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 8 - Saptamah khatavyavaharah
saptamah khatavyavaharah . sarvamarendramakutarcitapadapitham sarvajnamavyayama cintyamanantarupam | bhavyaprajasarasijakara balabhanum bhaktya namami sirasa jinavardhamanam || 1 || ksetrani yani vividhani puroditani tesam phalani gunitanyavagahanani (nena ) | karmanti kaundra phalasuksmavikalpitani vaksyami saptamamidam vyavaharakhatam || 2 || suksmaganitam . atra paribhasaslokah- hastaghane pamsunam dvatrimsatpalasatani puryani | utkiryante tasmat sattrimsatpalasataniha || 3 || khataganitaphalanayanasutram- 14 ksetraphalam vedhagunam samaravate vyavaharikam ganitam | mukhatalayutidalamatha satsankhyaptam syatsamikaranam || 4 || atroddesakah . | samacaturasrasyastau bahuh pratibahukasca vedhasca | ksetrasya vataganitam samaravate kim bhavedatra || 5 || tribhujasya ksetrasya dvatrimsadvahukasya vedhe tu | sattrimsadrstaste sadangulanyasya kim ganitam || 6 || sastasatavyasasya ksetrasya hi pancasastisahitasatam | vedho vrttasya tvam samaravate kim phalam kathaya || 7 || ayatacaturasrasya vyasah pancagravimsatirbahuh | sastirvedho'stasatam kathayasu samasya vatasya || 8 || SSL
ganitasarasangrahah . asmin khataganite karmantikasamjnaphalam ca aundrasamjnaphalam ca jnatva tabhyam karmantikaundrasamjnaphalabhyam suksmakhataphalanayanasutram- bahyabhyantara samsthitatattatksetrasthabahukotibhuvah | svapratibahusameta bhaktastatksetragananayanyonyam || 9 || gunitasca vedhagunitah karmantikasamjnaganitam syat | tadvahyantarasamsthitatattatksetre phalam samaniya || 10 || samyojya sankhyayaptam ksetranam veghagunitam ca | aundraphalam tatphalayorvisesakasya tribhagena || samyuktam karmantikaphalameva hi bhavati suksmaphalam || 113 || atroddesakah | samacaturasra vapi vimsatirupariha sodasaiva tale | " vedho nava kim ganitam ganitavidacaksva me sighram || 123 || vapi samatribahurvimsatirupariha sodasaiva tale | vedho nava kim ganitam karmantikamaundmapi ca suksmaphalam || 133 || samavrttasi vapi vimsatirupariha sodasaiva tale | vedho dvadasa dandah kim syatkarmantikaundrasuksmaphalam || 143 || ayatacaturasrasya tvayamassastireva vistarah | dvadasa mukhe tale'rtham vedho'stau kim phalam bhavati || 113 || navatirasitih saptatirayamascordhvamabhyamulesu | vistaro dvavimsat sodasa dasa sapta vedho'yam || 163 || vyasah sastirvadane madhye trimsattale tu pascadasa | samavrttasya ca vedhah sodasa kim tasya ganitaphalam || 173 ||
bahutraye'pi vedho nava kim tasyapi bhavati ganitaphalam || 183|| khatikayah khataganitaphalanayanasya ca khatikaya madhye suci- muravakaravat utsedhe sati khataganitaphalanayanasya ca sutram-- parivamukhena sahito viskambhastribhujavrttayostrigunat | ayamacaturasre caturguno vyasa sangunitah || 193 || sucimukhavadvedhe parikha madhye tu parivardham | mukhasahitamatho karanam pragvattalasucivedhe ca || 203 || atroddesakah . tribhujacaturbhujavrttam puroditam parikhaya pariksiptam | dandasitya vyasah parikhascatururvikastrivedhah syuh || 21 || ayatacaturayamo visatyuttarasatam punarvyasah | catvarimsat parikha catururvika trivedha syat || 223 || utsedhe bahuprakaravati sati khataphalanayanasya ca yasya kasyacit khataphalam jnatva tatkhataphalat anyaksetrasya khataphalanayanasya ca sutram- vedhayutih sthanahrta vedho mukhaphalagunah svavataphalam | tricaturbhujavrttanam phalamanyaksetraphalahatam vedhah || 233 || atroddesakah | samacaturasraksetre bhumicaturhastamatra vistare | tatraikadvitricaturhastanikhate kiyan hi samavedhah || 24 || 14-A.
