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________________ 20826000008 208001806942328788 858588888888888888888 vartamAna saMdarbha meM jaina gaNita kI upAdeyatA 868808535888888888888 * DaoN. paramezvara jhA gaNita kI vyApakatA sArvabhauma hai| vedAMga jyotiSa (1200 I.pU.) meM ise sabase U~cA sthAna pradAna kiyA gayA hai -'gaNitaM muurdhnisthitm'| isakI mahattA ke sambandha me jaina gaNitajJa mahAvIrAcArya kI ukti hai 'laukike vaidike vApi tatA sAmAyike'pi yH| vyApArastatra sarvatra sNkhyaanmupyujyte||" arthAt 'sAMsArika, vaidika tathA dhArmika Adi sabhI kAryoM meM gaNita upayogI hai| punaH unhoMne udghoSaNA kI hai - 'bahubhirvipralApaiH kiM trailokye scraacre| yaktiMcigdastu tatsarvaM gaNitena vinA na hi||' __ arthAt jo kucha ina tInoM lokoM meM carAcara (gatizIla evaM sthira) vastueM haiM, unakA astitva gaNita se vilaga nhiiN|' vastutaH saMkhyA kA jJAna jIvana ke hara pahalU ke lie Avazyaka hai| sRSTi ke Arambha se hI isakI upayogitA siddha huii| vizva ke prAcIna sabhya dezoM bebiloniyA, mizra, yUnAna, bhArata Adi meM isakA vikAsa samAna rUpa se hotA rhaa| bhArata meM gaNita-jJAna kI jhA~kI yahA~ ke prAcIna graMthoM-veda, brAhmaNa graMtha, purANa Adi meM milatI hai| bhAratIya saMskRti ke saMvarddhana evaM saMrakSaNa meM jainAcAryoM kA mahAn yogadAna hai| gaNita bhI unake ciMtana evaM manana kA viSaya rahA hai| gaNitIya siddhAntoM dvArA sRSTi-saMracanA ko spaSTa karanA tathA karma siddhAnta kI vyAkhyA karanA jainAcAryoM kA pramukha dRSTikoNa hai| phalasvarUpa jaina Agama graMthoM meM gaNitIya sAmagrI pratyakSa evaM parokSa rUpa meM vipula parimANa meM vidyamAna hai| yaha to aba nirvivAda rUpa se pramANita ho cukA hai ki bhAratIya gaNita ke aMdha yuga (500 I.pU.-500 I.) meM bhI yahA~ gaNita kA vikAsa hotA rahA jisameM jainAcAryoM kA amUlya yogadAna hai| sacamuca jaina Agama graMtha bhAratIya gaNita jyotiSa kI zrRMkhalA kI TUTI huI kar3I ko jor3ane kA kArya karate haiN| ina graMthoM ke avalokana se isa tathya kI puSTi hotI hai ki jina siddhAntoM ke AviSkAra kA zreya pAzcAtya gaNitajJoM ko diyA jAtA hai unameM se bahuta sAre siddhAntoM ko kaI zatAbdiyA~ pUrva hI jainAcAryoM ne lipibaddha kara rakhA hai| paravartI vidvAnoM ne pUrNataH gaNitIya granthoM kA bhI kSetramiti Adi zAkhAoM se sambandhita maulika evaM mahattvapUrNa siddhAntoM-sUtroM kA vivecana milatA hai| vartamAna saMdarbha meM ina gaNitIya siddhAntoM kI prAsaMgikatA evaM upAdeyatA kA vizleSaNa karanA hI isa nibaMdha kA abhISTa hai| ___ isa silasile meM sarvaprathama jainAcAryoM kI gaNitI upalabdhiyoM kA siMhAvalokana karanA Avazyaka pratIta hotA hai| jaina dharma ke mahatvapUrNa graMtha sthAnAMga sUtra (324 I.pU.) ke nimna sUtra meM gaNita vijJAna ke daza viSayoM kI carcA hai : (148)
