Ganita-sara-sangraha by Mahavira-Acharya

by M. Rangacharya | 1912 | 117,278 words

This is the English translation of the Ganita-sara-sangraha by Mahavira Acharya—an ancient Sanskrit text dealing with mathematics and mathematical problems from the 9th century. The Ganitasarasangraha includes significant mathematical concepts, like the decimal notation system and operations involving zero, highlighting the embedded rich mathematic...

Chapter 4 - Trtiyah prakirnaka vyavaharah

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trtiyah prakirnaka vyavaharah . pranutanantagunaugham pranipatya jinesvaram mahaviram | pranatajagatrayavaradam prakirnakam ganitamabhidhasye || 1 || 'vidhvastadurnayadhvantah siddhah syadvadasasanah | vidyanando jino jiyadvadindro munipungavah || 2 || itah param prakirnakam trtiyavyavaharamudaharisyamah-- bhagasseso mulakam sesamulam syatam jati he dviragramsamule | bhagabhyaso'nom'savargo'tha mula- misram tasmadvinnadrsyam dasamuh || 3 || tatra bhagajatisesajatyossutram- bhagonarupabhaktam drsyam phalamatra bhagajatividhau | amsonitarupahatihatamagram sesajatividhau || 4 || bhagajata vuddesakah | drsto'stamam stathivyam stambhasya tryamsako maya toye | padamsah saivale kah stambhah sapta hastah khe || 5 || saddagah patalisu bhramaravaratatestavibhagah kadambe padasrutadrumesu pradalitakusume campake pancamamsah | protphullambhojasande ravikara dalite trimsadaso'bhirame SL 47 tatraiko mattabhrngo bhramati nabhasi ka tasya brndasya sankhya || 6 || B and M omit this stanza

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ganitasarasangrahah . adayambhoruhani stutisatamukharah sravakastirtha krdbhayah pujam cakre caturbhyam vrsabhajinavarata tryamsamesamamusya | tryamsam turyam sadamsam tadanu sumataye tannavadvadasamsau sesebhyo dvidvipadmam pramuditamanasadatta kim tatpramanam || 7 || svavasikrtendriyanam durikrtavisakasayadosanam | silagunabharananam dayanganalingitanganam || 8 || sadhunam sadvrndam sandrstam dvadaso'sya tarkajnah | svatryamsavarjito'yam saiddhantaschandasastayossesah || 9 || panno'yam dharmakathi sa eva naimittikah khapadonah | vadi tayorvisesah sadgunito'yam tapasvi syat || 10 || girisikharatate mayopadrsta yatipatayo navasangunastasankhyah | ravikara paritapitojjvalangah kathaya munindrasamuhamasu me tvam || 11 || phalabharanamrakamre saliksetre sukassamupavistah | sahasotthita manusyaih sarve santrasitassantah || 12 || tesamartham pracimagneyim prati jagama sadbhagah | purvagreyasesah svadalonah svardhavarjito yamim || 13 || yamyayisesah sa nairrti svadvipancabhagonah | yaminairrtyasakapariseso varunimasam || 14 || nairrtyaparaviseso vayavyam sasvakatrisaptamsah | vayavyaparaviseso yutastvasaptastamah saumim || 11 ||

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prakirnakavyavaharah . vayavyuttarayoryutiraisanim svatribhagayugahina | dasagunitastavimsatiravasista vyomni kati kirah || 16 || kacidvasantamase prasunaphalagucchabhara namrodyane | kusumasavarasaranjitasukakokilamadhupamadhuranisvananicite || 17 || himakaradhavale prthule saudhatale sandrarundramrdutalpe | phaniphananitambabimba kanadamalabharanasobhangi || 18 || pathinajatharanayana kathinastanaharanamratanumadhya | saha nijapatina yuvati ratrau prityanuramamana || 19 || pranayakalahe samutthe muktamayakanthika tadabalayah | chinnavanau nipatita tatryasascetikam prapat || 20 || sadbhagah sayyayamanantaranantarardhamitibhagah | satsankhyanastasyah sarve sarvatra sampatitah || 21 || ekagrasastisatayutasahasramuktaphalani drstani | tanmauktikapramanam prakirnakam vetsi cet kathaya || 22 || sphuradindranilavarna satpadavrndam praphullitodyane | drstam tasyastamso'soke kutaje sadamsako linah || 23 || kutajasokavisesah sadgunito vipulapatalisande | patalyasokasesah svanavamsono visalasalavane || 24 || patalyasokaseso yutassvasaptamsakena madhukavane | pancasastandrsto vakulesutphullamukulesu || 25 || tilakesu kuravakesu ca saralesagresu padmasandesu | vanakarikapolamulesupi santasthe sa evamsah || 26 || 1 M roads sphuratendra

