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________________ jaina gaNita ane tenI mahattA narasiMha mULajIbhAI zAha jenonA dhArmika sAhityagraMthomAM bhagavAna mahAvIranI vANI prathamAnuyoga, caraNAnuyoga, karaNAnuyoga " ane dravyAnuyoga ema cAra anuyogomAM vaheMcI nAkhavAmAM AvI che. caraNanuyogamAM iSTa upAsanA ane sAdhunA AcArane lagatA kriyAkAMDono ane dravyAnuyogamAM tattvajJAna, nItizAstra, mAnasazAstra, jIvajIvazAstra vagereno samAveza thAya che. karaNAnuyogamAM alaukika ane laukika gaNitazAstranAM tattvono vicAra karavAmAM Avyo che eTale karaNAnuyogane gaNitAnuyoga paNa kahevAmAM Ave che. A batAve che ke jaina darzanamAM gaNitane UMcuM sthAna apAyeluM che. jainonAM laukika gaNitanI maulikatA ane mahattA aMge aneka vidvAnoe potAnA vicAro pragaTa karelA che. "gaNitatilakanI bhUmikAmAM prophehIrAlAla kApaDiyAe lakhyuM che ke sAmAnya rIte bhAratIo, ane vizeSe karIne jeno, gaNitanI bAbatamAM dhyAna ApavAmAM anya koI deza ke prajAthI pachAta nahotA. dakSiNa bhAratanA gaNitazAstrI mahAvIrAcArya(I. sa. 850)nuM "gaNitasArasaMgraha" A bAbata puravAra karI batAve che. temAM teoe saMgIta, nyAyatarka, nATyavidyA, sthApatya, auSadhivijJAna, rasoI vidyA, vyAkaraNa, kAvyazAstra (piMgaLa), arthazAstra, premavijJAna vageremAM gaNitazAstra yA "gaNatarInuM vijJAnanI upayogitA darzAvI che. trikoNa ane catukoNanA gaNitanuM vizleSaNa mahAvIrAcArye kareluM che, jemAM e aMge keTalIka vizeSatAo sUcavI che. A uparathI spaSTa thAya che ke jainAcAyoMe kevaLa dharma aMge gaNitano upayoga maryAdita rAkhyo nathI paNa aneka vyavahArika bAbatomAM teno prayoga karyo che. bhAratIya gaNitanA viSayamAM tenA vikAsamAM jainAcAryono hisso pradhAna che. je samayamAM gaNita prAraMbhika svarUpamAM hatuM te vakhate jaina gaNitIoe bIjagaNita ane mApakaraNa(mesyurezana)nI samasyAo hala karavAmAM upayogI hisso Apela che. gaNitamAM jenonA phALAnI prazaMsA karatAM DaoN. jI. thIboe sUryaprajJapti aMgenA potAnA nibaMdhamAM lakhyuM che ke grIkonuM bhAratamAM Agamana thayuM te pUrve A graMtha racAyo hovo joIe, kAraNake temAM grIkonI asaranI chAMTa paNa nathI. This work must have been composed before the Greeks came to India as there is no trace of Greek influence in it.