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________________ _ 'parikamma vavahAroM rajju rAsI klaasvnnnnoy| jAvantAvati vaggo ghaNo tataH vaggAvaggo vikappo v|| 5 arthAt 'parikarma (mUlabhUta prakriyAe~), vyavahAra (vibhinna viSaya), rajju (jyAmiti), rAzi (samuccaya, trairAzika), kalA savarNa (bhinna sambandhI kalana), yAvata-tAvata (sarala samIkaraNa), varga (varga samIkaraNa), dhana (dhana samIkaraNa), varga-varga (dvivarga samIkaraNa) evaM vikalpa (kramacaya-saMcaya) gaNita ke ye daza viSaya haiN| isase spaSTa hotA hai, ki IsA ke 400 varSa pUrva hI jainAcAryoM ko ina viSayoM kA samucita jJAna ho gayA thaa| paravartI vidvAnoM ne paryApta rUpa se inheM pallavita evaM puSpita kiyaa| gaNita meM abhI taka sabase adhika krAMtikArI kadama huA hai sthAna-mAna-saMketa kI dazamalava paddhati kA AviSkAra jo bhAratavAsiyoM kI hI dena hai| kisI bhI saMkhyA ko saralatA se likhane ke lie daza aMka (zUnya evaM 1 se v.taka) paryApta haiN| upalabdha purAlekha sambandha pramANoM meM yaha pramANita hotA hai ki isakA AviSkAra prathama zatAbdI I.pU. yA isase pUrva hI ho cukA thaa| jaina Agama graMthoM se bhI isakI puSTi hotI hai| jainoM ko aMtarikSa evaM samaya kI mApa ke lie bahuta bar3I-bar3I saMkhyAoM kI AvazyakatA par3atI thI jisake lie yaha paddhati bahuta hI lAbhaprada siddha huii| anuyogadvAra sUtra (prathama zatAbdI I.pU.) ke anusAra eka zIrSa prahelikA = (8400000)28 pUrvI 5 / AryabhaTa prathama (476 I.) ke samakAlIna athavA samIpavartI jaina dArzanika yativRSabha kI kRti tiloya paNNatI meM kAla-mApa evaM loka mApa ke lie vizAla saMkhyAoM evaM ikAiyoM ko paribhASita kiyA gayA hai| inameM se kAla kI sabase bar3I saMkhyAta ikAI acalAtma hai jisakA mAna (84)314(10)deg varSa hai| pakhaMDAgama (prathamazatAbdI) isa para likhI TIkA dhavalA (9vIM zatAbdI) gaNita sAra-saMgraha Adi graMthoM meM to sthAnamAna paddhati kA upayoga huA hai tathA usakI vistRta rUpa se carcA bhI hai| ina graMthoM meM 40 padoM taka sthAnamAna kI sUcI prastuta kI gayI hai| jahA~ bhArata meM yaha praNAlI bahuta pUrva se hI pracalita thI, vahA~ pAzcAtya dezoM meM phivonakI, jona Apha hailIphAksa, pIsA ke kyonArDoM Adi vidvAnoM kI racanAoM meM 12vI 13vIM zatAbdI meM isakA ullekha milatA hai| isa taraha yUropa ke vibhinna dezoM ne isa paddhati ko apanAyA jo Aja prAyaH samasta saMsAra meM pracalita hai| __ pUrNAMka saMkhyAoM kI taraha bhitroM ke vikAsa meM bhI jainAcAryoM kA ati viziSTa sthAna hai| bhinnoM kA lekhana evaM tatsambandhI saMkriyAoM ke sAtha-sAtha vibhinna sUtra bhI sUryaprajJapti (5 vIM zatAbdI I.pU.), sthAnAMga sUtra, tiloya paNNatI, SaTkhaMDAgama, dhavalA Adi prAcIna graMthoM meM upalabdha hai| mahAvIrAcArya ne to bhitroM se sambandhita sAre tatvoM ko pratipAdita kiyA hai|" uttarAdhyayana sUtra (300 I.pU.) evaM anuyogadvAra sUtra meM gaNitIya rAzi kI ghAtoM ko darzAne kI vidhi spaSTa rUpa se aMkita