Jain Agamo me Nihit Ganitiya Adhyayan ke Vishay

Author(s): Anupam Jain, Sureshchandra Agarwal
Publisher: USA Federation of JAINA
Catalog link: https://jainqq.org/explore/210579/1

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jaina AgamoM meM nihita gaNitIya adhyayana ke viSaya anupama jaina* evaM surezacandra agravAla" jaina paramparA meM tIrthaMkaroM ke upadezoM evaM una upadezoM kI unake pradhAna ziSyoM ( gaNadharoM) dvArA kI gaI vyAkhyA ko samAhita karane vAle samasta zAstra Agama kI saMjJA se abhihita kiye jAte haiM / vartamAna meM upalabdha samasta AgamoM kI racanA 5vIM zatI I0 pU0 se 5 vIM zatI I0 ke madhya jaina paramparA ke variSTha AcAryoM dvArA bhagavAn mahAvIra ke upadezoM ke AdhAra para kI gayI hai| jainadharma kI donoM dhArAe~ ( digambara evaM zvetAmbara ) AgamoM kI nAmAvalI ke sandarbha meM ekamata nahIM haiN| jahA~ digambara paramparA SaDkhaMDAgama, kaSAya.prAbhRti evaM AcArya kundakunda ke sAhitya ko Agama ke rUpa meM mAnyatA detI hai, vahIM zvetAmbara paramparA devaddhigaNi kSamAzramaNa ( 453-456 I0 ) kI adhyakSatA meM sampanna vallabho vAcanA meM skhalita evaM vilupta hote hue paramparAgata jJAna ko AdhAra banAkara likhe gaye aMga, upAMga sAhitya ko Agama kI mAnyatA deto hai / ye aMga, upAMga ardhamAgadhI prAkRta bhASA meM nibaddha haiM / yahA~ para hama inhIM AgamoM ko Agama ke rUpa meM carcA kreNge| jaina Agama granthoM meM sthAnAMga ( ThANaM ) kA mahattvapUrNa sthAna hai| aMga sAhitya meM yaha tRtIya sthAna para AtA hai| mUla rUpa se lagabhaga 300 I0 pU0 meM sRjita evaM 5 vIM zatI I0 meM apane vartamAna rUpa meM saMkalita isa aMga ke dasaveM adhyAya meM nihita 100vIM gAthA gaNitajJoM ko dRSTi se mahattvapUrNa hai| isa gAthA se hameM gaNita ke antargata adhyayana ke viSayoM kI jAnakArI milatI hai| parokSa rUpa se yaha mAnA jA sakatA hai ki ye viSaya Agama meM bhI upalabdha hoMge, kyoMki tIrthaMkara mahAvIra ko saMkhyAjJAna kA vizeSajJa mAnA gayA hai evaM Agama grantha unake paraMparAgata jJAna ke saMkalana mAtra haiN| sthAnAMgasUtra meM upalabdha yaha gAthA sthAnAMga ke vividha mudrita saMskaraNoM meM nimna prakAra pAI jAtI hai| dasa vidhe saMkhANe paNNatte taM jahA parikammaM vavahAro rajju rAsI kalAsavaNNe ya / jAvaMtAvati vaggo ghaNo ya (ta) taha vaggavaggo vi (kappo pa0 t-1)|| uparyukta rUpa ke atirikta kaI gaNita itihAsajJoM ne ise nimna rUpa meM uddhRta kiyA hai| parikammaM vavahAro rajju rAsI kalAsavanne ( kalAsavaNNe ) yA jAvaMtAvati vaggo ghano tataha vagga vaggo vikappo ta / -(2) * vyAkhyAtA (gaNita) zAsakIya mahAvidyAlaya, thyAvarA ( rAjagar3ha ) ma0 pra0 465674 / *rIDara, gaNita vibhAga, uccazikSA saMsthAna, meraTha, vi0vi0 meraTha (u0 pra0) 1. gaNitasArasaMgraha-maMgalAcaraNa 1/1, pR0 1 / 2. ThANaM pR0 926 10.100 / -

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76 anupama jaina evaM surezacandra agravAla (2) isa rUpa meM gAthA ko datta', jaina evaM upAdhyAya ne uddhRta kiyA hai jabaki kApaDiyA' ne ise nimna rUpa meM uddhRta kiyA hai| parikamma (1) vavahAro, (2) rajju, (3) rAsI, (4) kalAsavanne, (5) ya / jAvaMtavati, (6) vaggo, (7) ghaNo (8) ta taha vaggavaggo (9) vi kappota / / 3 / / ThANaM" meM (1) kI saMskRta chAyA nimna prakAra dI gaI hai| parikarma vyavahAraH rajju rAziH kalAsavarNa ca / yAvat tAvat iti vargaH ghanazca tathA vargavargopi // kalpazca // 4 // sthAnAMga kI isa gAthA kI vartamAna meM upalabdha sarvaprathama vyAkhyA abhayadeva sUri (10vIM zatI I0) dvArA kI gii| sthAnAMga kI TIkA meM uparyukta gAthA meM Aye viSayoM kA artha spaSTa karate huye unhoMne nirdhArita kiyA ki : 1. parikammaM = saMkalana Adi / 2. vavahAro -zreNI vyavahAra yA pATI gaNita / 3. rajju samatala jyAmiti / 4. rAso = annoM kI DherI / 5. kalAsavaNNe - prAkRtika saMkhyAoM kA guNana yA saMkalana / 6. vaggo . = vrg| 7. dhaNo = dhana / 8. vaggavaggo - caturthaghAta / 9. kappo = krakacikA vyavahAra / datta' ( 1929 ) ne lagabhaga 900 varSoM ke uparAnta upayukta vyAkhyA ko apUrNa evaM ekAMgI ghoSita karate hue apanI vyAkhyA prastuta kii| datta ke samaya meM bhI jaina gaNita kA jJAna atyanta prAraMbhika thA evaM gaNitIya dRSTi se mahattvapUrNa, vartamAna meM upalabdha grantha usa samaya taka aprakAzita evaM ajJAta the tathApi unakI vyAkhyA abhayadevasUri kI vyAkhyA kI apekSA tarkasaMgata pratIta hotI hai / unhoMne uparyukta dasa zabdoM kI vyAkhyA nimna prakAra dii| 1. dekheM saM0--3, pR0 119 / 2. dekheM saM0-8, pR0 37 inhoMne kalAsavaNNo ke sthAna para "kalAsavanne" pATha liyA hai| 3. dekheM saM-11 pR0 26 / ( Apane vikappo ta ko vikappota rUpa meM likhA hai| ina donoM pAThAntaroM se koI antara nahIM pdd'taa| jabaki (1) evaM (2) ke pAThoM meM......."vi // 'kappo ya' tathA 'vikappo ta' kA aMtara draSTavya hai| 4. dekheM saM0-10, pR0 12 / 5. ThANaM, pR0 926 / 6. dekheM saM0 3, pR0 119-122 /

