Mahavir ki Rekha Ganitiya Uppattiya

Author(s): Satyaprakash Saravsati
Publisher: Z_Kailashchandra_Shastri_Abhinandan_Granth_012048.pdf
Catalog link: https://jainqq.org/explore/210193/1

Page #1
AcArya mahAvIrakI rekhAgaNitIya upapattiyA~ svAmI satyaprakAza sarasvatI, ilAhAbAda jaina gaNitajJoMmeM sabase adhika khyAti gaNitasAra saMgrahake racayitA mahAvIrakI hai| anya jaina gaNitajJoMmeM abhayadevasUri, siMhatilaka sUri aura amarasiMha yatike nAma prasiddha haiM / trizatikAko TIkA karanevAle vallabha bhI jaina the, aura unhone TIkA telagu bhASAmeM kI thI / siMhatilaka suri, (1275 I0) ne zrIpati gaNitatilakakI TIkA kI, kucha jainavidvAnoMne zrIdharAcAryako bhI jaina mAnA kintu spaSTatayA pATIgaNita ke racayitA zrIdharajI zaiva hindU the / abhayadevasUri (1050 I0) ne prasiddha jainagrantha sthAnAMgasUtrakI TIkAmeM zrIdharakA nAma to nahIM liyA, kintu zrIdharakI pATIgaNita aura trizatikA -- ina donoM granthoMse uddharaNa diye haiM ( sadRza dvirAzighAta; 24, 28; samatrirAzihati; 11, 15) / prAcIna bhAratIya gaNitajJoMkI pUrvAparatA nimna san-saMvatoMse prakaTa hotI hai / vakhasAlI hastalipi 200 I0, prathama AryabhaTakA AryabhaTIya (janma 476 I0), bhAskara prathama (629 I0), brahmaguptakA brahmasphuTasiddhAnta, (628 I0), pRthUdaka svAmI nAmaka bhASyakAra ( 860 I0), skandasena (jisakA ullekha pRthUdakasvAmIne apane bhASyameM kiyA hai) navIM zatI I0 se pUrva, lallakI pATIgaNiva aura siddhAntatilaka (8vIM zatI I0), govindakI govindakRti ( 9vIM zatI I0 ), laghubhAskarIyake TIkAkAra zaMkara nArAyaNa (869 I0 ) aura udayadivAkara (1073 I0), mahAvIrakA gaNitasArasaMgraha ( 850 I0), zrIpatikA gaNitatilaka aura siddhAntazekhara (1039 I0), bhAskara dvitIyakI lIlAvatI (1150 I0), AryabhaTTa dvitIyakA mahAsiddhAnta (950 I0), aura nArAyaNakI gaNitakaumudI (1356 I0 ) mahAvIrakA gaNitasAra-saMgraha grantha gaNitake vizeSajJoMke liye bar3e kAmakI vastu hai / yaha prAcArya kannar3a pradezakA jaina vidvAn thA / AryabhaTTa aura bhAskara evaM brahmaguptake samAna AcAryoMne gaNitakA adhyayana jyotiSake pariprekSya meM kiyA thA, kintu mahAvIrakA gaNitasArasaMgraha aura zrIdharAcAryake pATIgaNita aura trizatikA grantha vizuddha gaNitake grantha haiM / jainadharmake AcArya gaNitazAstra ke svatantra adhyayanako bhI prArambhase mahattva dete Aye haiM / yaha ThIka hai ki ve yaha bhI svIkAra karate haiM ki gaNitakA jyotiSameM bhI upayoga hai, para gaNitake adhyayanakA svataH apanA bhI eka kSetra hai / mahAvIrake samaya taka brahmaguptakI pratiSThA sarvamAnya ho gayI thI, pRthUdaka svAmIne brahmasphuTasiddhAntakA bhASya kiyA / yaha AcArya bhI mahAvIrakA lagabhaga samakAlIna thA / donoM hI 850-860 I0 ke kAlake haiM / zrIdharAcArya mahAvIra ke granthase paricita thA, kaI kSetroMmeM usane mahAvIrake gaNitIya kAryako parivaddhita bhI kiyA / gaNitasAra-saMgrahameM jo bAta mahAvIrane 6 zlokoM meM dI hai, zrIdharane use apanI trizatikAmeM 4 paMktiyoMmeM hI samApta kara diyA hai / zrIdharakI ye cAra paMktiyA~ nimna haiM (trizatikA, udAharaNa 26 ) : kAminyA hAravallayAH suratakalahatAmoktikAnAM truTitvA / bhUmI yAtastribhAgaH zayanatalagataH paJcamAMzazca AttaH SaSThaH sukezyA dRSTaH gaNakadazamakaH saMgRhItaH priyeNa / kathaya katipaya mauktikaireSa hAraH // dRSTaM SaTkaJca sUtre gaNitasAra-saMgraha meM yahI prazna 12 paktiyoMmeM hai / ( 4 / 17-22) - 417 - 53.