hai jisase jJAta hotA hai ki prathama zatAbdI i.pU. yA usake pUrva hI jainAcAryoM ko ghAtAMkoM ke niyamoM kA jJAna ho gayA thaa| anuyogadvAra sUtra meM prathama varga, dvitIya varga Adi prathama mUla, dvitIya mUla Adi kA prayoga pAyA jAtA hai| sAtha hI saMsAra kI janasaMkhyA batAne ke lie 2644232=2 6 kA vyavahAra huA hai| dhavalA meM to ghAtAMka sambandhI vibhinna niyamoM kA upayoga bhI huA hai jinheM nimna rUpa meM vyakta kiyA jA sakatA hai :-xm. xn = x m+n, xm/xn = xm-n, (xmon = xmn aadi| 10 ina niyamoM ke ullekha se yaha sunizcita hotA hai ki tatkAlIna jainAcAryoM ko ghAtAMka ke ina niyamoM kA jJAna ho gayA thaa| ye niyama isI rUpa meM Aja bhI pracalita haiN| (149)
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________________ bhagavatI sUtra (300 I.pU.), sthAnAMga sUtra, anuyogadvAra sUtra Adi jaina graMthoM meM ati prAcIna kAla se hI kramacaya-saMcaya sambandhI viSaya bhaMga evaM vikalpa zIrSakoM ke antargata vizadatA ke sAtha pratipAdita kiyA gayA hai| bhagavatI sUtra meM isakA vivecana vyApaka rUpa meM kiyA gayA hai| ekaka saMyoga, dvika saMyoga, trika saMyoga Adi mUlabhUta pramANa die gae haiM jinheM nimnalikhita rUpa meM vyakti kiyA jA sakatA hai : '"c1- n, = n, n = n(n-1),n . = n(n-1)(n-2) '", "c2 1.2 ' "3 1.2.3 tathA "p, = n, "p, = n (n-1) aadi| yativRSabha, vIrasenAcArya, zIlAMka, nemicandra siddhAnta cakravartI Adi jaina vidvAnoM ne tatsambandhI niyamoM kA vivecana kiyA hai tathA vibhinna pahaluoM para bhI vicAra kiyA hai| kramacaya saMcaya sambandhI se niyama abhI bhI prayoga meM lAe jAte haiN| isake sAtha hI dvipada prameya ke vikAsa kA bhI una logoM ne patha prazasta kiyA hai| vibhinna prakAra ke samIkaraNoM yathA sarala, dvighAtI evaM anirNita prathama ghAtIya samIkaraNoM ko hala karane kI vidhiyA~ bhI jainAcAryoM ko jJAta thii| sthAnAMga sUtra meM prayukta yAvata-tAvata, varga, dhana, varga-varga Adi zabdoM meM isakI puSTi hotI hai| laghugaNaka siddhAnta ke janmadAtA jAne nepiyara (1550-1617 I.) evaM vargI (1600 I.) mAne jAte haiM, para unase lagabhaga sAta sau varSa pahale hI dhavalA meM isakA prayoga pAyA jAtA hai| saMkriyAoM kA upayoga milatA hai jo laghugaNaka ke nimnalikhita niyamoM ke paricAyaka haiM 12: ___ log, (x/y) = Log,x -log,y, log, (xy) = log,x+logy log2* = x, log, (2*)x* = x* log, (z*) Adi AdhAra 2 kI jagaha 3, 4 Adi kie jA sakate haiM tathA unheM sAmAnyIkRta bhI kiyA jA sakatA hai| . Aja rAzi siddhAnta (samuccaya) itanA vikasita ho cukA hai ki koI vijJAna isase na achUtA hai aura na hI isake binA AdhArita hai| isake pravartaka jArja kenTara (1885-1915) mAne jAte haiM, para usa rAzi siddhAnta kA vivecana ati prAcIna kAla meM hI jaina graMthoM meM upalabdha hai| SaTkhaMDAgama tiloya paNNatI, dhavalA, trilokasAra Adi graMthoM meM tatsambandhI abhidhAraNA, bheda-upabheda, udAharaNa