Sūrya Siddhānta

अचिन्त्याव्यक्तरूपाय निर्गुणाय गुणात्मने । समस्तजगदाधारमूर्तये ब्रह्मणे नमः ॥

acintyāvyaktarūpāya nirguṇāya guṇātmane | samastajagadādhāramūrtaye brahmaṇe namaḥ ||

To him whose form is unthinkable and unmanifest, who is without qualities and yet is the self of ⟨all⟩ qualities, whose embodied form is the support of the entire world — to Brahman, salutation.

अल्पावशिष्टे तु कृते मयो नाम महासुरः । रहस्यं परमं पुण्यं जिज्ञासुर् ज्ञानम् उत्तमम् ॥

alpāvaśiṣṭe tu kṛte mayo nāma mahāsuraḥ | rahasyaṃ paramaṃ puṇyaṃ jijñāsur jñānam uttamam ||

When but little of the Kṛta ⟨yuga⟩ remained, a great asura named Maya, desiring to know the supreme, holy, secret and highest knowledge —

वेदाङ्गम् अग्र्यम् अखिलं ज्योतिषां गतिकारणम् । आराधयन् विवस्वन्तं तपस् तेपे सुदुश्चरम् ॥

vedāṅgam agryam akhilaṃ jyotiṣāṃ gatikāraṇam | ārādhayan vivasvantaṃ tapas tepe suduścaram ||

— the foremost and entire Vedāṅga, the cause of the motions of the luminaries — worshipping Vivasvat ⟨the Sun⟩, performed austerity most hard to accomplish.

तोषितस् तपसा तेन प्रीतस् तस्मै वरार्थिने । ग्रहाणां चरितं प्रादान् मयाय सविता स्वयम् ॥

toṣitas tapasā tena prītas tasmai varārthine | grahāṇāṃ caritaṃ prādān mayāya savitā svayam ||

Gratified by that austerity and pleased, Savitṛ ⟨the Sun⟩ himself bestowed upon Maya, who sought a boon, the courses of the grahas.

विदितस् ते मया भावस् तोषितस् तपसा ह्य् अहम् । दद्यां कालाश्रयं ज्ञानं ग्रहाणां चरितं महत् ॥

viditas te mayā bhāvas toṣitas tapasā hy aham | dadyāṃ kālāśrayaṃ jñānaṃ grahāṇāṃ caritaṃ mahat ||

Your intention is known to me; I am indeed gratified by ⟨your⟩ austerity. I shall give ⟨you⟩ the knowledge that rests upon Time, the great course of the grahas.

न मे तेजःसहः कश्चिद् आख्यातुं नास्ति मे क्षणः । मदंशः पुरुषोऽयं ते निःशेषं कथयिष्यति ॥

na me tejaḥsahaḥ kaścid ākhyātuṃ nāsti me kṣaṇaḥ | madaṃśaḥ puruṣo'yaṃ te niḥśeṣaṃ kathayiṣyati ||

There is no one who can bear my radiance, and I have no leisure to declare ⟨it⟩. This Puruṣa, a portion of myself, will tell you the whole without remainder.

इत्य् उक्त्वान्तर्दधे देवः समादिश्यांशम् आत्मनः । स पुमान् मयम् आहेदं प्रणतं प्राञ्जलिस्थितम् ॥

ity uktvāntardadhe devaḥ samādiśyāṃśam ātmanaḥ | sa pumān mayam āhedaṃ praṇataṃ prāñjalisthitam ||

Having spoken thus, and having instructed a portion of himself, the god vanished. That Puruṣa said this to Maya, who stood bowed with joined palms —

शृणुष्वैकमनाः पूर्वं यद् उक्तं ज्ञानम् उत्तमम् । युगे युगे महर्षीणां स्वयम् एव विवस्वता ॥

śṛṇuṣvaikamanāḥ pūrvaṃ yad uktaṃ jñānam uttamam | yuge yuge maharṣīṇāṃ svayam eva vivasvatā ||

Listen with undivided mind to that highest knowledge which Vivasvat himself declared of old, in age after age, to the great sages.

शास्त्रम् आद्यं तद् एवेदं यत् पूर्वं प्राह भास्करः । युगानां परिवर्तेन कालभेदोऽत्र केवलः ॥

śāstram ādyaṃ tad evedaṃ yat pūrvaṃ prāha bhāskaraḥ | yugānāṃ parivartena kālabhedo'tra kevalaḥ ||

This is that very same primeval śāstra which Bhāskara ⟨the Sun⟩ declared before; here there is only a difference of time, through the revolution of the yugas.

लोकानाम् अन्तकृत् कालः कालोऽन्यः कलनात्मकः । स द्विधा स्थूलसूक्ष्मत्वान् मूर्तश् चामूर्त उच्यते ॥

lokānām antakṛt kālaḥ kālo'nyaḥ kalanātmakaḥ | sa dvidhā sthūlasūkṣmatvān mūrtaś cāmūrta ucyate ||

Time is the maker of the end of the worlds; another Time is of the nature of reckoning. That ⟨second Time⟩ is twofold, by reason of grossness and subtlety: it is called mūrta ⟨embodied⟩ and amūrta ⟨unembodied⟩.

प्राणादिः कथितो मूर्तस् त्रुट्याद्योऽमूर्तसंज्ञकः । षड्भिः प्राणैर् विनाडी स्यात् तत्षष्ट्या नाडिका स्मृता ॥

prāṇādiḥ kathito mūrtas truṭyādyo'mūrtasaṃjñakaḥ | ṣaḍbhiḥ prāṇair vināḍī syāt tatṣaṣṭyā nāḍikā smṛtā ||

That which begins with the prāṇa is declared mūrta; that which begins with the truṭi bears the name amūrta. By six prāṇas a vināḍī is made; by sixty of those a nāḍikā is recorded.

नाडीषष्ट्या तु नाक्षत्रम् अहोरात्रं प्रकीर्तितम् । तत्त्रिंशता भवेन् मासः सावनोऽर्कोदयैस् तथा ॥

nāḍīṣaṣṭyā tu nākṣatram ahorātraṃ prakīrtitam | tattriṃśatā bhaven māsaḥ sāvano'rkodayais tathā ||

By sixty nāḍīs a sidereal (nākṣatra) day-and-night is proclaimed. By thirty of those a month comes to be; and so too the civil (sāvana) ⟨month⟩, by ⟨thirty⟩ sunrises.

ऐन्दवस् तिथिभिस् तद्वत् संक्रान्त्या सौर उच्यते । मासैर् द्वादशभिर् वर्षं दिव्यं तद् अह उच्यते ॥

aindavas tithibhis tadvat saṃkrāntyā saura ucyate | māsair dvādaśabhir varṣaṃ divyaṃ tad aha ucyate ||

The lunar (aindava) ⟨month is reckoned⟩ likewise by tithis, and the solar (saura) is spoken of by the saṃkrānti. By twelve months a year ⟨comes to be⟩; that is called a divine (divya) day.

सुरासुराणाम् अन्योन्यम् अहोरात्रं विपर्ययात् । तत्षष्टिः षड्गुणा दिव्यं वर्षम् आसुरम् एव च ॥

surāsurāṇām anyonyam ahorātraṃ viparyayāt | tatṣaṣṭiḥ ṣaḍguṇā divyaṃ varṣam āsuram eva ca ||

For the gods and the asuras, day and night are mutually reversed. Sixty of those, multiplied by six ⟨= 360⟩, ⟨make⟩ a divine year, and likewise an āsura ⟨year⟩.

तद्द्वादशसहस्राणि चतुर्युगम् उदाहृतम् । सूर्याब्दसंख्यया द्वित्रिसागरैर् अयुताहतैः ॥

taddvādaśasahasrāṇi caturyugam udāhṛtam | sūryābdasaṃkhyayā dvitrisāgarair ayutāhataiḥ ||

Twelve thousand of those is declared a caturyuga. In the count of solar years it is 'two, three, oceans' ⟨= 432⟩ multiplied by ten thousand ⟨= 4,320,000⟩.

सन्ध्यासन्ध्यांशसहितं विज्ञेयं तच्चतुर्युगम् । कृतादीनां व्यवस्थेयं धर्मपादव्यवस्थया ॥

sandhyāsandhyāṃśasahitaṃ vijñeyaṃ taccaturyugam | kṛtādīnāṃ vyavastheyaṃ dharmapādavyavasthayā ||

That caturyuga is to be known as including its sandhyā and sandhyāṃśa. This arrangement of the Kṛta and the rest ⟨follows⟩ the arrangement of the quarters of dharma.

युगस्य दशमो भागश् चतुस्त्रिद्व्येकसङ्गुणः । क्रमात् कृतयुगादीनां षष्ठांशः सन्ध्ययोः स्वकः ॥

yugasya daśamo bhāgaś catustridvyekasaṅguṇaḥ | kramāt kṛtayugādīnāṃ ṣaṣṭhāṃśaḥ sandhyayoḥ svakaḥ ||

A tenth part of the yuga, multiplied by four, three, two and one in order, ⟨gives the measures⟩ of the Kṛta yuga and the rest; a sixth part ⟨of each⟩ is its own for the two twilights.

युगानां सप्ततिः सैका मन्वन्तरम् इहोच्यते । कृताब्दसंख्यस् तस्यान्ते सन्धिः प्रोक्तो जलप्लवः ॥

yugānāṃ saptatiḥ saikā manvantaram ihocyate | kṛtābdasaṃkhyas tasyānte sandhiḥ prokto jalaplavaḥ ||

Seventy-one yugas are here called a manvantara. At the end of it is declared a sandhi having the number of years of a Kṛta ⟨yuga⟩, which is a deluge of water.

ससन्धयस् ते मनवः कल्पे ज्ञेयाश् चतुर्दश । कृतप्रमाणः कल्पादौ सन्धिः पञ्चदशः स्मृतः ॥

sasandhayas te manavaḥ kalpe jñeyāś caturdaśa | kṛtapramāṇaḥ kalpādau sandhiḥ pañcadaśaḥ smṛtaḥ ||

Those Manus, together with their sandhis, are to be known as fourteen in a kalpa. At the beginning of the kalpa a fifteenth sandhi, of the measure of a Kṛta, is recorded.

