye vekA, mAsko, 1661. 1. 2. da0 yA0 stroika, kAskI grocerka istorI mAtemAtikI, i0 ba0 pogrevisskI dvArA jarmana se anUdita aura saMvaddhita, mAsko, 1664. 3. ka0 pra0 rivnikova, istoriyA mAtemAtikI, khaNDa 1, mAsko, 1960. 4. zrIdhara, patigaNita pro0 pha0 volkovA tathA pra0 i0 bolodArakI dvArA saMskRta se anUdita pra0 i0 bolodArakI dvArA paricayAtmaka lekha aura 6. 7. " rUsI se anuvAda -- suzrI maMjarI sahAya anuvAda saMzodhana - pro0 hemacaMda pAMDe TippaNiyAM " phIjiko - mate mAtIceskiye naUki va snAnAkha vostokA" 1966, vipu0, I (IV), pR0 141-246. a0 pa0 yUkyevica aura ba0 pra0 rojenpayelda, mAtemAtikA va svAnAkha vostokA va sarayedaniye vekA "Ija istorI naUki i tenika va strAnAkha vostokA, " 1960, vipu0 I, pR0 346-421. B. Datta, A.N. Singh, History of Hindu Mathematics, Vol. 1-2, Bombay, 1962. D.E. Smith, History of Mathematics, Vol. 1-2, Boston - London, 1930. 8. G. Sarton, Introduction to the History of Science, Vol. 1-3, Baltimore, 1927-1947. e. M. Rangacarya, The Ganita - Sara - Sangraha of Mahaviracarya, Ed. with English translation and notes, Madras, 1912. 10. W.E. Clark, The Aryabhatiya of Aryabhata, An Ancient Indian Work on Mathematics and Astronomic, Chicago, 1930. 99. "Algebra with Arithmatics and Mensuration from the Sanskrit of Brahmagupta and Bhascara" Translated by H.T. Colebrooke, London, 1817. 12. " The Maha - Bhaskariya by Bhaskara I" Ed. and translated into English with notes and comments by K.S. Shukla, Lucknow, 1960. 13. " The Maha-Siddhanta by aryabhata II", Ed. with explanatory notes by Sudhakara Dwivedi, Benaras, 1910: 14. " The Ganita tilaka by Sripati", Ed. with comment of Simhatilaka Suri by H.R. Kapadia, Baroda, 1935. 15. "The Ganita- Kaumudi by Narayana", Pt. 1, Ed. by Padmakara Dwvedi Jyautishacharya, Benaras, 1936. hai 8 AcArya ratna zrI dezabhUSaNa jI mahArAja abhinandana grantha

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Sumatiharsa Gani and Some Other Jaina Jvotisis -Prof. David Pingree Sumatiharsa Gani was a member of the Ancalagacchal who flourished in Rajasthan in the early seventeeth century. Between about 1610 and 1621 he composed commentaries on a number of jyotisa texts; in this paper, which is based on the information given at the beginning and end of the surviving commentaries, on a perusal of those manuscripts presently accessible to me, and on the colophons, an attempt is made to elucidate the history of his life and to establish bis relationships to other members of the Ancalagaccha. His surviving works are the following: I. A vsitti on the Vivahapatala composed by Brahmarka or Brahmaditya of the Valalya family before 1605, the date of the oldest known manuscript; this Brahmaditya may be identical with the author of the Prasnajnana, also named Brahmarka or Brahmaditya, who was the son of Moksesvara and the grandson of Jyotihsudana;3 he belonged to the Balambha (read Balalya ?) family. For the Vivahapatalavrtti I have used the fragmentary manuscript at Harvard, Sanskrit 405, which consists of ff. 5-16 and 18-19 containing I 14-111 41 and III 45-V 10. The colophons to this manuscript, which begin : ity amcalikamahopadhyayasri 5 sriharsaratnaganinam sisyapamditavadirajasumatiharsaratnaganiviracitayam, inform us of the fact that Sumatiharsa's teacher was the obscure Mahopadhyaya Harsaratna Gani. The only indication of a date in this manuscript is a horoscope which can be dated 5 October 1576 and provides an early terminus post quem; one wonders if it is the horoscope of Sumatiharsa himself (it is entitled simply srijan malagnam). Planets Text (sidereal) Computation (tropical) Saturn Jupiter Mars Sun Venus Mercury Moon Node Sagittarius Leo Capricorn Libra Libra Libra Pisces Aries Sagittarius 26deg Virgo 6deg Aquarius 7deg Libra 22deg Libra 25deg Libra 25deg Pisces 27deg Aries 30deg 1. 2. This gaccha, founded in 1166, had branches at Jaisalmer, Udayapura, Jirauala in Sirohi, and Nagara in Marwar, as well as at other localities in Rajasthan; see K.C. Jain, Jainism in Rajasthan, Sholapur 1963, p. 59. D. Pingree, Census of the Exact Sciences in Sanskrit (henceforth CESS), Philadelphia 1970 and following, A4, 261b. CESS, A4, 2610-262b. 3. jaina prAcya vidyAeM