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________________ 262 : zrI mahAvIra jaina vidyAlaya suvarNamahotsava grantha bhAratamAM gaNita--aMkagaNita, khIjagaNita, mApakaraNa, khagoLa vagereno abhyAsa ati prAcIna kALathI cAlato Avyo che. bhAratIya gaNitIoe A viSayomAM saMgIna phALo Apelo che. vastutaH teo Adhunika aMkagaNita ane khIjagaNitanA praNetAo hatA. paraMtu evo eka khyAla sAmAnya thaI gayo che ke hiMdanI vizALa vasatimAMthI mAtra vaizviko gaNitano abhyAsa karatA ane temAM rasa letA : bhAratIya prajAnA anyadharmI samUho, dAkhalA tarIke, bauddo ane jaino, A pratye lakSa na ApatA. A mAnyatA pracalita thavAnuM kAraNa e lAge che ke yuddha ane jainadharmI gaNitIoe lakhelAM gaNitanAM jUnAM pustako (kadAca sAMpradAyika hovAnA kAraNe) ochAM jANItAM che : emanI prato sArA pramANamAM maLI AvI nathI. paraMtu jainonA Agamo ane anya dharmazAstrone tapAsavAthI dekhAI Ave che ke jainoe gaNitanA viSayamAM rasa laI tenA abhyAsa dvArA potAno phALo ApavAmAM pAchI pAnI karI nathI. vastutaH gaNita ane khagoLanuM jJAna jaina sAdhu saMsthAnI siddhiomAM eka viziSTa aMga gaNAyuM che (juo bhagavatI sUtra : sUtra 90 : abhayadevasUrInI TIkA : mahesANA Agamodaya samiti : 1919). gaNitanA atyAre prApya sAhityanA purAvA parathI ema kahI zakAya ke pATalIputra (paTaNA), ujjaina, khaMbhAta, maisUra, malabAra, valabhI ane sAmAnyataH vANArasI, takSazilA ane anya keTalAMka sthaLoe gaNita aMgenA abhyAsa mATe samRddha mathako astitvamAM hatAM. A badhAM vacce kevA prakArano saMbaMdha hato e cokasa kahevA mATe atyAre ApaNI pAse pUrato purAvo nathI. A viSaya vizeSa saMzodhana mAgI le che. paNa judAM judAM mathakoethI maLI AvatAM gaNitika pustakonI tapAsa dvArA mAlUma paDe che ke vividha mathakoe thatuM gaNitika kAma sAmAnyataH maLatuM AvatuM hatuM--jo ke keTalIka vigatonI khAbatamAM krUraka spaSTa mAlUma paDe che. A uparathI ema kahI zakAya ke A badhAM mathakomAM gaNitanA abhyAsamAM paDelA vidvAno vacce arasaparasa saMbaMdhano vyavahAra haze : vidvAno eka mathakethI bIje mathake jatA haze : eka jagyAe thayela zodhanA pariNAmo bIjA mathake jaNAvavAmAM AvatAM haze ane vicAravinimaya thato haze. jaina ane buddha dharmanA prasArathI vidhavidha vijJAna ane kaLAonA abhyAsane uttejana maLyuM che. bhAratanuM dhArmika sAhitya, ane vizeSataH khuddha ane jaina dharmanA sAhitya graMtho, tapAsatAM A aMge purAvA maLI Ave che. gaNitanI bAbata laI e to moTI saMkhyA darzAvatA AMkaDA A pustakomAM vAraMvAra vaparAyelA mAlUma paDe che. AvA gaMjAvara AMkaDAno upayoga ane e lakhavA mATe sAdI saMjJApaddhatinI khilavaNI jo na hoya to, AvA AMkaDA lakhavA--darzAvavA muzkela che, ane AMkaDA goThavavAnI atyAre pracalita dazAMka paddhatinI zodha ene AbhArI che. have susthApita thayuM che ke dazAMza paddhati IsavI sananA prAraMbhamAM bhAratamAM zodhavAmAM AvI