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jaina AgamoM meM nihita gaNitIya adhyayana ke viSaya 77 1. aMka gaNita ke parikarma ( Fundamental Operation ) 2. aMka gaNita ke vyavahAra ( Subject of Treatment ) 3. rekhAgaNita ( Geometry ) 4. rAziyoM kA Ayatana Adi nikAlanA ( Mensuration of Solid bodies ) 5. bhinna ( Fraction ) 6. sarala samIkaraNa ( Simple Equation ) 7. varga samIkaraNa (Quadratic Equation ) 8. ghana samIkaraNa ( Cubic Equation ) 9. caturtha ghAta samoraNa ( Biquadratic Equation ) 10. vikalpa gaNita yA kramacaya-saMcaya ( Combination & Permutation ) datta dvArA viSaya kI vyApaka rUpa se samIkSA kiye jAne ke uparAMta sarvaprathama kApar3iyA ( 1937) ne isa viSaya kA sparza kiyA kintu nirNaya hetu atirikta sAmagrI prAcIna jaina gaNitIya granthoM Adi ke abhAva meM Apane apanA nirNaya surakSita rakhA / Apane likhA ki :. It is extremely difficult to reconcile these two views especially when we have at present neither any acess to a commentary prior to the one mentioned above nor to any mathematical works of Jaina authorship which is earlier to Ganita Sara Samgraha. So under these circumstances I shall be excused if I reserve this matter for further research.' AyaMgara ( 1967)2 upAdhyAya ( 1971 )3 agravAla ( 1972 )4 jaina ( lakSmIcaMda) ( 1980) ne apanI kRtiyoM/lekhoM meM isa viSaya kA UhApoha kiyA hai| sthAnAMgasUtra ke vigata 2-3 dazakoM meM prakAzita aneka saTIka saMskaraNoM meM abhayadevasUri kI hI mAnyatA kA poSaNa kiyA gayA hai / jaina vizva bhAratI, lADanUM se prakAzita saMskaraNa meM 3 pRSThIya vistRta pariziSTa meM isa viSaya kI vivecanA kI gaI hai kintu vaha bhI paraMparAnurUpa hI hai / hama yahA~ kramika rUpa se parikarma, vyavahAra Adi zabdoM kI adyAvadhi prakAzita vyAkhyAoM kI samIkSA kara niSkarSa nikAlane kA prayAsa kreNge| parikamma (saM0 parikarma) parikriyate asmita iti parikarmaH / arthAt jisameM gaNita kI mUla kriyA sampanna kI jAye use parikarma kahate haiN| parikarma zabda jaina vAGmaya ke liye nayA nahIM hai| aMga sAhitya ke antargata dRSTivAda aMga ( 12vAM aMga ) kA eka bheda parikarma hai| A0 kandakunda (dvitIya-tRtIya zatI I0) 1. dekheM saM0 10, pR013 / 2. dekheM saM0-13, pR0 25-27 / 3. dekheM saM0-11, pR0 26 / 4. dekheM saM0-1, pR0 30-57 / 5. dekheM saM0-8, pR0 37-41, 42 / 6. dekheM saM0-1, pR0 32 /

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78 anupama jaina evaM surezacandra agravAla ne SaTkhaNDAgama ke prathama tIna adhyAyoM para 12000 zloka pramANa parikarma nAmaka TIkA likhI thii| vIrasena ( 826 I0) kRta dhavalA meM 'pariyamma suttaM' nAmaka grantha kA gaNita grantha ke rUpa meM anekazaH ullekha haA hai| mahAvIrAcArya (850 I0) kRta gaNitasArasaMgraha kA eka adhyAya bhI parikarma vyavahAra hai jisameM aSTa parikarmoM kI carcA hai|' yadyapi brahmagupta ( 628 I0 ) ne 20 parikarmoM kA ullekha kiyA hai| tathApi bhAratIya gaNitajJoM ne maulika parikarma 8 hI mAne haiM jo ki brahmagupta ke nimnAMkita 20 parikarmoM meM se prathama 8 haiN| 1. saMkalana ( jor3a) 9-13. pA~ca jAtiyA~ ( bhinna saMbaMdhI) 2. vyakalana ( ghaTAnA) 14. rAzika 3. guNana 15. vyasta rAzika 4. bhAga 16. paMca rAzika 5. varga 17. sapta rAzika 6. vargamUla 18. nava rAzika 7. dhana 19. ekAdaza rAzika 8. ghanamUla 20. bhANDapratibhANDa vastutaH mUlaparikarma to saMkalana evaM vyakalana hI hai| anya to unase vikasita kiye jA sakate haiN| misra, yUnAna evaM arabavAsiyoM ne dviguNIkaraNa evaM ardhIkaraNa ko bhI maulika parikarma mAnA hai| kintu bhAratavAsiyoM ne nahIM mAnA hai, kyoMki dAzamika sthAna mAna paddhati se bhijJa logoM ke lie ina parikarmoM kA koI mahattva nahIM hai| abhidhAna rAjendra koza meM cuNi ko uddhRta karate hue likhA gayA hai ki parikarma gaNita kI vaha mUlabhUta kriyA hai jo ki vidyArthI ko vijJAna ke zeSa evaM vAstavika bhAga meM praveza ke yogya banAtI hai| inakI saMkhyA 16 hai / 3 bhAratIya gaNitajJoM ke liye ye parikarma itane sarala evaM sahaja the ki uccastarIya granthoM meM inakA koI vizeSa vivaraNa nahIM miltaa| iso tathya ke AdhAra para datta mahodaya ne likhA hai ki ina sAdhAraNa parikarmoM meM se adhikAMza kA ullekha siddhAMta granthoM meM nahIM miltaa| agravAla ne likhA hai ki "isase yaha pratIta hotA hai ki gaNita kI mUla prakriyAyeM cAra hI mAnI gaI hai-saMkalana, vyakalana, gaNana evaM bhajana / ina cAroM kriyAoM ke AdhAra para hI parikarmASTaka kA gaNita vikasita huA hai| uparokta vivecana se spaSTa hai parikamma kA artha gaNita ko mUlabhUta prakriyAyeM hI haiM evaM parikamma zabda kA Azaya aMkagaNita ke parikarma se hI hai| 1. Apane atyaMta sarala hone ke kAraNa saMkalana evaM vyakalana kI vidhiyoM kI carcA nahIM kI hai| 2. dekheM saM0-4, pR0 118 / 3. dekheM saM0-3, pR. 24 / 4. dekheM saM0-1, pR0 33 /