इत्थम् युगसहस्रेण भूतसंहारकारकः । कल्पो ब्राह्मम् अहः प्रोक्तं शर्वरी तस्य तावती ॥

ittham yugasahasreṇa bhūtasaṃhārakārakaḥ | kalpo brāhmam ahaḥ proktaṃ śarvarī tasya tāvatī ||

Thus the kalpa, ⟨measured⟩ by a thousand yugas and bringing about the destruction of beings, is declared to be a day of Brahmā; his night is of the same length.

परमायुः शतं तस्य तयाहोरात्रसंख्यया । आयुषोऽर्धमितं तस्य शेषकल्पोऽयम् आदिमः ॥

paramāyuḥ śataṃ tasya tayāhorātrasaṃkhyayā | āyuṣo'rdhamitaṃ tasya śeṣakalpo'yam ādimaḥ ||

His full lifetime is a hundred ⟨years⟩ by that reckoning of days and nights. Half of that lifetime of his has passed; of the remainder, this is the first kalpa.

कल्पाद् अस्माच् च मनवः षड् व्यतीताः ससन्धयः । वैवस्वतस्य च मनोर् युगानां त्रिघनो गतः ॥

kalpād asmāc ca manavaḥ ṣaḍ vyatītāḥ sasandhayaḥ | vaivasvatasya ca manor yugānāṃ trighano gataḥ ||

And of this kalpa six Manus, with their sandhis, have gone by; and of the Manu Vaivasvata, the cube of three ⟨= 27⟩ of the yugas has elapsed.

अष्टाविंशाद् युगाद् अस्माद् यातम् एतत् कृतं युगम् । अतः कालं प्रसंख्याय संख्याम् एकत्र पिण्डयेत् ॥

aṣṭāviṃśād yugād asmād yātam etat kṛtaṃ yugam | ataḥ kālaṃ prasaṃkhyāya saṃkhyām ekatra piṇḍayet ||

Of this twenty-eighth yuga, this Kṛta yuga has passed. From this ⟨point⟩, having reckoned up the time, one should collect the number into one ⟨sum⟩.

ग्रहर्क्षदेवदैत्यादि सृजतोऽस्य चराचरम् । कृताद्रिवेदा दिव्याब्दाः शतघ्ना वेधसो गताः ॥

graharkṣadevadaityādi sṛjato'sya carācaram | kṛtādrivedā divyābdāḥ śataghnā vedhaso gatāḥ ||

Of him ⟨the Creator⟩, creating the grahas, the nakṣatras, the gods, the daityas and the rest, and ⟨all⟩ that moves and does not move — of Vedhas there have passed divine years ⟨numbering⟩ 'Kṛta, mountains, Vedas' ⟨= 474⟩ multiplied by a hundred ⟨= 47,400⟩.

पश्चाद् व्रजन्तोऽतिजवान् नक्षत्रैः सततं ग्रहाः । जीयमानास् तु लम्बन्ते तुल्यम् एव स्वमार्गगाः ॥

paścād vrajanto'tijavān nakṣatraiḥ satataṃ grahāḥ | jīyamānās tu lambante tulyam eva svamārgagāḥ ||

The grahas, moving westward continually, being overcome by the nakṣatras through ⟨their⟩ exceeding speed, fall behind equally, ⟨each⟩ travelling in its own path.

प्राग्गतित्वम् अतस् तेषां भगणैः प्रत्यहं गतिः । परिणाहवशाद् भिन्ना तद्वशाद् भानि भुञ्जते ॥

prāggatitvam atas teṣāṃ bhagaṇaiḥ pratyahaṃ gatiḥ | pariṇāhavaśād bhinnā tadvaśād bhāni bhuñjate ||

Hence comes their eastward motion. Their daily motion, ⟨derived⟩ from their revolutions, differs by reason of the circumference ⟨of each orbit⟩; and according to that they traverse the asterisms.

शीघ्रगस् तान्य् अथाल्पेन कालेन महताल्पगः । तेषां तु परिवर्तेन पौष्णान्ते भगणः स्मृतः ॥

śīghragas tāny athālpena kālena mahatālpagaḥ | teṣāṃ tu parivartena pauṣṇānte bhagaṇaḥ smṛtaḥ ||

The swift-moving ⟨graha traverses⟩ them in a short time, the slow-moving in a long one. By one revolution of these ⟨grahas⟩ a bhagaṇa is reckoned ⟨complete⟩ at the end of Pauṣṇa ⟨Revatī⟩.

विकलानां कला षष्ट्या तत्षष्ट्या भाग उच्यते । तत्त्रिंशता भवेद् राशिर् भगणो द्वादशैव ते ॥

vikalānāṃ kalā ṣaṣṭyā tatṣaṣṭyā bhāga ucyate | tattriṃśatā bhaved rāśir bhagaṇo dvādaśaiva te ||

By sixty vikalās a kalā ⟨is made⟩; by sixty of those a bhāga ⟨degree⟩ is spoken of. By thirty of those a rāśi comes to be; and twelve of them are a bhagaṇa ⟨revolution⟩.

युगे सूर्यज्ञशुक्राणाम् खचतुष्करदार्णवाः । कुजार्किगुरुशीघ्राणां भगणाः पूर्वयायिनाम् ॥

yuge sūryajñaśukrāṇām khacatuṣkaradārṇavāḥ | kujārkiguruśīghrāṇāṃ bhagaṇāḥ pūrvayāyinām ||

In a yuga, the revolutions of the Sun, Mercury and Venus, and of the śīghras of Mars, Saturn and Jupiter, which move eastward, are 'a set of four skies, teeth, ocean' ⟨= 4,320,000⟩.

इन्दो रसाग्नित्रित्रीषुसप्तभूधरमार्गणाः । दस्रत्र्यष्टरसाङ्काक्षिलोचनानि कुजस्य तु ॥

indo rasāgnitritrīṣusaptabhūdharamārgaṇāḥ | dasratryaṣṭarasāṅkākṣilocanāni kujasya tu ||

Of the Moon ⟨the revolutions are⟩ 'flavours, fires, three, three, arrows, seven, mountains, arrows' ⟨= 57,753,336⟩; but of Mars, 'Aśvins, three, eight, flavours, marks, eyes, eyes' ⟨= 2,296,832⟩.

बुधशीघ्रस्य शून्यर्तुखाद्रित्र्यङ्कनगेन्दवः । बृहस्पतेः खदस्राक्षिवेदषड्वह्नयस् तथा ॥

budhaśīghrasya śūnyartukhādritryaṅkanagendavaḥ | bṛhaspateḥ khadasrākṣivedaṣaḍvahnayas tathā ||

Of Mercury's śīghra ⟨apex, the revolutions in a yuga are⟩ 17,937,060; and of Jupiter, likewise, 364,220.

सितशीघ्रस्य षट्सप्तत्रियमाश्विखभूधराः । शनेर् भुजङ्गषट्पञ्चरसवेदनिशाकराः ॥

sitaśīghrasya ṣaṭsaptatriyamāśvikhabhūdharāḥ | śaner bhujaṅgaṣaṭpañcarasavedaniśākarāḥ ||

Of Venus's śīghra ⟨apex⟩, 7,022,376; of Saturn, 146,568.

चन्द्रोच्चस्याग्निशून्याश्विवसुसर्पार्णवा युगे । वामं पातस्य वस्वग्नियमाश्विशिखिदस्रकाः ॥

candroccasyāgniśūnyāśvivasusarpārṇavā yuge | vāmaṃ pātasya vasvagniyamāśviśikhidasrakāḥ ||

Of the Moon's apogee (candrocca), 488,203 in the yuga; and of the node (pāta), ⟨moving⟩ to the left — that is, retrograde — 232,238.

भानाम् अष्टाक्षिवस्वद्रित्रिद्विद्व्यष्टशरेन्दवः । भोदया भगणैः स्वैः स्वैर् ऊनाः स्वस्वोदया युगे ॥

bhānām aṣṭākṣivasvadritridvidvyaṣṭaśarendavaḥ | bhodayā bhagaṇaiḥ svaiḥ svair ūnāḥ svasvodayā yuge ||

Of the asterisms (bhāni), 1,582,237,828. The risings of the asterisms, each diminished by ⟨each graha's⟩ own revolutions, are the risings of each ⟨graha⟩ in the yuga.

भवन्ति शशिनो मासाः सूर्येन्दुभगणान्तरम् । रविमासोनितास् ते तु शेषाः स्युर् अधिमासकाः ॥

bhavanti śaśino māsāḥ sūryendubhagaṇāntaram | ravimāsonitās te tu śeṣāḥ syur adhimāsakāḥ ||

The difference between the revolutions of the Sun and of the Moon ⟨gives⟩ the lunar months. Those, diminished by the solar months — the remainders are the intercalary months (adhimāsa).

सावनाहानि चान्द्रेभ्यो द्युभ्यः प्रोज्झ्य तिथिक्षयाः । उदयाद् उदयं भानोर् भूमिसावनवासरः ॥

sāvanāhāni cāndrebhyo dyubhyaḥ projjhya tithikṣayāḥ | udayād udayaṃ bhānor bhūmisāvanavāsaraḥ ||

Having cast out the civil days from the lunar days, ⟨the remainders are⟩ the omitted lunar days (tithikṣaya). From the Sun's rising to ⟨its next⟩ rising is a terrestrial civil day.

वसुद्व्यष्टाद्रिरूपाङ्कसप्ताद्रितिथयो युगे । चान्द्राः खाष्टखखव्योमखाग्निखर्तुनिशाकराः ॥

vasudvyaṣṭādrirūpāṅkasaptādritithayo yuge | cāndrāḥ khāṣṭakhakhavyomakhāgnikhartuniśākarāḥ ||

In a yuga ⟨the civil days are⟩ 1,577,917,828; the lunar ⟨days⟩ 1,603,000,080.

