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컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴커 � THIS TEXT FILE IS FOR REFERENCE PURPOSES ONLY! � � COPYRIGHT AND TERMS OF USAGE AS FOR SOURCE FILE. � � � � Text converted to Classical Sanskrit Extended � � (CSX) encoding: � � � � description character = ASCII � � � � long a � 224 � � long A � 226 � � long i � 227 � � long I � 228 � � long u � 229 � � long U � 230 � � vocalic r � 231 � � vocalic R � 232 � � long vocalic r � 233 � � vocalic l � 235 � � long vocalic l � 237 � � velar n � 239 � � velar N � 240 � � palatal n � 164 � � palatal N � 165 � � retroflex t � 241 � � retroflex T � 242 � � retroflex d � 243 � � retroflex D � 244 � � retroflex n � 245 � � retroflex N � 246 � � palatal s � 247 � � palatal S � 248 � � retroflex s � 249 � � retroflex S � 250 � � anusvara � 252 � � anusvara (overdot) � 167 � � capital anusvara � 253 � � visarga � 254 � � (capital visarga 255) � � � � Other characters of the CSX encoding table are � � not included. Accents have been dropped in order � � to facilitate word search. � 읕컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴켸 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-adhy�yas] [parikarma-vi嚆atis] BSS_12.1a/ parikarma-%vi嚆atim yas sa�kalita-�dy�m p�thak vij�n�ti/ BSS_12.1c/ %a亢au ca vyavah�r�n ch�y�-ant�n bhavati ga�akas sas// BSS_12.2a/ vipar�ta-cheda-gu鎚s r成yos cheda-a嚆ak�s sama-ched�s/ BSS_12.2c/ sa�kalite a嚆�s yojy�s vyavakalite a嚆a-antaram k�ryam// BSS_12.3a/ r�p性i cheda-gu鎚ni a嚆a-yut�ni %dvayos bah�n�m v�/ BSS_12.3c/ pratyutpannas bhavati cheda-vadhena uddh�tas a嚆a-vadhas// BSS_12.4a/ parivartya bh�ga-h�ra-cheda-a嚆au cheda-sa�gu�a-chedas/ [D: parivarttya h�d-m�tram] BSS_18.100c/ anyais datt�n pra�n�n ukty� evam s�dhayet kara�ais// [Cb.101] BSS_18.101a/ jana-sa�sadi daiva-vid�m tejas n成ayati bh�nus iva bh�n�m/ BSS_18.101c/ ku葺�k�ra-pra�nais pathitais api kim punar %�ata-�as// [Cb.102, �: �ata-�as > s�trais] BSS_18.102a/ prati-s�tram am� pra�n�s pathit�s sa-udde�ake�u s�tre�u/ BSS_18.102c/ �ry�-%tri-adhika-%�atena ca ku葺as ca %a亢�da�as adhy�yas// [Cb.103] BSS_18.102p/ iti �r�-br�hmasphu�asiddh�nte ku葺aka-adhy�yas %a亢�da�as// [�a�ku-ch�y�-�di-jㅰnam] [pra�n�s] BSS_19.1a/ d敖�v� dina-%ardha-gha�ik� yas arka-j쨅s ak�a-a嚆ak�n vij�n�ti/ BSS_19.1c/ udaya-antara-gha�ik�bhis jㅰt�t j쨎yam sas tantra-j쨅s// BSS_19.2a/ asta-antara-gha�ik�bhis yas jㅰt�t j쨎yam �nayati tastm�t/ BSS_19.2c/ madhya-gatim yuga-bha-ga鎚n �nayati tatas sas tantra-j쨅s// BSS_19.3a/ �nayati yas tamas-ravi-�a�a-a�ka-m�n�ni d�paka-�ikha-auccy�t/ BSS_19.3c/ �a�ku-tala-antara-bh�mi-jㅰne ch�y�m sas tantra-j쨅s// BSS_19.4a/ i亢a-g�ha-auccya-j쨅s yas tad-antara-j쨅s nir�k�yate tu jale/ BSS_19.4c/ g�ha-bhitti-agram dar�ayati darpa�e v� sas tantra-j쨅s// BSS_19.5a/ ch�y�-%dvit�ya-bh�-agra-antara-vijㅰnena vetti d�pa-aucyam/ BSS_19.5c/ �a�ku-ch�y�-j쨅s v� bh�mes ch�y�m sas tantra-j쨅s// [D: �a�ka- < �a�ku-] BSS_19.6a/ d敖�v� g�ha-tala-antara-j�labhos d敖�v� agram g�hasya bh�mi-j쨅s/ [D: d敖�v� g�ha-tala-antara-j�labhos > g�ha-puru�a-antara-salile yas] BSS_19.6c/ vetti g�ha-auccyam d敖�v� taila-stham v� sas tantra-j쨅s// BSS_19.7a/ v�k�ya g�ha-agram salile pras�rya salilam punar sva-bh�-jㅰne/ BSS_19.7c/ �nayati jal�t bh�mim g�hasya v� auccyam sas tantra-j쨅s// BSS_19.8a/ jㅰtais ch�y�-puru�ais vijㅰte toya-ku�yayos vivare/ BSS_19.8c/ ku�ye arka-tejasas yas vetti �r掩him sas tantra-j쨅s// [uttar性i] BSS_19.9a/ i亢a-divasa-%ardha-gha�ik� gha�ik�-%pa쨇ada�a-antara-pr性�s/ BSS_19.9c/ tad-divasa-cara-pr性�s tais ak�am s�dhayet pr�k-vat// BSS_19.10a/ jㅰta-j쨎ya-grahayos udaya-antara-n姓ik�bhis adhika-�nas/ BSS_19.10c/ udayais jㅰtas jㅰt�t j쨎yas pr�k-aparayos j쨎yas// BSS_19.11a/ jㅰtas sa-bha-%ardhas udayais asta-antara-n姓ik�bhis adhika-�nas/ BSS_19.11c/ jㅰt�t p�rva-aparayos j쨎yas bha-%ardha-�nake j쨎yas// BSS_19.12a/ jㅰtam k�tv� madhyam bh�yas anya-dine tad-antaram bhuktis/ BSS_19.12c/ trair成ikena bhukty� kalpa-graha-ma出ala-�nayanam// BSS_19.13a/ sthiti-%ardh�t vipar�tam tamas-pram性am sphu�am graha�e/ BSS_19.13c/ m�na-uday�t ravi-indvos gha�ik�-avayavena bha-udaya-tas// BSS_19.14a/ d�pa-tala-�a�ku-talayos antaram i亢a-pram性a-�a�ku-gu�am/ BSS_19.14c/ d�pa-�ikha-auccy�t �a�kum vi�odhya �e�a-uddh�tam ch�y�// BSS_19.15a/ �a�ku-antare�a gu�it� ch�y� ch�y�-antare�a bhakt� bh�s / BSS_19.15c/ sa-ch�y� �a�ku-gu鎚 d�pa-auccyam ch�yay� bhakt�// BSS_19.16a/ jㅰtv� �a�ku-ch�y�m anup�t�t s�dhayet samucchr�y�n/ BSS_19.16c/ g�ha-caitya-taru-nag�n�m auccyam vijㅰya v� ch�y�m// BSS_19.17a/ yuta-d敖�i-g�ha-auccya-h�t� hi antara-bh�mis d�k-auccya-sa�gu�it�// BSS_19.17c/ phala-bh�s nyaste toye prati-r�pa-agram g�hasya nar�t// BSS_19.18a/ g�ha-puru�a-antara-salile v�k�ya g�ha-agram d�k-auccya-sa�gu�itam/ BSS_19.18c/ g�ha-toya-antaram auccyam g�hasya n�-jala-antare�a h�tam// BSS_19.19a/ %prathama-%dvit�ya-n�-jala-antara-antare�a uddh�t� jala-apas�tis/ BSS_19.19c/ d敖�i-auccya-gu鎚 ucchr�yas toy�t n�-jala-antara-gu鎚 bh�s// BSS_19.20a/ ch�y�-puru�a-chinnam jala-ku�ya-antaram av�ptam �r掩his/ BSS_19.20c/ adhy�yas %vi嚆ati-�ry性�m %ekonavi嚆as ayam// [chandas-citi-uttaram] BSS_20.1a/ �gvarga� pary�ya� sam�hayog�vayuk�u yugme�u/ BSS_20.1c/ soy筬 pr�gvatpr�pt�d成catu�kak筬 �e�ayuktyontya�// BSS_20.2a/ ek�diyutavih�n�v�dyantau tadviparyayau y�vat/ BSS_20.2c/ varg�di�u vi�amayuj盛 kramotkram�dvardhayetp�d�n// BSS_20.3a/ ekaikena dvy�dvy筬 soppappadhike�u tatprati亢he�u/ BSS_20.3c/ varg�dirabh實焌nta� prast�ro bhavati yavamadhya�// BSS_20.4a/ s�nontyo dvipad�gra� tripad�dy�n�madha� p�thak sa�khy�/ BSS_20.4c/ tacchodhyo vyeka� p�thagnt�dr�pam�rdhvayutam// BSS_20.5a/ y�vat p�d�vyek�gacch�dvar�e�vathaikav�ddhe�u/ BSS_20.5c/ r�p�dyutagh�te varg�dy�n盛 par� sa�khy�// BSS_20.6a/ r�p�dhikap�d�rdhevi�ame緘rdhva� same�u p�d�rdhe/ BSS_20.6c/ ardh�dvigu鎚vyek盛yul�nyadhastasya sarve咸m// BSS_20.7a/ m�dhyais tath�rdhah�nai� kramap�dair vyastatulyap�d�dya�/ BSS_20.7c/ vi�ameravyeka� madhye prohy�dy�nyata� kury�t// BSS_20.8a/ saikakramatuly�dyair ny�so'bhyadhiko vi�odhita� c�dha�/ BSS_20.8c/ sa�khyaikya� t�d�k y�d�k prathamas trirahito na亢e// BSS_20.9a/ m�dhyai� k�tai� ca dalitai� samasa�khy�y盛 kramotkram�t k�eppam/ BSS_20.9c/ vi�am�y盛 vyek�y盛 dalam kram�d uttkram�t saikam// BSS_20.10a/ samasa�khy�y盛 sop�nakramotkram�bhy盛 tathaiva vi�am�bhy�m/ BSS_20.10c/ kalpy� pacite d敖�e prathama� �e咸k�ar性yante// BSS_20.11a/ samadalasamavi�am性盛 sa�khy�p�d�rdhasarvakalpavadha�/ BSS_20.11c/ sv�dyavadho'nyai� p�dai� svaparasya pr�gvadha� saikai�// BSS_20.12a/ �dy�danantaro'dha� kalppo'nyatulyam�dya� pr�k/ BSS_20.12c/ ny�so vargo'nyona� prast�ro'rdhasamavi�am性�m// BSS_20.13a/ na亢enty�t sv�dhasthonakalpagh�to'rdhatulyavi�am性�m/ BSS_20.13c/ vyeka� p�thak svavargoddh�ta� phala� tulyakaly�n�m// BSS_20.14a/ uddi亢e kalpah�te't�tai� prathama� phale sar�pe 'nya�/ BSS_20.14c/ asak�dvarg盛�ayute saike v�rdhasamavi�am性�m// BSS_20.15a/ kape�u p�thak gurulaghusa�khyaik�dibh�jit� pr�gvat/ BSS_20.15c/ vi�ame�v�dyalagh�no laghubhir meru� sam�d�n�m// BSS_20.16a/ ekadvitayo� parato dvisa�gu�o'nantar�dvir�po'dha�/ BSS_20.16c/ vargadhar�dyonodalasamavi�am性盛 dhvajo laghubhi�// BSS_20.17a/ laghusa�khy� padadalit� parato'dho'dha� ca �udhyati h�t� yai�/ BSS_20.17c/ dvigu鎚ntai� �uddhair vargaparair mandaro laghubhi�// BSS_20.18a/ k�tv�dho'dha� kalpy�nyek�dyekottar�nadhaste咸m/ BSS_20.18c/ sv�t parato'nyaikyam adha� prast�r�d uktavad ih�dyai�// BSS_20.19a/ guru�a亢yek�nigha蠢dvigu鎚nyek盛gul�ni sa�khy� sy�t/ BSS_20.19c/ dr�vi嚆atir �ry性盛 chanda�cityuttaro'dhy�ya�// BSS_20.19p/ iti �r�-br�hmasphu�a-siddh�nte chanda�cityuttar�dhy�yo vi嚆atitama�// [jy�-prakara�am] BSS_21.17a/ r成i-%a亢a-a嚆e�u a�k�n pada-sandhibhyas krama-utkram�t k�tv�/ BSS_21.17c/ badhn�y�t s�tr性i %dvayos %dvayos jy�s tad-%ardh�ni// BSS_21.18a/ jy�-%ardh�ni jy�-%ardh�n�m jy�-kha出�ni antar性i/ BSS_21.18c/ vyast�ni anty�t atha v� i�us utkrama-jy� dhanus t�bhy�m// BSS_21.19a/ %eka-%dvi-%tri-gu鎚y�s vy�sa-%ardha-k�tes p�thak %caturthebhyas/ BSS_21.19c/ m�l�ni %a亢a-%dv�da�a-%�o�a�a-kha出�ni atas any�ni// BSS_21.20a/ tulya-krama-utkrama-jy�-sama-kha出aka-varga-yuti-%catur-bh�gam/ BSS_21.20c/ prohya ana亢am vy�sa-%ardha-vargatas tad-pade %prathamam// BSS_21.21a/ tad-#dala-kha出�ni tad-�na-#jina-sam�ni %dvit�yam utpattau/ BSS_21.21c/ #k�ta-#yamala-%eka-#di�-#失a-#i�u-%sapta-#rasa-#gu�a-%nava-�d�n�m// BSS_21.22a/ evam j�v�-kha出�ni alp�ni bah�ni v� �dya-kha出�ni/ BSS_21.22c/ jy�-%ardh�ni v�tta-paridhes %�a亢ha-%caturtha-%tri-bh�g�n�m// BSS_21.23a/ utkrama-sama-kha出a-gu鎚t vy�s�t atha v� %caturtha-bh�g�t yat/ BSS_21.23c/ k�tv� ukta-kha出ak�ni jy�-%ardha-�nayanam na laghu asm�t//