Jain Ganit Vigyan ki Shodh Dishaye

Author(s): Lakshmichandra Jain
Publisher: Z_Tirthankar_Mahavir_Smruti_Granth_012001.pdf
Catalog link: https://jainqq.org/explore/210632/1

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bhiin Uini-bini bi ga saJIU menter * vartamAna vaijJAnika AdhAroM para huI khojoM ke vijJAna para prakAzita ho cuke haiM / ye lekha satahI saMdarbha meM abhinava avadhi meM aneka lekha jaina gaNita evaM athavA sAhityika nahIM haiM, kintu eka vaijJAnika dRSTikoNa 1. (a) Datta B. B., The Jaina School of Mathematics, Bull. Cal. Maths. Soc., 21 (1929) pp. 115-145. (a) Datta B. B., Mathematics of Nemicandra, The Jaina Antiquary, Arrah, 1, no. ii (1935) pp. 25-44. (#) Singh A. N., Mathematics of Dhavala - I, Satkhandagama, book iv, edited by Dr. H. L. Jain and others, Amaraoti, 1942. pp, v- xxi. (a) Singh, A. N., History of Mathematics in India from Jaina Sources, The Jaina Antiqary, 15, no. ii, (1949), pp. 46-53; and 16, no. ii (1950), pp. 54-69. The Central Jaina Oriental Library, Arrah. (6) Jain, L. C., Tiloapannatti ka Ganita, Reprinted from introduction to Jambu Divapannatli Samgaho, Jivaraj Granthamala. Sholapur, 1958, pp. 1-109. (*) Jain L. C., On the Jaina School of Mathematics, Babu Chotelal Jaina Smriti Grantha, Calcutta, 1967, pp. 265-292. (*) Jain, L. F., Set Theory in Jaina School of Mathematics, I. J. H. S. vol, 8, no. 1, 1973, pp 1-27. (a) Jain, L. C., The Kinematic Motion of astral real and counter Bodies in Trilok asara, I. J. H. S., vol. II, no. 1, 1976, pp. 58-74. () Das, S. R., The Jaina Calendar, The Jaina Antiquary, Arrah, vol. 3, no. ii, sep. 1973, pp. 31-36

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apanAkara prastuta kiye gaye haiM / balodarkI ne zrIdhara tathA mahAvIrAcArya para vizeSa zodha lekha likhe haiM / sikadAra ke lekhoM meM jahA~ darzana aura vijJAna ko yathAyogya maryAdAoM taka vistRta kara navInatA prakhara uThI hai, vahA~ mahendra kumAra evaM jaina ke lekhoM meM itihAsa gaNita evaM vijJAna ke vibhinna pahaluoM ko saMyukta kSetroM kI khoja prastuta kI gayI hai| datta aura siMha ne buniyAdI kArya kiyA hai gaNita itihAsa kA, tathA guptA ne gaNita itihAsa kI ajJAta gaharAiyoM meM pahuMca kI hai| lika evaM zarmA ne jaina jyotiSa ke gaNitAnuyoga para kArya kiyA hai tathA sarasvatI ne prAkRta graMthoM ke gaNita para abhivyaMjanA kI hai| zuklA ne AryabhaTTa prathama ke TIkAkAra bhAskara prathama kI TIkA meM pUrvavartI prAkRta graMthoM kI AryAoM aura gAthAoM ko khojA hai| agravAla kA zodha prabandha vistRta rUpa meM jaina gaNita aura jyotiSa kI jAnakArI detA hai| isa prakAra aba taka jo kArya ho cukA hai vaha naI zodha dizAoM kI ora iMgita karatA hai tathA vibhinna vidyA ke kendroM meM jaina gaNitavijJAna meM zodha hetu yathocita prabandha karAne kI ora preraNA detA hai| dhyAna rahe ki yaha saba zodha mukhyataH aise sthAnoM meM huA hai jahA~ jaina graMtha kendra nahIM haiM ataH ye aneka graMthoM ke abhAva meM hue haiN| gommaTasAradi graMthoM kI vRhad TIkAoM kI sAmagrI meM paMDita ToDaramala dvArA bar3A aMzadAna hai aura ukta prAyaH 3000 pRSThoM kI (gha) Shastri, N. C., Bhartiya Jyotisa ka Posaka Jaina Jyotisa, Varni Abhinandana Grantha, Saugor, 1962. pp. () Sikdara, J. C., Jaina Atomic Theory, I. J. H. S., 5.2 (1970), pp. 197-218. () Shukla, K. S. Hindu Mathematics in the seventh century as found in Bhaskara. I's commentary on Aryabhatiya (iv), Ganita, vo'. 