hatI. A samaya yuddha ane jaina dharmono madhyAhnakALa hato. A pati vedasamayanI prAthamika avasthAmAMthI pAMcamA saikAnA 'AryabhaTa ane varAhamihira jevA gaNitanonAM pustakomAM maLI Ave che. ethI gaNitika pragatimAM vega Avyo ane teno vikAsa thayo. game evaDI moTI saMkhyA darzAvatA AMkaDA Aje ApaNe sahelAIpUrvaka lakhI zakIe chIe. koIpaNa AMkaDAnI jamaNI bAjue lakhatAM hAtha thAkI jAya eTalA AMkaDA ke mIMDAM mUko; ane cokasa saMkhyA darzAvatA AMkaDA banAvI zakAze. jUnA kALamAM misaravAsIo koI saMkhyA darzAvato AMkaDo lakhavA e AMkaDo eTalIvAra lakhI darzAvatA. jemake, 8732 lakhavuM hoya to AvAra 8nA AMkaDAnI, sAtavAra chanA AMkaDAnI, traNavAra 3nA AMkaDAnI, evAra enA AMkaDAnI saMjJA lakhavI paDatI. A rIta ati kaMTALA bharelI ane kilaSTa paNa che. tyAra bAda romanoe saMkhyA darzAvavA kakkAnA akSarano
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________________ jaina gaNita ane tenI mahattA : 3 upayoga dAkhala karyo. romana paddhati pramANe 1ne mATe 1, 1ne mATe x, 100ne mATe c, 500 mATe D ane 1000 mATe c evI saMjJAo vAparavAmAM AvatI. romana paddhati pramANe 8732 lakhavuM hoya to, 8 hajAra mATe MMMMMMMM, chaso mATe DCC, trIsa mATe XXX ane e mATe II, eTale MMMMMMMMDcCXXXII eTaluM lakhavuM paDe. romana AMkaDA hajI paNa pustakomAM prakaraNanI saMkhyA, ghaDiyALanA DAyala para AMkaDA darzAvavA upayogamAM levAya che. Adhunika ekama, dazaka, so, hajArane krama sUcavatI paddhati pramANe AMkaDAo vaDe saMkhyA darzAvavAnI dazAMka paddhati dAkhala karavAnuM mAna jaina gaNitione jAya che. gaNitanA itihAsakAronI dhyAna bahAra rahelI eka bAbatano ulalekha ahIMyAM asthAne nahi gaNAya. vedika, bauddha ane jaina sAhitya I. sa. pUrve trIjA ke cothA saikAthI mAMDIne madhyayuganA kALa sudhI sAtatya jALave che-dareka saikAnuM pratinidhitva dharAvatuM sAhitya maLI AvyuM che. paNa gaNitanI bAbatamAM e sAtatya sacAvatuM nathI-moTA gAbaDAM paDelAM che. I. sa. 499mAM racAyela AryabhaTTIyanA pUrvenuM eka paNa gaNitika pustakanI prata bhAgye ja maLI Ave che. AmAM eka apavAda che vakSazAlI tarIke oLakhAtI tUTaka hastapratano. A vakSazAlI prata I. sa. bIjA ke trIjA saikAmAM lakhAyela lAge che. e vakhate gaNitanA jJAna saMbaMdhI zI paristhiti hatI e aMge vigatavAra mAhitI temAMthI maLatI nathI. AryabhaTTa, brahmagupta ke zrIdharanAM pustakomAM che tevuM gaNitika vivaraNa emAM nathI. emAMthI mAtra eTaluM maLe che ke saMkhyA lakhavA mATe AMkaDAnI goThavaNapaddhati te vakhate jANItI hatI. AryabhaTTIyamAMthI maLatAM gaNitanA siddhAMto khUba AgaLa vadhelAM mAluma paDe che. Adhunika aMkagaNita-vyAja, trirAzI, dvighAta(quadratic)samIkaraNonA nirAkaraNa (solution) mATe bIjagaNita, anizcita samIkaraNa (indeterminate equations)-A badhA viSayonuM nirUpaNa temAM AveluM che. I. sa. 1912mAM raMgAcAryane gaNitasAra saMgrahanI prata maLI : temaNe