The brAhmasphuTasiddhAnta of brahmagupta (A.D.628). ========================================== Digitized by Takao Hayashi, 18 June 1993. Based on S. Dvivedin's edition, Benares 1902. Revised 29 June 1993. Revised 19 January 2002. ========================================== The brAhmasphuTasiddhAnta consists of 24 chapters, but this digitized version contains mathematical chapters only, that is, 1. Chpater 12 (gaNita), 2. Chapter 18 (kuTTaka), 3. Chapter 19 (zaGku-chAyA-vijJAna), 4. Chapter 20 (chandas-citi-uttara), and 5. jyA-prakaraNa (verses 17--23) of Chpater 21 (gola). Colebrooke's translation is available for Chapters 12 and 18. ========================================== Notation (local rules) [D: x > y] means that the editor (Dvivedin) suggests y for x. In Chapter 18: [Cb.n] means that the verse is given the number, n, in Colebrooke's translation. [Cb.@] means that the verse does not exist in Colebrooke's translation. Otherwise, the verse number coincides with Colebrooke's. In Chapter 12, all the verse numbers given by Dvivedin coincide with Colebrooke's . The text of Chapter 20, on combinatrics concerning Sanskrit prosody, is left exactly as it appears in Dvivedin's edition without the decomposition of compounds and sandhi, as the chapter has not been deciphered yet. ========================================== [atha gaNita-adhyAyas] [parikarma-viMzatis] BSS12.001a/ parikarma-%viMzatim yas saGkalita-AdyAm pRthak vijAnAti/ BSS12.001c/ %aSTau ca vyavahArAn chAyA-antAn bhavati gaNakas sas// BSS12.002a/ viparIta-cheda-guNAs rAzyos cheda-aMzakAs sama-chedAs/ BSS12.002c/ saGkalite aMzAs yojyAs vyavakalite aMza-antaram kAryam// BSS12.003a/ rUpANi cheda-guNAni aMza-yutAni %dvayos bahUnAm vA/ BSS12.003c/ pratyutpannas bhavati cheda-vadhena uddhRtas aMza-vadhas// BSS12.004a/ parivartya bhAga-hAra-cheda-aMzau cheda-saMguNa-chedas/ [D: parivarttya hRd-mAtram] BSS18.100c/ anyais dattAn praznAn uktyA evam sAdhayet karaNais// [Cb.101] BSS18.101a/ jana-saMsadi daiva-vidAm tejas nAzayati bhAnus iva bhAnAm/ BSS18.101c/ kuTTAkAra-praznais pathitais api kim punar %zata-zas// [Cb.102, D: zata-zas > sUtrais] BSS18.102a/ prati-sUtram amI praznAs pathitAs sa-uddezakeSu sUtreSu/ BSS18.102c/ AryA-%tri-adhika-%zatena ca kuTTas ca %aSTAdazas adhyAyas// [Cb.103] BSS18.102p/ iti zrI-brAhmasphuTasiddhAnte kuTTaka-adhyAyas %aSTAdazas// [zaGku-chAyA-Adi-jJAnam] [praznAs] BSS19.001a/ dRSTvA dina-%ardha-ghaTikA yas arka-jJas akSa-aMzakAn vijAnAti/ BSS19.001c/ udaya-antara-ghaTikAbhis jJAtAt jJeyam sas tantra-jJas// BSS19.002a/ asta-antara-ghaTikAbhis yas jJAtAt jJeyam Anayati tastmAt/ BSS19.002c/ madhya-gatim yuga-bha-gaNAn Anayati tatas sas tantra-jJas// BSS19.003a/ Anayati yas tamas-ravi-zaza-aGka-mAnAni dIpaka-zikha-auccyAt/ BSS19.003c/ zaGku-tala-antara-bhUmi-jJAne chAyAm sas tantra-jJas// BSS19.004a/ iSTa-gRha-auccya-jJas yas tad-antara-jJas nirIkSyate tu jale/ BSS19.004c/ gRha-bhitti-agram darzayati darpaNe vA sas