षड्वह्नित्रिहुताशाङ्कतिथयश् चाधिमासकाः । तिथिक्षया यमार्थाश्विद्व्यष्टव्योमशराश्विनः ॥

ṣaḍvahnitrihutāśāṅkatithayaś cādhimāsakāḥ | tithikṣayā yamārthāśvidvyaṣṭavyomaśarāśvinaḥ ||

And the intercalary months are 1,593,336; the omitted lunar days, 25,082,252.

खचतुष्कसमुद्राष्टकुपञ्च रविमासकाः । भवन्ति भोदया भानुभगणैर् ऊनिताः क्वहाः ॥

khacatuṣkasamudrāṣṭakupañca ravimāsakāḥ | bhavanti bhodayā bhānubhagaṇair ūnitāḥ kvahāḥ ||

The solar months are 51,840,000. The risings of the asterisms, diminished by the Sun's revolutions, are the terrestrial days.

अधिमासोनरात्र्यार्क्षचान्द्रसावनवासराः । एते सहस्रगुणिताः कल्पे स्युर् भगणादयः ॥

adhimāsonarātryārkṣacāndrasāvanavāsarāḥ | ete sahasraguṇitāḥ kalpe syur bhagaṇādayaḥ ||

The intercalary months, the omitted days (ūnarātra), and the sidereal, lunar and civil days — these, multiplied by a thousand, are the revolutions and the rest in a kalpa.

प्राग्गतेः सूर्यमन्दस्य कल्पे सप्ताष्टवह्नयः । कौजस्य वेदखयमा बौधस्याष्टर्तुवह्नयः ॥

prāggateḥ sūryamandasya kalpe saptāṣṭavahnayaḥ | kaujasya vedakhayamā baudhasyāṣṭartuvahnayaḥ ||

Of the Sun's manda ⟨apex⟩, whose motion is eastward, in a kalpa: 387; of Mars's, 204; of Mercury's, 368.

खखरन्ध्राणि जैवस्य शौक्रस्यार्थगुणेषवः । गोऽग्नयः शनिमन्दस्य पातानाम् अथ वामतः ॥

khakharandhrāṇi jaivasya śaukrasyārthaguṇeṣavaḥ | go'gnayaḥ śanimandasya pātānām atha vāmataḥ ||

Of Jupiter's, 900; of Venus's, 535; of Saturn's manda ⟨apex⟩, 39. Now ⟨the revolutions⟩ of the nodes, ⟨which go⟩ to the left — that is, retrograde:

मनुदस्रास् तु कौजस्य बौधस्याष्टाष्टसागराः । कृताद्रिचन्द्रा जैवस्य त्रिखाङ्काश् च तथा भृगोस् ॥

manudasrās tu kaujasya baudhasyāṣṭāṣṭasāgarāḥ | kṛtādricandrā jaivasya trikhāṅkāś ca tathā bhṛgos ||

Of Mars's, 214; of Mercury's, 488; of Jupiter's, 174; and likewise of Venus's, 903.

शनिपातस्य भगणाः कल्पे यमरसर्तवः । भगणाः पूर्वम् एवात्र प्रोक्ताश् चन्द्रोच्चपातयोः ॥

śanipātasya bhagaṇāḥ kalpe yamarasartavaḥ | bhagaṇāḥ pūrvam evātra proktāś candroccapātayoḥ ||

The revolutions of Saturn's node in a kalpa are 662. The revolutions of the Moon's apogee and node have already been stated above.

षण्मनूनां तु सम्पीड्य कालं तत्सन्धिभिः सह । कल्पादिसन्धिना सार्धं वैवस्वतमनोस् तथा ॥

ṣaṇmanūnāṃ tu sampīḍya kālaṃ tatsandhibhiḥ saha | kalpādisandhinā sārdhaṃ vaivasvatamanos tathā ||

Having summed the time of the six Manus together with their junctions (sandhi), along with the junction at the beginning of the kalpa, and likewise ⟨the elapsed time⟩ of the Vaivasvata Manu —

युगानाम् त्रिघनं यातं तथा कृतयुगं त्व् इदम् । प्रोज्झ्य सृष्टेस् ततः कालं पूर्वोक्तं दिव्यसंख्यया ॥

yugānām trighanaṃ yātaṃ tathā kṛtayugaṃ tv idam | projjhya sṛṣṭes tataḥ kālaṃ pūrvoktaṃ divyasaṃkhyayā ||

— the twenty-seven ⟨mahā⟩yugas elapsed, and likewise this ⟨present⟩ Kṛta yuga; then, having cast out from that the time of the creation stated before, in divine reckoning,

सूर्याब्दसंख्यया ज्ञेयाः कृतस्यान्ते गता अमी । खचतुष्कयमाद्र्यग्निशररन्ध्रनिशाकराः ॥

sūryābdasaṃkhyayā jñeyāḥ kṛtasyānte gatā amī | khacatuṣkayamādryagniśararandhraniśākarāḥ ||

— these are to be known, in the reckoning of solar years, as elapsed at the end of the Kṛta ⟨yuga⟩: 1,953,720,000.

अत ऊर्ध्वम् अमी युक्ता गतकालाब्दसंख्यया । मासीकृता युता मासैर् मधुशुक्लादिभिर् गतैः ॥

ata ūrdhvam amī yuktā gatakālābdasaṃkhyayā | māsīkṛtā yutā māsair madhuśuklādibhir gataiḥ ||

From this point onward, these ⟨years⟩, joined with the number of years of time elapsed ⟨since⟩ and converted into months, are increased by the elapsed months beginning with the bright fortnight of Madhu ⟨Caitra⟩.

पृथक्स्थास् तेऽधिमासघ्नाः सूर्यमासविभाजिताः । लब्धाधिमासकैर् युक्ता दिनीकृत्य दिनान्विताः ॥

pṛthaksthās te'dhimāsaghnāḥ sūryamāsavibhājitāḥ | labdhādhimāsakair yuktā dinīkṛtya dinānvitāḥ ||

Those, set down separately, are multiplied by the intercalary months and divided by the solar months; joined with the intercalary months so obtained, converted into days, and increased by the ⟨elapsed⟩ days —

द्विष्ठास् तिथिक्षयाभ्यस्ताश् चान्द्रवासरभाजिताः । लब्धोनरात्रिरहिता लङ्कायाम् आर्धरात्रिकः ॥

dviṣṭhās tithikṣayābhyastāś cāndravāsarabhājitāḥ | labdhonarātrirahitā laṅkāyām ārdharātrikaḥ ||

— ⟨that total⟩ set down in two places, ⟨one copy⟩ multiplied by the omitted lunar days and divided by the lunar days; diminished by the omitted days (ūnarātra) so obtained, ⟨the result is the day-count⟩ reckoned from midnight at Laṅkā.

सावनो द्युगणः सूर्याद् दिनमासाब्दपास् ततः । सप्तभिः क्षयितः शेषः सूर्याद्यो वासरेश्वरः ॥

sāvano dyugaṇaḥ sūryād dinamāsābdapās tataḥ | saptabhiḥ kṣayitaḥ śeṣaḥ sūryādyo vāsareśvaraḥ ||

⟨This is⟩ the civil day-count (ahargaṇa), ⟨reckoned⟩ from the Sun; from it ⟨come⟩ the lords of the day, the month and the year. Reduced by sevens, the remainder, ⟨counted⟩ from the Sun onward, is the lord of the weekday.

मासाब्ददिनसंख्याप्तं द्वित्रिघ्नं रूपसंयुतम् । सप्तोद्धृतावशेषौ तु विज्ञेयौ मासवर्षपौ ॥

māsābdadinasaṃkhyāptaṃ dvitrighnaṃ rūpasaṃyutam | saptoddhṛtāvaśeṣau tu vijñeyau māsavarṣapau ||

⟨The day-count⟩ divided by the number of days in a month and in a year, ⟨the quotients⟩ multiplied by two and by three ⟨respectively⟩ and increased by one — the two remainders after division by seven are to be known as the lords of the month and of the year.

यथा स्वभगणाभ्यस्तो दिनराशिः कुवासरैः । विभाजितो मध्यगत्या भगणादिर् ग्रहो भवेत् ॥

yathā svabhagaṇābhyasto dinarāśiḥ kuvāsaraiḥ | vibhājito madhyagatyā bhagaṇādir graho bhavet ||

Just as ⟨has been said⟩: the heap of days (ahargaṇa), multiplied by ⟨a graha's⟩ own revolutions and divided by the terrestrial days, gives, by the mean motion, the graha ⟨expressed⟩ in revolutions and the rest.

एवं स्वशीघ्रमन्दोच्चा ये प्रोक्ताः पूर्वयायिनः । विलोमगतयः पातास् तद्वच् चक्राद् विशोधिताः ॥

evaṃ svaśīghramandoccā ye proktāḥ pūrvayāyinaḥ | vilomagatayaḥ pātās tadvac cakrād viśodhitāḥ ||

In the same way ⟨are found⟩ their own śīghra and manda apices, which were declared to move eastward; the nodes, whose motion is retrograde, are ⟨found⟩ likewise and then subtracted from the circle.

द्वादशघ्ना गुरोर् याता भगणा वर्तमानकैः । राशिभिः सहिताः शुद्धाः षष्ट्या स्युर् विजयादयः ॥

dvādaśaghnā guror yātā bhagaṇā vartamānakaiḥ | rāśibhiḥ sahitāḥ śuddhāḥ ṣaṣṭyā syur vijayādayaḥ ||

Jupiter's elapsed revolutions, multiplied by twelve and added to the current ⟨elapsed⟩ signs, ⟨then⟩ cleared by sixty, give the ⟨years of the sixty-year cycle⟩ beginning with Vijaya.

विस्तरेणैतद् उदितं संक्षेपाद् व्यावहारिकम् । मध्यमानयनं कार्यं ग्रहाणाम् इष्टतो युगात् ॥

vistareṇaitad uditaṃ saṃkṣepād vyāvahārikam | madhyamānayanaṃ kāryaṃ grahāṇām iṣṭato yugāt ||

This has been set forth at length; ⟨what follows is⟩ in brief, for practical use. The mean ⟨places⟩ of the grahas are to be computed from whichever yuga is desired.

