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________________ : 546 : jaina sAhitya meM gANitika saMketana zrI jaina divAkara- smRti-grantha jaina sAhitya meM gANitika saMketana Mathematical Notations ma - DA0 mukuTa bihArIlAla agravAla, esa-sI0, pI-eca0 DI0 [jaina tattvavidyA meM 'gaNitAnuyoga' eka svatantra anuyoga (viSaya) hai / prAcIna jaina manISI AtmA-paramAtmA Adi viSayoM para gaNita ko bhASA meM kisa prakAra vizleSaNa karate the, unakI zailI, unake saMketana Adi ke prasiddha vidvAn tathA lekhaka DA0 agravAla kA yaha lekha eka naye DAlatA hai / ] sambandha meM gaNita ke viSaya para prakAza * pUrvAbhAsa - mAnavIya jIvana meM saMketa kI mahattA prAyaH dekhI jAtI haiM / bhASA ne jaba taka zabdoM kI pakar3a nahIM kI thI taba bhI abhivyakti (Expression ) hotI rahatI thI / yaha abhivyakti kevala saMketoM ke kAraNa hI thI- yaha sarvavidita hI hai| yadi kahA jAye ki bhASA kA janma hI saMketoM se huA hai to asaMgati na hogii| jIvana meM gaNita kA apanA viziSTa mahatva hai, kyoMki mAnava apanI A~kheM kholate hI gaNa ( ginanA) ke cakkara meM pha~sa jAtA hai / yaha cakkara itanA sarala to nahIM hai ki vaha AsAnI se samajha sake / parantu kucha aise sAdhana haiM jo isa kArya ko sarala banA dete haiM; ve haiN| gaNita saMketa arthAt gaNita sambandhI saMketa / isI gANitika sAMketikatA ke vikAsa para vicAra karanA apanA parama lakSyamaya karttavya hai / prayukta ye ve saMketa hote haiM jo kisI gaNita sambandhI kriyA ko vyakta karane meM, kisI gaNitIya rAzi ko darzAne meM athavA gaNita meM prayukta hone vAlI gaNitIya rAzi ko nirdiSTa karane ke lie kiye jAte haiM / yathA a: b meM, bhAga kA cihna ( : ) nirdiSTa karatA hai ki a meM b kA bhAga denA hai | a b meM asamatA kA cihna
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________________ zrI jaina divAkara smRti grantha saMkhyA ke anta meM likhA jAtA thaa| jaise 4 aura 9 jor3ane hote the to isa prakAra likhA jAtA thA -- ha 1 1 yu 'bakSAlI hastalipi' meM pUrNAMka likhane kI yaha paddhati thI ki aGka ke nIce 1 likha diyA jAtA thA, kintu donoM ke bIca bhAga rekhA nahIM lagAI jAtI thii| jaina grantha 'tiloyapaNNatti' (IsA kI dUsarI zatAbdI kA grantha) meM jor3ane ke lie 'dhaNa' zabda likhA hai kyoMki prAcIna sAhitya meM dhana ke lie 'dhaNa' zabda prayoga hotA thA / jor3ane ke lie paM0 ToDaramala ne 'arthasaMdRSTi' meM log log (aM) + 1 ke lie usameM isa prakAra likhA hai' cihna kA prayoga kiyA hai / yathA 1va 2 jor3ane ke lie, vizeSakara bhinnoM ke yoga meM, 'arthasaMdRSTi' meM khar3I lakIra kA prayoga milatA haM / yathA cintana ke vividha bindu : 550 : ---- 1 kA Azaya 1 + se hai / ghaTAne ke lie saMketa - 'bakSAlI hastalipi' meM ghaTAne ke lie + saMketa kA prayoga kiyA gayA hai / yaha + cihna usa aGka ke bAda likhA jAtA yA jise ghaTAnA hotA thA / jaise 20 meM se 3 ghaTAne ke lie isa prakAra likhA jAtA thA -- 3+ 1 kucha jaina granthoM meM bhI ghaTAne ke lie uparokta saMketa kA prayoga milatA hai parantu yaha + cihna ghaTAyI jAne vAlI saMkhyA ke Upara likhA jAtA thA / AcArya vIrasena ne 'dhavalA' (IsA kI navIM zatAbdI kA grantha) meM isa prakAra ke saMketa kA prayoga kiyA hai jo nimnalikhita udAharaNa