OF CULTURE MINISTRY OF CUL Of VERNEINDIA. krtima bharata sarakara 146 ganitasarasangrahah . samacaturasrastadasahastabhuja vapika caturvedha | vapi tajjalapurnanya navabahatra ko vedhah || 293 || SSL yasya kasyacitkhatasya urdhvasthitabhujasankhyam ca adhassthita - bhujasankhyam ca utsedhapramanam ca jnatva, tatkhate istotsedhasankhyayah bhujasankhyanayanasya, aghassucivedhasya ca sankhyanayanasya sutram- mukhagunavedho mukhatalasesahato'traiva sucivedhah syat | viparitavedhagunamurakhatalayutyavalambahrvyasah || 263 || atroddesakah | samacaturasra vapi vimsatirurdhve caturdasadhasca | vedho mukhe navadhastrayo bhujah ke'tra sucivedhah kah || 273 || golakakaraksetrasya phalanayana sutram- vyasarthaghanardhaguna nava golavyavaharikam ganitam | taddasamamsam navagunamasesasuksmam phalam bhavati || 283 || atroddesakah | sodasaviskambhasya ca golakavrttasya viganayya | kim vyavaharikaphalam suksmaphalam capi me kathaya || 293 || srngatakaksetrasya vatavyavaharikaphalasya vatasuksmaphalasya nva sutram - bhuna krtidalaghanagunadasapadanavahrdyavaharikam ganitam | trigunam dasapadabhaktam srngatakasuksmaghanaganitam || 20 || atroddesakah | vyasrasya ca srngatakasadubahughanasya ganayitva | kim vyavaharikaphalam ganitam suksmam bhavetkathaya || 31 ||
khatavyavaharah . vapaprinalikanam vimocane tattadistapranalikasamyoge tajjalena vapyam purnayam satyam tattatkalanayanasutram --- vapipranalikah svavakalabhaktah savarnavicchedah | tadyutibhaktam rupam dinamsakah syatpranalikayutya || taddina bhagahataste tajjalagatayo bhavanti tadvapyam || 33 || atroddesakah | catastrah pranalikah syustatraikaika prapurayati vapim | dvitricatuhpancasardinasya katibhirdinamsaistah || 34 || trairasikakhyacaturthaganitavyavahare sucanamatrodaharanameva ; atra samyagvistarya pravaksyate- samacaturasra vapi navahastaghana nagasya tale | tacchikharajjaladhara caturasrangulasamanaviskambha || 35 || patitagre vicchinna taya ghana santaralajalapurna | sailotsedham vayam jalapramanam ca me bruhi || 36 || vapi samacaturasra navahastaghana nagasya tale | angulasamavrttaghana jaladhara nipatita ca tacchikharat || 37 || agre vicchinnabhuttasya vapya mukham pravista hi | sa purnantaragata jaladharotsedhena sailasya | utsedham kathaya sarakhe jalapramanam ca viganayya || 38 || samacaturasra vapi navahasaghana nagasya tale | tacchikharajjaladhara patitangulaghanatrikona sa || 393 || vapimukhapravistha sagre chinnantaralajalapurna | kathaya sarakhe viganayya ca giryutsedham jalapramanam ca || 40 ||
ganitasarasangrahah . samacaturasra vapa navahastaghana nagasya tale | angulavistarangulakhatalayugaladirghajaladhara || 41 || patitagre vicchinna vapimukhasamsthitantaralajalaih | sampurna svadvapi giryutsedho jalapramanam kim || 423 || iti khatavyavahare suksmaganitam sampurnam | citiganitam . itah param svatavyavahare citiganitamudaharisyamah | atra pari- bhasa-- sutram hasto dirgho vyasastadardhamangalacatuskamutsedhah | drstastathestakayastabhih karmani karyani || 43 || istaksetrasya khataphalanayane ca tasya khataphalasya istakanayane ca mukhaphalamudayena gunam tadistakaganita bhaktalabdham yat | citiganitam tadvidyattadeva bhavatistakasankhya || 44 || atroddesakah | vedih samacaturasra sastabhuja hastanavakamutsedhah | ghatita tadistakabhih katistakah kathaya ganitajna || 49 || astakarasamatrikonanavahastotsedhavedika racita | purvestakabhirasyam katistakah kathaya viganayya || 46 || samavrttakrtive dina vahastordhva karastakavyasa | ghatitestakabhirasyam kartistakah kathaya ganitajna || 47 || ayatacaturasrasya tvayamah sastireva vistarah | pancakrtih sad vedhastadistakacitimihacaksva || 48 ||