अस्मिन् कृतयुगस्यान्ते सर्वे मध्यगता ग्रहाः । विना तु पातमन्दोच्चान् मेषादौ तुल्यताम् इताः ॥

asmin kṛtayugasyānte sarve madhyagatā grahāḥ | vinā tu pātamandoccān meṣādau tulyatām itāḥ ||

At the end of this Kṛta yuga all the grahas in mean motion — except the nodes and the manda apices — came to equality at the beginning of Meṣa ⟨Aries⟩.

मकरादौ शशाङ्कोच्चं तत्पातस् तु तुलादिगः । निरंशत्वम् गताश् चान्ये नोक्तास् ते मन्दचारिणः ॥

makarādau śaśāṅkoccaṃ tatpātas tu tulādigaḥ | niraṃśatvam gatāś cānye noktās te mandacāriṇaḥ ||

The Moon's apogee ⟨stood⟩ at the beginning of Makara ⟨Capricorn⟩, and its node at the beginning of Tulā ⟨Libra⟩; the others had reached zero degrees. Those not stated are the slow-moving ones.

योजनानि शतान्य् अष्टौ भूकर्णो द्विगुणानि तु । तद्वर्गतो दशगुणात् पदं भूपरिधिर् भवेत् ॥

yojanāni śatāny aṣṭau bhūkarṇo dviguṇāni tu | tadvargato daśaguṇāt padaṃ bhūparidhir bhavet ||

The Earth's diameter is eight hundred yojanas doubled ⟨1,600⟩. The square root of ten times the square of that is the Earth's circumference.

लम्बज्याघ्नस् त्रिजीवाप्तः स्फुटो भूपरिधिः स्वकः । तेन देशान्तराभ्यस्ता ग्रहभुक्तिर् विभाजिता ॥

lambajyāghnas trijīvāptaḥ sphuṭo bhūparidhiḥ svakaḥ | tena deśāntarābhyastā grahabhuktir vibhājitā ||

Multiplied by the sine of co-latitude (lambajyā) and divided by the radius (trijīvā), ⟨that circumference becomes⟩ one's own corrected circumference of the Earth. By it the graha's daily motion, multiplied by the longitudinal difference (deśāntara), is divided.

कलादि तत् फलं प्राच्यां ग्रहेभ्यः परिशोधयेत् । रेखाप्रतीचीसंस्थाने प्रक्षिपेत् स्युः स्वदेशजा ॥

kalādi tat phalaṃ prācyāṃ grahebhyaḥ pariśodhayet | rekhāpratīcīsaṃsthāne prakṣipet syuḥ svadeśajā ||

That result, ⟨reckoned⟩ in minutes and so forth, is to be subtracted from the grahas (planets) ⟨for a place⟩ in the east; when ⟨one's place⟩ is situated west of the ⟨prime-meridian⟩ line, it is to be added. ⟨So corrected,⟩ they become ⟨the planets⟩ born of one's own place.

राक्षसालयदेवौकःशैलयोर् मध्यसूत्रगाः । रोहीतकम् अवन्ती च यथा सन्निहितं सरः ॥

rākṣasālayadevaukaḥśailayor madhyasūtragāḥ | rohītakam avantī ca yathā sannihitaṃ saraḥ ||

Lying upon the middle line ⟨drawn⟩ between the abode of the Rākṣasas ⟨Laṅkā⟩ and the mountain that is the dwelling of the gods ⟨Meru⟩ are Rohītaka and Avantī ⟨Ujjayinī⟩, and likewise the Sannihita lake.

अतीत्योन्मीलनाद् इन्दोः पश्चात् तद्गणितागतात् । यदा भवेत् तदा प्राच्यां स्वस्थानं मध्यतो भवेत् ॥

atītyonmīlanād indoḥ paścāt tadgaṇitāgatāt | yadā bhavet tadā prācyāṃ svasthānaṃ madhyato bhavet ||

When ⟨in a lunar eclipse the observed⟩ emergence of the Moon occurs afterwards, having passed beyond that ⟨emergence⟩ arrived at by computation, then one's own place is east of the middle ⟨meridian⟩.

अप्राप्य च भवेत् पश्चाद् एवं वापि निमीलनात् । तयोर् अन्तरनाडीभिर् हन्याद् भूपरिधिं स्फुटम् ॥

aprāpya ca bhavet paścād evaṃ vāpi nimīlanāt | tayor antaranāḍībhir hanyād bhūparidhiṃ sphuṭam ||

And if ⟨the emergence⟩ occurs without having reached ⟨the computed time⟩, ⟨one's own place is⟩ to the west; and in the same way also from the immersion ⟨the rule holds⟩. By the nāḍīs of the interval between the two, one should multiply the corrected circumference of the Earth ⟨at one's own latitude⟩.

षष्ट्या विभज्य लब्धैस् तु योजनैः प्राग् अथापरैः । स्वदेशः परिधौ ज्ञेयः कुर्याद् देशान्तरं हि तैः ॥

ṣaṣṭyā vibhajya labdhais tu yojanaiḥ prāg athāparaiḥ | svadeśaḥ paridhau jñeyaḥ kuryād deśāntaraṃ hi taiḥ ||

Dividing by sixty, one's own place is to be known upon the circumference by the yojanas obtained, ⟨measured⟩ eastward or else westward; and by those ⟨yojanas⟩ one should indeed make the deśāntara ⟨correction⟩.

वारप्रवृत्तिः प्राग्देशे क्षपार्धेऽभ्यधिके भवेत् । तद्देशान्तरनाडीभिः पश्चाद् ऊने विनिर्दिशेत् ॥

vārapravṛttiḥ prāgdeśe kṣapārdhe'bhyadhike bhavet | taddeśāntaranāḍībhiḥ paścād ūne vinirdiśet ||

In an eastern place the commencement of the weekday falls when midnight is exceeded by the nāḍīs of that place's deśāntara; to the west, one should declare it when ⟨midnight⟩ falls short ⟨by those same nāḍīs⟩.

इष्टनाडीगुणा भुक्तिः षष्ट्या भक्ता कलादिकम् । गते शोध्यं युतं गम्ये कृत्वा तात्कालिको भवेत् ॥

iṣṭanāḍīguṇā bhuktiḥ ṣaṣṭyā bhaktā kalādikam | gate śodhyaṃ yutaṃ gamye kṛtvā tātkāliko bhavet ||

The daily motion multiplied by the desired nāḍīs and divided by sixty gives ⟨a quantity⟩ in minutes and so forth. It is to be subtracted when ⟨the time is⟩ elapsed, added when ⟨it is⟩ yet to come; having done this, ⟨the planet⟩ becomes ⟨the planet⟩ of that moment.

भचक्रलिप्ताशीत्यंशं परमं दक्षिणोत्तरम् । विक्षिप्यते स्वपातेन स्वक्रान्त्यन्ताद् अनुष्णगुः ॥

bhacakraliptāśītyaṃśaṃ paramaṃ dakṣiṇottaram | vikṣipyate svapātena svakrāntyantād anuṣṇaguḥ ||

An eightieth part of the minutes of the zodiacal circle ⟨270 minutes⟩ is the greatest ⟨latitude⟩, south and north; the cool-rayed one ⟨the Moon⟩ is deflected by its own node away from the end of its own declination ⟨-circle, the ecliptic⟩.

तन्नवांशं द्विगुणितं जीवस् त्रिगुणितं कुजः । बुधशुक्रार्कजाः पातैर् विक्षिप्यन्ते चतुर्गुणम् ॥

tannavāṃśaṃ dviguṇitaṃ jīvas triguṇitaṃ kujaḥ | budhaśukrārkajāḥ pātair vikṣipyante caturguṇam ||

A ninth part of that ⟨30 minutes⟩, doubled, ⟨is⟩ Jupiter's; tripled, Mars'; Mercury, Venus and the Sun's son ⟨Saturn⟩ are deflected by their nodes fourfold.

एवम् त्रिघनरन्ध्रार्करसार्कार्का दशाहताः । चन्द्रादीनां क्रमाद् उक्ता मध्यविक्षेपलिप्तिकाः ॥

evam trighanarandhrārkarasārkārkā daśāhatāḥ | candrādīnāṃ kramād uktā madhyavikṣepaliptikāḥ ||

Thus three-cubed ⟨27⟩, the apertures ⟨9⟩, the Suns ⟨12⟩, the tastes ⟨6⟩, the Suns ⟨12⟩, the Suns ⟨12⟩, multiplied by ten, are declared to be, in order, the minutes of mean latitude of the Moon and the rest.

अदृश्यरूपाः कालस्य मूर्तयो भगणाश्रिताः । शीघ्रमन्दोच्चपाताख्या ग्रहाणां गतिहेतवः ॥

adṛśyarūpāḥ kālasya mūrtayo bhagaṇāśritāḥ | śīghramandoccapātākhyā grahāṇāṃ gatihetavaḥ ||

The embodiments of Time, invisible in form, abiding in the circle of the constellations, named the śīghrocca, the mandocca and the pāta ⟨the node⟩, are the causes of the motion of the grahas.

तद्वातरश्मिभिर् बद्धास् तैस् सव्येतरपाणिभिः । प्राक् पश्चाद् अपकृष्यन्ते यथासन्नं स्वदिङ्मुखम् ॥

tadvātaraśmibhir baddhās tais savyetarapāṇibhiḥ | prāk paścād apakṛṣyante yathāsannaṃ svadiṅmukham ||

Bound by cords of wind ⟨issuing⟩ from those ⟨embodiments⟩, ⟨the grahas⟩ are drawn by them, with their right and left hands, forward or backward, each according to its nearness, facing toward its own quarter.

प्रवहाख्यो मरुत् तांस् तु स्वोच्चाभिमुखम् ईरयेत् । पूर्वापरापकृष्टास् ते गतिं यान्ति पृथग्विधाः ॥

pravahākhyo marut tāṃs tu svoccābhimukham īrayet | pūrvāparāpakṛṣṭās te gatiṃ yānti pṛthagvidhāḥ ||

But the wind called pravaha drives them toward their own ucca ⟨apex⟩; drawn ⟨thus⟩ eastward and westward, they proceed with motions of several kinds.