se spaSTa hai' |1| sojjJa mANAvo evisse riNa saNNA" arthAt 1 zoSyamAna (arthAt ghaTAne yogya) hone se isakI RNa saMjJA hai / ghaTAne ke lie + cinha kI utpatti ke bAre meM prophesara lakSmIcandajI jaina kA mata hai ki yaha cinha brAhmI bhASA se banA hai / brAhmI bhASA meM RNa ke lie 'riNa' likhA jAtA hai aura riNa kA prathama akSara ri brAhmIbhASA meM likhA jAtA hai| adhika prayoga hote-hote isakA rUpa + ho gayA hai / + jaina granthoM meM ghaTAne ke lie 2 cinha bhI milatA hai| yaha cinha jisa aGka ko 20 1 1 paM0 ToDaramala kI arthasaMdRSTi, pRSTha 6, 7, 8, 15, 18, 20, 21 2 arthasaMdRSTi, pRSTha 11 ku dhavalA, pustaka 10, san 1654, pRSTha 151
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________________ : 551 : jaina sAhitya meM gANitika saMketana ghaTAnA hotA thA usake bAda likhA jAtA thA / yathA kA Azaya jaghanya yukta asaMkheya - 1 se hai / yahA~ para 2 kA Azaya jaghanya yukta asaMkheya se hai / 'arthadRSTi' meM isI prakAra ke aneka udAharaNa milate haiM / " yathA - yadi lA55413 kA Azaya la X 5 x 4 X 3 arthAt 60 lAkha se hai aura 1 lAkha isa rAzi meM se ghaTAyA jAve to zeSaphala ko isa prakAra likhate haiM goldeu la zrI jaina divAkara smRti grantha 'trilokasAra' (dazavIM zatAbdI kA jaina grantha) meM bhI ghaTAne ke lie isI prakAra kA saMketa milatA hai / isameM likhA hai ki mUlarAzi ke Upara ghaTAI jAne vAlI saMkhyA likho aura usake Age pUchar3I kA sA AkAra bindI sahita karo jaise 200 meM se 2 ghaTAne ke lie isa prakAra likhA hai-- 2 200 8 ghaTAne ke lie meM se 2 ghaTAne ke lie isa prakAra likhA hai - ghaTAne ke lie uparokta cinha 10 5/4/3 saMketa bhI jaina granthoM meM prayoga kiyA gayA hai / yathA 1 karor3a ko bhara hotA hai|" kahIM-kahIM ghaTAne ke lie * saMketa kA bhI prayoga kiyA gayA hai| paM0 ToDaramalajI ne isa saMketa kA prayoga isa prakAra kiyA hai-- I0 pU0 tIsarI zatAbdI meM bhI dRSTigocara 4 arthasaMdRSTi, pRSTha 4; tiloyapaNNatti, bhAga 2, pRSTha 606, 717 5 vahI, pRSTha 20 6 trilokasAra, pariziSTa, pRSTha 2 7 arthasaMdRSTi, pRSTha gaurIzaMkara hIrAcandra ojhA, bhAratIya prAcInalipi mAlA 1956, pleTa 1
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________________ zrI jaina divAkara smRti grantha * 1 ko isakA Azaya 1 karor3a - 1 hai / eka karor3a meM se 2 ghaTAne ke lie isa prakAra bhI likhA hai ko 2 ghanaloka meM se 2 ghaTAne ke lie isa prakAra likhA hai 0 2 = yahA~ para saMketa panaloka ke lie prayoga kiyA gayA hai| eka lAkha meM se 1 ghaTAne ke lie isa prakAra likhA hai' la 1 o 'trilokasAra' meM bhI ghaTAne ke lie uparokta cinha milatA hai| usameM likhA hai ki mUla rAzi (jisameM se ghaTAnA ho) ke nIce bindI likho aura phira bindI ke nIce RNa rAzi (ghaTAI jAne vAlI saMkhyA) likho / yathA yadi 200 meM se 2 ghaTAne hoM to isa prakAra likhate hai" tathA 6. arthasaMdRSTi, pRSTha 6 10 trilokasAra, pariziSTa, pRSTha 2 11 arthasaMdRSTi, pRSTha 6 12 tiloyapaNNatti, bhAga 1, pRSTha 20 o cintana ke vividha vindu 552 200 ghaTAne ke lie 'arthasaMdRSTi' meM kiyA hai| jaise eka lAkha meM la 75 ghaTAne ke lie saMketa ke sthAna para RNa zabda kA pratIkAtmaka prathama akSara bhI prayoga kiyA gayA hai| prAcIna sAhitya meM RNa ke lie riNa likhA jAtA thA / ataH ghaTAne ke lie 'ri' aura kahIM-kahIM 'riNa' kA prayoga hotA thA parantu yaha akSara jisa a ko ghaTAnA hotA thA, usake bAda meM likhA jAtA thaa| 'tiloyapaNNatti' meM aise udAharaNa aneka jagaha milate haiN| yathA saMketoM kA prayoga bhI paM0 ToDaramala ne se 5 ghaTAne ke lie isa prakAra likhA hai" lu) tathA