Page #2
kAcid vasantamAse prasUnaphalagucchabhAranamrodyAne / tanmauktika-pramANaM prakIrNakaM vetsi ceta kAthaya / hamane yahA~ prathama aura antima paktiyA~ hI uddhRta kI hai| mahAvIrake gaNitasAra-saMgrahakA prabhAva lagabhaga sabhI uttarakAlIna gaNitIya granthoMpara haiM, yaha to mAnanA hI par3egA / apane racanAkAlake Der3ha sau varSoM ke bhItara hI isa granthakI khyAti dakSiNa bhAratameM bahuta phaila gayI thI, rAjAmundarIke adhIza rAjarAjanarendrake saMrakSaNameM isakA telagumeM padyAnuvAda pAvalUri mallane kiyA thA, madrAsake rAjakIya pustakAlayameM isa anuvAdako pratilipi vidyamAna hai / 1912meM ema0 raMgAcAryane gaNitasAra-saMgrahakA aMgrejI anuvAda (praznottara sahita) kiyA jo madrAsa sarakArakI orase prakAzita huA thA / kolambiyA vizvavidyAlaya, nyUyArkake DeviDa yUjIna smithane isakI bhUmikA likhI thii| kSetramiti aura kSetraphala bhAratavarSa meM rekhAgaNitakI paramparA vaidika zrotakAlase calI A rahI hai| yajJakI citiyoM aura vediyoMke nirmANake sambandhameM, pichale katipaya varSoMse mero ruci zalbagranthoMke prati rhii| abhI kucha mAsa hI huye, cAra zulbasUtrakA saMgraha maine DA0 USAjyotiSmatIke sahayogase prakAzita kiyA-baudhAyana-zulbasUtra, Apastamba-zulbasUtra, kAtyAyana-zulbasUtra aura bhAmaha-zulbasUtra / baudhAyana aura Apastamba-zulbasUtroMkI prAcIna katipaya TIkAe~ bhI hama loga prakAzita kara cuke haiN| ina zulbasUtroMmeM prasaMgavaza vRtta, dIrghacaturasra, samacaturasra aura prauga (tribhujoM) kI rekhAgaNita aura unake kSetraphaloMkA acchA vidhAna hai| zalbasUtrakI vaidika paramparAmeM hI taraha-tarahakI iSTaka banAnekI paramparA Arambha haI aura kSetramiti kA bhI isI paramparAmeM janma huaa| pATIgaNitoMmeM bhI eka-do adhyAya kSetramitike rahate Aye haiN| zrIdharAcAryake grantha pATIgaNitameM zrIDhI vyavahArake bAda antima adhyAya kSetra vyavahArakA hai| kSetra jAtibhedase daza prakArake mAne gaye haiM : taba daza kSetrajAtayo bhavanti, samatribhujaM, dvisamatribhujaM, viSamatribhujaM, samacaturasraM, trisamacaturasra, dvisamacaturasraM viSamacaturasraM, dvidvisamacaturasraM, AyatacaturasraM, vRttaM, dhanuriti / ina kSetroMke sambandhameM aneka pAribhASika zabdoMkA prayoga hotA hai, jaise bhuja, bhUmi, mukhaM, koTi, karNa, lamba, avadhA, hRdayaM, paridhi, vyAsa, jyA, zarazcApa ityAdi / mahAvIrane gaNitasAra-saMgrahameM 16 jAtiyoMke kSetroMkA ullekha kiyA hai : 1. tIna jAtiyoMke tribhuja-(ka) sama (tInoM bhujA barAbara), dvisama (do bhujAe~ barAbara), aura viSama (tInoM bhujAe~ alaga-alaga mApa kii)| 2. pA~ca jAtiyoMke caturasra-(ka) sama, (kha) dvi-dvi-sama (equidichostic), (ga) dvisama (equibilateral), (gha) trisama (equitritilateral), (Ga) viSama (inequilateral). 