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Note that the ayanamsa in 1576 was about 14', which places all of the tropical longitudes within the sidereal Jongitudes indicated in the text. II. The Subodha, a vitti on the Jatakakarmapaddhati composed by Sripati in about 1050.1 The final verses are edited below on the authority of manuscripts in this British Library (Or. 5208) and in the LD Jnstitute (2538) : srimadancalagano'sti vivekacchedako bhuvi munisasarojah manasah pravitatagamapakso durato gatakubodhavipaksah 11 jayanti hi cidananda mahanandapradayinah srimanto 'traikakaiyanasagara manasaukasah 11 asams ca tacchasanakarino budhah sriharsaratnabhidhapathakottama siddhantapatiganitadikagamajnanapravina vidita yasasvinah 11 siddhantabrahmatulyadigrahasadhanahetave sukhopayah krto yaih susisyanam anukampaya 11 tacchisyena vinirmame sumatiyuggharsena satpaddhateh vsttair daivavidam sukharthajanani srimadguror bhavatah srimatparsvasivaprasattinibhsta padmavati pattane varse ramamunisasodasamite subhre 'svasasthidine 11 These verses begin by extolling the Ancalagaccha and its leader, the well-known and prolific author, Kalyanasagara Suri, one of whose patrons was Bhoja, Maharaja of Kaccha from 1631 to 1645.2 There still survive a number of manuscripts copied during his spiritual rule of the Ancalagaccha, which I list below in chronological order. Prasasti refers to Amotalala Maganalala Saha, Sriprasastisangraha, Ahmedabad 1936, Vol. 2. 1. Prasasti p. 173 no. 690. Santinathacaritra. Copied for Manikyalabha, pupil of Jayalabha Gani, pupil of Gajalabba Gani, on Thursday 7 November 1611 during rule of Kalyanasagara. 2. LDI 2631. Punyapalakathanaka. Copied by Kalyanasagara's pupil, Matinidhana, in 1614. 3. Berlin or. fol. 2591.3 Camda pannatti. Copied by Rajasika, a resident of Navyanagara, at the command of Kalyanasagara on 21 February 1620. 4. LDI 5692. Jyotisaratnamala of Sripati. Copied by Jnansekhara, the pupil of Kalyanasagara's pupil, Saubhagyasagara Suri, at Bhujadranga in 1620. 5. Prasasti p. 187 no. 745. Dasavaikalikasutra. Copied for Sangaka, a resident of Bhujanagara, in 1621 during the reign of Kalyanasagara. 6. Prasasti p. 188 no. 748. Simhasanadyatrimsika. Copied by Jnanasagara, pupil of Viracandra, at Mandavi on Friday 14 September 1621 during the reign of Kalyanasagara. 7. Prasasti p. 188 no. 749. Uttaradhyayanasutra. Copied for Hirajika, a resident of Pattananagara, and given to Lavanyasagara by Kalyanasagara on Thursday 3 October 1622. 1. The Jatakakarmapaddhati was also commented on by Sumatiharsa's contemporary, Krsna, at Kasi, this. was published by J.B. Chaudhari, Calcutta 1955. See also CESS A2, 55a-55b, and A4, 596-60a. 2. NCC vol. 3, pp. 259-260. 3. CESS A4, 387a. 900 AcAryaratna zrI dezabhUSaNa jI mahArAja abhinandana grantha

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8. LDI 7836. Uttaradhyayanasutra. Copied for Kasturai, wife of Sura, a resident of Bhinnamala, and given to Visalakirti Gani by Kalyanasagara in 1625. 9. Prasasti p. 195 no. 682. Uttaradhyayanasutra. Given to Ratnasimha Gani by Kalyanasagara at Radrahanagara on Wednesday 20 June 1627. 10. Prasasti p. 209 no. 748. Candarajano rasa. Copied for Devamurti, pupil of Premaji Gani, at Bhujanagara in 1641 during the rule of Kalyanasagara. 11. LDI (255. Lilavart of Bhaskaral with a vstti. Copied by Bhuvanasekhara Gani, pupil of Bhavasekhara Gani, at Bhujanagara in 1652 during the rule of Kalyanasagara. 12. LDI 3181. Subhasitaslokasangraha of Sakalakirti. Copied by Amimuni 1656 during the rule of Kalyanasagara. 13. LDI 8402. Sutrakstanga. Copied Bhavasekhara Gani, pupil of Vivekasekhara Gani, at Navanagara in 1657 during the rule of Kalyanasagara. 