23. Dec, 1972, no. 2, pp. 41-50. (ja) Gupta. R. C, Circumference of the Jambudvipa in Jaina Cosmography, vol. 10, no. 1, 1975, 38-46. () Volodarsky, A. I.. Articles on Sridhara and Mahavira, Fiziko matematicheskie nauki V stranakh vostoka 1 (1966) and 2 (1969). Cf. also a special chapter on India, History of Mathematics from the earliest Times to the Beginning of the 19th Century, vol. I, edited by A. P. Yushkevich (Moscow 1970-1972). (e) Lishk S. S., and Sharma S. D., The Evolution of Measures in Jain Astronomy, Tirthankar, vol 1, nos. 7-12, Jul.-Dec. 1975, pp. 83-92. (8) Jain, L. C.. Aryabhata the Astronomer and Yativrsabha, the Cosmographer, ibid, pp. 102-106. (Da) pramukha zodha prabandhoM meM mukuTa bihArI agravAla dvArA prastuta, "gaNita evaM jyotiSa ke vikAsa meM jainAcAyoM kA yogadAna" AgarA vizvavidyAlaya 1972 hai, tathA lika, sajjanasiMha dvArA jaina jyotiSa - bedAMgottara evaM helenayugapUrva nAmaka zodha prabandha paMjAba vizvavidyAlaya meM akTUbara 176 meM prastuta hone jA rahA hai| mahAvIrarAja gelar3A dvArA bhI rasAyana vijJAna meM zoSa agrasara hai| 282

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sAmagrI zodha chAtroM hetu zIghra hI chapAnA aba ati Avazyaka pratIta ho rahA hai / " jaina laukika gaNita evaM jyotiSa ko (vyAvahArika) gaNita rUpa meM mahAvIrAcArya, zrIdharAcArya tathA rAjAditya Thakkara pherU ne vikasita kiyA / jyotiSa ke gaNita ko vikasita karane meM pramukha rUpa se kAlakAcArya, haribhadra, candralekha, mahendra sUrI, labdhacandra gaNi ke aMzadAna bhI ullekhanIya haiM / 3 uparokta laukika rUpa lokottara gaNita - jyotiSa se bhinna rUpa se vikasita huA pratIta hotA hai| vizeSakara karma siddhAnta sambandhI gaNita ko vikasita karane ke lie tiloya paNNattI' jaise graMthoM meM AdhAra nirmita kiyA gayA hai| paTakhaMDAgama ke prathama pA~ca khaMDoM meM bhUmikA DAlI gayI hai tathA mahAbandha graMthoM meM bandha tattva kA nirUpaNa rAzi siddhAnta ke Azraya se kiyA gayA hai / punaH kasAya pAhuDa' meM upazama aura kSapaNA ke gaNitIya rUpa kA nikhAra hai / ina graMthoM ke sAra rUpa evaM TIkA rUpa graMthoM meM tathA itara zvetAmvara kAryAdi graMthoM meM gaNita vijJAna kI sAmagrI itihAsa tathA prayoga evaM vizleSaNa zodha kArya hetu advitIya hai / itihAsa sambandhI gaNita jyotiSa evaM karmagaNita siddhAnta ko zodha - 2. gommaTasAra, labdhisAra evaM kSapaNAsAra, (vR. tIna TIkAoM sahita ), gAMdhI haribhAI devakaraNa graMthamAlA, kalakattA, 1919 / inameM paM ToDaramala kRtaM samyakjJAna candrikA TIkA hai jisameM artha saMdRSTi adhikAra alaga se diye gaye haiM / 3. dekhiye, nemicandra zAstrI, bhAratIya jyotiSa, jJAnapITha, vArANasI, 1970 pR. 125-160 1 4. tiloya paNNattI bhAga 1 ( 1943 ), tathA bhAga 2 (1952), zolApura / 5. isa lekha meM hama mukhyataH lokottara gaNita-vijJAna zodha kA vivaraNa prastuta kreNge| lokottara gaNitAdi ke pramANa yUnAna, bhArata aura cIna meM bebilanIya srota ke kucha aMza lekara prakaTa hue haiM, jinameM ravAnI lAne kA zreya varddhamAna mahAvIrakAlIna muni maMDala ko hai jinake aMzadAna pazcima aura pUrva ke ucca mastiSkoM ke lie preraNA evaM kautUhala kI vastu bana gaye / yaha nizcata hai ki mahAvIra pUrva paramparAoM kI abhilekhabaddha sAmagrI mizra, cIna, bebilina, sumeru Adi sthaloM para jisa rUpa meM upalabdha hai vaha bhArata meM sindhu har3appA ke ajJAta rUpa meM dikhAI detI hai, kintu una sabhI meM vaha zakti nahIM thI ki ve vizva kI mahAvIrakAlIna jAgRti kI jyoti meM naye gaNita kA udbhava kara skeN| isI hetu itihAsa kA yaha pakSa ubhAranA zreyaskara hogA ki karma siddhAnta kA nirmANa karane meM jisa gaNita vidyA kI AvazyakatA huI vaha lokopakArI