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jaina AgamoM meM nihita gaNitIya adhyayana ke viSaya 79 2. vavahAro ( saM0 vyavahAra ) : isa zabda kI vyAkhyA abhayadevasUri ne zreNI vyavahAra Adi pATIgaNita ke rUpa meM tathA datta mahodaya ne aMkagaNita ke vyavahAra rUpa meM kI hai| brahmagupta ne vyavahAra ke 8 prakAra batAye haiN| 1. mizraka vyavahAra, 5. citi vyavahAra, 2. zreNI vyavahAra, 6.krakacikA vyavahAra, 3. kSetra vyavahAra, 7. rAzi vyavahAra, 4. khAta vyavahAra, 8. chAyA vyavahAra mahAvIrAcArya ke gaNitasArasaMgraha meM bhI sabhI prakaraNa upalabdha haiM usase inakI viSayavastu kA sugamatA se nirdhAraNa kiyA jA sakatA hai| zreNI vyavahAra gaNitake kSetra meM jaina-matAvalambiyoM kA lAghava zlAghanIya hai tiloyapaNNatti evaM dhavalA ke sAtha hI trilokasAra ke antaHsAkSya ke anusAra prAcIna kAla meM mAtra dhArAoM para hI eka vistRta grantha upalabdha thaa| phalataH vibhinna vyavahAroM meM zreNI vyavahAra ke pramukha hone ke kAraNa zabda ke spaSTIkaraNa meM usako pramukhatA dete hue likhanA svAbhAvika pratIta hotA hai| pATIgaNita zabda to jaina gaNita sahita sampUrNa bhAratIya gaNita meM pracalita hai / zrIdhara ( 750 I0 ) kRta pATIgaNita, gaNitasAra, gaNitatilaka; bhAskara (1150 I0) kRta lIlAvatI nArAyaNa (1356 I0) kRta gaNitakaumudI; munIzvara ( 1658 I0 ) kRta pATIsAra isa viSaya ke prasiddha grantha haiN| ina granthoM meM bIsa parikarma evaM ATha vyavahAroM kA varNana hai| ataH kahA jA sakatA hai ki gaNitasArasaMgraha kI sampUrNa sAmagrI parikarma evaM vyavahAra ina donoM meM hI samAhita hai| vartamAna meM vyavahAragaNita zabda kA prayoga pATIgaNita kI usa prakriyA ke lie hotA hai jisameM guNaka saMkhyA ke yogAtmaka khaNDa karake guNya se guNA kiyA jaaye| jisa samaya bar3I saMkhyAoM kI guNanavidhi kA pracalana nahIM huA thA usa samaya guNaka saMkhyA ko kaI samatulya khaNDoM meM vibhA thaka-pathaka gaNA karake usa gaNanaphala ko joDa diyA jAtA thA. kinta jainoM kI guNana kriyA meM dakSatA evaM gaNitIya jJAna kI paripakvatA ko dRSTigata karate yaha anumAna karanA nirarthaka hI hai ki vyavahAra gaNita gaNana ke isa sandarbha meM AyA ho sakatA hai| upAdhyAya, vyavahAra gaNita kA artha Practical Arithmatics karate haiN| jaba ki Srinivas Iengar ne feat & fi "Vyavahar means application of arithmatics to concrete problems (Applied Mathematics)' saMkSepa meM vavahAro kA artha pATIgaNita ke vyavahAra karanA upayukta hai| 3. rajju :-isa pAribhASika zabda kA viSaya-sUcI meM upayoga atyanta mahatvapUrNa hai| abhayadevasUri ne isakA artha rassI dvArA kI jAne vAlI gaNanAoM se sambandhita arthAt samatala jyAmiti se kiyA thA / 5 datta ne isako kiMcit vistRta karate hue isakI paridhi meM sampUrNa 1. zreNInoM vyavahAra vigere pATIgaNita prasiddha aneka prakAre vyavahAra gaNitecha / 2. trilokasAra, gAthA-91 / 3. dhArA kA artha Sequence hai / 4. dekheM saM0-13, pR0 32 5. rAjavar3e je saMkhyAna te rajju kahavAya che-te kSetra gaNita ch|

