Āryabhaṭīya with the Commentary (with commentary) · Chapter 32

chedāḥ parasparahatāḥ bhavanti guṇakārabhāgahārāṇām |
trayaḥ rāśayaḥ samāhṛtāḥ trirāśiḥ | trirāśiḥ prayojanam asya gaṇitasya iti trairāśikaḥ | trairāśike phalarāśiḥ trairāśikaphalarāśiḥ | tam trairāśikaphalarāśim | athaśabdaḥ parijñānavastuparigrahe uttaragranthapratipādane vartate | atra evaṃprakāraḥ arthaḥ kaḥ atra pratipāditaḥ ? ucyate ã paribhāṣā | sā ca lokavyavahārāt prativiṣayam bhinnā iti lokaprayogāt eva pradarśitā | anyathā hi prativiṣayam bhinnāḥ paribhāṣāḥ viṣayāḥ ca saṃkhyātītāḥ | tena upadeṣṭum
aśeṣataḥ sā na śakyate | ataḥ athaśabdena lokaprasiddhām paribhāṣām pratipādayati | icchārāśinā hatam kṛtvā, yaḥ asau phalarāśiḥ sa icchārāśinā hataḥ kriyate, tam icchārāśinā hatam guṇitam kṛtvā | labdham, labdham āptam | katham iti āha ã pramāṇabhajitam, pramāṇarāśinā bhajitam pramāṇabhajitam | tasmāt evaṃvidhāt rāśeḥ pramāṇabhajitāt | icchāphalam, icchāyāḥ phalam, icchāphalam, icchārāśiphalam iti arthaḥ | idam iti labdham pratyakṣīkṛtya uktam |
atra trairāśikam eva kevalam abhihitam ācāryāryabhaṭena, pañcarāśikādayaḥ anupātaviśeṣāḥ katham avagantavyāḥ ? ucyate ã anupātabījamātram eva ācāryeṇa upadiṣṭam ; tena anupātabījena sarvam eva pañcarāśyādikam siddhyati | kutaḥ ? pañcarāśikādīnām trairāśikasaṅghātatvāt | kasmāt pañcarāśyādayaḥ trairāśikasaṃhatāḥ ? pañcarāśike trairāśikadvayam saṃhatam, saptarāśike trairāśikatrayam, navarāśike trairāśikacatuṣṭayam iti ādi uddeśakeṣu
eva upadekṣyāmaḥ |
yadā punaḥ rāśayaḥ sacchedāḥ syuḥ tadā katham kartavyam iti āha ã
chedāḥ parasparahatāḥ bhavanti guṇakārabhāgahārāṇām |
chedāḥ parasparasya hatāḥ anyonyahatāḥ | keṣām iti ataḥ āha ã guṇakārabhāgahārāṇām | guṇyaguṇakārayoḥ parasparāpekṣayā guṇakāratvam , yasmāt guṇyaḥ guṇakāreṇa guṇyate, guṇakāraḥ api guṇyena, na kaścit phalaviśeṣaḥ | tena uktam guṇyaguṇakārau guṇakāraśabdena | guṇakārau ca bhāgahāraḥ ca guṇakārabhāgahārāḥ | ataḥ teṣām guṇakārabhāgahārāṇām chekāḥ parasparahatāḥ ye guṇakāracchedāḥ bhāgahārahatāḥ te bhāgahārāḥ bhavanti, bhāgahāracchedāḥ
ca guṇakārahatāḥ guṇakārāḥ bhavanti iti etat anuktam api avagamyate eva, yasmāt taddharmāya chedāḥ parasparam nīyante | bhāgahārāṇām saṃvargaḥ bhāgahāraḥ | guṇakārāṇām saṃvargaḥ guṇakāraḥ iti arthāt avagamyate |
uddeśakaḥ ã
candanapalāni pañca krītāni mayā hi rūpakaiḥ navabhiḥ |
candanam ekena tadā labhyam [ kim ] rūpakeṇa eva

tatra yathākrameṇa sthāpanā | uktam ca ã
ādyantayoḥ tu sadṛśau vijñeyau sthāpanāsu rāśīnām |
asadṛśarāśiḥ madhye trairāśikasādhanāya buddheḥ ||
iti |
nyāsaḥ ã 9 5 1
karaṇam ã rūpakaiḥ navabhiḥ pañcacandanapalāni iti nava pramāṇarāśiḥ, pañca phalarāśiḥ | ekena rūpeṇa kim iti ekam icchārāśiḥ | tena ekena icchārāśinā phalarāśiḥ guṇitaḥ 5, pramāṇarāśinā navakena vibhajyate
5
9 |
tatra phaleṣu bhāgam na prayacchati iti "catuṣkarṣam palam" iti caturbhiḥ guṇitam
20
9 |
labdham karṣadvayam karṣabhāgau ca [ navānām] | karṣab 2 karṣabhāgaḥ
2
9 |
uddeśakaḥ ã
ārdrakabhāraḥ daśabhiḥ sapañcabhāgaiḥ yadā abhivikrītaḥ |
palaśatamūlyam śīghram sārdhapalasya atra me vācyam