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ganitasarasangrahah . kinjalkapunjapinjarakanjavane madhukarastrayastrimsat | drsta bhramarakulasya pramanamacaksva ganaka tvam || 27 || goyuthasya ksitibhuti dalam taddalam sailamule sat tasyamsa vipulavipine purvapurvardhamanah | santisthante nagaranikate ghenavo drsyamana SL dvatrimsat tvam vada mama sarakhe gokulasya pramanam || 28 || iti magajatyuddesakah || sesajatavrddesakah | sadbhagamamrarase raja sesasya pancamam rajni | turyatryamsadalani trayo'grahisuh kumaravarah || 29 || sesani trini cutani kanistho darako'grahit | tasya pramanamacaksva prakirnakavisarada || 30 || carati girau saptamsah karinam sasthadimardhapascatyah | pratisesamsa vipine saddrstassarasi kati te syuh || 31 || kosthasya leme navamamsamekah pare'stabhagadidalantimamsan | sesasya sesasya punah purana drsta maya dvadasa tatprama ka || 32 || iti sesajatyuddesakah || atha mulajatau sutram- mularthamye chindyadamsonaikena yuktamulakrteh | drsyasya padam sapadam vargitamaha mulajatau svam || 33 ||

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tryamsah sesasya sastho varavakulavane panca mulani tasthuh punnage panca drsta mana ganaka ganam barhinam sanganayya || 35 || carati kamalasande sarasanam caturtho navamacarana bhagau sapta mulani cadri | vikacavakulamadhye saptaninnastamanah kati kathaya sarave tvam paksino daksa saksat || 36 || na bhagah kapivrndasya trini mulani parvate | catvarimsadvane drsta vanarastadganah kiyan || 37 || kalakanthanamartham sahakarataroh praphullasakhayam | tilake'stadasa tasthuna mulam kathaya pikanikaram || 38 || hamsakulasya dalam vakule'sthat panca padani tamalakujaye | 1 B reads hasti . ● B reads kim syattesam kunjaranam pramanam | • B reads nagah-

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CULTURE MINISTRY OF CULT GOVERNMENT ( GF INDIA SL sara 52 ganitasarasangrahah . atra na kiscidapi pratidrstam tatpramitim kathaya priya sighram || 39 || iti mulajatih || atha sesamulajati sutram padadalavargayutagranmulam saprakpadardhamasya krtih | drsye mulam prapte phalamiha bhagam tu bhagajatividhih || 40 || atroddesakah || gajayuthasya tryamsa 'ssesapadam ca trisanganam sanau | sarasi trihastinibhirnago drstah katiha gajah || 41 || nirjantukapradese nanadrumasandamanditodyane | asinanam yaminam mulam tarumulayogayutam || 42 || sesasya dasamabhago mulam navamo'tha mulamastamsah | mulam saptamamulam sastho mulam ca pancamo mulam || 43 || ete bhagah kavyapravacanadharmapramananayavidyah | vadacchando jyotisamantralankarasabdajnah || 44 || dvadasatapahprabhava dvadasabhedangasastra kusaladhiyah | dvadasa munayo drstah kiyati municandra yatisa mitih || 45 || mulani panca caranena yutani sanau sesasya pascanavamah karinam nagagre | mulani panca sarasijavane ramante nadyastathe sadiha te dviradah kiyantah || 46 || iti sesamulajatih || • B reads sesasya padam trisamguna .

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CULTURE TAINISTRY OF CULT GOVERNMENT OF bharata saraka prakirnakavyavaharah . atha dviggrasesamulajati sutram- mulam drsyam ca bhajedasakaparihanarupaghatena | purvagramagrarasau ksipedatassesamulavidhih || 47 || atroddesakah | madhukara eko drstah khe padme sesapancamacaturthi | sesacyaso mulam dvavamre te kiyantah syuh || 48 || simhascatvaro'drau pratisesasadamsakadimarghantah | mule catvaro'pi ca vipine drstah kiyantaste || 49 || tarunahariniyugmam drstam dvisangati bane kudharanikate sesah pancamsakadidalantimah | vipulakalamaksetre tasam padam tribhirahatam kamalasarasitire tasthurdasaiva ganah kiyan || 50 || iti dvisyasesamulajatih || athamsamulajati sutram- bhagagune mulagre nyasya padapraptadrsyakaranena | yalubdham bhagahrtam dhanam bhavedamsamulavidhau || 51 || anyadapi sutram- drsyadesaka bhaktaccaturgunanmulakrtiyutanmulam | sapamda dalitam vargitamamsabhyastam bhavet saram || 52 || 1 Breads dvau camre . SSL 53