tenuM saMzodhana karI tenuM zana karyuM tyArathI vidvAnone lAgyuM ke jaina gaNitanI paraMparA hovI joIe. "jaina skUla oNpha methemeTikasa' nAmanA lekhamAM (buleTina kalakattA metha0 sosAyaTI, 1929, 21, 115-145) prophesara bI do jenonAM sUtrono abhyAsa karI jaina gaNita viSe ane te aMgenAM e pustakomAMnA aneka saMdarbho prakAzamAM ANyA. AmAMthI keTalAya jaina gaNitajJoe lakhelAM gaNitanAM pustako adyApi prApya nathI. jena bhaMDAromAM saMgrahAyelI hastapratone tapAsI gaNitane lagatAM jainoe lakhelAM pustako prakAzamAM ANavAno samaya pAkI gayo che. "sarva vijJAnonuM udgama sthAne grIsa ke roma che' e pazcimI vidvAnoe pracalita karela siddhAMta have lAMbo vakhata TakI zake ema nathI. I. sa. pUrve 278mAM mRtyu pAmela bhadrabAhu (1) sUryaprAptinI TIkA ane (2) bhadrabAhavI saMhitAnA lekhaka hatA. siddhasenanuM nAma jaina khagoLavidomAM jANItuM che. ardhamAgadhI ane prAkRta sAhityamAM gaNita aMge temanA kAryanA ullekho vAraMvAra maLI Ave che. zvetAMbaronA karmagraMtha jevo digaMbarono graMtha vakhaMDAgama che. tenI TIkA vIrasene navamA saikAmAM prAraMbhanA varSomAM lakhI hatI. A TIkAgraMtha dhavalA nAme suvidita che. vIrasena eka dArzanika hatA ke temane gaNitazAstrI kahI na zakAya. eTale dhavalAmAM ApelI gaNitika bAbato agAu thaI gayelA gaNitajJonA AdhAre apAyela hovI joIe. dhavalAmAM Apela gaNita Isa. 200-600nI AsapAsanA samayanuM che ema gaNitanA vidvAnono abhiprAya che, eTale bhAratIya gaNitanA aMdhArayuga aMge te mAhitI pUrI pADe che. dhavalAnI gaNatika sAmagrI I satra 500nA jamAnAnI pahelAMnI che evuM teno vigatavAra abhyAsa karIne vidvAnoe
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________________ 264: zrI mahAvIra jaina vidyAlaya suvaNamahasava cantha puravAra karI batAvyuM che. dhavalAmAM varNavela gaNitanI ghaNu rIto anya koI gaNitika graMthamAM maLatI nathI. dhavalAnuM gaNita AryabhaTTIya ane pachInA graMthomAM che teTaluM saMkRta thayeluM nathI. ApaNI saMkhyA-paddhati sthAnamUlyanA siddhAMta para racAyela che. A paddhatinA be phAyadA che. eka te game teTalI moTI rakama ApaNe daza AMkaDA(saMketo)nI madadathI lakhI zakIe chIe; bIjuM enAthI saravALA-bAdabAkInA niyamo ati saraLa thaI gayA che. dhavalAnA lekhaka dazAMka paddhati, sthAnamUlya paddhati(place value system of notation)thI pUrepUrA vAkephagAra che evo purAvo puratamAM badheya maLI Ave che. dAkhalA tarIke, moTA AMkaDAvALI saMkhyA lakhavAnI nIce ApelI traNa rIto temAMthI maLI Ave che? (1) 79999998 jevI saMkhyAnI rakama lakhavA zarUAtamAM 7, cheDe 8 ane vacamAM 6 navaDA mIne e saMkhyA darzAvAI che. A rIta jaina sAhityamAM badheya ane gaNita sArasaMgrahamAM keTalIka jagyAe mAluma paDe che, ane sthAna-mUlya-kanyAsa paddhati sAthe paricaya darzAve che. (2) 46666664nA AMkaDAne 64, 600, 66 hajAra, 66 lAkha ane 4 koTi (karoDa) ema lakhavAmAM Avyo