nyāsaḥ ã
2000 10 100
1 1
5 2
savarṇite sthāpanā ã
2000 51 201
5 2
"chedāḥ parasparahatāḥ" iti guṇakārayoḥ chedāḥ bhāgahāram gatāḥ | 5, 2 etābhyām chedābhyām bhāgahāraḥ guṇitaḥ jātaḥ 20000 | [ guṇakārayoḥ 201, 51 anayoḥ ghātaḥ ] 10251 | pūrvavat labdham viṃśopakāḥ 10, viṃśopakabhāgāḥ ca
251
1000 |
uddeśakaḥ ã
aṣṭābhiḥ satryaṃśaiḥ mṛganābhyā labhyate palam sadalam |
kṛtavīryeṇa vigaṇyam sapañcabhāgena kim mayā labhyam

nyāsaḥ ã
[ 8 1 1
1 1 1
3 2 5 ]
savarṇitena ã
[ 25 3 6
3 2 5 ]
[pūrvavat karaṇena ] kṛtavīryalabdham mṛganābhyā māṣakāḥ 13, guñjāḥ 4, guñjābhāgāḥ
3
25 |
uddeśakaḥ ã
nāgaḥ viṃśatihastaḥ praviśati ardhāṅgulam muhūrttena |
pratyeti ca pañcāṃśam katibhiḥ ahobhiḥ bilam prāptam

nyāsaḥ ã sarpaḥ 480 aṅgulātmakaḥ, praviśati ardhāṅgulam
1
2,
pratiyeti [ca aṅgulapañcabhāgaḥ
1
5 ] |
atra pañcabhāgaviśuddham ardhāṅgulam sarpasya mauhūrttikī gatiḥ iti pañcabhāgam ardhāt viśodhya sthāpanā ã 9
10,
muhūrtaḥ 1, sarpapramāṇāṅgulāni 480 |
labdham divasāḥ
53
1
3
miśrarāśiṣu api etat eva anupātabījam | tat yathā ã
uddeśakaḥ ã
aṣṭau dāntāḥ trayaḥ damyāḥ iti gāvaḥ prakīrtitāḥ |
ekāgrasya sahasrasya kati dāntāḥ kati itare

nyāsaḥ ã aṣṭau dantāḥ 8, trayaḥ damyāḥ 3, dantadamyānām ekottaram sahasram 1001 |
atra ayam trairāśikanyāsaḥ ã
dāntadamyāḥ 11, dāntāḥ 8, sarvasamudāyaḥ 1001 |
atra iyam vācaḥ yuktiḥ ã ekādaśabhiḥ dāntadamyaiḥ aṣṭau dāntāḥ labhyante, tat ekāgreṇa sahasreṇa kiyantaḥ dāntāḥ iti labdhāḥ dāntāḥ 728 tathā eva damyāḥ 273 |
evam prakṣepakaraṇeṣu api uddeśakaḥ ã
samavāyakāḥ tu vaṇijaḥ pañcaikaikottarādimūladhanāḥ |
lābhaḥ sahasrasaṃkhyaḥ vada kasmai tatra kim deyam

nyāsaḥ ã dhanāni 1, 2, 3, 4, 5 | lābhaḥ sahasram 1000 |
karaṇam ã prakṣepakadhanena anena 15, ayam lābhaḥ 1000 | yathākrameṇa ekena dvābhyām iti ādi labdhāḥ lābhāḥ [ prathamasya ]
66
2
3,
dvitīyasya
133
1
3,
tṛtīyasya 200, caturthasya
266
2
3,
pañcamasya
333
1
3 |
bhinne api uddeśakaḥ ã
ardhena tṛtīyena prakṣepeṇa aṣṭamena ye vaṇijaḥ |
saptatiḥ ekena ūnā lābhaḥ teṣām kiyān kasya

nyāsaḥ ã
1 1 1 | lābhaḥ 69 |
2 3 8
atra bhinnagaṇitanyāyena "chedaguṇaḥ sacchedam" iti savarṇite jātāḥ
12 8 9
24 24 24 | chedaiḥ prayojanam na asti iti aṃśāḥ kevalāḥ 12, 8, 3 | eteṣām pūrvavat prakṣepanyāyena ekatra [ yogaḥ ] 23 | anena prakṣepeṇa asya lābhasya 69 bhāgaḥ svāṃśaiḥ pṛthak pṛthak guṇitasya trairāśikavibhāgena labdhāḥ bhāgāḥ 36, 24, 9 |
[ pañcarāśikam ]
pañcarāśike uddeśakaḥ ã
śatavṛddhiḥ māse syāt pañca kiyān māsaṣaṭprayuktāyāḥ |
vṛddhim vada viṃśatyā yadi bhaṭagaṇitam tvayā buddham