pravRtti ko lekara huI tathA use unnata karane meM vizva ke pratyeka bhAga meM vibhinna gaNita kI zAkhAe~ prasphuTita hotI calI gayIM / alaukika preraNA kA srota bhArata, yUnAna tathA SaTkhaNDAgama, (dhavala TIkA sa.) bhAga 1 - 16, DA. hIrAlAla Adi, (amarAvatI vidizA 1939 -- 1959) 6. mahAbaMdha bhAga 1-7, jJAnapITha - kAzI (paM. su. caM. divAkara evaM paM. phU. caM. siddhAntazAstrI dvArA sampAdita), 1947 - 1958 7. kasAya pAhuDa - sUtra aura cUrNi anuvAdAdi, paM. hIrAlAla si. zA. kalakattA- 1955 / sAtha hI, kasAya pAhuDa ( jayadhavala TIkA ), mathurA 1944 Adi / 8. dekhiye, B. L. Vander Waerden, Science Awakening, Holland, 1945 283

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RD cIna rahA, kintu ahiMsA aura satya ke rUpoM kA kA AdhAra banate haiN| (dhavala pu. 3 evaM 4) / kaNAdA citraNa jisa rUpa meM varddhamAnakAlIna bhArata meM huA, se prAyaH 200 varSa pUrva jahA~ umAsvAti ne pudgala tathA unakI vicAradhArA meM haA vaha anyatra upalabdha paramANu aura usake avibhAgI praticcheda (zakti-aMzoM) kI carcA kI hai vahAM usI AdhAra para sImita kSetra meM ananta-vibhAjyatA kA khaNDana karane vAle jInoM ke tarka vija ke gaNita-itihAsakAra bhale hI aise srota kI __ aura moziMga (370 I. pU.) kI bindu-paribhASA sahanikAlapasthiti kI parikalpanA bebilana meM kyoM na kareM sambandhita pratIta hote haiN| avibhAgI samaya sambandhI kintu gaNitIya vidhiyoM meM AmUla-cUla parivartana prAkRta prakaraNa jInoM ke aMtima do tarkoM kA viSaya banate haiN| thoM meM hI-nyAyAyika samanvaya lie, paryApta rUpa meM prAkRta graMthoM meM aneka prakAra ke avibhAgI praticcheda lumA AvazyakIya kAraNoM se huA dRSTigata hotA hai / yathArtha anantoM ke itihAsa kA nirmANa karate haiM tathA karma siddhAnta meM hI anAdi ananta viSayaka dravya, kSetra, aneka prakAra ke dravyAtmaka, bhAvAtmaka, kAlAtmaka evaM kArata evaM bhAva rAziyA~, unake alpa-bahatva, unakA kSetrAtmaka anantoM ke alpa-bahatva ko dekara itihAsa meM AchAdi salagA gaNana, unakA vaizleSika adhyayana / amaratva pradAna karate haiN| (ye prakaraNa dhavala pu. 3 tathA Adi kiyA gayA hai| sarvAdhika rahasya usa itihAsa 4 meM tathA mahAbandha granyoM meM vizeSa rUpa se nirvacanIta kAhI lo krAMtikArI sisTama siddhAnta ke tathyoM ko kA kiye gaye haiN|) karmoM ke sAmayika vilakSaNa parivartanoM meM prakaTa karatA hai| " jahAM iTalI meM jIno (460 I. pU.) ke anaMta- anantoM ke alpa bahutva ke prakaraNa yUropa meM punaH vibhAjyatA sambandhI tarka vismaya aura kautUhala utpanna gaililiyo (1564 --1642) kI eka-eka saMvAda tathA yUnAniyoM ko ananta kI gaNanA se carcAoM meM prakaTa hote haiM 14 tathA jArja keNTara (1845. bhayabhIta karate haiM, tathA jahA~ cIna meM 'huI ziha' (pAMcavI 1958) ke jIvana bhara ke athaka, aTUTa, dussAhasapUrNa sadI I. pU.) ke asadbhAsa 11 se sahasambaddha pratIta hote prayAsoM meM janma lete haiM 15 tathA vRkSa rUpa meM pallavita haiM vahA~ prAkRta graMthoM meM ve siddhAnta rUpa se upadhArita hote haiN| usake phalasvarUpa prAyaH 25 varSa se prasphuTita kiye jAkara dravya, kSetra, kAla aura bhAva kI prarUpaNA hae sisTama-sAyabarneTika siddhAnta haiM jinheM karma-siddhAnta 951dekhiye, mahAvIrAcArya-gaNita sAra saMgraha prastAvanA, zolApura 1963 / 10. T: Heath, Greek History of Mathematics, vol. I (1921) pp. 275 et seq. 11. Needham J. and Ling W., Science and Civilization in China, vol. 1, Cambridge, p. 144 (1954), vol. 3. (1959). 12. dekhie Ray, P., History of Chemistry in Ancient and Medieval India, Calcutta, 1956. pp. 46, 291, et seq. 13.15 dekhiye, nIdhama, bhAga 1, pR. 155 / dhavalA pustaka 3 tathA 4 bhI dekhie| Aja kA gaNita apari bhASita bindu ko lekara vyavahAra karatA hai| 14. Bell E. T.. Development of Mathematics, 1945, p. 273. 15. Fraenkel A. A., Abstract Set Theory, 1953, introduction, . 284