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80 anupama jaina evaM surezacandra agravAla jyAmiti ko samAhita kara liyaa| agravAla ne likhA hai ki ta kA abhiprAya kSetragaNita se hai| kSetragaNita meM palya sAgara Adi kA jJAna apekSita hai| Arambha meM isa gaNita ko sImA kevala kSetra paribhASAoM taka hI sImita thI para vikasita hote-hote yaha samatala jyAmiti ke rUpa meM vRddhigata ho gaI hai|'' AyaMgara ke anusAra : Rajju is the ancient Hindu name for geometry which was called Sulva in the Vedic literature. arthAt rajju rekhAgaNita kI prAcIna hindu saMjJA hai jo ki vaidika kAla meM zulva nAma se jAnI jAto thii| kAtyAyana zulvasUtra meM jyAmiti ko rajju samAsa kahA gayA hai / pro0 lakSmIcanda jaina ne rajju ke saMdarbha meM likhA hai :-'isa prakAra rajju ke upayoga kA abhiprAya jaina sAhitya meM zulva granthoM se bilkula bhinna hai / rajju kA jaina sAhitya meM mAna rAziparaka siddhAntoM se nikAlA gayA hai aura usase na kevala loka ke AyAma nirUpita kiye gaye haiM kintu yaha mApa bhI diyA gayA hai ki ukta raikhika mApa meM kitane pradezoM kI rAzi samAI huI hai| usakA mambandha jagazreNI se jagapratara evaM dhanaloka se bhI hai|" ___ Apane saMdarbhita gAthA ke viSayoM kI vyAkhyA karate hue rajju kA artha vizva mApa kI ikAI likhA hai| __ vastutaH usa sthiti meM jabaki vyavahAra ke 8 bhedoM meM se eka bheda kSetra vyavahAra bhI hai aura usameM jyAmiti kA viSaya samAhita ho jAtA hai evaM khAta, citi, rAzi evaM krAka cika, vyavahAra ke antargata menzurezana ( Mensuration. ) kA viSaya bhI A jAtA hai| taba kSetragaNita ke liye svatantra adhyAya kI itanI AvazyakatA nahIM raha gaI jitanI loka ke pramANa vistAra Adi se sambaddha jaTilatAoM, asaMkhyAta viSayaka rAziyoM ke gaNita se sambandhita viSaya kii| ina viSayoM kA vyApaka evaM vyavasthita vivecana jaina granthoM meM milatA hai| jabaki yaha anya kisI samakAlIna grantha meM nahIM miltaa| vividha dhArmika-arddhadhArmika jaina viSayoM ke spaSTIkaraNa meM inakI aparihArya AvazyakatA varaNAnuyoga athavA dravyAnuyoga ke kisI bhI grantha meM dekhI jA sakatI hai| etadviSayaka gaNita kI jana jagat meM pratiSThA kA Akalana isa bAta se bhI kiyA jA sakatA hai ki hemarAja ne saMkhyAta, asaMkhyAta evaM ananta viSayaka gaNita para 17vIM zatAbdI meM gaNitasAra nAmaka svatantra grantha kI racanA kI / asaMkhyAta evaM ananta ke jaTila viSayoM ko parikarma ke antargata mAnanA kiMcit bhI ucita nahIM, kyoMki parikarma meM to gaNita ( laukika gaNita ) kI mUlabhUta kriyAyeM AtI haiN| 1. dekheM saM0-1. pR0 36 / 2. dekheM saM.-13 pR0 26 / 3. rajju samAsa vakSyAma, kAtyAyana zulbasUtra 1.1 / 4. dekheM saM0-8, pR0 45 /

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jaina AgamoM meM nihita gaNitIya adhyayana ke viSaya rajju, palya Adi kI gaNanA sAmAnya parikarmoM se asaMbhava hai| dhanAMgula, jagazreNI evaM pralya ko apane sAmAnya artha meM prayukta karane parapalyopama ke arhaccheda asaMkhyAta jagazreNI = 7 rAjU = dhanAMgula yadi palyopama P hoto log2p/asaMkhyAta rAjU- dhanAMgula spaSTataH rAjU ( rajju ) eka asaMkhyAta rAzi' huii| asaMkhyAta saMkendro valayAkAra vRttoM kI zRMkhalA meM antima svayaMbhUramaNa dvIpa kA vyAsa rajju batAyA gayA hai| phalataH isa vidhi se bhI isakA mAna asaMkhyAta hI milatA hai| pro0 ghAsIrAma jaina ne AiMsTIna ke vivAdAspada saMkhyAta phailane vAle loka kI trijyA ke AdhAra se prApta ghanaphala kI loka ke Ayatana sa tulanA karake rajju ( rAjU ) kA mAna prApta kiyaa| yaha mAna 1.45 x 1021 mIla evaM 1.63 x 1021 mIla hai / eka anya rIti se yaha mAna 1.154101 mIla prApta hotA hai| kintu ghAsIrAma jaina dvArA uddhRta mAna apUrNa hai, kyoMki ye sabhI kalpanAoM evaM abhidhAraNAoM para Azrita haiN| rajju ko to asaMkhyAta rUpa meM ho svIkAra karanA upayukta hai| yaha svIkAra karane meM kiMcit bhI saMkoca nahIM honA cAhiye ki rajju zabda zulva kAla ke turanta bAda se bhAratIya gaNita meM kSetragaNita ke sandarbha meM AyA hai| bhale hI vaha mApane vAlI rassI rahA ho yA mApana kriyaa| yaha zabda rekhAgaNita tathA tribhuja, caturbhuja kI cAroM bhujAoM ke yoga ke rUpa meM bhI prayukta huA hai| tathApi yaha Avazyaka nahIM hai ki yaha isa gAthA yA siddhAnta granthoM meM bhI isI artha meM AyA ho| isa viSaya ke vistAra meM na jAkara hama yahA~ itanA kahanA , ucita samajhate haiM ki prastuta gAthA meM rajju zIrSaka hameM usa viSaya kI ora iMgita karatA hai jisameM loka ke vistAra, loka saMracanA, jaghanya parIta evaM jaghanya yukta evaM jaghanya asaMkhyAta kA gaNita samAhita hai| yadi hama yaha kaheM ki rajju kA pramANa lokottara pramANa kI ora iMgita karatA hai to anupayukta na hogaa| zabdoM ke artha kAla parivartana.viSaya parivartana. sandarbha parivartana se kitane badala jAte haiN| yaha viSaya bhASAvijJAna ke vettAoM hetu nayA nahIM hai| hamAre vicAra se rajju kI vyAkhyA meM abhayadeva evaM datta donoM hI asaphala rahe haiM evaM lakSmIcanda jaina ne sahI dizA kI ora saMketa kiyA hai| 1. dekheM saM0-6, pR0 22-23 / 2. dekheM saM0-5, pR0 92 / 3. dekhe saM0-11 pR0 215, 216 / 11

