TITUS
Author: Brahm. 
Brahmagupta
Text: Brsph. 
Brāhmasphuṭasiddhānta

(A.D. 628)

On the basis of the edition by
S. Dvivedin,
Benares 1902

digitized by Takao Hayashi,
Kyōtō, 18.6.1993;
TITUS version by Jost Gippert,
Frankfurt a/M, 18.5.2000 / 1.6.2000 / 3.12.2008



The brāhmaspʰuṭasiddʰānta consists of 24 chapters, but this digitaliśed version contains mathematical chapters only, that is,
   1. Chapter 12 (gaṇita),
   2. Chapter 18 (kuṭṭaka),
   3. Chapter 19 (śaṅku-cʰāyā-vijñāna),
   4. Chapter 20 (cʰandas-citi-uttara), and
   5. jyā-prakaraṇa (stanśas 17--23) of Chpater 21 (gola).



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.


[Different from the original version, the symbols and are replaced by ՙ and ^ in the TITUS edition.





Chapter: 12 
[atʰa gaṇita-adʰyāyas]
[parikarma-viṃśatis]


Verse: 1a    parikarma-ՙviṃśatim yas saṅkalita-ādyām pr̥tʰak vijānāti /
Verse: 1c    
ՙaṣṭau ca vyavahārān cʰāyā-antān bʰavati gaṇakas sas //
Verse: 2a    
viparīta-cʰeda-guṇās rāśyos cʰeda-aṃśakās sama-cʰedās /
Verse: 2c    
saṅkalite aṃśās yojyās vyavakalite aṃśa-antaram kāryam //
Verse: 3a    
rūpāṇi cʰeda-guṇāni aṃśa-yutāni ՙdvayos bahūnām /
Verse: 3c    
pratyutpannas bʰavati cʰeda-vadʰena uddʰr̥tas aṃśa-vadʰas //
Verse: 4a    
parivartya bʰāga-hāra-cʰeda-aṃśau cʰeda-saṃguṇa-cʰedas / [D: parivarttya<parivartya]
Verse: 4c    
aṃśas aṃśa-guṇas bʰājyasya bʰāga-hāras savarṇitayos //
Verse: 5a    
saṃvarṇita--aṃśa-vargas cʰeda-kr̥ti-vibʰājitas bʰavati vargas /
Verse: 5c    
saṃvarṇita-aṃśa-mūlam cʰeda-padena uddʰr̥tam mūlam //
Verse: 6a    
stʰāpyas antya-gʰanas antya-kr̥tis ՙtri-guṇa-uttara-saṅguṇā ca tad-ՙpratʰamāt /
Verse: 6c    
uttara-kr̥tis antya-guṇā ՙtri-guṇā ca uttara-gʰanas ca gʰanas //
Verse: 7a    
cʰedas gʰanāt ՙdvitīyāt gʰana-mūla-kr̥tis ՙtri-saṅguṇā āpta-kr̥tis /
Verse: 7c    
śodʰyā ՙtri-pūrva-guṇitā ՙpratʰamāt gʰanatas gʰanas mūlam //
Verse: 8a    
sadr̥śa-cʰeda-aṃśa-yutis cʰeda-vibʰaktā pʰalam ՙpratʰama-jātau /
Verse: 8c    
aṃśais aṃśās guṇitās cʰedais cʰedās ՙdvitīyāyām //
Verse: 9a    
ūrdʰva-aṃśās cʰeda-guṇās ՙtr̥tīya-jātau ՙdvayos ՙpratʰama-parayos /
Verse: 9c    
cʰedais cʰedās guṇitās sva-aṃśa-yuta-ūnais upari-ga-aṃśās //
Verse: 10a    
trairāśike pramāṇam pʰalam iccā ādi-antayos sadr̥śa-rāśī /
Verse: 10c    
iccʰā pʰalena guṇitā pramāṇa-bʰaktā pʰalam bʰavati //
Verse: 11a    
vyasta-trairāśika-pʰalam iccʰā-bʰaktas pramāṇa-pʰala-gʰātas /
Verse: 11c    
trairāśika-ādiṣu pʰalam viṣameṣu ՙekādaśa-anteṣu //
Verse: 12a    
pʰala-saṅkramaṇam ubʰaya-tas bahu-rāśi-vadʰas alpa-vadʰa-hr̥tas jñeyam /
Verse: 12c    
sakaleṣu evam bʰinneṣu ubʰaya-tas cʰeda-saṅkramaṇam //
Verse: 13a    
prāk mūlya-vyatyāsas bʰāṇḍapratibʰāṇḍake anyat ukta-samam /
Verse: 13c    
parikarmāṇi ՙaṣṭānām vyavahārāṇām abʰihitāni //



