The Brahmasphutasiddhanta of Brahmagupta (A.D.628). ========================================== Digitalized by Takao Hayashi, 18 June 1993. Based on S. Dvivedin's edition, Benares 1902. Revised 29 June 1993. ========================================== The Brahmasphutasiddhanta consists of 24 chapters, but this digitalized version contains mathematical chapters only, that is, 1. Chpater 12 (ganita), 2. Chapter 18 (kuttaka), 3. Chapter 19 (sanku-chaya-vijnana), 4. Chapter 20 (chandas-citi-uttara), and 5. jna-prakarana (stanzas 17--23) of Chpater 21 (gola). ========================================== 旼컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴� � THIS TEXT FILE IS FOR REFERENCE PURPOSES ONLY! � � COPYRIGHT AND TERMS OF USAGE AS FOR SOURCE FILE. � � � � Text converted to Ronald E. Emmerick's encoding for � � WordPerfect 5.1 DOS and related utility programmes � � BHELA, CARAKA etc. (DOS versions): � � � � description character = ASCII � � � � long a � 195 � � long A � 249 � � long i � 197 � � long I � 253 � � long u � 198 � � long U � 244 � � vocalic r � 173 � � vocalic R � 227 � � long vocalic r � 204 � � vocalic l � 202 � � long vocalic l � 203 � � velar n � 199 � � velar N � 167 � � palatal n � 164 � � palatal N � 165 � � retroflex t � 194 � � retroflex T � 232 � � retroflex d � 172 � � retroflex D � 214 � � retroflex n � 239 � � retroflex N � 215 � � palatal s � 211 � � palatal S � 193 � � retroflex s � 171 � � retroflex S � 229 � � anusvara � 230 � � capital anusvara � 245 � � visarga � 247 � � capital visarga � 234 � 읕컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴� Notation (local rules) [D: x > y] indicates that Dvivedin, the editor, suggests the reading, y, instead of x. In Chapter 18: [Cb.n] indicates that the stanza is given the number, n, in Colebrooke's translation. [Cb.@] indicates that the stanza does not exist in Colebrooke's translation. Otherwise, the stanza number coincides with Colebrooke's one. (Colebrooke's translation is available for Chapters 12 and 18 only. In Chapter 12, all the stanza numbers given by Dvivedin coincide with Colebrooke's .) As Chapter 20, on combinatrics concerning Sanskrit prosody, has not been deciphered yet, the text of that chapter is left exactly as it is in Dvivedin's edition without decomposition of compounds