tathA una para saMkriyAe~ dRSTigocara hotI haiM 12 vibhinna prakAra kI rAziyoM kA ullekha haiM tathA parimita aparimita, rikta evaM ekala samuccayoM ke udAharaNa bhI upalabdha hai| zreNiyoM ke sambandha meM jainAcAryoM kA yogadAna advitIya hai| tiloyapaNNatI evaM trilokasAra meM vibhinna prakAra kI zreNiyoM kA vizada vivecana hai| nemicandra siddhAnta cakravartI (10 vIM zatAbdI) ne dhArAoM kA prakaraNa vistAra pUrvaka likhA hai| unhoMne 14 prakAra kI dhArAoM kI vistRta carcA ke sAtha-sAtha sUtroM kA vizleSaNa bhI kiyA hai| unake graMtha triloka sAra meM to vRhatdhArA parikarma nAmaka eka gaNitIya graMtha kI bhI carcA hai| isase isa tathya kI puSTi hotI hai ki usa samaya taka dhArAoM se sambandhita svataMtra jaina graMtha upalabdha thaa| (150)
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________________ (8) jaina graMthoM meM jyAmitIya vivecana kA bAhulya hai tathA kSetramiti viSayaka sAmagrI vipula parimANa meM upalabdha hai| sUrya-prajJapti meM vibhinna jyAmitIya AkRtiyoM kI carcA hai| bhagavatI sUtra evaM anuyogadvAra sUtra meM Thosa AkRti dhanatrayas, dhanacaturasra, dhanAyata, dhana varga evaM dhana parimaMDala, Ayata, gola, velana, sambandhI sUtroM kA prayoga milatA hai|" umAsvAmI (150 I.pU.) kI racanA tatvArthAdhigamasUtra bhASya meM aneka mApikI sUtra vidyAmAna haiM jinheM nimna rUpa meM likhA jA sakatA hai| 16 :- yadi kisI vRtta kI paridhi ke lie p, jIvA = c, vRttakhaMDa ke cApa kI lambAI = s, vRttakhaMDa kI U~cAI =H, vRtta kI trijyA =R, vyAsa =D, kSetrapha7 =A vyakta kiyA jAya to P = 10D; A =1 PD, C = 4H (D-H)H=1 (D/D--c'), S= 6h-c2 aura D= {h2 +2 In tiloyaNNatI meM kucha pramukha prayukta sUtra nimnalikhita haiM 16 :- (1) lambavRttIya belana kA Ayatana 10r h; (2) lamba prijma ke chinnaka kA Ayatana = AdhAra kA kSetraphala x prijya kI lambAI, (3) vRtta kI paridhi Dx 10 (4) vRtta ke caturthAMza kI jIvA kA varga =2R', (5) vRtta kI jIvA =ADP- Pc (6) vRttakhaMDa kA cApa = 5 =/26(dth)-12 (7) = H =PT2ii vRttakhaMDa kI U~cAI vRttakhaMDa kA kSetraphala = A-HD V10 trilokasAra meM bhI aise aneka sUtra upalabdha haiN|18 ina sUtroM meM se prAyaH sabhI kA vyavahAra abhI bhI kiyA jAtA hai| vRtta kI paridhi evaM usake vyAsa ke anupAta arthAt ke mAna kI vivecanA ati prAcIna kAla se hI jaina Agama graMthoM meM kI jAtI rahI hai| jaina paramparAnusAra isakA sthUla mAna 3 tathA sUkSma mAna V10 svIkata kiyA gayA hai| sarya prajJapti meM ina donoM mAnoM kI carcA hai 12 / bhagavatI satra anapa sUtra, tatvArthAdhigama sUtra bhAgya, tiloyapaNNatI, trilokasAra Adi jaina graMthoM meM bhI ye mAna upalabdha hai| dhavalA meM to kA mAna 355/113 diyA gAya hai jo Adhunika mAna se bahuta hI nikaTa hai| ise cInI mAna kahA jAtA hai, para aisA anumAna hai ki cIna meM prayoga hone se pUrva hI jainAcAryoM ne isakA upayoga kiyA