14. Prasasti p. 226 no. 834. Upadesacintamani with a vrtti. Copied by Bhavasekhara Gani, pupil of Vivekasekhara Gani, at Anjara on 5 November 1660 during the rule of Kalyanasagara. These 14 manuscripts establish the fact that Kalyanasagara was the head of the Ancalagaccha for about 50 years; nos. 3. 4, and 11 further confirm his interest (and that of the Ancalagaccha) in jyotihsastra. The scribe of nos. 13 and 14, Bhavasekhara Gani, copied another manuscript of the Sripatipaddhati with Sumatiharsa's Subodha in the LD Institute (891) for Bhuvanasekhara, the scribe of no. 11, at Sivapurinagara in 1693. The next padas extol Sumatiharsa's guru, Harsaratna, as a teacher of astronomy (sidhanta) and mathematics (patiganita) and as the commentator on, among other, unnamed works, the Brahmatulya or Karanakutuhala of Bhaskara. Unfortunately, no copy of the commentary has yet been located, nor is any other work of Harsaratna known to be extant. Finally, Sumatiharsa states that he completed his vrtti on the Sripatipaddhati at Padmavati on 6 October 1616. This Padmavati probably the same as that in which Dhanaraja wrote, as we shall see shortly; it has been identified with Puskara Dear Ajmer). The epithet srimatparsvasivaprasattinibhrta makes one think it possible that Padmavati is Vindhyavali (modern Bijaulia) on the Reva River in the Uparamala range between Chitor and Bundi; for it was a center of the worship of Parsvanatha and of Siva,' but so also was Puskara. More will be said of this below. III. The Karika, a tika on the Tajikasara composed by Haribhadra or Haribhatta, apparently in 1523. I have used manuscript 2541C of the India Office Library; the following edition of the final verses is based on that manuscript together with others at Gottingen (Kielhorn 121) and the LD Institute (6664): subodha sripatimahadevibrahmarkaparvanam 1 etasya vrttayo jneyah svasara hsdayamgamah Il varse sailahayangabhuparimite mase tatha phalgune pak se suklatare tithau dasamite srikherava purvare rajye srimati visnudasanrpater vairibhavsnde harer vsttim brigurubarsaratnakrpaya samantanamakarot 11 gurubandhavaratnahvadirghayurdhanarajayoh nirantaragrahad esa racita tanutac ciram 11 1. CESS A4, 300b. 2. CESS A+, 322a-326a. 3. K.C. Jain, Ancient Cities and Towns of Rajasthan, Delhi 1972, p. 104. 4. Ibid. pp 400-404. maina prAcya vidyAeM

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Sumatiharsa here lists his previous commentaries as being on the Sripatipaddhati (no. II), the Mahadevi composed by Mahadeva in 1316, the Vivahapatala of Brahmarka (no 1), and the Byhatparvamala composed by Purusottama before 1490. It is regrettable that two of these four are no longer in existence. He then states that he completed the Karika at Kherava on 21 February 1621 during the reign of Visnudasa Nrpati, a ruler of whom I have so far succeeded in discovering no other trace. Sumatiharsa himself here assumes the title Samanta or feudatory. Finally, he claims to have written this tika upon the insistence of Ratpa, a relative of his guru, Harsaratna, and of Dhanaraja, whom we will discuss later. The colophon to the Karika names Harsaratna's guru Mahopadhyaya Udayaraja Gani; this information is also given in the colophon of the next work. In the text itself Sumatiharsa uses as his example the horoscope of an individual born on 7 May 1535 and his fifty-ninth anniversary horoscope, dated 7 May 1594. Planets Text Computation (7 May 1535) Text Saturn Jupiter Mars Sun Venus Mercury Moon Node Cancer Aquarius Pisces Taurus Taurus Taurus Cancer Cancer Leo 4deg Pisces 5o Aries 12deg Taurus 26deg Gemini 10deg Gemini 6deg Cancer 25deg Cancer 21deg Cancer Aquarius Gemini Taurus Taurus Taurus Aries Taurus Computation (7 May 1594) Leo 6deg Aquarius 26deg Cancer 5deg Taurus 26deg Taurus 230 Gemini 11 Aries 26deg Taurus 20deg IV. The Ganakakumudakaumudi, a commentary on the Karanakutuhala composed by Bhaskara in 1183. This is the only work of Sumatiharsa's to have been printed; the edition by Madhava Sastri Purohita was published