ग्रहात् प्राग्भगणार्धस्थः प्राङ्मुखं कर्षति ग्रहम् । उच्चसंज्ञोऽपरार्धस्थस् तद्वत् पश्चान्मुखं ग्रहम् ॥

grahāt prāgbhagaṇārdhasthaḥ prāṅmukhaṃ karṣati graham | uccasaṃjño'parārdhasthas tadvat paścānmukhaṃ graham ||

⟨The being⟩ named the ucca, standing in that half of the circle which is east of the graha, draws the graha eastward; standing in the western half, it likewise draws the graha westward.

स्वोच्चापकृष्टा भगणैः प्राङ्मुखं यान्ति यद् ग्रहाः । तत् तेषु धनम् इत्य् उक्तम् ऋणं पश्चान्मुखेषु च ॥

svoccāpakṛṣṭā bhagaṇaiḥ prāṅmukhaṃ yānti yad grahāḥ | tat teṣu dhanam ity uktam ṛṇaṃ paścānmukheṣu ca ||

By whatever ⟨arc⟩ of the circle the grahas, drawn by their own ucca, move eastward, that is declared to be additive (dhana) in their case; and subtractive (ṛṇa) for those ⟨moving⟩ westward.

दक्षिणोत्तरतोऽप्य् एवं पातो राहुः स्वरंहसा । विक्षिपत्य् एष विक्षेपं चन्द्रादीनाम् अपक्रमात् ॥

dakṣiṇottarato'py evaṃ pāto rāhuḥ svaraṃhasā | vikṣipaty eṣa vikṣepaṃ candrādīnām apakramāt ||

In the same way to the south and north as well, the node — Rāhu — by its own force casts the deflection ⟨in latitude⟩ of the Moon and the rest away from the ecliptic.

उत्तराभिमुखं पातो विक्षिपत्य् अपरार्धगः । ग्रहं प्राग्भगणार्धस्थो याम्यायाम् अपकर्षति ॥

uttarābhimukhaṃ pāto vikṣipaty aparārdhagaḥ | grahaṃ prāgbhagaṇārdhastho yāmyāyām apakarṣati ||

The pāta, when it lies in the western half, deflects ⟨the graha⟩ toward the north; standing in the half of the circle east ⟨of the graha⟩, it draws the graha toward the south.

बुधभार्गवयोः शीघ्रात् तद्वत् पातो यदा स्थितः । तच्छीघ्राकर्षणात् तौ तु विक्षिप्येते यथोक्तवत् ॥

budhabhārgavayoḥ śīghrāt tadvat pāto yadā sthitaḥ | tacchīghrākarṣaṇāt tau tu vikṣipyete yathoktavat ||

For Mercury and Venus, when the pāta stands in like manner ⟨reckoned⟩ from the śīghra, those two are deflected as has been stated, through the drawing of that śīghra.

महत्त्वान् मण्डलस्यार्कः स्वल्पम् एवापकृष्यते । मण्डलाल्पतया चन्द्रस् ततो बह्व् अपकृष्यते ।

mahattvān maṇḍalasyārkaḥ svalpam evāpakṛṣyate | maṇḍalālpatayā candras tato bahv apakṛṣyate |

Owing to the greatness of its orbit the Sun is drawn aside but very little; the Moon, by reason of the smallness of its orbit, is drawn aside far more than that.

भौमादयोऽल्पमूर्तित्वाच् छीघ्रमन्दोच्चसञ्ज्ञकैः । दैवतैर् अपकृष्यन्ते सुदूरम् अतिवेगिताः ॥

bhaumādayo'lpamūrtitvāc chīghramandoccasañjñakaiḥ | daivatair apakṛṣyante sudūram ativegitāḥ ||

Mars and the rest, because of the smallness of their bodies, are drawn far aside by the deities named the śīghrocca and the mandocca, and are made exceedingly swift.

अतो धनर्णं सुमहत् तेषां गतिवशाद् भवेत् । आकृष्यमाणास् तैर् एवं व्योम्नि यान्त्य् अनिलाहताः ॥

ato dhanarṇaṃ sumahat teṣāṃ gativaśād bhavet | ākṛṣyamāṇās tair evaṃ vyomni yānty anilāhatāḥ ||

Hence their additive-and-subtractive ⟨equation⟩ becomes very great, by force of their motion. Being drawn thus by those ⟨deities⟩ and struck by the wind, they travel in the sky.

वक्रातिवक्रा विकला मन्दा मन्दतरा समा । तथा शीघ्रतरा शीघ्रा ग्रहाणाम् अष्टधा गतिः ॥

vakrātivakrā vikalā mandā mandatarā samā | tathā śīghratarā śīghrā grahāṇām aṣṭadhā gatiḥ ||

Retrograde, very retrograde, motionless, slow, slower, even, and likewise swifter and swift — the motion of the grahas is eightfold.

तत्रातिशीघ्रा शीघ्राख्या मन्दा मन्दतरा समा । ऋज्वीति पञ्चधा ज्ञेया या वक्रा सातिवक्रगा ॥

tatrātiśīghrā śīghrākhyā mandā mandatarā samā | ṛjvīti pañcadhā jñeyā yā vakrā sātivakragā ||

Among these the very swift, that called swift, the slow, the slower and the even are to be known as direct ⟨motion⟩ in its five kinds; and that which is retrograde is ⟨the one⟩ that goes very retrograde.

तत्तद्गतिवशान् नित्यं यथा दृक्तुल्यतां ग्रहाः । प्रयान्ति तत् प्रवक्ष्यामि स्फुटीकरणम् आदरात् ॥

tattadgativaśān nityaṃ yathā dṛktulyatāṃ grahāḥ | prayānti tat pravakṣyāmi sphuṭīkaraṇam ādarāt ||

How the grahas, ever by force of those several motions, are brought into agreement with observation — that ⟨process of⟩ making true (sphuṭīkaraṇa) I shall now declare with care.

राशिलिप्ताष्टमो भागः प्रथमं ज्यार्धम् उच्यते । तत् तद्विभक्तलब्धोनमिश्रितं तद् द्वितीयकम् ॥

rāśiliptāṣṭamo bhāgaḥ prathamaṃ jyārdham ucyate | tat tadvibhaktalabdhonamiśritaṃ tad dvitīyakam ||

The eighth part of the minutes of a rāśi ⟨225⟩ is called the first half-chord ⟨Sine⟩. That ⟨first Sine⟩, combined with itself lessened by the quotient obtained on dividing ⟨it⟩ by that ⟨first Sine⟩, is the second.

आद्येनैवं क्रमात् पिण्डान् भक्त्वा लब्धोनसंयुताः । खण्डकाः स्युश् चतुर्विंशज्यार्धपिण्डाः क्रमाद् अमी ॥

ādyenaivaṃ kramāt piṇḍān bhaktvā labdhonasaṃyutāḥ | khaṇḍakāḥ syuś caturviṃśajyārdhapiṇḍāḥ kramād amī ||

Dividing the ⟨Sine⟩ aggregates in this way, in order, by the first ⟨225⟩, and taking ⟨each increment⟩ lessened by the quotient and then added on, the khaṇḍas ⟨increments⟩ arise; these, in order, are the twenty-four aggregates of half-chords.

तत्त्वाश्विनोऽङ्काब्धिकृता रूपभूमिधरर्तवः । खाङ्काष्टौ पञ्चशून्येशा बाणरूपगुणेन्दवः ॥

tattvāśvino'ṅkābdhikṛtā rūpabhūmidharartavaḥ | khāṅkāṣṭau pañcaśūnyeśā bāṇarūpaguṇendavaḥ ||

⟨The twenty-four Sines are:⟩ 225, 449, 671; 890, 1105, 1315.

शून्यलोचनपञ्चैकाश् छिद्ररूपमुनीन्दवः । वियच्चन्द्रातिधृतयो गुणरन्ध्राम्बराश्विनः ॥

śūnyalocanapañcaikāś chidrarūpamunīndavaḥ | viyaccandrātidhṛtayo guṇarandhrāmbarāśvinaḥ ||

1520, 1719; 1910, 2093.

मुनिषड्यमनेत्राणि चन्द्राग्निकृतदस्रकाः । पञ्चाष्टविषयाक्षीणि कुञ्जराश्विनगाश्विनः ॥

muniṣaḍyamanetrāṇi candrāgnikṛtadasrakāḥ | pañcāṣṭaviṣayākṣīṇi kuñjarāśvinagāśvinaḥ ||

2267, 2431; 2585, 2728.

रन्ध्रपञ्चाष्टकयमा वस्वद्र्यङ्कयमास् तथा । कृताष्टशून्यज्वलना नगाद्रिशशिवह्नयः ॥

randhrapañcāṣṭakayamā vasvadryaṅkayamās tathā | kṛtāṣṭaśūnyajvalanā nagādriśaśivahnayaḥ ||

2859, 2978; 3084, 3177.

षट्पञ्चलोचनगुणाश् चन्द्रनेत्राग्निवह्नयः । यमाद्रिवह्निज्वलना रन्ध्रशून्यार्णवाग्नयः ॥

ṣaṭpañcalocanaguṇāś candranetrāgnivahnayaḥ | yamādrivahnijvalanā randhraśūnyārṇavāgnayaḥ ||

3256, 3321; 3372, 3409.

रूपाग्निसागरगुणा वस्वग्निकृतवह्नयः । प्रोज्झ्योत्क्रमेण व्यासार्धाद् उत्क्रमज्यार्धपिण्डिकाः ॥

rūpāgnisāgaraguṇā vasvagnikṛtavahnayaḥ | projjhyotkrameṇa vyāsārdhād utkramajyārdhapiṇḍikāḥ ||

3431, 3438. Subtracting ⟨these Sines⟩ from the radius ⟨3438⟩ in the inverse order, ⟨one obtains⟩ the aggregates of the versed half-chords ⟨versed Sines⟩.

मुनयो रन्ध्रयमला रसषट्का मुनीश्वराः । द्व्यष्टैका रूपषड्दस्राः सागरार्थहुताशनाः ।

munayo randhrayamalā rasaṣaṭkā munīśvarāḥ | dvyaṣṭaikā rūpaṣaḍdasrāḥ sāgarārthahutāśanāḥ |

7, 29, 66, 117; 182, 261, 354.

