Āryabhaṭīya with the Commentary (with commentary) · Chapter 42

ye ravimāsebhyaḥ adhikāḥ cāndramāsāḥ te yuge yuge adhimāsāḥ bhavanti, ye ca bhūdivasonāḥ śaśidivasāḥ te yuge tithipralayāḥ | pralayaḥ vināśaḥ | tithīnām pralayāḥ tithipralayāḥ | avamarātrāṇi iti arthaḥ | evam bruvatā etat pradarśitam bhavati ã sauryacāndrāntaram adhimāsabhogaḥ, sāvamam sāvanam cāndram mānam iti | adhikāvamayoḥ madhyamagatyā upacayaḥ iti uktam | yadi sphuṭagatyā syāt tadā dvitīyāyām pravṛttāyām pratipat tṛtīyā [ni]vṛttipravṛttī
na staḥ | adhimāsāvamaiḥ kim nirvartyate? ahargaṇaḥ iti āha | na etat asti, vinā api adhimāsāvamaiḥ ahargaṇasya nirvartitatvāt | na eṣaḥ doṣaḥ, upāyāntaratvāt | adhimāsāvamaiḥ vinā ahargaṇasya sādhanam pradarśitam | yena ca adhimāsāvamaiḥ ahargaṇaḥ labhyate sa upāyaḥ pradarśayitavyaḥ | na etat asti, ekopāyatvāt | sa ca ayam ca ekaḥ upāyaḥ | katham ekopāyatā? ye cāndramāsāḥ te sādhikāḥ teṣām sādhikatvāt sādhikaḥ eva māsarāśiḥ labhyate | punar api ca bhūdivasānām
rahitāvamatvāt trairāśikena rahitāvamaḥ ahargaṇaḥ labhyate | atha kaścit laghūkaraṇārthī guṇakārāt bhāgahāram apanayet tasya śeṣaguṇite labdham pratirāśitaguṇye [kṣipet] | yadi bhāgahārāt avaśiṣyate tatra śeṣaguṇite labdham guṇyāt pratirāśitāt apanīyam iti eṣaḥ gaṇitanyāyaḥ | atha atra guṇakārādhikatvāt māsāḥ kṣipyante bhāgahārādhikatvāt divasāḥ apacīyante iti ekopāyatā | tasmāt na arthaḥ anayā kārikayā, tathāpi lokavyavahārārtham adhimāsāvamānām
upadeśaḥ kartavyaḥ | lokaḥ ca adhimāsāvamaiḥ vyavaharati | uktam ca ã "karaṇādhiṣṭhitam adhimāsakam kuryāt", "triśatam sacatuṣpañcāśa[tam a]horātrāṇām karma sāṃvatsaraḥ" iti | adhimāsārtham trairāśikam ã yadi yugavarṣaiḥ māsaiḥ vā yugādhimāsakāḥ labhyante, tataḥ yātavarṣādibhiḥ kiyantaḥ iti adhimāsakalabdhiḥ | evam eva avamānām cāndradivasaiḥ iti |
atra ca ayam praśnaḥ ã "tena divākaroḍupau" iti ahargaṇena vinā candrādityānayanam | tat yathā ã yātavarṣeṣu dvādaśaguṇiteṣu gatamāsān kṣipet | tataḥ triṃśadguṇiteṣu divasān prakṣipya trairāśikam ã yadi pūrṇaviyadambarajaladharapayodharayamaśaraviṣayeṣucandraiḥ [1555200000] yugasauradivasaiḥ yugādhimāsakāḥ labhyante, tataḥ etaiḥ divasaiḥ kiyantaḥ iti, labhdam adhimāsakāḥ | śeṣe kṣepaḥ ucyate ã yadi bhūdivasatulyena avamaśeṣeṇa yugādhimāsatulyaḥ
upacayaḥ adhimāsakaśeṣasya labhyate, tadā anena avamaśeṣeṇa kiyān iti | yat labdham tat adhimāsakaśeṣe prakṣipya yugacāndramāsaiḥ rasarāmāgnigutāśanatrikṛtatriviṣayaiḥ [5343336] bhāgalabdham bhāgāḥ, ṣaṣṭiguṇite liptāḥ | triṃśaguṇādhikayutam divasarāśim kṛtvā trairāśikam ã yadi yugacāndradinaiḥ yugāvamadināni labhyante, tataḥ etaiḥ kim iti labhdam avamaḥ | śeṣam ṣaṣṭyā saṃguṇya bhūdivasaiḥ pūrṇāmbaraśaranagaśaśirandhramunigiriviṣayarūpaiḥ [1577917500]
vibhajet, labdham ghaṭikāḥ |
atha kim artham adhikāvamaśeṣayoḥ śaśimāsabhūdivasaiḥ bhāgaḥ hriyate? ucyate ã yaḥ asau adhimāsaśeṣaḥ sa cāndramāsāvayavaḥ | ataḥ tena sacchedena trairāśikam ã yadi yugaśaśimāsaiḥ sūryabhagaṇāḥ labhyante, tataḥ anena śaśimāsāvayavena kiyantaḥ iti | tatra śaśimāsāvayavacchedena saha ravibhagaṇena apavartanam ã ravibhagaṇānām ravibhagaṇabhāgena ekaḥ guṇakāraḥ, chedasya tāvat bhāgena ṣaṣṭiśatatrayam | tatra bhagaṇeṣu bhāgam na prayacchati