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2. saMkhyAe~ likhane tathA vyakta karane meM dasAA~ Adi paddhatiyoM kA prayoga kA gaNita, navIna sAmagrI apane rAzi siddhAnta para AdhArita kara de skegii| 16 (dekhiye labdhisAra evaM ksspnnaasaar-vhdttiikaaeN|) jahAM jArja kenTara ko koI aisI AvazyakatA kA koI AdhAra nahIM thA vahA~ prAkRta graMthoM ke isa gaNita ko karma-siddhAnta pratipAdita karane kI kaThora AvazyakatA kA vizAla evaM gahana AdhAra thA / pariNAmoM kI atIba nirmalatA kA uddezya jagata itihAsa kI upekSA karane meM apane nAmoM ko chipAkara amara ho gayA / prAyaH pratyeka ghaTanA meM sAMtatA, anumAna aura abhibindutA prasthApita kara samAdhAna kara liyA jAtA hai| kintu asIma gaharAiyoM aura ananta UcAiyoM meM pahuMca karane hetu nabIna gaNitIya upakaraNoM kA AviSkAra karanA hotA hai-vaha Aja kI Adhunika jyAmiti aura bIjagaNita jinakA sahasambandha prAkRta graMthoM ke kSetroM aura bIjoM se karane parane para itihAsa ke pRSTha svaNima kie jA sakate haiN| 3. hrAsita guNya rAziyoM ke likhane meM sthAnArhA paddhati kA prayoga (a. saM.) ___4. salAgA gaNana kA upayoga (dhavala, pu. 3-4) 5. eka-eka, eka-bahu tathA bahu-bahu saMvAda vidhi kA prayoga (dhavala, pu.-3) 6. viralana-deya guNana tathA vargana saMvargana vidhiyoM kA prayoga (dhavala evaM tiloyapaNNattI) 7. kSetra prayoga vidhi tathA kAla prayoga vidhi kA upayoga (dhavala, pu. 3) 8. vargAdi sthAnoM meM khaNDita, bhAjita, varalita, apahrata, pramANa, kAraNa, nirukti evaM vikalpa vidhiyoM kA prayoga / dhavala, pu. 3, pR. 40, Adi) _spaSTa hai ki varddhamAna yuga meM eka navIna patha kI ora mor3a dene ke lie, sarvadaSTiyoM se Adarza ko taulane ke liye, bhArata tathA videzoM meM bhI pracalita laukika gaNitoM ko sAdhana rUpa meM avazya cunA gayA hogA / usameM navIna prasAdhana apane sAdhyoM ke AdhAra para AviSkRta kiye gaye hoMge aura yugAntara meM unakA pracalana puna:-punaH hAramonIya bhAvoM meM deza-dezAntaroM meM hotA cala gayA hogA / abhilekhabaddha sAmagrI se pratIta hotA hai ki navIna paddhatiyoM kA upayoga sambhavataH nimnarUpa meM vikasita huA hogA :-- 9. dhArAoM dvArA aneka anantAtmaka evaM asaMkhyA tmaka tathA saMkhyeya rAziyoM ke pada evaM padasthAnoM kA niruupnn|" (trilokasAra, pra. adhyAya ) 10. sUcyaMgula jagazreNi, aMtarmuhUrta, palya, sAgara, avibhAgI praticcheda, pradeza, samaya Adi ikAiyoM evaM saMkhyA tathA upamA mAnoM ke nirUpaNa aura tInoM loka ke khaMDoM dvArA vibhinna rAziyoM ke nirUpaNa / 1. vividha pratIkatva kA vikAsa (dekhie ti. pa. evaM a. saM.) 16. Kalman R. E., Falb, P. L. and Arbib M. A.. Topics in Mathematical System Theory, T M H, Bombay, 1969. 17. AcArya nemicaMdra si. ca., "trilokasAra" mAdhavacaMdra bhaividya kRta TIkA, bambaI, 1920 / 285

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11. 