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________________ : 553 : jaina sAhitya meM gANitika saMketana || zrI jaina divAkara- smRti-grantha % 3D 14- ri0 yo0 100000 / 3 arthAt-madhyaloka ke UparI bhAga se saudharma vimAna ke dhvajadaNDa taka 1 lAkha yojana kama Der3ha rAjU UMcAI pramANa hai / isameM spaSTa hai ki 'ri0' kA Azaya yahA~ para ghaTAne se hai| yahA~ 14-3 kA artha Der3ha rAjU se hai| guNA ke lie saMketa-guNA ke lie 'bakSAlI hastalipi' meM 'gu' saMketa kA prayoga milatA hai| yaha saMketa 'gu' zabda 'guNA' athavA 'guNita' kA prathama akSara hai / yathA-13 isakA Azaya 34343XX 34343410 hai| 'tiloyapaNNatti' meM guNA ke lie eka khar3I lakIra kA prayoga kiyA gayA hai / yathA 1000x 66X500XCXCXCXCXCXCXX8 ke lie isa prakAra likhA hai|" %66.500 / 88888888 / yahA~ para%0 kA Azaya 1000 hai| 'arthasaMdaSTi' meM bhI guNA ke lie yahI cihna milatA hai / yathA-16 ko 2 se guNA karane ke lie 16 / 2 likhA hai / trilokasAra' meM bhI guNA ke lie yahI cihna milatA hai / yathA--128 ko 64 se guNA karane ke lie 128 / 64 likhA hai / 16 bhAga ke lie saMketa-bhAga ke lie 'bakSAlI hastalipi' meM 'bhA' saMketa kA prayoga milatA hai| yaha saMketa 'bhA' zabda 'mAga' athavA 'bhAjita' kA prathama akSara hai| yathA-10 isakA Azaya 40 mA 160 | 13 | mh b isakA Azaya 130-41310 se hai| | 1 1 bhinnoM ko pradarzita karane ke lie prAcIna jaina sAhitya meM aMza aura hara ke bIca rekhA kA prayoga nahIM milatA hai / 'tiloyapaNNatti' meM belana kA Ayatana mAlama kiyA hai jo AyA hai| isa 19 ko isa grantha meM isa prakAra likhA hai-- 24 13 bakSAlI hastalipi Folio 47, recto 14 tiloyapaNNatti, bhAga 1, gAthA 1, 123-124 15 arthasaMdRSTi, pRSTha 6 16 trilokasAra, pariziSTa, pRSTha 3 17 bakSAlI hastalipi Folio 42, recto 18 triloyapaNNatti, bhAga 1, gAthA 1,118
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________________ // zrI jaina divAkara-smRti-grantha / cintana ke vividha bindu : 554; 'trilokasAra' meM bhI isI prakAra ke udAharaNa upalabdha hote haiM / isameM likhA hai ki ikyAsI sau vANavai kA cauMsaThavA~ bhAga isa prakAra likhiye 8162 64 _ 'trilokasAra' meM bhAga dekara zeSa bacane para usako likhane kI vidhi kA bhI ullekha kiyA hai, jo Adhunika vidhi se bhinna hai / yathA 8164 meM 64 kA bhAga deM to 128 bAra bhAga jAvegA aura 2 zeSa raheMge / arthAt 128 2 ko isa grantha meM isa prakAra likhA hai 128 / 2 zUnya kA prayoga-0 kA prayoga Adi saMkhyA ke rUpa meM prArambha nahIM huA apitu rikta sthAna kI pUrti hetu pratIka ke rUpa meM prayoga huA thA / Adhunika saMketa lipi meM jahA~ * likhA jAtA hai vahA~ para prAcInakAla meM 0 saMketa na likhakara usa sthAna ko khAlI chor3a diyA jAtA thaa| jaise 46 kA artha hotA thA chiyAlIsa aura 4 6 kA artha hotA thA cAra sau chaH / yadi donoM aMkoM ke madhya jitanA upayukta sthAna chor3anA cAhie usase