iti dvādaśa triṃśat ca guṇakāraḥ | tatra ṣaṣṭiśatatrayabhāgena rūpam, tāvat bhāgena eva chedasya api rūpam eva | śaśimāsāḥ eva kevalāḥ bhāgahārāḥ iti | avamaśeṣaḥ api bhūdināvayavaḥ iti trairāśikam ã yadi bhūdinaiḥ cāndradivasāḥ labhyante, tataḥ anena bhūdivasāvayavena cāndradivasacchedena kim iti | tatra guṇakārabhāgahārayoḥ tulyatvāt nāśaḥ | śeṣe ṣaṣṭiguṇe bhūdivasabhakte ghaṭikāḥ iti | atha yātavarṣāṇi bhagaṇāḥ, māsāḥ rāśayaḥ, dināni bhāgāḥ iti parikalpya
avamaśeṣalabdhaghaṭikāḥ ca liptāḥ | ebhyaḥ adhikaśeṣalabdham viśodhayet | śeṣam madhyamasūryaḥ | tebhyaḥ eva trayodaśaguṇitebhyaḥ adhikaśeṣaphalam viśodhayet | śeṣam madhyamacandraḥ |
adhimāsakaiḥ api avamāḥ ānīyante | tat yathā ã abhīṣṭavarṣāṇi dinīkṛtya trairāśikam ã [yadi] yugasūryadivasaiḥ yugādhimāsakāḥ labhyante, tataḥ etaiḥ abhīṣṭasūryadivasaiḥ kiyantaḥ iti, adhimāsakāḥ samatikrāntāḥ labhyante, vartamānasya ca śeṣaḥ | tat etat trairāśikam ã yadi yugādhimāsaiḥ yugāvamarātrā[ṇi] labhyante tataḥ etaiḥ adhimāsakaiḥ abhīṣṭaiḥ kiyantaḥ iti gaṇitanyāyena savarṇīkṛtya yugāvamaiḥ guṇayet | athavā abhīṣṭādhimāsarāśim aṃśarāśim
ca pṛthak pṛthak yugāvamaiḥ saṃguṇayya aṃśarāśim yugasūryadivasaiḥ vibhajya labhdam upari kṣiptvā yugādhimāsakaiḥ bhāgalabdham abhīṣṭakālāvamāḥ | athavā trairāśikadvayam bhaṅktvā api ānīyante ã yadi yugasūryadivasaiḥ adhimāsakāḥ labhyante, tataḥ abhīṣṭadivasaiḥ kiyantaḥ iti ekam trairāśikam | tataḥ punar api ã yadi yugādhimāsakaiḥ yugāvamāḥ labhyante, tataḥ trairāsikanyāyaviracitarāśyutpannādhimāsakaiḥ kiyantaḥ iti | tatra pūrvatrairāśike yugādhimāsakaḥ
guṇakāraḥ dvitīyatrairāśike bhāgahāraḥ | ataḥ guṇakārabhāgahārayoḥ tulyatvāt naṣṭayoḥ abhīṣṭadivasānām yugāvamaḥ guṇakāraḥ, yugasauryadivasaḥ bhāgahāraḥ, labdham abhīṣṭāvamāḥ |
abhīṣṭāvamaiḥ api adhimāsakāḥ ānīyante | abhīṣṭavarṣamāseṣu tat utpannādhimāsakān prakṣipya triṃśatā saṃguṇayya trairāśikadvayam kriyate ã yadi yugaśaśidivasaiḥ yugāvamāḥ labhyante tataḥ abhīṣṭaśaśidivasaiḥ kiyantaḥ iti avamāḥ | evam ekam trairāsikam | punar ã yadi yugāvamaiḥ yugādhimāsakāḥ labhyante tataḥ abhīṣṭāvamaiḥ pūrvatrairāśikaviracitaiḥ kiyantaḥ iti, adhimāsakāḥ labhyante | tatra pūrvatrairāśike yugāvamāḥ guṇakāraḥ, iha bhāgahāraḥ
| ataḥ guṇakārabhāgahārayoḥ tulyatvāt naṣṭayoḥ yugaśaśidivasaḥ bhāgahāraḥ, yugādhimāsakaḥ guṇakāraḥ, phalam abhīṣṭādhimāsakāḥ | pūrvavat vā pṛthak pṛthak trairāśikena api karaṇīyam |
atha adhimāsakaiḥ abhīṣṭagrahāḥ api ānīyante | tat yathā ã yadi yugādhimāsakaiḥ abhīṣṭagrahabhagaṇāḥ labhyante, tadā iṣṭādhimāsakaiḥ kiyantaḥ iti | adhimāsapatanakālāvadheḥ abhīṣṭagrahabhagaṇādayaḥ labhyante | asau eva abhīṣṭakālikaḥ kriyate | katham? adhimāsaka[śeṣeṇa] abhīṣṭagrahabhagaṇān saṃguṇayya adhimāsakaiḥ guṇitaśaśidivasaiḥ vibhajet | tatra bhagaṇādayaḥ labhyante, [te] pūrvalabdhādhimāsakagrahabhagaṇeṣu yojyante tadā