and sandhi. [atha ga�ita-adhy홿as] [parikarma-vi烟atis] BSS_12.1a/ parikarma-%vi烟atim yas sa�kalita-홥y홲 p춗hak vij홳홺i/ BSS_12.1c/ %aヂau ca vyavah홸홳 ch홿�-ant홳 bhavati ga�akas sas// BSS_12.2a/ vipar흓a-cheda-gu点s r촨yos cheda-a烟ak홹 sama-ched홹/ BSS_12.2c/ sa�kalite a烟홹 yojy홹 vyavakalite a烟a-antaram k홸yam// BSS_12.3a/ r�p췹i cheda-gu点ni a烟a-yut홳i %dvayos bah�n홲 v�/ BSS_12.3c/ pratyutpannas bhavati cheda-vadhena uddh춗as a烟a-vadhas// BSS_12.4a/ parivartya bh홪a-h홸a-cheda-a烟au cheda-sa�gu�a-chedas/ [D: parivarttya h춄-m홺ram] BSS_18.100c/ anyais datt홳 pra�n홳 ukty� evam s홥hayet kara�ais// [Cb.101] BSS_18.101a/ jana-sa�sadi daiva-vid홲 tejas n촨ayati bh홳us iva bh홳홲/ BSS_18.101c/ ku쩟홮홸a-pra�nais pathitais api kim punar %�ata-�as// [Cb.102, �: �ata-�as > s�trais] BSS_18.102a/ prati-s�tram am� pra�n홹 pathit홹 sa-udde�ake쳕 s�tre쳕/ BSS_18.102c/ 홸y�-%tri-adhika-%�atena ca ku쩟as ca %aヂ홥a�as adhy홿as// [Cb.103] BSS_18.102p/ iti �r�-br홫masphu헯siddh홳te ku쩟aka-adhy홿as %aヂ홥a�as// [�a�ku-ch홿�-홥i-jㅓnam] [pra�n홹] BSS_19.1a/ d�ヂv� dina-%ardha-gha헻k� yas arka-j쨅s ak첺-a烟ak홳 vij홳홺i/ BSS_19.1c/ udaya-antara-gha헻k홣his jㅓt홺 j쨎yam sas tantra-j쨅s// BSS_19.2a/ asta-antara-gha헻k홣his yas jㅓt홺 j쨎yam 홳ayati tastm홺/ BSS_19.2c/ madhya-gatim yuga-bha-ga点n 홳ayati tatas sas tantra-j쨅s// BSS_19.3a/ 홳ayati yas tamas-ravi-�a�a-a�ka-m홳홳i d흍aka-�ikha-auccy홺/ BSS_19.3c/ �a�ku-tala-antara-bh�mi-jㅓne ch홿홲 sas tantra-j쨅s// BSS_19.4a/ iヂa-g춉a-auccya-j쨅s yas tad-antara-j쨅s nir흆쳙ate tu jale/ BSS_19.4c/ g춉a-bhitti-agram dar�ayati darpa�e v� sas tantra-j쨅s// BSS_19.5a/ ch홿�-%dvit흝a-bh�-agra-antara-vijㅓnena vetti d흍a-aucyam/ BSS_19.5c/ �a�ku-ch홿�-j쨅s v� bh�mes ch홿홲 sas tantra-j쨅s// [D: �a�ka- < �a�ku-] BSS_19.6a/ d�ヂv� g춉a-tala-antara-j홯abhos d�ヂv� agram g춉asya bh�mi-j쨅s/ [D: d�ヂv� g춉a-tala-antara-j홯abhos > g춉a-puru첺-antara-salile yas] BSS_19.6c/ vetti g춉a-auccyam d�ヂv� taila-stham v� sas tantra-j쨅s// BSS_19.7a/ v흆쳙a g춉a-agram salile pras홸ya salilam punar sva-bh�-jㅓne/ BSS_19.7c/ 홳ayati jal홺 bh�mim g춉asya v� auccyam sas tantra-j쨅s// BSS_19.8a/ jㅓtais ch홿�-puru첺is vijㅓte toya-ku촽ayos vivare/ BSS_19.8c/ ku촽e arka-tejasas yas vetti 홸튬him sas tantra-j쨅s// [uttar췹i] BSS_19.9a/ iヂa-divasa-%ardha-gha헻k� gha헻k�-%pa쨇ada�a-antara-pr췹홹/ BSS_19.9c/ tad-divasa-cara-pr췹홹 tais ak첺m s홥hayet pr홮-vat// BSS_19.10a/ jㅓta-j쨎ya-grahayos udaya-antara-n챙ik홣his