tantra-jJas// BSS19.005a/ chAyA-%dvitIya-bhA-agra-antara-vijJAnena vetti dIpa-aucyam/ BSS19.005c/ zaGku-chAyA-jJas vA bhUmes chAyAm sas tantra-jJas// [D: zaGka- < zaGku-] BSS19.006a/ dRSTvA gRha-tala-antara-jAlabhos dRSTvA agram gRhasya bhUmi-jJas/ [D: dRSTvA gRha-tala-antara-jAlabhos > gRha-puruSa-antara-salile yas] BSS19.006c/ vetti gRha-auccyam dRSTvA taila-stham vA sas tantra-jJas// BSS19.007a/ vIkSya gRha-agram salile prasArya salilam punar sva-bhU-jJAne/ BSS19.007c/ Anayati jalAt bhUmim gRhasya vA auccyam sas tantra-jJas// BSS19.008a/ jJAtais chAyA-puruSais vijJAte toya-kuDyayos vivare/ BSS19.008c/ kuDye arka-tejasas yas vetti ArUDhim sas tantra-jJas// [uttarANi] BSS19.009a/ iSTa-divasa-%ardha-ghaTikA ghaTikA-%paJcadaza-antara-prANAs/ BSS19.009c/ tad-divasa-cara-prANAs tais akSam sAdhayet prAk-vat// BSS19.010a/ jJAta-jJeya-grahayos udaya-antara-nADikAbhis adhika-Unas/ BSS19.010c/ udayais jJAtas jJAtAt jJeyas prAk-aparayos jJeyas// BSS19.011a/ jJAtas sa-bha-%ardhas udayais asta-antara-nADikAbhis adhika-Unas/ BSS19.011c/ jJAtAt pUrva-aparayos jJeyas bha-%ardha-Unake jJeyas// BSS19.012a/ jJAtam kRtvA madhyam bhUyas anya-dine tad-antaram bhuktis/ BSS19.012c/ trairAzikena bhuktyA kalpa-graha-maNDala-Anayanam// BSS19.013a/ sthiti-%ardhAt viparItam tamas-pramANam sphuTam grahaNe/ BSS19.013c/ mAna-udayAt ravi-indvos ghaTikA-avayavena bha-udaya-tas// BSS19.014a/ dIpa-tala-zaGku-talayos antaram iSTa-pramANa-zaGku-guNam/ BSS19.014c/ dIpa-zikha-auccyAt zaGkum vizodhya zeSa-uddhRtam chAyA// BSS19.015a/ zaGku-antareNa guNitA chAyA chAyA-antareNa bhaktA bhUs / BSS19.015c/ sa-chAyA zaGku-guNA dIpa-auccyam chAyayA bhaktA// BSS19.016a/ jJAtvA zaGku-chAyAm anupAtAt sAdhayet samucchrAyAn/ BSS19.016c/ gRha-caitya-taru-nagAnAm auccyam vijJAya vA chAyAm// BSS19.017a/ yuta-dRSTi-gRha-auccya-hRtA hi antara-bhUmis dRk-auccya-saGguNitA// BSS19.017c/ phala-bhUs nyaste toye prati-rUpa-agram gRhasya narAt// BSS19.018a/ gRha-puruSa-antara-salile vIkSya gRha-agram dRk-auccya-saGguNitam/ BSS19.018c/ gRha-toya-antaram auccyam gRhasya nR-jala-antareNa hRtam// BSS19.019a/ %prathama-%dvitIya-nR-jala-antara-antareNa uddhRtA jala-apasRtis/ BSS19.019c/ dRSTi-auccya-guNA ucchrAyas toyAt nR-jala-antara-guNA bhUs// BSS19.020a/ chAyA-puruSa-chinnam jala-kuDya-antaram avAptam ArUDhis/ BSS19.020c/ adhyAyas %viMzati-AryANAm %ekonaviMzas ayam// [chandas-citi-uttaram] BSS20.001a/ RgvargaH paryAyaH samUhayogAvayukSu yugmeSu/ BSS20.001c/ soyAH prAgvatprAptAdAzcatuSkakAH zeSayuktyontyaH// BSS20.002a/ ekAdiyutavihInAvAdyantau tadviparyayau yAvat/ BSS20.002c/ vargAdiSu viSamayujAM kramotkramAdvardhayetpAdAn// BSS20.003a/ ekaikena dvyAdvyAH soppappadhikeSu tatpratiSTheSu/ BSS20.003c/ vargAdirabhISTAntaH prastAro bhavati yavamadhyaH// BSS20.004a/ sUnontyo dvipadAgraM tripadAdyAnAmadhaH pRthak saMkhyA/ BSS20.004c/ tacchodhyo vyekaH pRthagntAdrUpamUrdhvayutam// BSS20.005a/ yAvat pAdAvyekAgacchAdvarNeSvathaikavRddheSu/ BSS20.005c/ rUpAdyutaghAte vargAdyAnAM parA