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anupama jaina evaM surezacandra agravAla rAsI ( saM0 rAzi): isa zabda kI vyAkhyA meM abhayadeva evaM datta meM gambhIra matabheda hai| abhayadeva ne rAsI kA artha annoM kI DherI kiyA hai jabaki datta ne unakI vyAkhyA ko pUrNataH nirasta karate hue likhA 'The term rasi appears in later Hindu works, except this last mentioned one (G. S. S.) and means measurement of mounds of grains. But I do not think that it has been used in the same sense in the cononical works for measurement of heaps of grain has never been given any prominence in later mathematical works and indeed it does not deserves any prominance. arthAt rAzi zabda gaNitasAra saMgraha ke bAda ke sabhI granthoM meM annoM kI DherI ke mApana ke sandarbha meM AyA hai kintu maiM nahIM samajhatA ki yaha prAcIna siddhAnta-granthoM meM bhI isI sandarbha meM prayukta huA hogaa| annoM kI DherI ke mApana ko bAda ke granthoM meM bhI koI mahattva nahIM diyA gayA aura na yaha diyA jAne yogya hai| unhoMne Age likhA hai ki rAzi kA artha annoM kI DherI saMkucita hai evaM yaha zabda vyApaka rUpa se jyAmiti kI ora iMgita karatA hai| paravartI hindU gaNita granthoM meM yaha prakaraNa khAta vyavahAra ke antargata AyA hai evaM rAzi isakA eka choTA bhAga hai| pro0 lakSmIcanda jaina ne eka sthAna para rAsI kA artha samuccaya/annoM kI DherI likhA hai| hamAre vicAra meM sUri evaM datta donoM ke artha samIcIna nahIM haiN| samuccaya artha aneka kAraNoM se jyAdA upayukta lagatA hai| rAzi zabda kI vyAkhyA karate hae jaina ne likhA hai ki isa pAribhASika zabda para gaNita itihAsajJoM ne dhyAna nahIM diyaa| rAzi ke abhivatta-seTa (Set) jaise hI haiN|4 rAzi ke paryAyavAcI zabda samUha, ogha, puMja, vRnda, sampAta, samudAya, piNDa, avazeSa tathA sAmAnya haiM / jaina karma evaM darzana sambandhI sAhitya meM vorasena (828 I0 lagabhaga) taka isakA upayoga atyadhika hone lagA thA / isakA upayoga paravartI hindU gaNita granthoM meM trairAzika paMcarAzi ke rUpa meM bhI huA hai / abhidhAna rAjendrakoSa meM rAzi kA prayoga samUha, ogha, puMja, sAmAnya vastuoM kA saMgraha, zAli, dhAnyarAzi, jIva, ajIva rAzi, saMkhyAna rAzi ke rUpa meM batalAyA gayA hai| tiloyapaNNatti (473-609) I0 meM sRSTi vijJAna ke sandarbha meM prayukta samuccayoM hetu rAzi kA anekazaH upayoga huA hai| kisI bhI rAzi ke avayava kA usI rAzi se sadasyatA viSayaka sambandha hotA hai| rAzi kI saMracanA karane vAle 6 dravya nimna haiM : 1. jIva, 2. pudgala paramANu, 3. dharma 4. adharma 5. AkAza 6. kAlANu 1. dhAnya bigerano Dhagalo tenA viSaya vAlaM saMkhyAna te rAzi paTimAM rAzivyavahAra nAma thI prasiddha cha / 2. dekheM saM0-3, pR0 120 / 3. dekheM saM0-1, pR0 35 / 4. dekheM saM0-8, pR0 43 /

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jaina AgamoM meM nihita gaNitIya adhyayana ke viSaya 83 rAzi racane vAlI ikAiyA~ samaya, pradeza, avibhAgI, praticcheda, varga evaM sampradAyabaddha haiM / apane lekha' meM jaina ne jainAgamoM evaM usakI TIkAoM meM pAye jAne vAle samuccayoM ke prakAra, udAharaNa likhane kI vidhi saMketAtmaka vidhi, paddhati, una para sampAdita kI jAne vAlI vividha saMkriyAoM kA vivaraNa diyA hai| isase spaSTa hai ki prAcIna jainagaNita meM Adhunika samuccaya gaNita ke bIja vidyamAna the kintu samucita pAribhASika zabdAvalI ( Terminology ) ke abhAva Adhunika cintaka use hRdayaMgama nahIM kara pA rahe haiN| prAcIna zabdAvalI evaM etadviSayaka vartamAna zabdAvalI meM atyadhika matabheda hai / niSkarSataH yaha kahA jA sakatA hai ki rAzi prayukta huA hai / isa tathya ko asvIkAra karane para kSetra, karma siddhAnta kA gaNita, upekSita raha jAtA hai / karatA hai / zabda sandarbhita gAthA meM samuccaya ke artha meM jaina gaNita kA eka ativiziSTa evaM advitIya yaha tathya bhI hamArI vicAradhArA ko puSTa 5. kalAsavanne (saM0 kalAsavarNa ) - bhinnoM se sambaddha gaNita ko vyakta karane vAlA yaha zabda nirvivAda hai kyoMki vakSAlI hastalipi se mahAvIrAcArya ( 850 I0 ) paryanta yaha zabda mAtra - isI artha meM prayukta huA hai / jo saMkhyA pUrNa na ho aMzoM meM ho use samAna karanA kalA savarNa kahalAtA hai / ise samacchedokaraNa, savarNana aura samaccheda vidhi bho kahate haiM / kalA zabda kA prayoga tiloyapaNatti meM bhinna ke artha meM huA hai / jaise eka baTe tIna ko "ekkalA tivihattA se vyakta kiyA gayA hai, ataH kalA savarNa viSaya ke antargata bhinnoM para aSTa parikarma, bhinnAtmaka zreNiyoM kA saMkalana prahasana evaM vividha jAtiyoM kA vivecana A jAtA hai / 6. jAvaMtAvati (saM0 yAvat tAvat ) - ise guNAkAra bhI kahA jAtA hai / abhayadevasUri ne isakI vyAkhyA prAkRtika saMkhyAoM kA guNana yA saMkalana ke rUpa meM kii| isakA nirvacana vyavahAra rUpa meM karate hue batAyA gayA ki yadi pahale jo saMkhyA socI jAtI hai use gaccha, icchAnusAra guNana karane vAlI saMkhyA vAccha yA iSTa saMkhyA kaheM to pahale gaccha saMkhyA ko iSTa saMkhyA se guNA karate haiM, usameM phira iSTa ko milAte haiM, usa saMkhyA ko punaH gaccha se guNA karate haiM / tadanantara guNanaphala meM iSTa ke dugune se bhAga dene para gaccha kA yoga A jAtA hai / arthAt yadi gaccha = n, iSTa = x to prAkRtika saMkhyAoM kA yoga / n(nx+x) 2x S= isI ko vivicchita, yAdRcchA, vAcchA, yAvat tAvat rAzi kahate haiM / isa sampUrNa kriyA ko yAvat tAvat kahate haiM / jaina ne likhA hai ki 'isa zabda kA prayoga una sImAoM ko vyakta karatA hai jina pariNAmoM ko vistRta karanA hotA hai; athavA sarala samIkaraNa kI racanA karanI hotI hai| isakA artha jahA~ 1. dekheM saM0-9, pR0 1 / 2. tiloyapaNNatti - 2 / 112 / 3. 'jAvaM tAvati vA guNA kaTauti vA egaTA' sthAnAMga vRtti - patra 471 /