hai| vartamAna samaya meM prAyikatA kI khoja kA zreya geliliyo, pharameTa, pAskala, baranaulI Adi pAzcAtya gaNitajJoM ko diyA jAtA hai, para prAyikatA ke siddhAntoM kI nIMva guNAtmaka rUpa se AcArya kundakunda (52 I.pU. se 44 I. taka) evaM samantabhadra (2rI zatAbdI) ne rakha dI thii| syAdvAda ke saptabhaMgoM meM sannihita isa siddhAnta kA prayoga bhI pAyA jAtA hai| deg isa dizA meM anya aneka maulikatAe~ evaM viziSTatAe~ jaina graMthoM meM yuga-yuga se pallavita hotI rahI hai| bhAratIya gaNita ke itihAsa meM jina do jaina gaNitajJoM kA mahattvapUrNa sthAna hai ve haiM zrI dharAcArya (8vIM zatAbdI) tathA mahAvIrAcArya (850 ii.)| zrIgharAcArya ne gaNita sambandhI svataMtra graMthoM pATIgaNita evaM triMzatikA kI racanA kara eka paramparA sthApita kii| ina graMthoM meM gaNita ke vibhinna viSayoM kI atyAdhanika vidhi kA vivecana kiyA gayA hai| sabase mahatvapUrNa bAta yaha hai ki dvighAtIya samIkaraNa ke hala karane kI aisI vaijJAnika vidhi kI unhoMne kalpanA kI jo abhI bhI usI rUpa meM prayoga kI jAtI hai| bhAskarAcArya (151)
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________________ (12 vIM zatAbdI) ne zrIdharAcArya dvArA sthApita isa vidhi ko nimna rUpa meM uddhata kiyA hai : 'caturAhata vargasamai rUpaiH pakSadvayaM gaNayet / avyakta varga rUpairyukto pakSoM tato mUlam // ' 21 arthAt 'samIkaraNa ke donoM pakSoM ko asAta rAzi ke varga ke guNAMka ke caugune se guNA kreN| donoM meM ajJAta rAzi ke maulika guNAMka varga ko jor3a deN| isa kriyA kI sahAyatA se dvighAtIya samIkaraNa -bb2-4ac 2a 2 ax + 4x + C = o ke mUla x = 22 24 mahAvIrAcArya kA gaNita ke kSetra meM zlAghanIya yogadAna hai| unakA gaNita sambandhI mahatvapUrNa graMtha hai gaNita-sAra-saMgraha jisakI racanA pAThya pustaka kI zailI meM kI gayI hai| isameM niyamoM kA pratipAdana udAharaNoM ke sAtha kiyA gayA hai| sarvaprathama unhoMne hI ghoSaNA kI ki RNAtmaka rAzi kA vargamUla nahIM ho sktaa| unhoMne isa sambandha meM pratibhApUrNa niSkarSa dekara kAlpanika rAziyoM kI khoja ke lie mArga prazasta kiyaa| kAlpanika rAzi kI jo parikalpanA unhoMne 9vIM zatAbdI meM kI vahI yUropa meM koMsI ne 1847 I. meM kii| vahIM sarvaprathama bhAratIya gaNitajJa haiM jinhoMne guNottara zreNI ke yoga ke lie vyApaka sUtra pratipAdita kiyA jo abhI taka pracalita hai 23 sAtha hI unhoMne kramacaya-saMcaya ke lie vyApaka sUtra kI sthApanA kI jo yUropa meM 1634 I. meM AviSkRta huA / isI taraha aMkagaNita jyAmiti kSetramiti Adi zAkhAoM meM bhI unakA yogadAna stutya hai / katipaya jyAmitIya AkRtiyoM ke kSetraphala ke sUtroM kI unhoMne hI sarvaprathama sthApanA kii| nimna vRtta, unnata vRtta, kaMbuka vRtta, dIrghavRtta, antazcakravAla vRtta, vRzcikravAla vRtta, hastaMdata kSetra, praNavAkAra, yavAkAra, murajAkAra, vajrAkAra kSetra Adi AkRtiyoM ke kSetraphala nikAlane kI vidhi