[miśraka-vyavahāras]



Verse: 14a    
kāla-guṇitam pramāṇam pʰala-bʰaktam vi-ՙeka-guṇa-hatam kālas /
Verse: 14c    
sva-pʰala-yuta-ʰrūpa-bʰaktam mūla-pʰala-aikyam bʰavati mūlam //
Verse: 15a    
kāla-pramāṇa-gʰātas para-kāla-hr̥tas dvidʰā ādya-miśra-vadʰāt /
Verse: 15c    
anya-ՙardʰa-kr̥ti-yutāt padam anya-ՙardʰa-ūnam pramāṇa-pʰalam //
Verse: 16a    
prakṣepa-yoga-hr̥tayā labdʰyā prakṣepakās guṇās lābʰās /
Verse: 16c    
ūna-adʰika-uttarās tad-yuta-ūnayā sva-pʰalam ūna-yutam //



[śreḍʰī-vyavahāras]



Verse: 17a    
padam ՙeka-hīnam uttara-guṇitam saṃyuktam ādinā antya-dʰanam /
Verse: 17c    
ādi-yuta-antya-dʰana-ՙardʰam madʰya-dʰanam pada-guṇam gaṇitam //
Verse: 18a    
uttara-hīna-ՙdvi-guṇa-ādi-śeṣa-vargam dʰana-uttara-ՙaṣṭa-vadʰe /
Verse: 18c    
prakṣipya padam śeṣa-ūnam ՙdvi-guṇa-uttara-hr̥tam gaccʰas //
Verse: 19a    
ՙeka-uttaram ՙeka-ādyam yadi iṣṭa-gaccʰasya bʰavati saṅkalitam /
Verse: 19c    
tat ՙdvi-yuta-gaccʰa-guṇitam ՙtri-hr̥tam saṅkalita-saṅkalitam //
Verse: 20a    
ՙdvi-guṇa-pada-sa-ՙeka-guṇitam tat ՙtri-hr̥tam bʰavati varga-saṅkalitam /
Verse: 20c    
gʰana-saṅkalitam tad-kr̥tis eṣām sama-golakais citayas //



[kṣetra-vyavahāras]