Page #10
anupama jaina evaM surezacandra agravAla taka vahA~ taka bhI hotA hai|" .... hindU bIjagaNita meM isa pAribhASika zabda kA bar3A mahatva hai. isa zabda kA udbhava yA to yadRcchA arthAt vivakSita rAzi se athavA vAcchA ( arthAt icchita ) rAzi se huA hai ? vakSAlI hastalipi meM isakA prayoga kUTasthiti niyama ko dhvanita karane hetu huA hai| yaha bhI sujhAva prApta huA hai ki isakA sambandha anirdhata (Indeterminate) athavA aparibhASita athavA aparibhASita ikAiyoM kI rAzi se bhI hai / isa prakAra jAvaM tAvaM se eka yaha artha bhI dhvanita hotA pratIta hotA hai ki koI bhI saMkhyA ko parimita sImA se lekara utkRSTa saMkhyeya taka le jAte haiM to jaghanya parIta asaMkhyeya ke kevala eka kama hotA hai|' AyaMgara (1967) bhI isa zabda kI vyAkhyA karate samaya jaTilatA kA anubhava karate haiM ve likhate haiM ki The Word Yavat Tavat is the word for the unknown quantity in ancient Hindu Mathematics and provides the algebric symbol Ya(at). It is difficult to account for this except by saying that it means the Science of Algebra in however redimentom form it may have existed. Besides the problem on indices in a general form. This subject may have included solutions of the problems of Arithmetics by assumi g unknown quantities simple Summations. S agravAla ne apane zodha-prabaMdha meM isa gAthA ke 9 viSayoM kI vivecanA to kI hai kintu yAvat tAvat ko sparza bhI nahIM kiyA / Akhira kyoM ? datta mahodaya ne isa gAthA ke prathama 5 zabdoM kI abhayadevari dvArA dI gaI vyAkhyAyeM katipaya godhanoM sahita svIkAra kara lI kinta bAda ke pA~ca zabdoM jAvatAvati vaggo. ghaNa evaM vikappota kI vyAkhyAoM ko pUrNataH nirasta karate hue likhA hai ki In the identification of the remaining terms (last five). The commentator is not only of no help but is, on the other hand, positively misleading.5 - datta mahodaya ne isa zabda kI vyAkhyA karate hue Age likhA hai ki : I venture to presume that the term Yavat-Tavat is connected with the rule of False position which in the early stage of Science of Algebra in every country, was the only method of solving linear equations. It is interesting to find that this method was once given so much importance in Hindu Algebra That the section dealing with it was named after it.& 1. dekheM saM08, pR0 37 / 2. vahIM pR046 / 3. dekheM saM0-13, pR0 26 / 4. dekheM saM0-10, pR0 48,49 / 5. dekheM saM0-3, pR0 122 / 6. dekheM saM0-3, pR0 122 /

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jaina AgamoM meM nihita gaNitIya adhyayana ke viSaya isa prakAra Apane yAvat tAvat ko sarala samIkaraNa se sambaddha kiyaa| jo ucita hI hai| kyoMki S= n(x+x) meM se x kAmana lekara aMza evaM hara meM se kATa dene para yaha banatA hai jo ki prAkRtika saMkhyAoM ke yoga kA sUtra hai| S = (n) (n + i) yaha viSaya to parikarma ke antargata A hI jAtA hai| ataH datta kI vyAkhyA vicAra adhika tarkasaMgata hai| 7-8-9 vaggo, ghaNo, vaggavaggo (varga, ghana evaM caturtha ghAta ): abhidhAna rAjendra meM ina tInoM zabdoM kI vyAkhyA Agamika uddharaNoM sahita dI gaI hai jahA~ inake artha kramazaH varga karanA, ghana karanA evaM varga kA varga karanA hai| agravAla ne bhI apane zodhaprabaMdha meM varga ke ullekhoM ko saMkalita kiyA hai|' una sabase svAbhAvika rUpa meM yaha pratIta hotA hai ki ye zabda nizcita rUpa se vartamAna meM pracalita arthoM ( jyAmitIya artha nahIM ) meM hI prayukta huye haiN| kintu yahA~ bhI hama apane pUrva tarka ko uddhRta karate haiM jaba varga evaM ghana karanA ye donoM kriyAyeM mUla parikarmoM meM A jAtI haiM taba unheM navIna viSaya ke rUpa meM pratiSThita karane kA kyA aucitya ? punaH anuyogadvAra sUtra, uttarAdhyayana sUtra Adi prAcIna granthoM meM jaba ghAtAMkoM ke siddhAnta upalabdha haiM evaM unameM 12vIM ghAta taka ke prayoga nirdiSTa haiM-taba caturtha ghAta ko hI kyoM vizeSa mahattva diyA gayA ? dhavalA meM nihita vagita saMgita kI prakriyA meM 256 taka ko ghAta A jAtI hai| caturtha ghAta nikAlane kI kriyA varga karane kI kriyA ko punarAvRtti ke samatulya hai| jainAcArya varga evaM ghana karane kI apekSA adhika jaTila kriyAoM vargamUla evaM ghanamUla nikAlane meM vizeSa siddhahasta the| yadi varga evaM dhana ko svataMtra viSaya kI mAnyatA dI gaI to unheM bhI dI jAnI cAhiye / lekina aisA nahIM kiyA gayA / Akhira kyoM ? saMbhavataH uparyukta praznoM evaM anya kAraNoM ko hI dRSTigata karate hue datta ne bhI likhA ki 'I have no doubt in my mind that Varga' refers to quadratic equation 'Ghan' refers to cubic equation and Vargavarga' to biquadratic equation'. yadyapi Aja ke upalabdha AgamoM meM hameM dhana samIkaraNa evaM caturthaghAta samIkaraNa ke spaSTa ullekha nahIM milate kintu vartamAna meM anupalabdha granthoM meM unakA pAyA jAnA asvAbhAvika nahIM hai / Agamika jJAna ke AdhAra para racita gaNitasAra saMgraha meM to aise ullekha pracura haiM ataH datta kA kathana asatya nahIM kahA jA sakatA hai / AyaMgara evaM jaina ne bhI unakA samarthana kiyA hai| 1. anuyogadvAra sUtra-142 / / 2. dhavalA, pustk-3| 3. dekheM saM0-3, pR0 172 / 4. dekheM saM0 13, pR0 28 /