149 khatavyavaharah . prakarasya vyasah sapta caturvimsatistadayamah | ghathitestakah kati syusvocchrayo vimsatistasya || 49 || vyasah prakarasyodhve sadagho'thasta tirthaka dirghah | ghatitestakah kati syussrocchrayo vimsatistasya || 103 || dvadasa sodasa vimsatirutsedhah sapta sat ca pancadhah | vyasa mukhe catustridvikascaturvimsatidirghah || 113 || istavedikayam patitayam satyam sthitasthane istakasa nkhyanayanasya ca patitasthane istakasankhyanayanasya ca sutram - mukhatalasesah patitotsedhagunah sakalavedhahrtsamukhah | mukhabhumyorbhumimukhe purvoktam karanamavasistam || 123 || atroddesakah | dvadasa dairghyam vyasah pascadhascordhvamekamutsedhah | dasa tasmin panca kara bhagnastatrestakah kati syustah || 133 || prakare karnakarena magre sati sthitestakanayanasya ca patitestaka- nayanasya ca sutram bhumimukhe dvigune murakhabhumiyute'bhagnabhudayayutone | dairyodayasasthamsanne sthitapatitestakah kramena syuh || 143 || atroddesakah | prakaro'yam mulanmadhyavartena vayuna viddhah | karnakrtya bhagnastatsthitapatitestakah kiyatyah syuh || 15 || prakaro'yam mulanmadhyavartena caikahastam gatva | karnakrtya bhagnah katistakah syuh sthitasca patitah kah || 163||
ganitasarasangrahah . prakaramadhyapradesotsedhe taravrddhacanayanasya prakarasya ubhayaparsvayoh tarahaneranayanasya ca sutram istestakodayahrto vedhasva tarapramaname honam | mukhatalasesena hrtam phalameva hi bhavati tarahanih || 57 || atroddesakah | prakarasya vyasah sapta tale vimsatistadutsedhah | ekenaye ghatitastaravrddhayune karodayestakaya || 18 || samavrttayam vapyam vyasacatuske'rdhayuktakarabhumih | ghatitestakabhirabhitastasyam vedhastrayah kah syuh | ghatitestakah sarakhe me viganayya bruhi yadi vetsi || 60 || istakaghatitasthale adhastalavyase sati urdhvatalavyase sati ca ganitanyayasutram dvigunaniveso vyasayamayuto dvigunitastadayamah | ayatacaturasre syadutsedhavyasasangunitah || 61 || atroddesakah | vidyadhara nagarasya vyaso'stau dvadasaiva cayamah | paca prakaratale mukhe tadekam dasotsedhah || 62 || iti khatavyavahare citiganitam samaptam | krakacikavyavaharah . itah param krakacika vyavaharamudaharisyamah | tatra paribhasa- hastadvayam sadangulahinam kiskahvayam bhavati | istadyantacchedana sankhyaiva hi margasamjna syat || 63 || atha sakakhyavyadidrumasamudayesu vaksyamanesu | vyasoda yamarganamangula samkhya parasparanapta || 64 ||
OF CULTURE MINISTRY OF CU GOVERNMENT bharata saraka E OF INDIA • khatavyavaharah . hastangulavargena krakacike pattikapramana syat | sakahayadrumadidrumesu parinahadairdhya hastanam || 61 || samkhya parasparana marganam samkhyaya gunita | tatpattikasamapta krakacakrta karmasamkhya syat || 66 || sakarjunamlavetasa saralasita sarja dundukakhyesu | sriparni ksakhyamesvami jekamargasya | sannavatirangulanamayamah kiskureva vistarah || 67 || atroddesakah | sakakhyatarau dirghah sodasa hastasca vistarah | sardhatrayasca margasvasti kanyatra karmani || 68 || iti khatavyavahare krakacikavyavaharah samaptah || SSL 151 iti sarasangrahe ganitasastre mahaviracaryasya krtau saptamah khata- vyavaharah samaptah ||