at Bombay ip 1901. I have also consulted the two Harvard manuscripts, Sanskrit 37 and 1105. The eighth introductory verse is : srisripatividitakesavapaddhati dve brahmarkasighrakhagasiddhim atho vivrtya ! mala ca parvasahita bihatiti tasyah sarasya taji kadhuro vivsti apudyam 11 This adds to the previously known commentaries on the Sripatipaddhati, the Vivahapatala, the Maha devi (sighrakhagasiddhi), the Brhatparvamala, and the Tajikasara, one on the Jatakapaddhati of Kesava" as is the case with so many other of Sumatiharsa's works no manuscript of this one is presently available. At the end of the tika are the following verses : vindhyadrim nikasa puri suvidita sarvarddhi vrddhyanvita tannetasti bhatah svavamsatilakas caulukyavamsodbhavah susriviramade sunitinipuno hemadrir evaparo yo 'bhud yavanabhupatin sthirataran pronmulya rajanyake! 1. CESS, A4, 374a-376b. 2. CESS, A4, 209b. 3. CESS, A4, 3222-326a. 4. CESS, A2, 666-70b; A3, 24a; and A4, 64-65a. AcAryaratna zrI dezabhUSaNa jI mahArAja abhinandana grantha

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velakhye khalu mantrini priyavrse dana prasak tau sati mangalyadrikalamite gatavati srivikramat samvati i mase prausthapade vinayakatithau daityejya vare vare cakre Srigurubhavatan sumatiyuggharsena caisa muda 11 The city near the Vindhyadri one might again guess to be it. yavali, ne moriern Bijauia in Mewar: this, however, was ruled by the Paramaras, whereas Sumatiharsa's lon! claimed to he l bo This chieftain, Viramadeva, a second Hemadri who beat the Muslims, remains totally obscure to me, though several Rajput rulers bearing this name are known. The date given for the completion of the Ganakakumudakaumudi is Friday 10 August 1621. Within the text are examples for Saturday 21 February 1596; Thursday 11 March 1596: Monday 13 October 1600; Saturday 20 June 1601; Friday 26 September 1617; Tuesday U November 1617: Friday 14 November 1617; Wednesday 29 November 1620; and Tuesday 17 July 1621. V. A vrtti on the Horamakaranda of Gunakara. Of this unusual work (it seems to be the only extant commentary on the Horamakaranda) there is only one extant manuscript, no. 3368 in the Oriental Institute. Baroda, which is incomplete and which I have not as yet been able to consult. Sumatiharsa's interest in the Horamakaranda is attested to by his citations from it in his vytti on the Sripatipaddhati; it should also be noted that Rajasekhara, the pupil of Buddhisekhara Gani, the pupil of Bhavsekhara Gani (who is probably the Bhavasekhara Gani connected with manuscripts 11, 13, and 14 in the list of manuscripts associated with Kalyanasagara Gani), copied one of the LD Institute's manuscripts (6510) of Gunakara's work in 1678--perhaps from Sumatiharsa's copy. This raises again the possibility--already apparent in the list of Kalyanasagara manuscripts-of the existence of a School of jyotihsastrins in the Ancalagaccha during the seventeenth century. Further evidence in this direction is provided by the Mahadevidipika, a vrtti on Mahadeva's Mahadevi (also commented on by Sumatiharsa, though his vitti is lost) composed by Dhanaraja of the Ancalagaccha at Padmavati in 1635. This Dhanaraja is undoubtedly the scholar who urged Sumatiharsa to compose his Karika on Haribhadra's Tajikasara, and Padmavati then is identical with the locality in which Sumatiharsa wrote his Subodha. For the Mahadevidipika I have used manuscript 689 at the Oriental Institute, Baroda. The upasamhara gives the date, place, and circumstances of Dhanaraja's composition : varse netran avangabhuparimite jyesthasya pakse site 'stamyam sadgunaprkthamannarayute padmavatipattanei raja hy utkatavairinagadamano rasprodavamsodbhavah sriman srigajasimha bhupativaro 'sti srimaror mandale | jaine sasana evam ancalagane satsajjanaih samstute kalyanodadhisurayah subhakara nandantu bhumandale tatsevakarabhojarajaga nayo vidvadvara vacaka asan sarvasudhimanahkamalinisambodhane bhanavah || khetanam ki pura krta budhamahadevena ya sarani tasya daivavidam sukharthajananim vrttim varam vistaram tacchisyo dhanaraja evam akarod dharsena bahvadarair bahvarthaih sahitam ca panditapadad aptaprasakter guroh || In these verses Dhanaraja informs us that he was the pupil of Bhojaraja Gani (called Bhuvanaraja Gani in the colophon), who honoured Kalyanasagara Suri, the ruler of the Ancalagaccha, and that he 1. CESS A2, 1276-128b; A3, 31b; and A4, 81a. 2. CESS, A3, 124a-124b, and A4, 1176. jaina prAcya vidyAeM 803