Verse: 21a    
stʰūla-pʰalam ՙtri-ՙcatur-bʰuja-bāhu-pratibāhu-yoga-ʰdala-gʰātas /
Verse: 21c    
bʰuja-yoga-ՙardʰa-ՙcatuṣṭaya-bʰuja-ūna-gʰātāt padam sūkṣmam //
Verse: 22a    
bʰuja-kr̥ti-antara-bʰū-hr̥ta-hīna-yutā bʰūs ՙdvi-bʰājitā āvādʰe / [D: -kr̥tyantyantara-<-kr̥ti-antara-]
Verse: 22c    
sva-āvādʰā-varga-ūnāt bʰuja-vargāt mūlam avalambas //
Verse: 23a    
aviṣama-ՙcatur-asra-bʰuja--pratibʰuja-vadʰayos yutes padam karṇas /
Verse: 23c    
karṇa-kr̥tis bʰū-mukʰa-yuti-ʰdala-varga-ūnā padam lambas //
Verse: 24a    
karṇa-kr̥tes koṭi-kr̥tim viśodʰya mūlam bʰujas bʰujasya kr̥tim /
Verse: 24c    
prohya padam koṭis koṭi-bāhu-kr̥ti-yuti-padam karṇas // [D: vāhu < bāhu]
Verse: 25a    
karṇa-yutau ūrdʰva-adʰara-kʰaṇḍe karṇa-avalamba-yoge /
Verse: 25c    
sva-āvādʰe sva-yuti-hr̥te dvidʰā pr̥tʰak karṇa-lamba-guṇe //
Verse: 26a    
aviṣama-pārśva-bʰuja-guṇas karṇas ՙdvi-guṇa-avalambaka-vibʰaktas /
Verse: 26c    
hr̥dayam viṣamasya bʰuja-pratibʰuja-kr̥ti-yoga-mūla-ՙardʰam //
Verse: 27a    
ՙtri-bʰujasya vadʰas bʰujayos ՙdvi-guṇita-lamba-uddʰr̥tas hr̥daya-rajjus /
Verse: 27c    
ՙdvi-guṇā ՙtri-ՙcatur-bʰuja-koṇa-spr̥k vr̥tta-viṣkambʰas //
Verse: 28a    
karṇa-āśrita-bʰuja-gʰāta-aikyam ubʰayatʰā anyonya-bʰājitam guṇayet /
Verse: 28c    
yogena bʰuja-pratibʰuja-vadʰayos karṇau pade viṣame //
Verse: 29a    
viṣama-ՙcatur-asra-madʰye viṣama-ՙtri-bʰuja-ՙdvayam prakalpya pr̥tʰak /
Verse: 29c    
karṇa-ՙdvayena pūrva-vat āvādʰe lambakau ca pr̥tʰak //
Verse: 30a    
viṣama-bʰuja-antar-ՙtri-bʰuje prakalpya karṇau bʰujau tad-āvādʰe /
Verse: 30c    
pr̥tʰak ūrdʰva-adʰara-kʰaṇḍe karṇa-yutau karṇayos adʰare //
Verse: 31a    
ՙtri-bʰje bʰujau tu bʰūmis tad-lambas lambaka-adʰaram kʰaṇḍam /
Verse: 31c    
ūrdʰvam avalamba-kʰaṇḍam lambaka-yoga-ՙardʰam adʰara-ūnam //
Verse: 32a    
karṇa-avalambaka-yutau kʰaṇḍe karṇa-avalambakayos adʰare /
Verse: 32c    
anupātena tad-ūne ūrdʰve sūcyām sa-pāṭāyām //
Verse: 33a    
kr̥ti-yutis asadr̥śa-rāśyos bāhus gʰātas ՙdvi-saṅguṇas lambas /
Verse: 33c    
kr̥ti-antaram asadr̥śayos ՙdvi-guṇam ՙdvi-sama-ՙtri-bʰuja-bʰūmis //
Verse: 34a    
iṣṭa-ՙdvayena bʰaktas dvidʰā iṣṭa-vargas pʰala-iṣṭa-yoga-ՙardʰe /
Verse: 34c    
viṣama-ՙtri-bʰujasya bʰujau iṣṭa-ūna-pʰala-ՙardʰa-yogas bʰūs //
Verse: 35a    
iṣṭasya bʰujasya kr̥tis bʰaktā ūnā iṣṭena tad-ʰdalam koṭis /
Verse: 35c    
āyata-ՙcatur-asrasya kṣetrasya iṣṭa-adʰikā karṇas //
Verse: 36a    
āyata-karṇas bāhū bʰuja-kr̥tis iṣṭena bʰājitā iṣṭa-ūnā /
Verse: 36c    
ՙdvi-hr̥tā koṭi-adʰikā bʰūs mukʰam ūnā ՙdvi-sama-ՙcatur-asre //
Verse: 37a    
karṇa-kr̥tis ՙtri-sama-hbujās ՙtrayas ՙcaturtʰas viśodʰya koṭi-kr̥tim /
Verse: 37c    
bāhu-kr̥tes ՙtri-guṇāyās yadi adʰikas bʰūs mukʰam hīnas //
Verse: 38a    
jātya-ՙdvaya-koṭi-bʰujās para-karṇa-guṇās bʰujās ՙcatur-viṣame /
Verse: 38c    
adʰikas bʰūs mukʰa-hīnas bāhu-ՙdvitayam bʰujau anyau //
Verse: 39a    
iṣṭa-guṇa-kāra-guṇitas giri-uccʰrāyas pura-antaram anaṣṭam /
Verse: 39c    
ՙdvi-yuta-guṇa-kāra-bʰājitam utpātas anyasya sama-gatyos //
Verse: 40a    
vyāsa-vyāsa-ՙardʰa-kr̥tī paridʰi-pʰale vyāvahārike ՙtri-guṇe /
Verse: 40c    
tad-vargābʰyām ՙdaśabʰis saṅguṇitābʰyām pade sūkṣme //
Verse: 41a    
vr̥tte śara-ūna-guṇitāt vyāsāt ՙcatur-āhatāt padam jīvā /
Verse: 41c    
jyā-vargas ՙcatur-āhata-śara-bʰaktas śara-yutas vyāsas //
Verse: 42a    
jyā-vyāsa-kr̥ti-viśeṣāt mūla-vyāsa-antara-ՙardʰam iṣus alpas /
Verse: 42c    
vyāsau grāsa-ūna-guṇau grāsa-ūna-aikya-uddʰr̥tau bāṇau //
Verse: 43a    
iṣṭa-śara-ՙdvaya-bʰakte jyā-ՙardʰa-kr̥tī śara-yute pʰale vyāsau /
Verse: 43c    
śarayos pʰalayos aikyam grāsas grāsa-ūnam aikyam tat //