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ganitasarasangrahah . atrodesakah | padmanalatribhagasya jale mulastakam sthitam | sodasangalamakase jalanaladayam vada || 53 || dvitribhagasya yanmulam navaghnam hastinam punah | sesatripathamamsasya mulam paddessamahatam || 54 || vigaladdana ' dharardra gandamandaladantinah | caturvimsatiradrsta mayatavyam kati dvipah || 55 || krodaugharthacatuh padani vipinam sardulavikridita prapussesadasamsamulayugalam sailam catustaditam | sasardhasya padam trivargagunitam vapram varaha vane drstastaptagunastakapramitayastesam pramanam vada || 56 || ityasamulajatih || atha bhagasamvargajatau sutram - 'svamsataharadunaccaturgunagrena taddharena hatat | mulam yojyam tyajyam tacchede taddalam vittam || 57 || atroddesakah | astamam sodasamsanam saliraseh krsivalah | caturvimsativahamsca leme rasih kriyan vada || 18 || Breads varai . After this stanza all the MSS. have the following stanza; but it is simply a paraphrase of stanza No. 57 :- anyaca- caturhatadrstenonaddhara hatyam sahrtaharat | tacchedana hatanmulam yojyam tyajyam tacchede tadardha vittam ||

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OF CULTURE MINISTRY OF CUL prakrti samprapta ERNMENT OF INDIA bharata saraka prakirnakavyavaharah . sikhinam sodasabhagah svagunasrute tamalasande'sthat | sesanavamsah svahatascaturagradasapi kati te syuh || 59 || jale trimsadasahato dvadasamsah sthitassesavimso hatah sodasena | trininena panke kara vimsatih khe sarakhe stambhadairghyasya manam vada tvam || 60 || iti bhagasamvargajatih || athonadhikamsavargajati sutram svamsakabhakta harardham nyunayugadhikonitam ca tadvargat | vyunadhikavargagranmulam svarna phalam parde'sahatam || 61 || hinalapa udaharanam | mahisinamastamso vyeko vargikrto vane ramate | pascadasadrau drstastrnam carantyah kiyantyastah || 62 || anekapanam dasamo dvivarjitah svatanganah kridati salakivane | caranti sadurgamita gaja girau kiyanta ete'tra bhavanti dantinah || 63 || adhikalapa udaharanam | jambuvrkse pancadasamso dvikayuktah khenabhyastah kekikalasya dvikrtighnah | 1 Momita hina . * M omits this as well as the following stanza. SL 55

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ganitasarasangrahah . pancapyanye mattamayurassahakare ramramyante mitra vadaisam parimanam || 64 || ityunadhikamsavargajatih || atha mulamisrajatau sutram - misrakrtirunayukka vyadhika ca dvigunamisrasammakta | vargikrta phalam syatkaranamidam mulamisravidhau || 65 || hinalapa uddesakah | mulam kapotavrndasya dvadasonasya napi yat | tayoryoga ' kapota sad drstastannikarah kiyan || 66 || paravatiyasanghe caturghanone'pi tatra yanmulam | tayayogah sodasa tadvrnde kati vihangah syuh || 67 || adhikalapa uddesakah | rajahamsanikarasya yatpadam sastasastisahitasya caitayoh | samyutirdvikavihina patkrti- stadgane kati maralaka vada || 68 || iti mulamisrajatih || atha bhinnadrsyajatau sutram-- drsyamsone rupe bhagabhyasena bhajite tatra | yallabdham tatsaram prajayate bhinnadrsyavidhau || 69 || • Broads yogah

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prakirnakavyavaharah atroddesakah | sikatayamastamsastandrsto'stadasamsasanganitah | stambhasyartham drstam stambhayamah kiyan kathaya || 70 || dvibhaktanavamamsakaprahatasaptavimsamsakah pramodamavatisthate karikulasya prthvitale | vinilajaladakrtirviharati tribhago nage vada tvamadhuna sarave karikulapramanam mama || 71 || sadhutkrtornivasati sodasamsaka- stribhajitah svakagunito vanantare | pado girau mama kathayasu tanmiti prottirnavan jaladhisamam prakirnakam || 02 || iti bhinnadrsyajatih || iti sarasanghahe ganitasastre mahaviracaryasya krti prakirnako nama trtiyavyavaharah samaptah || 1 B, M and K read gagane .

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