खर्तुवेदा नवाद्र्यर्था दिङ्नागास् त्र्यर्थकुञ्जराः । नगाम्बरवियच्चन्द्रा रूपभूधरशङ्कराः ॥

khartuvedā navādryarthā diṅnāgās tryarthakuñjarāḥ | nagāmbaraviyaccandrā rūpabhūdharaśaṅkarāḥ ||

460, 579, 710, 853; 1007, 1171.

शरार्णवहुताशैका भुजङ्गाक्षिशरेन्दवः । नवरूपमहीध्रैका गजैकाङ्कनिशाकराः ॥

śarārṇavahutāśaikā bhujaṅgākṣiśarendavaḥ | navarūpamahīdhraikā gajaikāṅkaniśākarāḥ ||

1345, 1528; 1719, 1918.

गुणाश्विरूपनेत्राणि पावकाग्निगुणाश्विनः । वस्वर्णवार्थयमलास् तुरङ्गर्तुनगाश्विनः ॥

guṇāśvirūpanetrāṇi pāvakāgniguṇāśvinaḥ | vasvarṇavārthayamalās turaṅgartunagāśvinaḥ ||

2123, 2333; 2548, 2767.

नवाष्टनवनेत्राणि पावकैकयमाग्नयः । गजाग्निसागरगुणा उत्क्रमज्यार्धपिण्डकाः ॥

navāṣṭanavanetrāṇi pāvakaikayamāgnayaḥ | gajāgnisāgaraguṇā utkramajyārdhapiṇḍakāḥ ||

2989, 3213; 3438 — ⟨these are⟩ the aggregates of the versed half-chords ⟨versed Sines⟩.

परमापक्रमज्या तु सप्तरन्ध्रगुणेन्दवः । तद्गुणा ज्या त्रिजीवाप्ता तच्चापं क्रान्तिर् उच्यते ॥

paramāpakramajyā tu saptarandhraguṇendavaḥ | tadguṇā jyā trijīvāptā taccāpaṃ krāntir ucyate ||

But the Sine of the greatest declination is 1397. A ⟨given⟩ Sine multiplied by that and divided by the radius ⟨trijīvā, 3438⟩ — the arc of that ⟨result⟩ is called the declination (krānti).

ग्रहं संशोध्य मन्दोच्चात् तथा शीघ्राद् विशोध्य च । शेषं केन्द्रपदं तस्माद् भुजज्या कोटिर् एव च ॥

grahaṃ saṃśodhya mandoccāt tathā śīghrād viśodhya ca | śeṣaṃ kendrapadaṃ tasmād bhujajyā koṭir eva ca ||

Subtracting the graha from the mandocca, and likewise subtracting ⟨it⟩ from the śīghra ⟨śīghrocca⟩, the remainder is the kendra; from that ⟨are had⟩ its quadrant (pada), and thence the base-Sine (bhujajyā) and the upright (koṭi).

गताद् भुजज्या विषमे गम्यात् कोटिः पदे भवेत् । युग्मे तु गम्याद् बाहुज्या कोटिज्या तु गताद् भवेत् ॥

gatād bhujajyā viṣame gamyāt koṭiḥ pade bhavet | yugme tu gamyād bāhujyā koṭijyā tu gatād bhavet ||

In an odd quadrant the base-Sine is ⟨taken⟩ from the elapsed ⟨part⟩ and the upright from the part yet to come; but in an even quadrant the base-Sine is from the part yet to come, and the upright-Sine from the elapsed.

लिप्तास् तत्त्वयमैर् भक्ता लब्धं ज्यापिण्डकं गतम् । गतगम्यान्तराभ्यस्तं विभजेत् तत्त्वलोचनैः ॥

liptās tattvayamair bhaktā labdhaṃ jyāpiṇḍakaṃ gatam | gatagamyāntarābhyastaṃ vibhajet tattvalocanaiḥ ||

The minutes ⟨of the given arc⟩, divided by 225, yield a quotient: ⟨that is the number of⟩ sine-elements (jyāpiṇḍa) already passed over. ⟨The remainder,⟩ multiplied by the difference between the sine passed and the sine yet to come, one should divide by 225.

तदवाप्तफलं योज्यं ज्यापिण्डे गतसंज्ञके । स्यात् क्रमज्याविधिर् अयम् उत्क्रमज्यास्व् अपि स्मृतः ॥

tadavāptaphalaṃ yojyaṃ jyāpiṇḍe gatasaṃjñake | syāt kramajyāvidhir ayam utkramajyāsv api smṛtaḥ ||

The result so obtained is to be added to the sine-element named 'passed' (gata). This is the rule for the sines (kramajyā); it is declared for the versed sines (utkramajyā) as well.

ज्यां प्रोज्झ्य शेषं तत्त्वाश्विहतं तद्विवरोद्धृतम् । संख्यातत्त्वाश्विसंवर्गे संयोज्य धनुर् उच्यते ॥

jyāṃ projjhya śeṣaṃ tattvāśvihataṃ tadvivaroddhṛtam | saṃkhyātattvāśvisaṃvarge saṃyojya dhanur ucyate ||

Having cast off the ⟨next lesser tabular⟩ sine, the remainder multiplied by 225 and divided by their difference, ⟨then⟩ added to the product of 225 and the number ⟨of sines passed over⟩ — that is called the arc.

रवेर् मन्दपरिध्यंशा मनवः शीतगो रदाः । युग्मान्ते विषमान्ते तु नखलिप्तोनितास् तयोः ॥

raver mandaparidhyaṃśā manavaḥ śītago radāḥ | yugmānte viṣamānte tu nakhaliptonitās tayoḥ ||

The degrees of the Sun's manda epicycle are 14; of the Moon (the cold-rayed), 32 — at the ends of the even ⟨quadrants⟩; but at the ends of the odd ⟨quadrants⟩ these two are diminished by 20 minutes.

युग्मान्तेऽर्थाद्रयः खाग्निसुराः सूर्या नवार्णवाः । ओजे द्व्यगा वसुयमा रदा रुद्रा गजाब्धयः ॥

yugmānte'rthādrayaḥ khāgnisurāḥ sūryā navārṇavāḥ | oje dvyagā vasuyamā radā rudrā gajābdhayaḥ ||

At the ends of the even ⟨quadrants, the manda epicycles are⟩ 75, 30, 33, 12, 49; in the odd, 72, 28, 32, 11, 48 ⟨degrees — for Mars, Mercury, Jupiter, Venus and Saturn in order⟩.

कुजादीनाम् अतः शीघ्रा युग्मान्तेऽर्थाग्निदस्रकाः । गुणाग्निचन्द्राः खनगा द्विरसाक्षीणि गोऽग्नयः ॥

kujādīnām ataḥ śīghrā yugmānte'rthāgnidasrakāḥ | guṇāgnicandrāḥ khanagā dvirasākṣīṇi go'gnayaḥ ||

Next, the śīghra ⟨epicycles⟩ of Mars and the rest: at the ends of the even ⟨quadrants⟩, 235, 133, 70, 262, 39.

ओजान्ते द्वित्रियमला द्विविश्वे यमपर्वताः । खर्तुदस्रा वियद्वेदाः शीघ्रकर्मणि कीर्तिताः ॥

ojānte dvitriyamalā dviviśve yamaparvatāḥ | khartudasrā viyadvedāḥ śīghrakarmaṇi kīrtitāḥ ||

At the ends of the odd ⟨quadrants⟩: 232, 132, 72, 260, 40 — these are declared for the śīghra operation.

ओजयुग्मान्तरगुणा भुजज्या त्रिज्ययोद्धृता । युग्मे वृत्ते धनर्णं स्याद् ओजाद् ऊनाधिके स्फुटम् ॥

ojayugmāntaraguṇā bhujajyā trijyayoddhṛtā | yugme vṛtte dhanarṇaṃ syād ojād ūnādhike sphuṭam ||

The base-sine (bhujajyā), multiplied by the difference between the odd and the even ⟨epicycles⟩ and divided by the radius (trijyā), is ⟨applied⟩ to the even circle, additively or subtractively according as it is less or greater than the odd — ⟨and so the epicycle becomes⟩ true.

तद्गुणे भुजकोटिज्ये भगणांशविभाजिते । तद्भुजज्याफलधनुर् मान्दं लिप्तादिकं फलम् ॥

tadguṇe bhujakoṭijye bhagaṇāṃśavibhājite | tadbhujajyāphaladhanur māndaṃ liptādikaṃ phalam ||

The base-sine and the koṭi-sine, multiplied by that ⟨true epicycle⟩ and divided by the degrees of a revolution ⟨360⟩: the arc of that base-sine result is the manda equation (phala), in minutes and so on.

शैघ्र्यं कोटिफलं केन्द्रे मकरादौ धनं स्मृतम् । संशोध्यं तु त्रिजीवायां कर्क्यादौ कोटिजं फलम् ॥

śaighryaṃ koṭiphalaṃ kendre makarādau dhanaṃ smṛtam | saṃśodhyaṃ tu trijīvāyāṃ karkyādau koṭijaṃ phalam ||

The śīghra koṭi-result, when the kendra ⟨the anomaly⟩ is in Makara and the signs following, is declared additive to the radius (trijīvā); but when in Karka and the signs following, the koṭi-result is to be subtracted ⟨from it⟩.

तद्बाहुफलवर्गैक्यान् मूलं कर्णश् चलाभिधः । त्रिज्याभ्यस्तं भुजफलं चलकर्णविभाजितम् ॥

tadbāhuphalavargaikyān mūlaṃ karṇaś calābhidhaḥ | trijyābhyastaṃ bhujaphalaṃ calakarṇavibhājitam ||

From the sum of the squares of that ⟨koṭi-result so applied⟩ and of the base-result, the square root is the hypotenuse called cala ⟨the variable one⟩. The base-result multiplied by the radius (trijyā) and divided by the cala hypotenuse —

लब्धस्य चापं लिप्तादिफलं शैघ्र्यम् इदं स्मृतम् । एतद् आद्ये कुजादीनां चतुर्थे चैव कर्मणि ॥

labdhasya cāpaṃ liptādiphalaṃ śaighryam idaṃ smṛtam | etad ādye kujādīnāṃ caturthe caiva karmaṇi ||

— the arc of the quotient is the result in minutes and so on: this is declared the śīghra ⟨equation⟩. It ⟨is used⟩ in the first, and likewise in the fourth, operation for Mars and the rest.