3, ATha jAtiyoMkI gheredAra AkRtiyA~ (vRtta):-(ka) samavRtta (circle), (kha) ardhavRtta, (ga) AyatavRtta (ellipse), (gha) kambukAvRtta (zaMkhakI AkRtikA), (Ga) nimnavRtta (concave circle), (ca) unnatavRtta (convex ciscle), (cha) bahicakravAlavRtta (outlying annulus), (ja) antazcakravAla vRtta (inlying annulus).

Page #3
solaha jAtiyoMke ina kSetroMke kSetraphala nikAlanekI do prakArakI vidhiyoMkA ullekha mahAvIrane kiyA hai :(ka) vyAvahArika (approximate) aura sUkSma (accurate): kSetraM jinapraNItaM phalAzrayAda vyAvahArika sUkSmamiti / bhedAd dvidhA vicintya vyavahAraM spaSTametadabhidhAsye // 7-2 // yaha kahanA kaThina hai ki yUkliDake prameyoMkA paricaya mahAvIra yA anya kSetrajJa gaNitajJoMko thA yA nhiiN| saMbhavatayA rekhAgaNitIya tarkakA usa prakArakA vikAsa isa dezameM nahIM huA, jaisA ki yUnAnameM / tribhajake koNoMko nApanekA koI paimAnA (DigarI yA samakoNoMkA) usa samaya nahIM thA kintu jyA (Sine) ke rUpakA anupAta unheM paricita thaa| jyAoMkI apekSAse hI koNa vyakta kiye jAte the| tribhujoM aura caturasroMke kSetraphala nikAlaneke sUtroMkA vikAsa mahAvIrane kiyaa| pratyeka tribhujake tInoM zIrSa eka vizeSa vRtta (parimaNDala, zulbasUtroMkI paribhASAmeM) para sthita hote haiN| kintu sabhI caturasroM (quadrialtarals) ke liye aisA honA Avazyaka nahIM hai| brahmaguptane bra0 sphu0 siH, 12 / 21 [1] aura mahAvIrane [ga.sA. saM0 9150 [1] ne isa bAtakA dhyAna nahIM rkkhaa| donoMne sabhI caturasroMke kSetraphalake liye nimna sUtra diyA : caturasrakA kSetraphala = Vs (s - a) (s - b) (s-c) (s - d) isa sUtrameM s = cAroM bhujAoMke yogakA AdhA; a, b, c,d= cAra bhujAoMkI pRthak pRthak lambAI / tribhujako aisA caturasra mAna sakate haiM, jisakI eka bhujAkI lambAI zUnya ho, arthAt d = 0 samIkaraNase, tribhujakA kSetraphala =Vs (s-a) (-b) (-) jahA~ a, b, c tInoM bhujAoMkI pRthaka pRthaka lambAI hai, aura 3 = 1 (a + b + c) vastutaH mahAvIra aura brahmaguptake ye samIkaraNa unhIM caturasroMke liye yathArtha hai jinake cAroM zIrSa vRttakI paridhi para hoM (eyclic quadrilateral) / sabhI caturasroMke liye sAmAnya samIkaraNa nimna hogA : ka ka ga citra 1. cakrIya caturasra c a +b+c+d citra 2. acakrIya aturasra Page #4