che. A rItamAM nAnI saMkhyA prathama mUkI che, je saMskRta sAhityamAM pracalita praNAlI mujaba che. jemake, 19 mATe ekoviMzati, 12 mATe dvAdaza. aMkanyAsano khela 100 che--nahi ke daza. prAkRta ane pAlI sAhityamAM 100no AMka skela tarIke sAmAnya rIte vaparAyo che. A (3) 2279949ne 2 koTi (karoDa), 27 lAkha, 99 hajAra, 400ne 98 tarIke darzAvAyo che. Adhunika pracalita rIte anusAra moTAmAM moTo mUlyAMka prathama mUkavAmAM Avyo che. jaina graMthomAM jIvarAzi, dravyapramANa vagerenI carcAmAM moTI saMkhyA darzAvatA AMkaDAo vAraMvAra maLI Ave che e suvidita che. karmagraMthamAM (ane digaMbaronA pakhaMDAgama ane tenI TIkA dhavalAmAM paNa) moTI moTI saMkhyA darzAvatA AMkaDAo maLI Ave che. koTi-koTi-koTi ane koTi-koTi-koTi-koTi AtmAonI saMkhyA A pustakamAM noMdhAyela che. saravALA, bAdabAkI, guNAkAra ane bhAgAkAranI mULabhUta rIte; vargamULa, ghanamULa vagere bAbatono ullekha maLI Ave che. Adhunika gaNitamAM laoNgerithame (laghugaNaka) mahattApUrNa sthAna prApta karyuM che. A aMge dhavalAmAM ApelI nIcenI keTalIka muddAnI bAbato laIe : (1) saMkhyAno ardhacchada eTale jeTalI vAra tene ardha karI zakAya te saMkhyAnI barAbara. A rIte mno ardhacchada = m. ardhacchedane TUMkAmAM Ac vaDe darzAvIe to, Adhunika paribhASAmAM koI saMkhyA(x)no ardhacchada Acx= log *, jemAM laoNgerithama benA pAye (beIjhamAM) che. [, (2) trikaraccheda : koI paNa saMkhyAno trikaccheda tene 3 vaDe jeTalIvAra bhAgI zakAya tenI barAbara. trikaccheda mATe TC saMkhyA laIe to koI paNa saMkhyA xno trikaccheda = Tex=log, 4, jemAM laoNgerithama unA beIjhamAM che. (3) vargasalAkA : koI saMkhyAnI varga salAkA eTale te saMkhyAnA ardhacchedano artha che. koI saMkhyA xnI varga salAkA (vs) eTale-- - - Vs= Ac Ac x=log log x, jemAM laoNgerithama benA beIjhamAM che.
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________________ jaina gaNita ane tenI mahattA : 265 (4) catucchedaH cAra vaDe jeTalIvAra bhAgI zakAya tenI barAbara. . koI saMkhyA (x)no caturthaccheda (cc) = cc x = logqx (jemAM laoNgerithama inA beIjhamAM che) laoNgerithama aMge dhavalAmAM nIcenAM pariNAma tAravavAmAM AvyAM che : (1) Log (m/n) = log m - log n (2) Log (m.n) = log m + log n (3) Log2 m =m () Log (x*) 2 = 2 x log x (4) log log (x*)2 = log (2 x log x) = log x + log 2 + log log x 4 log 2 = 1 = log x + 1 +log log x (6) log (xx) x =xx log xx A batAvI Ape che ke e jamAnAmAM jaina gaNitano Adhunika ghAtanA niyamo ane laoNgerathamanA siddhAMtothI paricita hovA joIe. have bIjI keTalIka bAbatono TUMkAmAM nirdeza karIe. apUrNAMka aMge paNa puSkaLa mAhitI maLI che. A mAhitI koI paNa anya gaNita-pustakamAMthI maLatI nathI. trirAzi aMge paNa ullekho che. A aMge phaLa, IcchA ane pramANa evA pAribhASika zabdono vaparAza karavAmAM Avyo che. prAcIna sAhityamAM anaMta infinite) zabda anekavidha arthomAM