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Couried the Mchaderepika at Padmavai on 13 May 1635 while the Rastroda Gajasimha was ruling Marwar (1619-1638); the word harsena in the last verse may be an oblique reference to Sumatibarsa or to Harsaratna. It is necessary now to consider again the question of the identification of Padmavati. That Puskara was called by this name in Jaina circles seems to be well attested; and Puskara, like Vindhyavali. had both Jaina and Saiva temples. However, Ajmer (and Puskara almost certainly went with it) was in the possession of the Moghuls from 1556 till 1720, and this fact makes it difficult to explain Dhanaraja's claim to be writing under Gajasimha in 1635, unless some sort of control over it had been granted to Gajasimha as a faithful supporter of the Moghuls. Vindhyavali, on the other hand, has some fainous Saiva temples dating back to the period of the Cauhanas, and an image of Parsvanatha was manifested there in the twelfth century: this fits in very well with the epithet given to Padmavati by Sumatiharsa in the Subodha, but neither is it known that Vindhyavali was called Padmavati nor was it ever in Marwar territory. Thus, the identification of Puskara with Padmavati must remain the more fikely explanation of the facts though Dhanaraja's mention of Gajasirnha remains a problem. This is not the only problem of the Mahadevidipika. For in this work not only does Dhanaraja refer to Thursday 9 March 1637, but also in several different places computations are given for Sirohi in 1063 (the Baroda manuscript was copied a year earlier, in 1662). This date--Saka 1585- is confirmed by the statement that it is 480 years from Saka 1105, the epoch of Bhaskara's Karanakutuhala. The explanation for its occurrence must lie in the fact that 480 years is eight cycles of sixty years, though none of them begins with Mahadeva's epoch, 1318 (Saka 1240). What Dhanaraja's connections with Sirohi might be are not as yet evident. But we do possess some remnants of his activities as a teacher of jyotisa in the form of manuscripts copied by his successors in the Ancalagaccha; these are listed in the Sriprasastisangraha utilized previously. 1. p. 238 no. 888. The Saspancasika of Psthuyabas! with the vstti of Bhattotpala." Copied by Subhagyaraja, the pupil of Harsaraja, the pupil of Dhanaraja on Sunday 25 April 1669. The same scribe had the Jambucaritra copied on Saturday 27 March 1669; p. 239 no. 884. Copied by Jinaraja, the 2. p. 277 no. 1061. The Vasantarajasakuna of Vasantaraja with a vrtti. pupil of Hirananda, the pupil of Dhanaraja on Wednesday 18 September 1706. One final monument that these Jaina jyotisis of Ancalagaccha have left is one of the manuscripts of Dhanaraja's Mahadevidipika preserved at the LD Institute (7129). For it was copied by Buddhisekhara Gani, the pupil of Bhavasekhara Gani, at Rajanagara in 1672 for Rajasekhara Gani of the Ancalagaccha; Rajasekhara, as we have seen, was the scribe of a manuscripts of the Horamak aranda and the pupil of Buddhisekhara. I have little doubt that future explorations of jyotisa manuscripts from Rajasthan will reveal much more concerning the activities of these teachers, commentators, and scribes of jyotisa works, though Sumatiharsa will undoubtedly remain their outstanding representative. 1. CESS, A4, 2126-221b. 2. CESS, A4. 277b-281b. 3. Prohably that of Bhanucandra: see CESS, A4, 292a-292b. AcAryaratna zrI dezabhUSaNa jI mahArAja abhinandana grantha