caturasrakA kSetraphala = V(s-a) (s - b) (s-c) (s-d)- abcd Cossa jahA~ a= caturasra ke Amane-sAmaneke koNoMke yogakA AdhA (cakrIya caturasrameM a = 90deg, Cos a = 0, citra 1) caturasroMkA kSetraphala nikAlaneke liye mahAvIrane nimna niyama pratipAdita kiyA hai : bhujAyatyardhacatuSkAd bhujahInAd ghAtitAt padaM sUkSma / athavA mukhatalayutidalamavalambaguNairna viSamacaturasra / / (ga0 sA0 saM0 750) yahI bAta zrIdharakI pATIgaNitameM isa prakAra kahI gayI hai : bhujayutidalaM caturdhA bhujahInaM tadavadhAtpadaM gaNitam sadRzAsamalambAnAmasadRzalambe viSamabAhI / (117) arthAt cAroM bhujAoMkA yoga nikAlakara usakA AdhA karo aura isa phalameM kramazaH pratyeka bhujAkI lambAI ghaTAo, phira cAroMko guNA karo, phira isakA vargamUla nikAla lo / aisA karanese caturasrakA kSetraphala nikala aavegaa| ___ yaha smaraNa rakhanA cAhiye ki yaha niyama sabhI caturasroMke liye lAgU nahIM hai / dvitIya AryabhaTTane spaSTatayA iMgita kiyA hai ki tribhujoMke liye to yaha niyama ThIka hai, kintu jaba taka karNa (diagonal) kA jJAna na ho, caturasrakA na to kSetraphala nikAlA jA sakatA hai aura na isake lambaka nirdhArita kiye jA sakate haiM : karNajJAnena vinA caturasra lambakaM phalaM yadvA / vaktuM vAJchati gaNako yo 'sau mUrkhaH pizAco vA // (mahAsiddhAnta, 25 / 70) binA karNake jAne jo gaNitajJa caturasra kSetrakA kSetraphala nikAlanA cAhate haiM, ve mUrkha aura pizAca haiM / aise kaThora zabda AryabhaTTa dvitIyane kahe haiN| mahAvIra, brahmagupta, zrIdhara Adine caturasroMke viSayameM jo kahA hai, vaha kevala cakrIya caturasroMke viSayameM hai| ___ pA~ca jAtiyoMke caturasroMke karNa jAnaneke liye mahAvIrane nimna niyama diyA hai : kSitihataviparItabhujA mukhaguNabhujamizritau guNacchedau / chedaguNau pratibhujayoH savargayuteH parda karNau // (ga0 sA0 saM0, 7 / 54) yaha niyama bhI kevala cakrIya caturasroMke lie yathArtha hai, Uparake zlokameM jo kahA hai, use hama bIjagaNitIya zabdoMmeM nimna prakAra vyakta kara sakate haiM : (cakrIya) caturasrakA karNa = / (ac + bd) (ab + cd) ad + bc athavA = /(ac + bd) (ad + bc) ab + cd vRttameM vyAsa aura paridhikA sambandha-mahAvIrake anusAra yadi vRttake vyAsako 10 ke varga mUlase guNA kara diyA jAya, to paridhikA mAna nikala AtA hai / Aja kala ke zabdoM meM V10 = 7 -paridhi = 3.16 vyAsa - 420 -

Page #5
vRttakSetra-vyAso dazapadaguNito bhavet parikSepaH / vyAsacaturbhAgaguNaH paridhiH phalamardhamarcetat / / (ga0 sA0 saM0, 760) vyAsax/104 vyAsa paridhi x vyAsa = vRttakA kSetraphala = - vyAsa = 2 vyAsArdha = 2r; vRtta kA kSetraphala = ruri AryabhaTa prathamane vRttakI paridhi aura usake vyAsakA sambandha nimna saMkhyAse vyakta kiyA hai : - -Tra pArASa vyAsa = 62632 = 3.1416 (AryabhaTa) 20000 16 4 3927 = 3.1416 (bhAskara) 1641250 AyatavRtta ( ellipse ) arthAt