मान्दं कर्मैकम् अर्केन्दोर् भौमादीनाम् अथोच्यते । शैघ्र्यं मान्दं पुनर् मान्दं शैघ्र्यं चत्वार्य् अनुक्रमात् ॥

māndaṃ karmaikam arkendor bhaumādīnām athocyate | śaighryaṃ māndaṃ punar māndaṃ śaighryaṃ catvāry anukramāt ||

For the Sun and the Moon there is a single operation, the manda. Now for Mars and the rest it is stated: śīghra, manda, manda again, śīghra — four, in order.

मध्ये शीघ्रफलस्यार्धं मान्दम् अर्धफलं तथा । मध्यग्रहे मन्दफलं सकलं शैघ्र्यम् एव च ॥

madhye śīghraphalasyārdhaṃ māndam ardhaphalaṃ tathā | madhyagrahe mandaphalaṃ sakalaṃ śaighryam eva ca ||

⟨Apply⟩ to the mean ⟨graha⟩ half the śīghra result, and likewise half the manda result; ⟨then⟩ to the mean graha the whole manda result, and the whole śīghra as well.

अजादिकेन्द्रे सर्वेषां शैघ्र्ये मान्दे च कर्मणि । धनं ग्रहाणां लिप्तादि तुलादाव् ऋणम् एव च ॥

ajādikendre sarveṣāṃ śaighrye mānde ca karmaṇi | dhanaṃ grahāṇāṃ liptādi tulādāv ṛṇam eva ca ||

When the kendra is in Aries (aja) and the signs following, for all ⟨the grahas⟩, in the śīghra and in the manda operation alike, the ⟨equation⟩ in minutes and so on is additive to the grahas; and when in Libra and the signs following, subtractive.

अर्कबाहुफलाभ्यस्ता ग्रहभुक्तिर् विभाजिता । भचक्रकलिकाभिस् तु लिप्ताः कार्या ग्रहेऽर्कवत् ॥

arkabāhuphalābhyastā grahabhuktir vibhājitā | bhacakrakalikābhis tu liptāḥ kāryā grahe'rkavat ||

The graha's daily motion, multiplied by the Sun's base-result (bāhuphala) and divided by the minutes of the zodiac circle ⟨21,600⟩, gives minutes that are to be applied to the graha as ⟨they are⟩ to the Sun.

स्वमन्दभुक्तिसंशुद्धा मध्यभुक्तिर् निशापतेः । दोर्ज्यान्तरादिकं कृत्वा भुक्ताव् ऋणधनं भवेत् ॥

svamandabhuktisaṃśuddhā madhyabhuktir niśāpateḥ | dorjyāntarādikaṃ kṛtvā bhuktāv ṛṇadhanaṃ bhavet ||

The Moon's (the night-lord's) mean daily motion, cleared of the daily motion of its own manda ⟨apsis⟩: having performed ⟨the operation with⟩ the difference of the base-sines and the rest, ⟨the result⟩ becomes subtractive or additive to the daily motion.

ग्रहभुक्तेः फलं कार्यं ग्रहवन् मन्दकर्मणि । दोर्ज्यान्तरगुणा भुक्तिस् तत्त्वनेत्रोद्धृता पुनः ॥

grahabhukteḥ phalaṃ kāryaṃ grahavan mandakarmaṇi | dorjyāntaraguṇā bhuktis tattvanetroddhṛtā punaḥ ||

The correction (phala) of a graha's daily motion is to be made as ⟨it is⟩ for the graha ⟨itself⟩ in the manda operation. The daily motion, multiplied by the difference of the base-sines and divided by 225, again —

स्वमन्दपरिधिक्षुण्णा भगणांशोद्धृता कलाः । कर्क्यादौ तु धनं तत्र मकरादाव् ऋणं स्मृतम् ॥

svamandaparidhikṣuṇṇā bhagaṇāṃśoddhṛtā kalāḥ | karkyādau tu dhanaṃ tatra makarādāv ṛṇaṃ smṛtam ||

— multiplied by its own manda epicycle and divided by the degrees of a revolution ⟨360⟩, ⟨gives⟩ minutes; there, in Cancer and the signs following it is additive, and in Capricorn and the signs following it is declared subtractive.

मन्दस्फुटीकृतां भुक्तिं प्रोज्झ्य शीघ्रोच्चभुक्तितः । तच्छेषं विवरेणाथ हन्यात् त्रिज्यान्त्यकर्णयोः ॥

mandasphuṭīkṛtāṃ bhuktiṃ projjhya śīghroccabhuktitaḥ | taccheṣaṃ vivareṇātha hanyāt trijyāntyakarṇayoḥ ||

Having subtracted the manda-corrected daily motion from the daily motion of the śīghra apex (śīghrocca), one should then multiply that remainder by the difference between the radius (trijyā) and the last hypotenuse (antyakarṇa).

चलकर्णहृतं भुक्तौ कर्णे त्रिज्याधिके धनम् । ऋणम् ऊनेऽधिके प्रोज्झ्य शेषं वक्रगतिर् भवेत् ॥

calakarṇahṛtaṃ bhuktau karṇe trijyādhike dhanam | ṛṇam ūne'dhike projjhya śeṣaṃ vakragatir bhavet ||

Divided by the cala hypotenuse, ⟨the result is⟩ additive to the daily motion when the hypotenuse is greater than the radius, subtractive when less; and when ⟨that subtractive quantity⟩ is the greater, having subtracted ⟨the motion from it⟩, the remainder is retrograde motion.

दूरस्थितः स्वशीघ्रोच्चाद् ग्रहः शिथिलरश्मिभिः । सव्येतराकृष्टतनुर् भवेद् वक्रगतिस् तदा ॥

dūrasthitaḥ svaśīghroccād grahaḥ śithilaraśmibhiḥ | savyetarākṛṣṭatanur bhaved vakragatis tadā ||

When a graha, standing far from its own śīghrocca, has its body drawn to the contrary side by the slackened reins ⟨of rays⟩, then its motion becomes retrograde.

कृतर्तुचन्द्रैर् वेदेन्द्रैः शून्यत्र्येकैर् गुणाष्टिभिः । शररुद्रैश् चतुर्थेषु केन्द्रांशैर् भूसुतादयः ॥

kṛtartucandrair vedendraiḥ śūnyatryekair guṇāṣṭibhiḥ | śararudraiś caturtheṣu kendrāṃśair bhūsutādayaḥ ||

Mars and the rest ⟨turn retrograde⟩ at kendra-degrees, in the fourth ⟨operation⟩, of 164, 144, 130, 163 and 115.

भवन्ति वक्रिणस् तैस् तु स्वैः स्वैश् चक्राद् विशोधितैः । अवशिष्टांशतुल्यैः स्वैः केन्द्रैर् उज्झन्ति वक्रताम् ॥

bhavanti vakriṇas tais tu svaiḥ svaiś cakrād viśodhitaiḥ | avaśiṣṭāṃśatulyaiḥ svaiḥ kendrair ujjhanti vakratām ||

By these ⟨degrees⟩, each its own, ⟨the grahas⟩ become retrograde; and when their own kendras equal the degrees left after ⟨these⟩ have been subtracted from a circle ⟨360°⟩, they give up retrogradation.

महत्त्वाच् छीघ्रपरिधेः सप्तमे भृगुभूसुतौ । अष्टमे जीवशशिजौ नवमे तु शनैश्चरः ॥

mahattvāc chīghraparidheḥ saptame bhṛgubhūsutau | aṣṭame jīvaśaśijau navame tu śanaiścaraḥ ||

Owing to the greatness of the śīghra epicycle, Venus and Mars ⟨are retrograde⟩ in the seventh ⟨sign of anomaly⟩, Jupiter and Mercury (the Moon's son) in the eighth, and Saturn in the ninth.

कुजार्किगुरुपातानां ग्रहवच् छीघ्रजं फलम् । वामं तृतीयकं मान्दं बुधभार्गवयोः फलम् ॥

kujārkigurupātānāṃ grahavac chīghrajaṃ phalam | vāmaṃ tṛtīyakaṃ māndaṃ budhabhārgavayoḥ phalam ||

For the nodes (pāta) of Mars, Saturn and Jupiter, the śīghra-born result is ⟨applied⟩ as for the graha ⟨itself⟩; the third ⟨operation's⟩ manda result is contrary — ⟨and so too⟩ the result for the nodes of Mercury and Venus.

स्वपातोनाद् ग्रहाज् जीवा शीघ्राद् भृगुजसौम्ययोः । विक्षेपघ्न्य् अन्त्यकर्णाप्ता विक्षेपस् त्रिज्यया विधोः ॥

svapātonād grahāj jīvā śīghrād bhṛgujasaumyayoḥ | vikṣepaghny antyakarṇāptā vikṣepas trijyayā vidhoḥ ||

The sine of the graha diminished by its own node — for Venus (bhṛguja) and Mercury (saumya), that of the śīghra ⟨so diminished⟩ — multiplied by the ⟨greatest⟩ latitude and divided by the last hypotenuse (antyakarṇa), is the latitude (vikṣepa); for the Moon, ⟨the divisor is⟩ the radius (trijyā).

विक्षेपापक्रमैकत्वे क्रान्तिर् विक्षेपसंयुता । दिग्भेदे वियुता स्पष्टा भास्करस्य यथागता ॥

vikṣepāpakramaikatve krāntir vikṣepasaṃyutā | digbhede viyutā spaṣṭā bhāskarasya yathāgatā ||

When the latitude (vikṣepa) and the declination (apakrama) are of one direction, the declination is joined with the latitude; when the directions differ, it is diminished ⟨by it⟩ — ⟨that is⟩ the true ⟨declination⟩. For the Sun (bhāskara) it stands as it was obtained.