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86 anupama jaina evaM surezacandra agravAla 10.vikappota yA kappo (vikalpa yA kalpa)-pATha (1) ko svIkAra karate hue abhayadevasUri ne isakI vyAkhyA meM likhA hai ki isase lakar3I kI cirAI evaM pattharoM kI cinAI kA jJAna hotA hai|' pATIgaNita meM ise krakacikA vyavahAra kahate haiN| abhayadeva ne isako udAharaNa se bhI samajhAyA hai| sthAnAMgasUtra ke sabhI upalabdha saMskaraNoM meM hameM yahI pATha evaM artha milatA hai kintu datta, kApar3iyA, upAdhyAya, agravAla evaM jaina Adi sabhI ne ise (2) rUpa meM uddhRta kiyA hai evaM isakA artha vikalpa (gaNita) kiyA hai| vikalpa evaM bhaMga jaina sAhitya meM kramacaya evaM saMcaya ke liye Aye haiM / jaina granthoM meM isa viSaya ko vizuddhatA evaM viziSTatA ke sAtha pratipAdita kiyA gayA hai| krakacikA vyavahAra, vyavahAroM kA hI eka bheda hone tathA vikalpa ( athavA bhaMga ) gaNita ke viSaya kA dArzanika viSayoM kI vyAkhyA meM pracuratA evaM atyanta svAbhAvika rUpa se prayoga, yaha mAnane ko vivaza karatA hai ki vikalpagaNita jainAcAryoM meM hI nahIM apitu prabuddha zrAvakoM ke jIvana meM bhI raca-paca gayA thA, tabhI to viSaya ke ulajhate hI ve vikalpagaNita ke mAdhyama se use samajhAne lagate the| aisI sthiti meM vikalpagaNita ko gaNita viSayoM kI sUcI meM bhI samAhita na karanA samIcIna nahIM kahA jA sktaa| ullekhanIya hai ki vikalpa gaNita koI sarala viSaya nahIM thA tabhI to anya samakAlIna logoM ne isakA itanA upayoga nahIM kiyaa| jaina hI isameM lAghava ko prApta the| ataH vikappota kA artha vikalpa ( gaNita ) hI hai / viSaya ke samApana se pUrva viSaya se sambaddha katipaya anya mahatvapUrNa tathyoM kA ullekha bhI Avazyaka hai| Agama granthoM meM carcita gaNitIya viSayoM kI jAnakArI dene vAlI eka anya gAthA zIlAMka ( 9vIM za0 I0 ) ne sUtrakRtAMga kI TIkA meM puNDarIka zabda ke nikSepa ke avasara para uddhRta kI hai / gAthA nimnavat hai parikamma rajju rAsI vavahAre taha kalA savaNNe (savanne) ya / / 5 / / ' (pudgala ) jAvaM tAvaM ghaNe ya dhaNe vagga vaggavagge ya / ' TIkA ke sampAdaka mahodaya ne uparyukta gAthA kI saMskRta chANa nimna prakAra kI hai| parikammaM rajju, rAzi vyavahArastayA kalAsavarNazca / pudgalAH yAvattAvat bhavanti dhanaM ghanamUlaM vargaH vargamUlaM / / -(6) (5) isase spaSTa hai ki isa gAthA meM bhI viSayoM kI saMkhyA 10 hI hai kintu usameM sthAnAMga meM AI gAthA ke vikappota ke sthAna para puggala zabda AyA hai| arthAt yahA~ pudgala ko gaNita adhyayana kA viSaya mAnA gayA hai, vikalpa ko nahIM / zeSa nau prakAra sthAnAMga ke samAna hI haiM / 1. kalpacheda gaNita karavataNDe kASThAnuM chedana tenA viSayavAlu je gaNita se pATiyAM krAkaca vyavahAra kahevAya che ( sthaanaaNgvRtti)| 2. sUtrakRtAMga-zru taskandha-2, adhyAya-1, sUtra-154 / 3, dekheM saM0-3 10 120 / 4. ThANaM, pR0 994 /

