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
vͤ
and
wͦ
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
vā
/
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
vā
/
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
sā
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
vā
//
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
vā
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
vā
//
[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
vā
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
vā
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 //
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.