saMkhyA// BSS20.006a/ rUpAdhikapAdArdheviSameSUrdhvaH sameSu pAdArdhe/ BSS20.006c/ ardhAdviguNAvyekAMyulAnyadhastasya sarveSAm// BSS20.007a/ mAdhyais tathArdhahInaiH kramapAdair vyastatulyapAdAdyaH/ BSS20.007c/ viSameravyekaM madhye prohyAdyAnyataH kuryAt// BSS20.008a/ saikakramatulyAdyair nyAso'bhyadhiko vizodhitaz cAdhaH/ BSS20.008c/ saMkhyaikyaM tAdRk yAdRk prathamas trirahito naSTe// BSS20.009a/ mAdhyaiH kRtaiz ca dalitaiH samasaMkhyAyAM kramotkramAt kSeppam/ BSS20.009c/ viSamAyAM vyekAyAM dalam kramAd uttkramAt saikam// BSS20.010a/ samasaMkhyAyAM sopAnakramotkramAbhyAM tathaiva viSamAbhyAm/ BSS20.010c/ kalpyA pacite dRSTe prathamaH zeSAkSarANyante// BSS20.011a/ samadalasamaviSamANAM saMkhyApAdArdhasarvakalpavadhaH/ BSS20.011c/ svAdyavadho'nyaiH pAdaiH svaparasya prAgvadhaH saikaiH// BSS20.012a/ AdyAdanantaro'dhaH kalppo'nyatulyamAdyaH prAk/ BSS20.012c/ nyAso vargo'nyonaH prastAro'rdhasamaviSamANAm// BSS20.013a/ naSTentyAt svAdhasthonakalpaghAto'rdhatulyaviSamANAm/ BSS20.013c/ vyekaH pRthak svavargoddhRtaH phalaM tulyakalyAnAm// BSS20.014a/ uddiSTe kalpahRte'tItaiH prathamaH phale sarUpe 'nyaH/ BSS20.014c/ asakRdvargAMzayute saike vArdhasamaviSamANAm// BSS20.015a/ kapeSu pRthak gurulaghusaMkhyaikAdibhAjitA prAgvat/ BSS20.015c/ viSameSvAdyalaghUno laghubhir meruH samAdInAm// BSS20.016a/ ekadvitayoH parato dvisaMguNo'nantarAdvirUpo'dhaH/ BSS20.016c/ vargadharAdyonodalasamaviSamANAM dhvajo laghubhiH// BSS20.017a/ laghusaMkhyA padadalitA parato'dho'dhaz ca zudhyati hRtA yaiH/ BSS20.017c/ dviguNAntaiH zuddhair vargaparair mandaro laghubhiH// BSS20.018a/ kRtvAdho'dhaH kalpyAnyekAdyekottarAnadhasteSAm/ BSS20.018c/ svAt parato'nyaikyam adhaH prastArAd uktavad ihAdyaiH// BSS20.019a/ guruSaSTyekAnighaTIdviguNAnyekAMgulAni saMkhyA syAt/ BSS20.019c/ drAviMzatir AryANAM chandazcityuttaro'dhyAyaH// BSS20.019p/ iti zrI-brAhmasphuTa-siddhAnte chandazcityuttarAdhyAyo viMzatitamaH// [jyA-prakaraNam] BSS21.017a/ rAzi-%aSTa-aMzeSu aGkAn pada-sandhibhyas krama-utkramAt kRtvA/ BSS21.017c/ badhnIyAt sUtrANi %dvayos %dvayos jyAs tad-%ardhAni// BSS21.018a/ jyA-%ardhAni jyA-%ardhAnAm jyA-khaNDAni antarANi/ BSS21.018c/ vyastAni antyAt atha vA iSus utkrama-jyA dhanus tAbhyAm// BSS21.019a/ %eka-%dvi-%tri-guNAyAs vyAsa-%ardha-kRtes pRthak %caturthebhyas/ BSS21.019c/ mUlAni %aSTa-%dvAdaza-%SoDaza-khaNDAni atas anyAni// BSS21.020a/ tulya-krama-utkrama-jyA-sama-khaNDaka-varga-yuti-%catur-bhAgam/ BSS21.020c/ prohya anaSTam vyAsa-%ardha-vargatas tad-pade %prathamam// BSS21.021a/ tad-#dala-khaNDAni tad-Una-#jina-samAni %dvitIyam utpattau/ BSS21.021c/ #kRta-#yamala-%eka-#diz-#Iza-#iSu-%sapta-#rasa-#guNa-%nava-AdInAm// BSS21.022a/ evam jIvA-khaNDAni alpAni bahUni vA Adya-khaNDAni/ BSS21.022c/ jyA-%ardhAni vRtta-paridhes %SaSTha-%caturtha-%tri-bhAgAnAm// BSS21.023a/ utkrama-sama-khaNDa-guNAt vyAsAt atha vA %caturtha-bhAgAt yat/ BSS21.023c/ kRtvA ukta-khaNDakAni jyA-%ardha-Anayanam na laghu asmAt// ========End=======End=======End========