avamarātrapatanakālāvadheḥ bhavati | tataḥ punar api avamarātraśeṣam ṣaṣṭyā saṃguṇayya śaśidivasaiḥ eva vibhajet | labdham ghaṭikāḥ | tataḥ ã yadi ṣaṣṭighaṭikābhiḥ abhīṣṭagrahabhuktiḥ labhyate, [tadā] ābhiḥ ghaṭikābhiḥ kim iti | labdham pūrvasthāpite grahe dadyāt, abhīṣṭadivasasya udayakālāvadheḥ [grahaḥ] bhavati |
atha avamaiḥ api ã yadi yugā[vamaiḥ abhīṣṭagrahabhagaṇāḥ] labhyante tataḥ yātāvamaiḥ kiyantaḥ iti | avamarātraparisamāptikālāvadheḥ abhīṣṭagrahabhagaṇādayaḥ labhyante, tataḥ iṣṭadivasaudayikaḥ kriyate | katham? avamarātraśeṣeṇa abhīṣṭagrahabhagaṇān saṃguṇayya yugāvamabhūdivasasaṃvargeṇa vibhajet | labdham bhagaṇādayaḥ | tān pūrvalabdhabhagaṇādiṣu kṣipet | audayikaḥ grahaḥ bhavati |
atra ayam praśnaḥ ã
avamaiḥ yaḥ adhikamāsān avamāni ca yaḥ karoti adhikamāsaiḥJ|
tābhyām vā graham iṣṭam tasya aham śiṣyatām yāmi

iti|
adhimāsāvamaśeṣābhyām sūryācandramasoḥ ānayanam uktam | idānīm avamaśeṣāt eva sarvagrahānayanam abhidhāsyate | tat yathā ã yugāvamam ṣaṣṭyā apavartya sthāpanā ã 418043 | atha ādityānayane tāvat ete apavartitāvamāḥ kena guṇitāḥ apavartitādityabhagaṇān apanīya tat apavartitabhūdinānām tu śuddham bhāgam dadyuḥ iti kuṭṭākāraḥ kriyate | tatra labdham kuṭṭākāraḥ saptendurasādrivasavaḥ, aṅkaiḥ api 87617 | anena avamaśeṣam saṃguṇayya
apavartitabhūdinaiḥ eva vibhajet | śeṣam tatra raveḥ maṇḍalaśeṣaḥ | etena ādityānayanam vyākhyātam |
uddeśakaḥ ã
ṣaṭsaptabāṇenduśarādriśūnyadasrapramāṇaḥ avamajātaśeṣaḥ |
etena śeṣaḥ ravimaṇḍalānām vācyaḥ vivasvān ca kalāntasaṅkhyam