adhika-�nas/ BSS_19.10c/ udayais jㅓtas jㅓt홺 j쨎yas pr홮-aparayos j쨎yas// BSS_19.11a/ jㅓtas sa-bha-%ardhas udayais asta-antara-n챙ik홣his adhika-�nas/ BSS_19.11c/ jㅓt홺 p�rva-aparayos j쨎yas bha-%ardha-�nake j쨎yas// BSS_19.12a/ jㅓtam k춗v� madhyam bh�yas anya-dine tad-antaram bhuktis/ BSS_19.12c/ trair촨ikena bhukty� kalpa-graha-ma詮ala-홳ayanam// BSS_19.13a/ sthiti-%ardh홺 vipar흓am tamas-pram췹am sphu헯m graha�e/ BSS_19.13c/ m홳a-uday홺 ravi-indvos gha헻k�-avayavena bha-udaya-tas// BSS_19.14a/ d흍a-tala-�a�ku-talayos antaram iヂa-pram췹a-�a�ku-gu�am/ BSS_19.14c/ d흍a-�ikha-auccy홺 �a�kum vi�odhya �e첺-uddh춗am ch홿�// BSS_19.15a/ �a�ku-antare�a gu�it� ch홿� ch홿�-antare�a bhakt� bh�s / BSS_19.15c/ sa-ch홿� �a�ku-gu点 d흍a-auccyam ch홿ay� bhakt�// BSS_19.16a/ jㅓtv� �a�ku-ch홿홲 anup홺홺 s홥hayet samucchr홿홳/ BSS_19.16c/ g춉a-caitya-taru-nag홳홲 auccyam vijㅓya v� ch홿홲// BSS_19.17a/ yuta-d�ヂi-g춉a-auccya-h춗� hi antara-bh�mis d춌-auccya-sa�gu�it�// BSS_19.17c/ phala-bh�s nyaste toye prati-r�pa-agram g춉asya nar홺// BSS_19.18a/ g춉a-puru첺-antara-salile v흆쳙a g춉a-agram d춌-auccya-sa�gu�itam/ BSS_19.18c/ g춉a-toya-antaram auccyam g춉asya n�-jala-antare�a h춗am// BSS_19.19a/ %prathama-%dvit흝a-n�-jala-antara-antare�a uddh춗� jala-apas춗is/ BSS_19.19c/ d�ヂi-auccya-gu点 ucchr홿as toy홺 n�-jala-antara-gu点 bh�s// BSS_19.20a/ ch홿�-puru첺-chinnam jala-ku촽a-antaram av홶tam 홸튬his/ BSS_19.20c/ adhy홿as %vi烟ati-홸y췹홲 %ekonavi烟as ayam// [chandas-citi-uttaram] BSS_20.1a/ 춇varga� pary홿a� sam�hayog홼ayuk쳕 yugme쳕/ BSS_20.1c/ soy츠 pr홪vatpr홶t홥촨catu쳈ak츠 �e첺yuktyontya�// BSS_20.2a/ ek홥iyutavih흋홼홥yantau tadviparyayau y홼at/ BSS_20.2c/ varg홥i쳕 vi첺mayuj충 kramotkram홥vardhayetp홥홳// BSS_20.3a/ ekaikena dvy홥vy츠 soppappadhike쳕 tatpratiヂhe쳕/ BSS_20.3c/ varg홥irabh큰쩠nta� prast홸o bhavati yavamadhya�// BSS_20.4a/ s�nontyo dvipad홪ra� tripad홥y홳홲adha� p춗hak sa�khy�/ BSS_20.4c/ tacchodhyo vyeka� p춗hagnt홥r�pam�rdhvayutam// BSS_20.5a/ y홼at p홥홼yek홪acch홥var�e쳖athaikav춄dhe쳕/ BSS_20.5c/ r�p홥yutagh홺e varg홥y홳충 par� sa�khy�// BSS_20.6a/ r�p홥hikap홥홸dhevi첺meテrdhva� same쳕 p홥홸dhe/ BSS_20.6c/ ardh홥vigu点vyek충yul홳yadhastasya sarveッm// BSS_20.7a/ m홥hyais tath홸dhah흋ai� kramap홥air vyastatulyap홥홥ya�/ BSS_20.7c/ vi첺meravyeka� madhye prohy홥y홳yata� kury홺// BSS_20.8a/ saikakramatuly홥yair ny홹o'bhyadhiko vi�odhita� c홥ha�/ BSS_20.8c/ sa�khyaikya� t홥춌 y홥춌 prathamas trirahito naヂe// BSS_20.9a/ m홥hyai� k춗ai� ca