dIrghavRttake vyAsa aura paridhi-AyatavRttako Aja hama dIrghavRtta kahate haiM / isake do vyAsa hote haiM / eka to bar3A aura dUsarA choTA / AyatavattakI paridhi aura kSetraphalake sambandhameM mahAvIrakA niyama nimna hai : gha citra 3. AyatavRtta AyAma = kakha = a, vyAsa yA viSkambha = gagha = b vyAsakRtiSSaDguNitA dviSaDguNAyAmakRtiyutA (paraM) paridhiH / vyAsacaturbhAgaguNAzcAyatavRttasya sUkSmaphalam // (ga0 sA0 saM0, 7 / 63) choTe vyAsa (viSkambha) ke vargako 6 se guNA karo aura lambe vyAsa (AyAma) ke dugunekA varga lekara isameM jodd'o| isa vargakA jo vargamUla hogA, vaha paridhikI lambAI hogii| paridhiko choTe vyAsake caturthAMzase guNA kareM, to AyatavRttakA kSetraphala nikala jaavegaa| isI bAtako hama bIjIya samIkaraNameM nimna prakAra vyakta kara sakate haiM: paridhi:/6b4ad jahA~ b = AyatavRttakA choTA vyAsa; a = AyAtavRtta kA bar3A vyAsa (AyAma) AyatavRttakA kSetraphala = paridhi x b/4 = b/4/6b* +4 (yaha smaraNa rakhanA cAhiye ki mUla zlokameM yaha nahIM likhA ki paridhi nikAlaneke lie 6b+4a'kA vargamUla nikAlanA hai)| -421

Page #6
mahAvIrane abhyAsake liye eka udAharaNa diyA hai : kSetrasya AyatavRttasya viSkambho dvAdazaiva tu / AyAmastatra SaTtriMzat paridhiH kaH phalaM ca kim // (ga0 sA0 saM0, 7 / 22) arthAt yadi eka Ayata vRttakA viSkambha (choTA vyAsa) 12 aura AyAma (bar3A vyAsa) 36 hai, to usakI paridhi aura kSetraphala btaao| paridhi =/6b* +4ad 3/6x12x12+4x36x36 =V36x24 +4x36x36 = 6x2/6+ 36 = 12/42 = 12x6.48 = 77.76 kSetraphala = b/4 x 12/42 = 3x 12/42 = 36x6.43 = 233.28 mahAvIrane AyatavRttoMkI paridhi aura kSetraphala nikAlaneko eka sthUla yA vyAvahArika vidhi bhI dI haiM : vyAsArdhayuto dviguNita AyatavRttasya paridhirAyAmaH / viSkambhacaturbhAgaH pariveSahato bhavetsAram / / (ga0 sA0 saM0, 7 / 21) arthAt bar3e vyAsa meM choTe vyAsakA AdhA jor3o aura ise dose guNA kro| aisA karanese AyatavRttakI paridhi milegii| isa paridhiko choTe vyAsa (viSkambha) ke cauthAI mAnase guNA karo, to kSetraphala milegaa| paridhi = 2 (a + b/2) kSetraphala = b/4 x 2 (a + b/2) Uparake udAharaNameM, a= 36, b= 12, phalataH paridhi =2 (36x12/2) =2x42 =84 kSetraphala =3x84-252 ye uttara sthUla arthAt truTipUrNa haiM; sUkSmamAnameM paridhi 77.76 aura kSetraphala 233.28 hai / kambuka kSetra (conchiform) kI paridhi aura kSetraphala nikAlanA-ina kSetroMke sambandhameM bhI mahAvIrane sthUla aura sUkSma mAnoM ke nikAlaneke pRthak-pRthak niyama diye haiN| kambukake samAna vRtta (citra 4.) kI adhikatama caur3AImeMse kambukake mukhakA AdhA ghaTAo aura ise phira tInase guNA kro| aisA karanese kambaka vRttako paridhi milegii| isa paridhike Adheke vargakA eka tihAI lo aura isameM mukhake AyAmake Adheke vargakA 3/4 jor3o, to kambuka vRttakA kSetraphala milegaa| vadanAGkhano vyAsastriguNaH paridhistu kambukAvRtte / valayAdhaM kRtitryaMzo mukhArdhavargatripAdayutaH // (ga0 sA0 saM0, 7 / 23) citra 4. kambukavRtta -422