avamaśeṣaḥ 20751576 | labdham raveḥ maṇḍalaśeṣaḥ 49665, raviḥ ca 2 | 24 | 58 |
candrasya api kuṭṭākārānayanam pūrvavat eva | apavartitāvamāḥ kena guṇitāḥ apavartitacandrabhagaṇān apanīyā apavartita[bhū]dinānām śuddham bhāgam prayacchati iti kuṭṭākāranyāyena labdham kuṭṭākāraḥ 2119236 | uddiṣṭāvamaśeṣeṇa candrānayanam |
athavā madhyamāt sūryāt sahayātabhagaṇaiḥ liptīkṛtya trairāśikam ã yadi yugaraviliptābhiḥ yugaśaśibhagaṇāḥ labhyante, [tadā] etābhiḥ yātaraviliptābhiḥ kiyantaḥ iti | labdham bhagaṇāḥ, śeṣe dvādaśādiguṇite madhyamaḥ candraḥ labhyate | athavā khakhaṣaḍghanena yadā yugaraviliptāḥ apavartitāḥ bhavanti [tadā] ravibhagaṇāḥ bhāgahāraḥ, śaśibhagaṇāḥ yātaraviliptānām guṇakāraḥ, phalam madhyamacandraliptāḥ | evam anena nyāyana candrāt abhīṣṭagrahāt
vā iṣṭagrahaḥ ānīyate | katham? nirjñātagrahayātaliptānām abhīṣṭagrahabhagaṇāḥ guṇakāraḥ nirjñātagrahayugaliptāḥ bhagaṇāḥ vā bhāgahāraḥ, phalam [bhagaṇāḥ] liptāḥ [vā] | atra ayam praśnaḥ ã
savituḥ śaśinam karoti yaḥ śaśinaḥ sthititaḥ tārakagrahān |
asmatsiddhāntavarjitāt kālajñapravaraḥ sa ucyate

iti

[ mānuṣapitṛdevavarṣapramāṇāni ]
mānuṣapitṛdevānām varṣapramāṇanirūpaṇāya āha ã
ravivarṣam mānuṣyam tat api triṃśadguṇam bhavati pitryam |
pitryam dvādaśaguṇitam divyam varṣam vinirdiṣṭam

ravivarṣam, raveḥ varṣam ravivarṣam | ravivarṣasya ca pramāṇam abhihitam ã "ravibhagaṇāḥ ravyabdāḥ" [kālakriyāí, 5] iti | raveḥ bhagaṇabhogaḥ mānuṣāṇām varṣam | yat eva raveḥ varṣam tat eva mānuṣāṇām varṣam iti | tat api triṃśadguṇam bhavati pitryam | tat mānuṣyam varṣam triṃśadguṇitam pitryam varṣam bhavati, yasmāt māsaḥ teṣām ahorātram | uktam ca ã "śaśimāsārdham pitaraḥ" [kālakriyāí, 17] iti | pitryam dvādaśaguṇitam divyam varṣam
vinirdiṣṭam | piṭrṇām yat varṣam tat dvādaśaguṇitam ekam varṣam devānām, yasmāt pitryam varṣam māsaḥ devānām | yathākrameṇa ekatriṃśatṣaṣṭiśatatraya[guṇam] ca [ravivarṣam] manujapitṛdevānām [varṣāṇi]

[yugamānam brahmadinapramāṇam ca]
caturyugabrahmadinajñāpanārtham āha ã
divyam varṣasahasram grahasāmānyam yugam dviṣaṭkaguṇam |
aṣṭottaram sahasram brāhmaḥ divasaḥ grahayugānām