vAparavAmAM Avyo che. enI yogya vyAkhyA ane anaMtatAno khyAla pAchaLathI dAkhala thayo. moTA AMkaDAvALI rakama vAparanArAoe athavA to potAnA darzanamAM AvA AMkaDA vAparavA TevAyelAoe enI vyAkhyA upajAvavA prayAsa karyo haze. anaMta zabdanI sAthe saMkaLAyela anekavidha khyAlonuM vargIkaraNa karavAmAM bhAratanA jaina dArzaniko saphaLa thayA ane pariNAme tenI vyAkhyA teoe upajAvI. A vargIkaraNa anusAra anaMtatAnA agiyAra prakAra che: (1) nAmAnanta (2) sthApanAnanta (3) dravyAnA (4) gaNanAnanta (sAMkhyika anaMta) (5) apradezikAnanta (6) ekAnanta (7) ubhayAnanta (8) vistArAnanta (9) sarvananta (10) bhAvanAnanta (11) zAzvatAnaH (avinAzI). A vargIkaraNa sarvagrAhI che ane jaina sAhityamAM je arthomAM anaMta zabda vaparAyo che te badhAno temAM samAveza thAya che. jaina sAhityamAM saMkhyAta (numerable), asaMkhyAta (innumerable) ane anaMta (infinite) saMkhyA prAraMbhathI ja vAparavAmAM AvI che. - yuropamAM ArkimiDIse samudrakAMThe retInA kaNonI saMkhyA nakkI karavA prayatna karyo. grIka tatvavettAoe anaMta ane maryAdA aMge aneka kalpanAo rajU karI. moTI saMkhyA darzAvavA anukULa saMjJAonI teone khabara nahotI-tenuM jJAna nahotuM. bhAratamAM vaidika, jaina ane buddha dArzanikoe A aMge yogya saMsAdarzako upajAvyA. khAsa karIne jenoe vizvamAM jIvasaMkhyA, samaya, sthaLa vagere aMge khyAla ApavA prayatna karyo.
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________________ 216 H zrI mahAvIra jaina vidyAlaya suvarNa mahotsava moTA AMkaDA darzAvavA nIce Apela traNa rIte upayogamAM levAtIH (1) sthAna-mUlya paribhASA : dazanuM dhoraNa vAparIne 1040 jevA moTA AMkaDAo darzAvavA 10nuM dhoraNa yojavAmAM AvyuM hatuM. (2) ghAtanA niyamo (varga-saMvarga) moTI saMkhyAo TUMkAmAM darzAvavA upayogamAM levAmAM AvatA. dAkhalA tarIke, (2)ra = 4 (22)= x = 256 (2)ra * ( rAya ? = 256256. Ane 2 no tRtIya vargIta-saMvargata kahevAyo che. A saMkhyA vizvamAM proTIna ane ilekTronanI saMkhyA karatAM paNa vadhAre che. (3) lagerithama (ardhacchada) yA laoNgeriyamano lageriyama (ardhacchada salAkA) moTA AMkaDAnA laoNgerithamanI kriyA dvArA nAne darzAvavA vAparavAmAM Avato. jemake, log22 = 2 log loga 2562 56 =11 log, log, 4 =3. A traNa rItomAMthI eka yA bIjIno upayoga ApaNe Aje karIe chIe. dazAMka paddhati AkhI duniyAmAM sAmAnya thaI paDI che. moTA AMkaDAvALI saMkhyAnI gaNatarI karavA laoNgeriyamano upayoga Aje sAmAnya rIte thAya che. dhAtanA niyamono upayoga Adhunika bhautika vijJAnamAM sAmAnya banI gayo che. vizvamAM proTonanI saMkhyAnI gaNatarI karIne AMkaDo 136-2256 vaDe darzAvAya che. A badhI Adhunika rItonA siddhAMto jainone jANItA hatA, kAraNake temano upayoga thayelo che, eTale sAtamA saikA pahelAM bhAratamAM A rIte jANatI haze ema phalita thAya che, ane emAM jene gaNitano phALo mahattApUrNa che. anaMtatAnA aneka prakAro astitvamAM