[kʰāta-vyavahāras]



Verse: 44a    
kṣetra-pʰalam vedʰa-guṇam sama-kʰāta-pʰalam hr̥tam ՙtribʰis sūcyās /
Verse: 44c    
mukʰa-tala-tulya-bʰuja-aikyāni ՙeka-agra-hr̥tāni sama-rajjus //
Verse: 45a    
mukʰa-tala-yuti-ʰdala-gaṇitam vedʰa-guṇam vyāvahārikam gaṇitam /
Verse: 45c    
mukʰa-tala-gaṇita-aikya-ՙardʰam vedʰa-guṇam syāt gaṇitam autram //
Verse: 46a    
autra-gaṇitāt viśodʰya vyavahāra-pʰalam bʰajet ՙtribʰis śeṣam /
Verse: 46c    
labdʰam vyavahāra-pʰale prakṣipya bʰavati pʰalam sūkṣmam //



[citi-vyavahāras]



Verse: 47a    
ākr̥ti-pʰalam auccya-āhatam agra-tala-aikya-ՙardʰam auccya-dairgʰya-guṇam /
Verse: 47c    
gʰana-gaṇitam iṣṭakā-gʰana-pʰalena hr̥tam iṣṭakā-gaṇitam //



[krākacika-vyavahāras]



Verse: 48a    
vistāra-āyāma-aṅgula-gʰātas mārga-āhatas ՙdvi-ʰveda-hr̥tas /
Verse: 48c    
kiṣku-aṅgulāni labdʰam tat ՙṣaṇṇavatis bʰavati karma //
Verse: 49a    
śākā-ādiṣu śālmalyām ՙśata-ՙdvayam bījake ՙśatam ՙviṃśam /
Verse: 49c    
śāla-sarala-ādiṣu ՙśatam atʰa avi-dāruṣu ՙcatuḥṣaṣṭis /



[rāśi-vyavahāras]



Verse: 50a    
ՙnavamas śūkiṣu ՙdaśamas stʰūleṣu ՙekādaśas bʰavati aṇuṣu /
Verse: 50c    
paridʰes vedʰas paridʰes ՙṣaṣ-aṃśa-varga-āhatas gaṇitam //
Verse: 51a    
ՙdvi-ՙcatur-sa-ՙtri-aṃśa-guṇas bʰitti-antar-vāhya-koṇa-gas paridʰis /
Verse: 51c    
prāk-vat kr̥tvā gaṇitam tad-gaṇitam sva-guṇa-kāra-hr̥tam //



[cʰāyā-vyavahāras]