kama chor3A jAtA thA to pAThakagaNa bhrama meM par3a jAte the ki lekhaka kA Azaya 46 se hai athavA 406 se / isa bhrama ko dUra karane ke lie usa saMkhyA ko 4 6 na likhakara 4.6 ke rUpa meM aMkita kiyA jAne lgaa| dhIre-dhIre isa praNAlI kA Adhanika rUpa 406 ho gyaa| isa prakAra ke prayoga kA ullekha prAcIna jaina granthoM evaM mandiroM Adi meM likhA milatA hai| udAharaNArtha AgarA ke hIMga kI maNDI meM gopInAtha jI ke jaina mandira meM eka jaina pratimA hai jisakA nirmANa kAla saM0 1506 hai, parantu isa pratimA para isakA nirmANa kAla 1506 na likhakara 15 // likhA hai| varga ke lie cihna-kisI saMkhyA ko varga karane ke lie 'va' cihna milatA hai| yaha cihna 'va' usa saMkhyA ke bAda likhA jAtA hai, jisakA varga karanA hotA hai / yathA 'ja ju a' eka saMkhyA hai jisakA artha jaghanya yukta ananta hai / yadi isakA varga kareMge to use isa prakAra likheMge -- ja ju ava isI prakAra dhana kA saMketa 'gha', caturtha ghAta ke lie 'va-ba' (varga-varga), pA~cavIM ghAta ke lie 'va-gha-ghA' (varga ghana ghAta), chaThavIM ghAta ke lie 'gha-va' (dhana varga), sAtavIM ghAta ke lie 'va-va-gha-ghA' (varga varga ghana ghAta) Adi saMketa upalabdha hote haiN| bagita-saMvagita ke liye cihna-vagita-saMvagita zabda kA tAtparya kisI saMkhyA kA usI saMkhyA tulya ghAta karane se hai| jaise 5 kA vargita-saMvargita 55 huaa| jaina granthoM meM isake liye vizeSa cihna prayoga kiyA hai| kisI saMkhyA ko prathama bAra vargita-saMgita karane ke lie isa prakAra likhA jAtA hai nA 16 trilokasAra, pariziSTa, pRSTha 5 20 vahI, pariziSTa, pRSTha 6 21 arthasaMdRSTi, pRSTha 5
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________________ : 555 : jaina sAhitya meM gANitika saMketa jana sAhitya meM mAsika patiH zrI jaila divakara smRti grantha / zrI jaina divAkara-smRti-grantha isakA Azaya hai na se hai / dvitIya vagita-saMgita ke lie isa prakAra likhA jAtA hai / isakA Azaya na ko vagita-saMgita karake prApta rAzi ko punaH vagita-saMvagita karanA hai / arthAt ( na') hai| jaise 2 kA dvitIya vagita-saMgita (22)huA / ataH kA 44 =256 huaa| dvitIya vargita-saMgita rAzi ko pUnaH eka bAra vagita-saMvagita karane para tRtIya vagita-saMvagita prApta hotA hai| 2 ke tRtIya vagita-saMvagita ko 'dhavalA' meM isa prakAra likhA hai22 // 256 (256) vargamUla ke lie saMketa-'tiloyapaNNatti' aura 'arthasaMdRSTi' Adi meM vargamUla ke lie 'ma' kA prayoga kiyA hai| 'tiloyapaNNa tti' ke nimnalikhita avataraNa meM 'mU0' saMketa vargamUla ke = 5864 riNa rA* : - ... paM0 ToDaramala kI 'arthasaMdRSTi' meM 'ke mU' prathama vargamUla aura 'ke mU,' vargamUla ke vargamUla ke lie prayoga kiyA gayA hai| __saMketa 'mU0' mUla arthAt vargamUla zabda kA prathama akSara hai / isa saMketa ko usa saMkhyA ke anta meM likhA jAtA thA jisakA vargamUla nikAlanA hotA thA / 'bakSAlI hastalipi' meM bhI 'mu0' kA prayoga milatA hai jo nimna udAharaNa se spaSTa hai | 11 yu0 5 mU0 4 22 dhavalA, pustaka 3, amarAvatI 1941, pariziSTa pR0 35 23 tiloyapaNNatti, bhAga 2, paMcama adhikAra, pRSTha 606 24 Bulletin of Mathematical Society, Calcutta, Vol. 21, 1929 patrikA meM prakAzita vibhUtibhUSaNadatta kA 'bakSAlI gaNita' para lekha, pRSTha 24