unhoMne dii| cakrIya caturbhuja sambandhI unake dvArA sthApita sUtra zata pratizata Adhunika rUpa kA hI hai| 26 mahAvIrAcArya ke atirikta rAjAditya, haribhadrasUri, ralekhara sUri, Thakkara pherU, somatilaka, mahimodaya, hemarAja, paM. ToDaramala Adi jainAcAryoM ne bhI apanI apanI racanAoM meM gaNitIya sUtroM kA vizleSaNa kiyA / phalasvarUpa jaina gaNita kA uttarottara vikAsa hotA rahA / 25 uparyukta siMhAvalokana se yaha aba spaSTa ho jAtA hai ki jainAcAryoM ne gaNita ke unnayana meM zlAghanIya yogadAna diyA hai| tathya bhI pramANita hotA hai ki unake dvArA pratipAdita sthApita maulika gaNitIya siddhAnta abhI bhI vyApaka rUpa meM pracalita hai| ataH vartamAna saMdarbha meM bhI jaina gaNita kI upAdeyatA usI rUpa meM hai jisa rUpa meM prAcIna kAla meM thI / AvazyakatA isa bAta kI hai ki vibhinna graMthAkaroM meM upalabdha, upekSita pAMDulipiyoM kA adhyayana evaM cintana-manana ho jisase gaNita meM jainAcAryoM ke avadAna kA sahI-sahI mUlyAMkana ho ske| saMdarbha sUcI 1. Ara. zAmazAstrI (saM.) vedAMga jyotiSa, maisUra, 1,36, zloka 4 2. lakSmIcandra jaina (saM.) gaNita-sAra-saMgraha, zolApura 1, 63, 1., pR. 2 3. 4. vahI, 1.16, pR. 3 paramezvara kA bhAratIya gaNita ke aMdha yuga meM jainAcAryoM kI upalabdhiyA~, sAdhvIrala kusumAvatI abhinandana graMtha, pRSTha 34 - 74 / (152)
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________________ sthAnAMga sUtra zloka 643 / 6. anuyoga dvAra sUtra zloka 116 / / 7. lakSmIcandra jaina, tiloyapaNNatI kA gaNita, zolApura, 1.58, pR. 54 / 8. gaNita-sAra-saMgraha, (saM. 2), 3.1-14, pR. 36-6 / anuyoga dvAra sUtra, zloka 142 // eca. ela. jaina (saM.) dhavalA, bhAga 3, pR. 253 tathA la. ca. jaina, maithamaiTikala TApika oNpha dhavalA, ja. esa. esa., 11.2 1.6, pRSTha-.-. 11. bhagavatI sUtra zloka 314 / 12. dhavalA, bhAga 3, pRSTha 20-24 evaM 56 / 13. anupama jaina jaina gaNita kI maulikatAe~ evaM bhAvI zodha dizAe~, arhatvacana, pravezAMka 188, pR. 120 / 14. trikolakasAra, mAdhavacanda (TIkA), bambaI, 1,20, pR. 14-15 / 15. bhagavatI sUtra, zloka 635-26 / 16. vizeSa vivaraNa ke lie drarUkhya anupama jaina evaM sureza candra agravAla, jaina gaNitIya sAhitya, arhat vacana, pravezAMka 1.88 evaM 26-28 evaM lakSmIcandra jaina, injaikTa sAinsesa phroma jaina sorseja, bhAga 1, jayapura 1.82, pR. 45 / 17. lakSmIcandra jaina (saM. 16), pR. 46 / / 18. vahI. pR. 46 / 19. vahI pR. 32-33 / 20. ramezacandra jaina, syAdvAda ke saprabhaMga evaM Adhunika gaNita-vijJAna, arhat vacana, pravezAMka 1.88, pR - / 21. sudhAkara dvivedI (saM.) bIjagaNita, banArasa, 1,27, pR 22. gaNita-sAra-saMgraha, 1.52, pR.| / 23. vahI, 2:3, pR. 28 // 24. vahI, 6.218, pR. 146 / 25. vahI, 7.1- 232 1/2, pRSTha 181-250 / 26. vahI, 7.50, pR. 1.3 // * * * * * pradhAnAcArya ko. opareTiva kaoNleja, begUsarAya (bihAra ) - 851101 (153)