Verse: 52a    
cʰāyā-nara-sa-ՙeka-hr̥tam dyu-ʰdalam prāk-aparayos dyu-gata-śeṣam /
Verse: 52c    
dina-gata-śeṣa-aṃśa-hr̥tam dyu-ʰdalam cʰāyā-nara-vi-ՙekam //
Verse: 53a    
dīpa-tala-śaṅku-talayos antaram iṣṭa-pramāṇa-śaṅku-guṇam /
Verse: 53c    
dīpa-śikʰa-auccyāt śaṅkum viśodʰya śeṣa-uddʰr̥tam cʰāyā //
Verse: 54a    
cʰāyā-agra-antara-guṇitā cʰāyā cʰāyā-antareṇa bʰaktā bʰūs /
Verse: 54c    
bʰūs śaṅku-guṇā cʰāyā-vibʰājitā dīpa-śikʰayā auccyam //



[pratyutpanna-ādayas]



Verse: 55a    
guṇa-kāra-kʰaṇḍa-tulyas guṇyas go-mūtrikā-kr̥tas guṇitas /
Verse: 55c    
sahitas pratyutpannas guṇa-kāraka-bʰeda-tulyas //
Verse: 56a    
guṇyas rāśis guṇa-kāra-rāśinā iṣṭa-adʰika-ūnakena guṇas /
Verse: 56c    
guṇya-iṣṭa-vadʰa-ūna-yutas guṇake abʰyadʰika-ūnake kāryas //
Verse: 57a    
cʰedena iṣṭa-yuta-ūnena āptam bʰājyāt anaṣṭam iṣṭa-guṇam /
Verse: 57c    
prakr̥ti-stʰa-cʰeda-hr̥tam labdʰyā yuta-hīnakam anaṣṭam //
Verse: 58a    
guṇyas cʰeda-pʰala-vadʰas guṇaka-hr̥tas guṇya-bʰājitas guṇakas /
Verse: 58c    
cʰeda-uddʰr̥tas pʰalam guṇya-guṇa-vadʰas pʰala-hr̥tas cʰedas //
Verse: 59a    
guṇya-guṇa-kārayos cʰeda-labdʰayos yadi ՙdvayos ՙdvayos nāśas /
Verse: 59c    
teṣām dr̥śyau vyastau kr̥tvā tad-stʰānayos ca iṣṭau //
Verse: 60a    
guṇyam guṇa-kāram guṇayet cʰedena bʰāga-hārasya /
Verse: 60c    
guṇya-guṇa-kāra-rāśyos cʰeda-guṇas bʰāga-hāras ca //
Verse: 61a    
accʰedasya cʰedam ^rūpam kr̥tvā anyat ukta-vat sarvam /
Verse: 61c    
apavartyau cʰeda-guṇau tulyena iṣṭena guṇyau // [D: avaparttyau < apavartyau]
Verse: 62a    
sva-vikala-ՙṣaṣṭi-aṃśa-guṇas sakalas ՙtriṃśa-uddʰr̥tas vikala-vargas /
Verse: 62c    
prakṣepyas sakala-kr̥tau varga-gʰanau ՙdvi-ՙtri-tulya-vadʰau //
Verse: 63a    
rāśes ūnam ՙdvi-guṇam bahutara-guṇam ūna-kr̥ti-yutam vargas /
Verse: 63c    
rāśes iṣṭa-yuta-ūnāt vadʰas kr̥tis iṣṭa-kr̥ti-yuktas //
Verse: 64a    
iṣṭa-alpa-rāśi-vargau yukta-ūnau itara-vikala-vargābʰyām /
Verse: 64c    
ՙdvi-guṇa-itara-rāśibʰyām bʰaktau tena adʰika-ūnābʰyām //
Verse: 65a    
stʰāna-antareṣu labdʰam yena samam pʰala-yuta-ūnaka-cʰedas /
Verse: 65c    
dalitas kr̥ti-yoga-antara-padam itaras pʰala-yuta-ūnas //
Verse: 66a    
dik-mātram etat anyat jyā-utpattau kuṭṭake ca katʰayiṣye /
Verse: 66c    
saṅkalita-ādiṣu āryās ՙṣaṭṣaṣṭis ՙdvādaśas adʰyāyas //
Verse: 66p    
iti śrī-brāhma-spʰuṭa-siddʰānte ՙdvādaśas adʰyāyas // 12 //



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This text is part of the TITUS edition of Brahmagupta, Brahmasphutasiddhanta.

Copyright TITUS Project, Frankfurt a/M, 8.12.2008. No parts of this document may be republished in any form without prior permission by the copyright holder.