yat etat divyam varṣam tat dvādaśabhiḥ sahasreṇa guṇitam grahasāmānyam yugam | grahāṇām sāmānyam grahasāmānyam | kim tat? yugam | yasmāt sarve grahāḥ sahaśīghroccaiḥ yugapat mīnameṣasandhau bhavanti, tasmāt yugam grahasāmānyam | tat ca viyadambarākāśaśūnyayamarāmavedāḥ [4320000] | etat eva kṛta-tretā-dvāpara-kalivarṣāṇām pramāṇam | asmākam tu yugapādāḥ sarve eva ca tulyakālāḥ | paurāṇikaiḥ tu bhinnakālāḥ vyākhyātāḥ ã
catvāri āhuḥ sahasrāṇi varṣāṇām yat kṛtam yugam |
tasya tāvat śatī sandhyā sandhyāṃśaḥ ca tathāvidhaḥ ||
itareṣu sasandhyeṣu sasandhyāṃśeṣu ca triṣu |
ekāpāyena vartante sahasrāṇi śatāni ca ||
[manusmṛtiḥ, 1.69-70]
iti | kṛtapramāṇam viyadambarākāśavasuyamamunicandrāḥ [1728000] | tretāpramāṇam viyadambarākāśarasanavārkāḥ [1296000] | dvāparapramāṇam viyadambarākāśavedarasavasavaḥ [864000] | kalipramāṇam viyadambarākāśayamarāmavedāḥ [432000] | samāsitāni viyadambarākāśaśūnyayamarāmavedāḥ [4320000]| kim punar atra yuktam ã purāṇakāraiḥ yathā bhinnapramāṇāni kṛtādīni vyākhyātāni tathā pratipattum, āhosvit yathā asmākam ācāryeṇa pratipāditāni samapramāṇāni
iti? yathā asmākam prasiddhāni tathā iti āha | yadi purāṇaprakriyāprasiddhāni yugapādapramāṇāni parigṛhyantām, tadā kaliyugādau grahāḥ mīnameṣasandhau yugapat madhyamagatyā na syuḥ | katham iti ucyate | yugapādānām trayāṇām ekatrapramāṇam viyadambarākāśāṣṭavasuvasurāmāḥ [3888000] iti etaiḥ ahargaṇam utpādya yathāvihitamadhyamagrahagaṇitaprakriyāyām yugapat mīnameṣasandhau madhyamagrahāḥ na labhyante | anayā eva prakriyayā idānīm
api grahagatyām sādhyamānāyām eva iṣṭagrahāṇām gatiḥ na labhyate | yadi punar samam eva kṛtādīnām pramāṇam tat idam trayāṇām api yugapādānām pramāṇam viyadambarākāśaśūnyakṛtayamāgnayaḥ [3240000], anena yātena sarvam iṣṭam upapadyate | tasmāt "yathā asmākam prasiddhāni " iti suṣṭhu uktam |
aṣṭottaram sahasram brāhmaḥ divasaḥ grahayugānām | grahayugam iti yat etat grahasāmānyam yugam tat parigṛhyate | tat aṣṭottareṇa sahasreṇa guṇitam prajāpateḥ ekadivasapramāṇam bhavati | nanu ca atra api paurāṇikaiḥ saha virudhyate | katham? paurāṇikaiḥ ã
sahasrayugaparyantam ahar yat brahmaṇaḥ viduḥ |
rātrim yugasahasrāntām te ahorātravidaḥ janāḥ ||
[bhagavadgītā, 8.17]
iti sahasrayugaparyantam brahmaṇaḥ divasapramāṇam uktam | atra ca aṣṭottaram sahasram caturyugānām iti | atra tāvat vicāryate | paurāṇikaiḥ ã "sahasrayugaparyantam ahar yat brahmaṇaḥ viduḥ" iti abhidhāya taiḥ eva ekasaptatiḥ caturyugānām manvantaram caturdaśa manavaḥ brāhmaḥ divasaḥ iti [abhihitam] | atra ekasaptatiḥ caturdaśaguṇitā sahasrasaṅkhyām na prāpnoti | ucyate ca ã caturdaśa manvantarāṇi brahmaṇaḥ divasaḥ, sahasram caturyugānām iti svavacanavirodhaḥ
| asmākam tu dvāsaptatiḥ caturyugānām manvantaram, aṣṭottarasahasram brāhmaḥ divasaḥ iti yuktisiddham etam | katham punar idam jñāyate dvāsaptatiḥ caturyugānām manvantaram iti? gītikāsūktatvāt |
kāhaḥ manavaḥ ḍha manuyugāḥ śkha | iti |
[gītikāí, 5]

[utsarpiṇyādiyugavibhāgaḥ]
utsarpiṇyapasarpiṇīsuṣamāduṣṣmāparijñānāya āha ãã
utsarpiṇī yugārdham paścāt apasarpiṇī yugārdham ca |
madhye yugasya suṣamā ādau ante duṣṣamā indūccāt