Page #7
R AHARI mAna lo kambuvRttakA vyAsa =a, mukhakA AyAma = m; tI paridhi = 3 (a-1 m) kSetraphala = [3 (a- m) ]x + (m/2) x2 eka anya sthala para mahAvIrane kambu-nibha vRttakI paridhi (parikSepa) aura kSetraphala donoMkA adhika sUkSma mAna nimna zabdoM meM diyA hai : vadanA?no vyAso dazapadaguNito bhavetparikSepaH / mukhadalarahitavyAsArdhe vargamukhacaraNakRtiyogaH / / dazapadaguNitA kSetrakambuni me sUkSmaphalametat / / (ga0 sA0 saM0,765-66) dazapadakA artha /10 arthAt 10 kA vargamUla hai| isa sUkSma mAnake AdhAra para kambu-vRttake liye parikSepa yA paridhi = /10x (a-m) kSetraphala = [ { (a-|m)x } + m/4] x /10 bahiH aura antazcakravAla vRttoMke kSetraphala-kisI vRttake bAhara dUsarA samakendraka vRtta khIMcA jA sakatA hai aura isI prakAra kabhI usI vRttake bhItara bhI eka samakendraka vRtta khIMcA jA sakatA hai| ina donoM sthitiyoMmeM do prakArake cakravAlavRtta prApta hote haiM-antaHzcakravAla vRtta aura bahiHcakravAla vRtta / donoM avasthAoMmeM do samakendraka vRttoMke bIcameM jo kSetra ghirA huA hai, usakA kSetraphala nikAlanA hai| mahAvIrane isake nikAlanekI sthUla aura sUkSma-donoM citra 5. (ka) citra 5. (kha) prakArakI gaNanAyeM dI haiM : antazcakravAlavRtta bahizcakravAlavRtta nirgamasahito vyAsastriguNo nirgamaguNo bahirgaNitam / / rahitAdhigamavyAsAdabhyantaracakravAlavRttasya / / (ga0 sA0 saM0, 7 / 28) bhItarake vRttake vyAsameM nirgamakI caur3AI (breadth of annular space) ko jor3a do aura ise tInase guNA kara do, to bahiHcakravAlavRttakA kSetraphala nikala aavegaa| isI prakAra, vRttake vyAsa meMse adhigamakI caur3AIko ghaTA do aura phira ise 3 se guNA karake adhigama caur3AIse guNA karo to antazcakravAlavRttakA kSetraphala nikala aavegaa| mAna lo ki diye vRttakA vyAsa d hai aura isake bAhara khIMce vRttakA nirgama a hai to bahiHcakravAlavRttakA kSetra = (d+a)x3xa 45955535363555755 HERESTHETHERETEERTHA

Page #8