109800 gagana khaMDoM ke koNIya mApa tathA yojana ke dUrIya mApadvArA jyotiSa bimboM kA sthira evaM gatizIla pramANoM kA nirdhAraNa | 18 12. jyotiSa bimboM kA yugmIya vidhi se sammukha prasthApana kara gatizIla ghaTanAoM ke Akalana | kuMtala - dIrghavRttIya bimbagamanazIlatA eka kSetrIya siddhAnta / " kA uparokta AviSkAroM ko Thoka tithiyA~ nirdhAraNa karanA kaThina hai, kintu smRti maMda hone ke phalasvarUpa unakA uttarottara abhilekhana varddhamAna ke bAda kI prakriyA avazya pratIta hotI hai, jisakA zrRMkhalAbaddha prasphuTana Aja kA vizAlatama vaijJAnika gaNitIya sAhitya rUpa meM darzanIya hai / uparokta sAmagrI kA aMtima aitihAsika rUpa paMDita ToDaramala kRta gommaTasArAdi kI vRhada TIkAoM meM dRSTavya hai / 30 isameM unhoMne RRNa pratIka ke lie pA~ca cinhoM kA prayoga batalAyA hai / zUnya kA vibhinna arthoM meM pratIkabaddha upayoga hai / usameM salagA gaNana ke bhI prayoga haiM jinameM phalana ke phalana ke pratIka kI avadhAraNA ko vikasita karane kI ora asaphalatA milI pratIta hotI hai / yadi ve prayAsa isa ora bar3hate aura bhAratIya gaNita vidvAnoM kA jhukAva isa ora adhika hotA, to kucha zatAbdiyoM pUrva hI Aja kA yuga upasthita hotA aura yaha zreya bhArata ko yathocita miltaa| isameM prayukta hue kucha pratIka giranAra eva azoka kAla se pUrva ke zilAlekha kAlIna pratIna hote haiM / azoka ke pUrva ke bar3alI grAma ( ajamera) tathA nepAla kI tarAI ke 18. dekhiye 1 ( kha ) / 19. vahI / 20. dekhiye 2 21. dekhiye 1 (pha) / 22. nIdhama, bhAga 1, pR. 150 - 151 Adi / pripAbA nAmaka sthAna meM upalabdha sAmagrI meM jo 'I' kA cinha hai, usase RNa ( riNa athavA ri) ke lie prayukta cinhoM kA saMbaMdha saMbhavataH sthApita kiyA jA sakatA hai / 21 (dekhiye, ojhA racita bhAratIya prAcIna lipimAlA, pR. 2, 47, 1959 dillI) / jahA~ arastU (384 I. pU. se 322 I. pU.) AtmAoM kI zraddhi ke siddhAnta kA prarUpaNa karate haiM, vahA~ cIna meM aisA hI siddhAnta zuinatjU ( 298 I. pU. - 238 I. pU., Hsun Tzu yA Hsun Chhing) dvArA prarUpita kiyA gayA hai, aura yahI bhArata meM jIvoM ke mArgaNA sthAnAdi rUpa meM nirUpita hai / ( nIdhama, bhAga 1, pR. 155 ) / cIna se lekara yUnAna taka aisI avadhAraNAoM kA yugapat prakaTa honA itihAsa kI samasyA hai| isI prakAra candramA ke bar3hane ghaTane ke kAraNa samudroM ke nIce kI pAtAla vAyu kA phailanA ( ti pa bhAga 1, 4-2403, zolApura, 1943 ), cIna aura yUnAna meM kramaza: lU ziha cuna viu (cauthI se tIsarI zatAbdI I. pU. ) aura arastU dvArA candramA kI kalAdi ke kAraNa samudrI rIr3hahIna jantuoM ke phailane Adi kI carcA se samanvaya rakhatA pratIta hotA hai / ina tathyoM ke hajAroM mIla dUra phailanevAlA srota kahA~ thA yaha itihAsa kI samasyA hai 122 bhArata se eka aura pithegorasa ora dUsarI ora kanphyUzana (chaThI sadI 50 ) dvArA pazcima aura pUrva meM navIna pratibhA kA netRtva saMcAlana eka adbhuta krAMti ko prakaTa karatA hai / pithegorasa sambandhI aneka kiMva 286

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daMtiyA~ unake ahiMsA patha aura gaNitAdi ke vilakSaNa jJAna ko batalAtI haiN| loka meM jIvasaMkhyA kI acalatA ke AdhAra para janatA ko hiMsA tathA mA~sAhAra kI ora se mor3akara zAkAhArI tathA hariyAlI rahita bhojana kI ora pravRtta karane kA prayatna pithegorasa kI nijI pratibhA kA dyotaka hai ( E. T. Bell, Magic of Numbers, 1946, pp. 87, 88, 91, 92 ) / yadi koI sAdhAraNa srota yUnAna aura cIna ke madhya rahA, to aise prakaraNa cIna meM kanphyUzasa yA tAo kAla meM dRSTigata honA caahie| nIdhama ke anusAra bauddha dharma kA cIna meM prathama praveza I. pazcAt 65 meM huA jisake prAyaH 100 varSa pazcAt prathama sUtroM kA cInI bhASA meM loyAMga meM anuvAda prArambha huA / ( nIghama, bhAga 1, pR. 112 ) / misra deza kI jAgRti kA kAla bhI prAyaH yahI hai, jabaki sAyaTika yuga ( 663-525 I.) meM vahA~ ahiMsaka kUpU kAlIna prAcIna paramparAoM kA akasmAta anusaraNa prArambha huA thA aura narasiMha ( Sphinx ) pratIka punaH pUjA kI vastu bana gayA thA / sambhavataH yahI AkarSaNa pithegorasa ke pUrva deza bhramaNa kA kAraNa banA hogA 123 avibhAgI pudgala paramANu ke AdhAra