nyāsaḥ ã 1001 20
1 6
5
karaṇam ã prathamatrairāśikam 100, 5, 20 | labdham rūpakaḥ 1 | dvitīyatrairāśikam ã yadi māsena rūpakaḥ, ṣaḍbhiḥ kiyantaḥ iti labdham rūpakāḥ ṣaṭ |
etat eva gaṇitam yugapat kriyamāṇam pañcarāśikam bhavati | tatra api śatasya māse iti [ śatam rūpam ca ] pramāṇarāśidvayam, pañca iti phalarāśiḥ viṃśatyā ṣaḍbhiḥ māsaiḥ kim iti viṃśatiḥ ṣaṭ ca icchārāśiḥ | tatra pūrvavat eva icchārāśiḥ phalarāśinā guṇitaḥ pramāṇarāśibhyām vibhajyate, phalam pūrvavat eva | trairāśikam eva etat dvidhā vyavasthitam | chedāḥ api pūrvavat guṇakārabhāgahārāṇām parasparam gacchanti |
[ uddeśakaḥ ] ã
[ śatasya māsadvaya]prayuktasya vṛddhiḥ paynnca | pañcaviṃśateḥ pañcamāsaprayuktāyāḥ kā vṛddhiḥ iti

nyāsaḥ ã 100 25 labdham 3
2 5 1
5 8
uddeśakaḥ ã
[śatasya ardhacatuṣka]māsaprayuktasya vṛddhiḥ ardhapañcakāḥ rūpakāḥ | tadā pañcāśataḥ daśamāsaprayuktasya kā vṛddhiḥ iti

nyāsaḥ ã 100 50
3 10
1
2
4
1
2
labdham rūpakāḥ ṣaṭ 6, saptabhāgāḥ trayaḥ ca
3
7 |
uddeśakaḥ ã
viṃśatyāḥ sārdhāyāḥ satryaṃśaḥ rūpakaḥ bhavet vṛddhiḥ |
māse sapañcabhāge pādonānām tu saptānām ||
māsaiḥ ṣaḍbhiḥ vācyam daśabhāgayutaiḥ tu kā bhavet vṛddhiḥ |
jñātvā chedavikalpam samyak bhaṭatantrasūtreṇa

savarṇite sthāpanā ã
41 27
2 4
6 61
5 10
4 0
3
labdham rūpakadvayam [ 2, viṃśopakāḥ ] 4, viṃśopakabhāgāḥ ca
26
41 |
[ saptarāśikam ]
saptarāśike uddeśakaḥ ã
saptocchritasya kariṇaḥ triṃśat paridheḥ navāyatasya yadā |
nava kuḍuvāḥ labhyante nityam saṃśuddhaśālipṛthukānām ||
pañcocchritasya vācyam saptāyām asya dantinaḥ kim syāt |
aṣṭāviṃśatiparidheḥ vācyāḥ pṛthukāḥ tadā labhyāḥ

sthāpanā ã 7 5
30 28
9 7
9 0
labdham pṛthukakuḍuvāḥ 4, setike 2, setikabhāgāḥ
2
3
uddeśakaḥ ã
hastyuttamasya caturhastocchritasya ṣaḍāyatasya pañcapariṇāhasya ardhatṛtīyāḥ kuḍuvāḥ labhyante māṣānām yadā tadā tryucchritasya pañcāyatasya ardhapañcamapariṇāhasya kim labhyam

nyāsaḥ ã 4 3
6 5
5 9
2
5 0
2
labdham kuḍuvaḥ 1, setikā 1, mānakau 2, ardhamānakam
1
2 |
evam navarāsyādiṣu yojyāḥ |
[ vyastatrairāśikam ]
vyastatrairāśikam api etat eva | tatra guṇakārabhāgahāraviparyāse viśeṣaḥ | tat yathā ã
[uddeśakaḥ ]
pañcasauvarṇike pale dṛṣṭāni ṣoḍaśā palāni suvarṇasya yadā tadā catussauvarṇike kiyanti iti

nyāsaḥ ã 5 16 4
atra pañcasauvarṇikena palena ṣoḍaśa palāni iti pañcabhiḥ ṣoḍaśa guṇitāḥ suvarṇāḥ bhavanti | ete suvarṇāḥ caturbhiḥ hrṭāḥ catussauvarṇikapalāni bhavanti | evam labdhāni palāni 20 |
svasiddhānte ca yadi vyāsārdhamaṇḍale bhujāphalam idam labhyate tadā tatkālotpannakarṇaviṣkambhārdhamaṇḍale kim iti tatra mahati karṇapramāṇe alpīyasyaḥ [ bhujāphalakalā ] bhavanti, alpakarṇe vahvyaḥ iti vyāsārdham guṇakāraḥ [ karṇaḥ bhāgahāraḥ ] |
uddeśakaḥ ã
aṣṭau piṭakāḥ dṛṣṭāḥ caturdaśaprasṛtikena mānena |
aṣṭaprasṛtikamāne piṭakāḥ ke syuḥ tadā vācyāḥ

nyāsaḥ ã 8 14 8
labdham piṭakāḥ 14 || 26-27 ||
[ kalāsavarṇanam ]
kalāsavarṇoddeśapradarśanārtham āryāpaścārdham āha ã
chedaguṇam sacchedam parasparam tat savarṇatvam