isI d vyAsake vRttake bhItara adhigama a ho, to antazcakravAla-vRttakA kSetra ___ = (d-a)x3xa mahAvIrane donoMkA eka udAharaNa diyA hai : vyAso'STAdazahastAH, punarbahinirgatAstrayastatra / vyAso'STAdazahastAzcAntaH putraradhigatAstrayaH kiM syAt / / (ga0 sA0 saM0, 7 / 29) yahA~ d = 18 aura a = 31 bahiHcakavAla-vRttakA kSetra = (18+ 3)x 3x3 ___-189 vargahasta antaHcakravAla-vRttakA kSetra = (18 - 3)x 3x3 = 135 vargahasta smaraNa rakhanA cAhiye ki ina saba udAharaNoMmeM pAI (ga) kA mAna sthUlatayA 3 mAnA gayA hai / ise /10 yA 3,1416 (AryabhaTakA) mAna lenepara praznoMke uttara kucha bhinna hoNge| mahAvIrane gaNitasAra-saMgrahake saptama adhyAyameM anya AkRtiyoMke kSetroM aura parikSepoMke nikAlane liye bhI niyama diye haiM jo gaNitajJoM ke vizeSa kAmake haiN| ye AkRtiyA~ nimna haiM : yatamurajapaNavazakrAyudhasaMsthAnapratiSThitAnAM tu| mukhamadhyasamAsArdhaM tvAyAmaguNaM phale bhavati // (ga0 sA0 saM0, 3 / 32) . yava, muraja (mRdaGga), paNava, vajra / inake liye sAmAnya niyama yaha hai : mukha para cor3AI = a, madhyameM caur3AI - b, pUrI lambAI (AyAma) =c, to kSetraphala = (a+b)xc yavasaMsthAnakSetrasyAyAmo'zItirasya viSkambhaH / madhyazcatvAriMzatphalaM bhavet ki samAcakSata / / (ga0 sA0 saM0, 7 / 33) ------+----- rakha mAna lo yava (jau ke AkArakA kSetra) kI lambAI 80 hai, bIca meM caur3AI 40 hai, donoM nokoM yA zIrSoM para caur3AI zUnya hai / ataH kSetraphala = (0+ 40x80)x citra 6. yava 80 = 1600 vargahasta / ka AyAmo'zItirayaM daNDAmukhasya viMzatimadhye / catvAriMzatkSetre mRdaMgasaMsthAnake brUhi / / (ga0 sA0 saM0, 7 / 34) bhRdaMgake AkArake kSetrakI lambAI 80 daNDa hai, kinAroM para mukha 20 daNDakA hai aura bIcameM mAna 40 daNDakA hai| citra 7. mRdaMga yA muraja phalataH kSetraphala = 1 (a + b)xc a = 20; b = 40; c= 80 kSetraphala = 1 (20 + 40)x 80 =2400 vargadaNDa -424

Page #9
isI prakAra hama eka udAharaNa vajra kA leMge / - --- --- - vajra bIcoMbIcameM zUnya moTAIkA hai, mukhakI caur3AI = a aura AyAma = c hai, ataH nimna udAharaNameM : vajrAkRtestathAsya kSetrasya SaDagranavatirAyAmaH / madhyesUcirmukhayo strayodazatryaMzasaMyutAH daNDAH / / (ga0 sA0 saM0, 7 / 26) citra 8. bajra yahA~ c= 96 daMDa, mukha para kA mAna = a = 133 daMDa; b = 0 kSetraphala = (49+0) x 96 = 640 vargadaNDa mahAvIrane apane grantha gaNitasAra-saMgrahake kSetrAdhyAyameM isI prakArakI aneka upapattiyoMkA vivaraNa diyA hai| vRttoM, tribhujoM aura caturbhujoMke itane vistAra diye haiM jinakA ullekha karanA yahA~ sambhava nahIM hai| prAcIna gaNitase sambandha rakhanevAle itihAsameM mahAvIrakA nAma amara hai aura koI bhI itihAsakAra isa gaNitajJakI upekSA nahIM kara sakatA hai| AryabhaTIya, vakhazAlI hastalipi, pATIgaNita ( zrIdharakI) aura brahmasphuTasiddhAntake samAna gaNitasAra-saMgraha amara grantha hai, jisase pratyeka bhAratIya gaNitapremIko paricita honA caahiye| VODA . . . 54 -425 -