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jaina AgamoM meM nihita gaNitIya adhyayana ke viSaya bosa ne apanI pustaka' meM uparyukta gAthA (6) ko uddhRta kiyA hai kintu usake AdhAra para nIce jo viSayoM kI sUcI banAyI hai usameM pudgala ko haTAkara vikalpa gaNita ko sammilita kara diyA hai athavA yaha kahA jAye ki sthAnAMga vAlI gAthA ke viSayoM ko de diyaa| isakA kyA kAraNa hai ? saMbhavataH truTivaza aisA huA hai| saMskRta chAyA ko dekhane se spaSTa hai ki gaNita adhyayana ke viSaya 11 haiM, arthAt parikarma, vyavahAra, rajju, rAzi, klAsavarNa, pudgala, yAvat tAvat, ghana, ghanamUla, varga, aura vargamUla / punaH draSTavya hai ki mUla gAthA (5) meM kahIM kucha aisA nahIM hai jo mUla zabda ko dhvanita karatA ho / datta ne bhI likhA hai There is nothing in the either form which could be informed a reference to roots (mula). Above all by that interpretation, he has made the number of topics for discussion to be eleven against the express injuction of the Canonical works that they are all together ten. So we shall reject the rendering of the verse (Sanskrit version).2 aba prazna yaha uThatA hai ki kyA pudgala ko gaNita adhyayana kA viSaya mAnA jAye ? isa saMdarbha meM datta mahodaya ne to spaSTa likhA hai ki Pudgala as a topic for discussion in mathematics is meaningless. 2 arthAt pudgala ko gaNita adhyayana kA viSaya svIkAra karanA nirarthaka hai| kintu vicAraNIya yaha hai ki yaha niSkarSa Apa ke dvArA taba diyA gayA thA jaba karma siddhAnta kA gaNita prakAza meM nahIM AyA thaa| usa samaya taka Relativity ke saMdarbha meM jainAcAryoM ke prayAsa bhI prakAzita nahIM huye the| Aja parivartita sthiti meM yaha niSkarSa itanI sugamatA se gale nahIM utaratA / kyoMki asaMkhyAta viSayaka gaNita, rAzi gaNita ( Set theory ) Adi kA mUla to pudgala hI hai / mApana kI paddhatiyA~ to yahIM se prArambha hotI haiN| eka tathya yaha bhI hai ki zIlAMka ne bhI to ise kisI prAcIna grantha se hI uddhRta kiyA hogaa| lekina samasyA yaha hai ki pudgala ko gaNita kA viSaya svIkAra karane para vikalpa chUTa jAtA hai| jabaki vikalpa to atyadhika evaM nirvikalpa rUpa se jaina granthoM meM AtA hai| yahAM hameM bRhatkalpa bhASya kI eka paMkti kucha madada karatI hai| "bhaMga gaNitAi gamika"4 malayagiri ne isakI vyAkhyA karate hue likhA hai ki bhaMga (vikalpa) evaM gaNita alagaalaga haiN| saMkSepa meM yaha viSaya vicAraNIya hai evaM abhI yaha nirNaya karanA upayukta nahIM hai ki pudgala ko gaNitIya adhyayana kA viSaya svIkAra kiyA jAye athavA nhiiN| sthAnAMgasUtra ke hI caturtha adhyAya meM etadviSayaka eka anya gAthA prApta hotI hai| gAthA nimnavat hai1. dekheM saM0-2, pR0 158 / 2. dekheM saM0-3, pR0 170 / 3. vahI, pR0 120 / 4. vRhatkalpa bhASya, 143 / 5. dekheM saM0 10, pR. XIII /

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88 anupama jaina evaM surezacandra agravAla cauvidhi saMkhANe paNNatte taM jahA | parikamma vavahAre rajju rAsI // '-7 isa gAthA para adyAvadhi kisI ne dhyAna nahIM diyA hai / eka hI grantha meM do prakAra ke ullekha kyoM haiM ? saMkhyAna ke cAra prakAra pichale pRSTha para uddhRta datta ke niSkarSa ke pratikUla haiN| kyA yahA~ saMkhyAna se koI bhinna artha dhvanita hotA hai ? athavA kyA yahA~ para iMgita saMkhyAna ke prakAra koI vizeSa guNa rakhate haiM ? isa viSaya para abhI aura vyApaka vicAra vimarza apekSita hai| 1. Agrawal, N. B. - 'gaNita evaM jyotiSa ke vikAsa meM jainAcAryoM kA yogadAna' AgarA vi. Lal vi0 meM prastuta zodha-prabandha 1972 / 2. Bose, D M. & - A Concise History of Sciences in India' Sen, S N I. N. S. A.--New Delhi. 1971 3. Dutt, B. B - 'The Jaina School of Mathematics' B. C. M. S. (Calcatta). 21 pp. 115-143, 1929 4. Dutt, B. B & - 'hindU gaNita zAstra kA itihAsa' (hindI saMskaraNa) anu0 DA0 kRpAzaMkara Singh A. N. zukla-u0 pra0 hindI grantha akAdamI, lakhanaU, 1967 / 5. Jain. G. R. 'Cosmology.Old & New' (Hindi Ed) Bhartiya Jnanpitha, New Delhi 1974. 6. Jain, L.C. 'tiloyapaNNatti kA gaNita' antargata jambaddIvapaNNattirAgate, jaina saMskRti saMrakSaka saMgha, zolApura 1950 / / 7. Jain, L. C. - 'Set Theory in Jaina School of Mathematics I. J. H. S. (Calcutta), 8-1, pp. 1-27. 1973 8. Jain, L. C. 'AgamoM meM nihita gaNitIya sAmagrI evaM usakA mUlyAMkana' 'tulasI pUjya' lADana pu0 35-74, 1980 9. Jain, L. C. - Exact Sciences from Jaina Sciences. Vol. I Rajasthan Prakrita Bharati, Jaipur 1983. 10. Kapadia, H. R. - Introduction of Gorilo Tilak' Gaek wad Oriental Series, Baroda 1937. 11. Upadhyaya,BL -- 'prAcIna bhAratIya gaNita' vijJAna bhAratI, dillI 1971 12. Shah, A L - 'jaina sAhitya kA bRhad itihAsa-bhAga 5 pA0 vi0 zodha-saMsthAna, vArANasI 1969 / 13. Srinivas, C P. - The History of Ancient Indian Mathematics National Iengar World Press Calcutta 1967. 14. - aMga suttANi-bhAga 1, jaina vizva bhAratI, lADana 1975 15. - - ThANaM (sthAnAMga sUtta) TIka, jaina vizva bhAratI, lADan 1980 16. - tilopapaNNatti-saTIka jaina saMskRti saMrakSaka saMgha, zolApura 1944 17. - - gaNitasAra saMgraha (hindI saMskaraNa) jaina saMskRti saMrakSaka saMgha, zolApura 1962 1. ThANaM 4, sUtra, 505, pR0 438 / Jain, L. C. -