para paribhASita bindu ke prayoga meM vIrasena dvArA katipaya navIna vidhiyoM kA upayoga prakaTa huA hai / inameM se nizzeSaNa vidhi vizeSa rUpa se mahattvapUrNa hai| isake dvArA zaMku ke samacchinnaka kA ghanaphala nikAlA gayA hai / isase kA mAna nikAlane ke aise sUtra kA upayoga kiyA gayA hai| jo cIna meM tsu zuMga - cihna ( prAya: pAMcavI sadI Tsu Chhung-Chih ) dvArA prayukta huA hai / jaina graMthoM - dhavala -- meM rAzi siddhAnta meM prayukta bhinna kalana cIna tathA mitra dezoM ke kalana se zreSTha hai| cIna meM salaga gaNana ( I. pU. 4thI zatAbdI meM ), bhArata meM prAyaH 6vIM sadI athavA katipaya graMthoM ( SaT khaNDAgamAdi) meM I. pazcAt 2rIM sadI meM upalabdha haiM / jahA~ cIna meM varga aura ghanamUla I. pU prathama sadI meM dRSTigata haiM vahA~ SaTkhaNDAgama meM sImita kSetra meM sthiti pradeza binduoM kI saMkhyA kA bArahavA~ vargamUla nikAlane kA ullekha hai aura jisake tulya mAna kSetra, kAla, bhAva meM pradatta haiM / cIna meM jyAmitIya sAmagrI I. pU. tRtIya sadI meM upalabdha hai, vahIM tiloyapaNNattI meM pAMcavI sadI tathA itara graMthoM I. pU. bhI dRSTigata hai| jahAM cIna meM prAyaH 1000 varSa pUrva bIjagaNita tathA jyAmiti kI mUlabhUta tAdAtmya prakaTa hai vahAM dhavala ( 9vIM sadI) tathA alakhvArijnI (9 vIM sadI) meM dRSTavya hai| cIna meM kUTa sthiti ke prayoga bhI prAkRta graMthoM meM upalabdha haiM / isI prakAra anirvRta vizleSaNa suna tjU ( 4thI sadI) tathA prAkRta graMthoM meM dRSTigata hai / 24. dekhiye 1 ( kha ) / lokottara gaNita vijJAna meM jyotiSa bimboM kI saMkhyA kA nirdhAraNa, unakI gamanazIlatA, sumeru se dUrI, citrAtala se UMcAI, bimboM ke AkAra, tathA mApa, Adi vividha prakAra kI sAmagrI vikasita kI gayI / ina prAcIna tatvoM ko hajAroM varSoM se aparivartita rakhA gayA (ti.pa., pR. 16-17 ) / yUnAna se ye vidhiyA~ atyaMta bhinna haiM | 24 23. Salem Hossan, The Sphinx, Its History in the Light of Recent Excavations, Cairo, pp. 219-221, (1949). karma siddhAnta ke gaNita kA itihAsa vigata 25 varSa ke vizva vijJAna meM prodbhUta gaNitIya sisTama siddhAnta se prArambha huA hai / niyaMtraNa yogyatA tathA pariNAma yogyatA ke Akalana gaNitIya rUpa meM vizva ke 287

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itihAsa meM kevala karma siddhAMta meM hI nihita haiN| isameM se phalita jyotiSa Adi kA vikAsa svAbhAvika hai 125 vijJAna - vikAsa sambandhI zodha dizA : jisa prakAra Aja ke vijJAna kA AdhAra rAzisiddhAnta hai, usI prakAra karma vijJAna kA AdhArabhUta gaNita rAzi saiddhAntika hai| sikadAra dvArA paramANu siddhAnta para vistRta zodha prabandha tathA aneka zodha lekha prastuta kiye gaye haiM jinameM vaijJAnika dRSTikoNa liyA gayA hai / vAstava meM karma siddhAnta kA eka AdhAra paramANu siddhAnta hai| karma siddhAnta eka-sUtrI tathA saMgata siddhAnta ke rUpa meM aneka upadhAraNAoM ( Postulates ) tathA parikalpanAoM (Hypothesis) kA AdhAra lekara nirmita kiyA gayA / yaha priMsapila thyorI ke rUpa meM vikasita huA na ki kansaTrakTiva thyorI ke rUpa meM 120 abhI taka jo vijJAna sambandhI adhyayana jI. Ara. jaina evaM kola je. epha. Adi dvArA hue haiM unase sthiti AzAjanaka to pratIta hotI hai / ghaTanAoM kA isa prakAra kA AMzika samAdhAna hI kisI siddhAnta ko saMgata siddha nahIM kara sakatA hai| apitu siddhAnta kA 26. mahattva taba siddha hotA hai, jaba ki vaha Adhunika siddhAntoM kI samasyAoM ko hala karane meM yogadAna dekara navIna phalita ko nikAlane kA patha-pradarzana kara sake / karma siddhAnta meM sannihita tattvoM meM nimnalikhita pramukha dhAraNAoM kA sanniveSa hai : 1. anantoM yA ananta rAziyoM kA pUrNAMkoM para AdhArita, dhArA jJAna se upacArita, alpabahutyAdi aneka rAzi sambandhI siddhAnta / 2. samaya kI avibhAjyatA ke AdhAra para mahattama evaM laghuttama pravega kI avadhAraNA, jisase kAla aura kSetra ke kvAMTama kA prAdurbhAva 129 288 3. pudgala paramANu kI avibhAjyatA tathA unakI rAzi kI yathArtha gaNAtmaka upadhAraNA yaha rAzi jIva rAzi se ananta gunI hai / 25. jyotiSa sambandhI cIna meM upalabdha sAmagrI hetu dekhiye, 11, bhAga 3 | mizra, yUnAna tathA bebilana Adi meM prApta sAmagrI hetu dekhiye Neugebauer, O, The Exact Sciences in Antiquity, Providence, 1957 / karma siddhAnta meM phalita jyotiSa saMvAda ke rUpa meM svabhAvataH upasthita ho jAtA hai / Aya vyaya, puNya, pApa Adi bhAvoM kA sattva, Asrava nirjarA se sambandha adhika upayukta pratIta hotA hai / ina siddhAntoM kA vivecana DA. AinsTAIna ne The London Times, Nov. 28, 1919 meM diyA thaa| 27. Jain, G. R., Cosmology, Old and New, Lucknow 1942, Kohl, J. F., Physikalische Lund Biologische Weltbild der Indischen Jaina Sekte, Aligang, 1956. 28. dhArAoM se sambandhita eka lekha zIghra prakAzita hone vAlA hai - Jain, L. C., Divergent Seque nces Locating Transfinite Sets in Trilokasara (I. J. H. S. Calcutta) 4. pudgala paramANu kA ananta pudgala paramANuoM ke sAtha eka hI pradeza meM avagAhana / 5. dravyoM tathA unake guNa paryAyoM kA eka-dUsare ke guNa paryAyoM meM anyonyAbhAva evaM atyantA 29. dekhiye Jain L. C, Mathematical Foundations of Jaina Karma System, Bhagwan Mahavira and his relevance in modern times, Bikaner, 1976, pp. 132-150.

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bhAvAdi / ise dravya svAtantrya bhI kahate haiM jo kevala jinAgama meM hI upalabdha hai, anyatra nhiiN| 11. yoga aura moha rUpI adhyavasAya (input functions) vicaraNa se guNa sthAnoM (control stations) sambandhI pariNAma (output functions) / inakA citraNa sisTama siddhAnta kA eka aMga hai| 6. sparza guNa ke avibhAgI praticchedoM (UrjA staroM) ke nizcita AdhAra para pudgala paramANuoM kA bandha / 7. samayoM ke bItane kI atIta-anAgata dizA athavA kramabaddha paryAyoM se saha sambandha / yaha Causality kA siddhAnta hai jisakA upayoga sisTama siddhAnta meM huA hai / / 12. Asrava (input values) tathA udayAdi nirjarA (output values) yukti se sattva (State) kA jJAna / isakA citraNa sisTama siddhAnta kA dUsarA aMga hai| 13. karma siddhAnta meM misTama siddhAnta kI apekSA bandhAdi tattvoM kA samAveza / isa prakAra karma siddhAnta ekasUtrI saMgata siddhAnta se sisTama siddhAnta meM aneka sujhAva tathA unnayana hetu navIna patha kA anusaraNa / 32 8. upAdAna zaktiyoM ke sivAya pudgala kA anya dravyoM se udAsIna anugraha (sahakAritA) se gamana, pariNamana, avagAhana tathA sthiratA honaa| 9. pudgala meM varNa, rasa, gaMdha, sparza vizeSa guNoM ke sivAya sAmAnya guNoM (prameyatva, agurulaghutva, ananta guNI hA nivRddhi, Adi) kA honA / 14. jyotiSa siddhAnta meM ekasUtrI siddhAnta (jo tiloya paNNattI prabhUti granthoM meM upalabdha hai) dvArA gaNitIya gamanazIlatA ke navIna niyamoM kI vyutpatti / kuntala-dIrghavRttIya jyotiSa bimbagamana dvArA paMcAMga sambandhI samasta jAnakArI kA Anayana 133 10. kevala jIva tathA pudgala meM kriyAvatI evaM bhAva vatI zakti kA astitva / (dravyoM ke dezAntara prApti hetu pradezoM ke halana-calanarUpa parirapanda ko kiyA kahate haiN| unameM honevAle avirala pravAha rUpa pariNamana ko bhAva kahate haiM / ) 15. Adhunikatama bIjagaNitIya evaM jyAmitIya jJAna ke upayoga se karma siddhAnta kI yathArtha gaharAiyoM meM pahu~ca kI pUrNa saMbhAvanA / 30. dekhiye, vhii| 31. dekhiye, Jain L. C., The Jaina Theory of Ultimate Particles, paper read at the univerity of Indore on 8-4-1976. 32. dekhiye, 291 33. dekhiye 1 (kha, / / rer at afga. Jain L. C.. On Spiro elliptic orbit of the Sun in Tiloyapanna paper read at the Univerity of Saugar. 34. isa viSaya para vistRta lekha System Theory in Jaina School of Mathematics prAyaH samApti para hai| 286