dalitai� samasa�khy홿충 kramotkram홺 k첿ppam/ BSS_20.9c/ vi첺m홿충 vyek홿충 dalam kram홥 uttkram홺 saikam// BSS_20.10a/ samasa�khy홿충 sop홳akramotkram홣hy충 tathaiva vi첺m홣hy홲/ BSS_20.10c/ kalpy� pacite d�ヂe prathama� �eッk첺r췹yante// BSS_20.11a/ samadalasamavi첺m췹충 sa�khy홶홥홸dhasarvakalpavadha�/ BSS_20.11c/ sv홥yavadho'nyai� p홥ai� svaparasya pr홪vadha� saikai�// BSS_20.12a/ 홥y홥anantaro'dha� kalppo'nyatulyam홥ya� pr홮/ BSS_20.12c/ ny홹o vargo'nyona� prast홸o'rdhasamavi첺m췹홲// BSS_20.13a/ naヂenty홺 sv홥hasthonakalpagh홺o'rdhatulyavi첺m췹홲/ BSS_20.13c/ vyeka� p춗hak svavargoddh춗a� phala� tulyakaly홳홲// BSS_20.14a/ uddiヂe kalpah춗e't흓ai� prathama� phale sar�pe 'nya�/ BSS_20.14c/ asak춄varg충�ayute saike v홸dhasamavi첺m췹홲// BSS_20.15a/ kape쳕 p춗hak gurulaghusa�khyaik홥ibh홭it� pr홪vat/ BSS_20.15c/ vi첺me쳖홥yalagh�no laghubhir meru� sam홥흋홲// BSS_20.16a/ ekadvitayo� parato dvisa�gu�o'nantar홥vir�po'dha�/ BSS_20.16c/ vargadhar홥yonodalasamavi첺m췹충 dhvajo laghubhi�// BSS_20.17a/ laghusa�khy� padadalit� parato'dho'dha� ca �udhyati h춗� yai�/ BSS_20.17c/ dvigu点ntai� �uddhair vargaparair mandaro laghubhi�// BSS_20.18a/ k춗v홥ho'dha� kalpy홳yek홥yekottar홳adhasteッm/ BSS_20.18c/ sv홺 parato'nyaikyam adha� prast홸홥 uktavad ih홥yai�// BSS_20.19a/ guru첺ヂyek홳igha쩨dvigu点nyek충gul홳i sa�khy� sy홺/ BSS_20.19c/ dr홼i烟atir 홸y췹충 chanda�cityuttaro'dhy홿a�// BSS_20.19p/ iti �r�-br홫masphu헯-siddh홳te chanda�cityuttar홥hy홿o vi烟atitama�// [jy�-prakara�am] BSS_21.17a/ r촨i-%aヂa-a烟e쳕 a�k홳 pada-sandhibhyas krama-utkram홺 k춗v�/ BSS_21.17c/ badhn흝홺 s�tr췹i %dvayos %dvayos jy홹 tad-%ardh홳i// BSS_21.18a/ jy�-%ardh홳i jy�-%ardh홳홲 jy�-kha詮홳i antar췹i/ BSS_21.18c/ vyast홳i anty홺 atha v� i쳕s utkrama-jy� dhanus t홣hy홲// BSS_21.19a/ %eka-%dvi-%tri-gu点y홹 vy홹a-%ardha-k춗es p춗hak %caturthebhyas/ BSS_21.19c/ m�l홳i %aヂa-%dv홥a�a-%쳍촡�a-kha詮홳i atas any홳i// BSS_21.20a/ tulya-krama-utkrama-jy�-sama-kha詮aka-varga-yuti-%catur-bh홪am/ BSS_21.20c/ prohya anaヂam vy홹a-%ardha-vargatas tad-pade %prathamam// BSS_21.21a/ tad-#dala-kha詮홳i tad-�na-#jina-sam홳i %dvit흝am utpattau/ BSS_21.21c/ #k춗a-#yamala-%eka-#di�-#텁a-#i쳕-%sapta-#rasa-#gu�a-%nava-홥흋홲// BSS_21.22a/ evam j흚�-kha詮홳i alp홳i bah�ni v� 홥ya-kha詮홳i/ BSS_21.22c/ jy�-%ardh홳i v춗ta-paridhes %첺ヂha-%caturtha-%tri-bh홪홳홲// BSS_21.23a/ utkrama-sama-kha詮a-gu点t vy홹홺 atha v� %caturtha-bh홪홺 yat/ BSS_21.23c/ k춗v� ukta-kha詮ak홳i jy�-%ardha-홳ayanam na laghu asm홺//