che ema jyorja kenTore ogaNIsamI sadInA madhyamAM darzAvyuM. Transfinite number(sAMta-atIta saMkhyA)no siddhAMta teNe rajU karyo. anaMta rAzio(aggregates)nA pradezomAM kenToranA saMzodhane gaNitane majabUta pAyo pUro pADyo; saMzodhana mATe eka prabaLa hathiyAra ApyuM ane gaNitanA ati gahana (abstruse) vicArone cokasAIpUrvaka abhivyakta karavAnI bhASA pUrI pADI. A AMkaDAonuM kalana (calculus) hajI vikAsa pAmyuM nathI eTale AvI saMkhyAone gaNitika vizleSaNamAM asarakAraka rIte upayogamAM laI zakAtI nathI. mULabhUta (cardinal) saMkhyA 9nA vargIta-saMvargIta cc no khyAla anaMta mULabhUta naMbarono siddhAMta upajAvavA mATe jenono prAthamika prayAsa che. jaina sAhityamAM utkRSTa-asaMkhyAtano vicAra anaMtatAnI najIka Ave che. gaNitanA vikAsamAM Avo prayatna zarUAtamAM niSphaLa ja nIvaDavAno. chatAM jaina gaNitIoe e prayatna karyo e ja adbhuta che. emAM ja jaina gaNitanI mahattA samAyelI che. - jainonA bhUmitika jJAna viSe be bAbatono TUMko ullekha asthAne nahi gaNAya. bhagavatI sUtra (sUtra726-727)mAM ekano ullekha mAlUma paDe che. jAtajAtanA bhUmitika AkAro banAvavA jarUrI pradeza
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________________ jaina gaNita ane tenI mahattA H 267 (pradeshas)nI laghutama saMkhyAnuM temAM vivaraNa che. bIjI bAbata budIpa prajJaptimAM meruparvatanA judA judA staro aMge savistara carcA karavAmAM AvI che. ja (pAI)nI kiMmata kADhavA jUnA kALathI pAzcAtyoe prayatno karelA ema gaNitanI tavArIkhamAMthI maLI Ave che. (pAI)nI kimata aMge jenonAM sUtromAM nIcenA traNa spaSTa AMkaDAo noMdhAyelA maLI Ave che: (1) V10; (2) traNa karatAM jarAka vadhAre tripui viroSam ane (3) 316. bhagavatI sUtramAM (sUtra 91), jIvAjIvAbhigamasUtramAM (sUtra 82 ane 109), jaMbuddIpaprajJaptimAM (sUtra 3), tattvArthIdhigamasUtrabhASyamAM (311) ane bIjA keTalAka graMthomAM prathama kimata(10)no nirdeza mAlUma paDe che. uttarAdhyayana sUtramAM (36, 59) nI bIjI kiMmata mAlUma paDe che. trIjI kiMmata chavAchavAbhigamasUtramAM (sUtra 112) sUcavAI che. ema noMdhavAmAM AvyuM che ke vartalanA vyAsa (diameter) mAM 100no vadhAro thatAM teno paridha (Circumference) 316 jeTalo vadhe che. vartuLano paridha tenA vyAsa pramANe phare che e bAbatathI jaino abhinna hovA joIe ema anumAna thAya che. digaMbaronA graMthomAM ja = 19/6 ema samIkaraNa ApyuM che. jenono gaNitanA vikAsamAM phALo e viSaya khUba saMzodhana mAge che. ApaNu apragaTa jUnA graMthonuM saMzodhana karI vizeSa purAvo bhego karavAnI AvazyakatA che. atyArasudhI sArA evA prayatno thayA che. paraMtu vizeSa vyavasthita savistara saMzodhana icchanIya cheApaNA junA bhaMDAromAM paDelI hastaprato ane graMtho tapAsIne. * jainataroe (hiMduoe) nAnI kiMmata kADhelI che. A mATe juo DaoN. dattano lekha (jarnala oNpha eziyATika sosAyaTI oNpha beMgAla, vaoNlyuma 22, 25-42 (1926)).