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jahA~ taka pratyakSa darzana aura jJAna kA prazna hai, kSaNa vastu hai| isase bhI vilakSaNa tathya hai sukamabaddhI unakI sambhAvyatA kA prAkRta graMthoM meM Adhunika kAla sAdhya (well-ordering theorem) gabhita prakriyA ke lie niSedha hai| taba mati aura zruta se parokSa kA astitva, "ki sarvadhArA meM 1, 2, 3, se prArasbha darzana aura jJAna kA prakaraNa sammukha AtA hai| pudgala karate hae, samasta saMkhyeya, asaMkhyeya tathA ananta rAziyA~ dravya viSayaka darzana jJAna kI upalabdhi zrata ke sivAya pAra karate hae kevala jJAna rAzi taka phNcnaa|" isa mati se hotI hai| gati kA AkAra saMdezavAhaka, sAdhya ko siddha karane kA AzvAsana jArja keNTara ne pudagalaka kriyAe~ haiN| saMdeza bAhana kAla para AdhArita diyA thaa| kintu yaha sAdhya aba kathaMcita siddha kiyA hone se sApekSatA siddhAnta kI AvazyakatA spaSTa hai| jA sakatA hai| sApekSatA siddhAnta meM jaba mahattama pravega kI upadhAraNA anantoM ke alpa-bahutva sthApita karane meM keNTara kI jAtI hai, to bhautika vijJAna ke prAraMbhika Adhunika aura DeDikeMDa kI jyAmitIya vidhiyoM meM spaSTa antara prayogoM kI puSTi hotI hai| sAtha hI alpatama kriyA hai| jahA~ Aja saralarekhA athavA vyavahAra kAla kI (action) ke kvANTama kI upadhAraNA se kvAMTama atIta-anAgata dizAyeM kinhIM bhI do binduoM ke yA~trikI kA AdhAra banatA hai, jisameM anizciti ke antarAla meM agaNya (non-denumerable) rAzi kI anubandha bhI prayukta hote haiM / 35 Adhunika sApekSatA siddhAnta meM jahA~ eka ora mahattama pravega ko upadhArita mAnyatA hai, vahA~ prAkRta graMthoM meM binduoM kI rAzi kI kiyA gayA hai, vahA~ use alpatama pravega tathA avibhAgI sImita (asaMkhyeya athavA saMkhyeya) saMkhyA kI mAnyatA samaya se achatA rakhA gayA hai| kvANTama yAMtrikI meM hai| 39 asaMkhyAta kAlANaoM se lokAkAza-dravya kI padagala kI daMtamaya (taraMgAtmaka evaM kaNikAtmaka) akhaDatA pUNarUpaNa sammAtA h| dazAoM tathA gati aura sthiti ke sambandha meM samAdhAna isI prakAra karma-siddhAnta viSayaka aneka tathyoM ko nahIM milatA hai kyoMki yaha kansTrakTiva thyorI hai, Adhunika tathyoM kI talanA meM rakhate hae navIna aMzadAna sApekSatA siddhAnta kI bhA~ti priMsIpala thyorI nahIM hai| kA prayAsa karanA hogA / jyAmiti kI apekSA sisTama ina samasyAoM kA samAdhAna jaina samaya tathA maMda tama / tathA karma siddhAnta meM bIjagaNitIya dRSTi vikasita kI pravega kI avadhAraNAe~ karatA pratIta hotA hai / gayI hai jo ghaTanA-cakra kI jAnakArI atyaMta sahaja DhaMga se detI hai| isa AdhAra para bIjagaNitIya adhyayana kA prAkRta graMthoM meM atIta kAla samaya rAzi se anAgata zodha-kSetra lAbhadAyaka siddha hotA pratIta hotA hai|" kAla rAzi anantaguNI batalAnA gaNita kI eka vila 35. dekhiye, 291 36. dekhiye, vhii| 37. dekhiye, z lot, W. L., The Role of the Axiom of Choice in the Development of the Abstract Theory of Sets, Library of Congress, Mic 57-2164, Columbia University Thsis (1957) 38. dekhie 1 (i)| 39. dekhiye, Kalman, R. E. Introduction to the Algebriac Theory of Linear Dynamical Systems, Lecture notes, vol. II, Springer Verlag, 1969. 260