ग्रहोदयप्राणहता खखाष्टैकोद्धृता गतिः । चक्रासवो लब्धयुताः स्वाहोरात्रासवः स्मृताः ॥

grahodayaprāṇahatā khakhāṣṭaikoddhṛtā gatiḥ | cakrāsavo labdhayutāḥ svāhorātrāsavaḥ smṛtāḥ ||

The ⟨graha's⟩ motion, multiplied by the prāṇas of the graha's rising and divided by 1,800; the asus of a circle ⟨21,600⟩ increased by the quotient are declared to be the asus of its own day-and-night.

क्रान्तेः क्रमोत्क्रमज्ये द्वे कृत्वा तत्रोत्क्रमज्यया । हीना त्रिज्या दिनव्यासदलं तद्दक्षिणोत्तरम् ॥

krānteḥ kramotkramajye dve kṛtvā tatrotkramajyayā | hīnā trijyā dinavyāsadalaṃ taddakṣiṇottaram ||

Having made the two — the sine (kramajyā) and the versed sine (utkramajyā) of the declination — the radius (trijyā) there diminished by the versed sine is the half-diameter of the day ⟨-circle⟩; that ⟨is⟩ southern or northern ⟨as the declination is⟩.

क्रान्तिज्या विषुवद्भाघ्नी क्षितिज्या द्वादशोद्धृता । त्रिज्यागुणाहोरात्रार्धकर्णाप्ता चरजासवः ॥

krāntijyā viṣuvadbhāghnī kṣitijyā dvādaśoddhṛtā | trijyāguṇāhorātrārdhakarṇāptā carajāsavaḥ ||

The Sine of declination (krāntijyā), multiplied by the equinoctial shadow and divided by twelve, is the earth-Sine (kṣitijyā); that, multiplied by the radius (trijyā) and divided by the hypotenuse of ⟨the circle of⟩ half the day-and-night — the day-radius — gives the asus arising from the ascensional difference (cara).

तत्कार्मुकम् उदक्क्रान्तौ धनहानी पृथक् स्थिते । स्वाहोरात्रचतुर्भागे दिनरात्रिदले स्मृते ॥

tatkārmukam udakkrāntau dhanahānī pṛthak sthite | svāhorātracaturbhāge dinarātridale smṛte ||

The arc of that, when the declination is north, ⟨stands as⟩ additive and subtractive, placed separately; ⟨applied thus⟩ to a fourth part of the ⟨sun's⟩ own day-and-night ⟨circle⟩, the two are declared to be the half-day and the half-night.

याम्यक्रान्तौ विपर्यस्ते द्विगुणे तु दिनक्षपे । विक्षेपयुक्तोनितया क्रान्त्या भानाम् अपि स्वके ॥

yāmyakrāntau viparyaste dviguṇe tu dinakṣape | vikṣepayuktonitayā krāntyā bhānām api svake ||

When the declination is south, the two are reversed; and doubled, they are the day and the night. By the declination increased or diminished by the ⟨celestial⟩ latitude, ⟨the same is to be computed⟩ for the asterisms also, in their own ⟨case⟩.

भभोगोऽष्टशतीलिप्ताः खाश्विशैलास् तथा तिथेः । ग्रहलिप्ताभभोगाप्ता भानि भुक्त्या दिनादिकम् ॥

bhabhogo'ṣṭaśatīliptāḥ khāśviśailās tathā titheḥ | grahaliptābhabhogāptā bhāni bhuktyā dinādikam ||

The nakṣatra-portion (bhabhoga) is eight hundred minutes, and that of a tithi is kha-aśvi-śaila — seven hundred and twenty. The minutes of a graha divided by the nakṣatra-portion give the nakṣatras ⟨elapsed⟩; ⟨the remainder⟩ by the ⟨daily⟩ motion gives days and the rest.

रवीन्दुयोगलिप्ताभ्यो योगा भभोगभाजिताः । गता गम्याश् च षष्टिघ्न्यो भुक्तियोगाप्तनाडिकाः ॥

ravīnduyogaliptābhyo yogā bhabhogabhājitāḥ | gatā gamyāś ca ṣaṣṭighnyo bhuktiyogāptanāḍikāḥ ||

From the minutes of the sum of Sun and Moon, divided by the nakṣatra-portion, come the yogas ⟨elapsed⟩; the elapsed and the remaining ⟨minutes⟩, multiplied by sixty and divided by the sum of the ⟨daily⟩ motions, are the nāḍikās.

अर्कोनचन्द्रलिप्ताभ्यस् तिथयो भोगभाजिताः । गता गम्याश् च षष्टिघ्न्यो नाड्यो भुक्त्यन्तरोद्धृताः ॥

arkonacandraliptābhyas tithayo bhogabhājitāḥ | gatā gamyāś ca ṣaṣṭighnyo nāḍyo bhuktyantaroddhṛtāḥ ||

From the minutes of the Moon diminished by the Sun, divided by the ⟨tithi-⟩portion, come the tithis ⟨elapsed⟩; the elapsed and the remaining, multiplied by sixty and divided by the difference of the ⟨daily⟩ motions, are the nāḍīs.

ध्रुवाणि शकुनिर् नागं तृतीयं तु चतुष्पदम् । किंस्तुघ्नं तु चतुर्दश्याः कृष्णायाश् चापरार्धतः ॥

dhruvāṇi śakunir nāgaṃ tṛtīyaṃ tu catuṣpadam | kiṃstughnaṃ tu caturdaśyāḥ kṛṣṇāyāś cāparārdhataḥ ||

The fixed ⟨karaṇas⟩ are Śakuni, Nāga, third Catuṣpada, and Kiṃstughna — ⟨reckoned in order⟩ from the latter half of the dark fourteenth.

बवादीनि ततः सप्त चराख्यकरणानि च । मासेऽष्टकृत्व एकैकं करणानां प्रवर्तते ॥

bavādīni tataḥ sapta carākhyakaraṇāni ca | māse'ṣṭakṛtva ekaikaṃ karaṇānāṃ pravartate ||

Thereafter the seven beginning with Bava, and these are the karaṇas called movable (cara). In a month each single one of the karaṇas comes round eight times.

तिथ्यर्धभोगं सर्वेषां करणानां प्रकल्पयेत् । एषा स्फुटगतिः प्रोक्ता सूर्यादीनां खचारिणाम् ॥

tithyardhabhogaṃ sarveṣāṃ karaṇānāṃ prakalpayet | eṣā sphuṭagatiḥ proktā sūryādīnāṃ khacāriṇām ||

For all the karaṇas one should reckon a duration of half a tithi. This has been declared the true motion (sphuṭa-gati) of the Sun and the rest that travel in the sky.

शिलातलेऽम्बुसंशुद्धे वज्रलेपेऽपि वा समे । तत्र शङ्क्वङ्गुलैर् इष्टैः समं मण्डलम् आलिखेत् ॥

śilātale'mbusaṃśuddhe vajralepe'pi vā same | tatra śaṅkvaṅgulair iṣṭaiḥ samaṃ maṇḍalam ālikhet ||

On a stone slab levelled with water, or else on ⟨a floor of⟩ hard plaster that is level — there, with a radius of as many gnomon-digits as one wishes, let him draw an even circle.

तन्मध्ये स्थापयेच् छङ्कुं कल्पनाद्वादशाङ्गुलम् । तच्छायाग्रं स्पृशेद् यत्र वृत्ते पूर्वापरार्धयोः ॥

tanmadhye sthāpayec chaṅkuṃ kalpanādvādaśāṅgulam | tacchāyāgraṃ spṛśed yatra vṛtte pūrvāparārdhayoḥ ||

At its centre let him set up a gnomon (śaṅku) taken by assumption as twelve digits. Where the tip of its shadow touches the circle, in the eastern and the western halves —

तत्र बिन्दू विधायोभौ वृत्ते पूर्वापराभिधौ । तन्मध्ये तिमिना रेखा कर्तव्या दक्षिणोत्तरा ॥

tatra bindū vidhāyobhau vṛtte pūrvāparābhidhau | tanmadhye timinā rekhā kartavyā dakṣiṇottarā ||

— there, marking both points on the circle, named east and west, a north–south line is to be made between them by means of a ‘fish’ (timi — the lens-figure formed where two arcs cut).

याम्योत्तरदिशोर् मध्ये तिमिना पूर्वपश्चिमा । दिङ्मध्यमत्स्यैः संसाध्या विदिशस् तद्वद् एव हि ॥

yāmyottaradiśor madhye timinā pūrvapaścimā | diṅmadhyamatsyaiḥ saṃsādhyā vidiśas tadvad eva hi ||

Between the south and north directions, by means of a fish, the east–west ⟨line is drawn⟩; and the intermediate directions are to be established in just the same way, by fishes ⟨constructed⟩ between the ⟨cardinal⟩ directions.

चतुरस्रं बहिः कुर्यात् सूत्रैर् मध्याद् विनिर्गतैः । भुजसूत्राङ्गुलैस् तत्र दत्तैर् इष्टप्रभा स्मृता ॥

caturasraṃ bahiḥ kuryāt sūtrair madhyād vinirgataiḥ | bhujasūtrāṅgulais tatra dattair iṣṭaprabhā smṛtā ||

Outside ⟨the circle⟩ let him make a square, by threads issuing from the centre. There, by the digits laid off upon the side-threads, the required shadow is reckoned.

प्राक्पश्चिमाश्रिता रेखा प्रोच्यते सममण्डले । उन्मण्डले च विषुवन्मण्डले परिकीर्त्यते ॥

prākpaścimāśritā rekhā procyate samamaṇḍale | unmaṇḍale ca viṣuvanmaṇḍale parikīrtyate ||

The line lying east and west is declared ⟨the trace⟩ of the prime vertical (sama-maṇḍala); and it is proclaimed ⟨the trace⟩ of the unmaṇḍala and of the equinoctial circle (viṣuvan-maṇḍala) as well.

रेखा प्राच्यपरा साध्या विषुवद्भाग्रगा तथा । इष्टच्छायाविषुवतोर् मध्यम् अग्राभिधीयते ॥

rekhā prācyaparā sādhyā viṣuvadbhāgragā tathā | iṣṭacchāyāviṣuvator madhyam agrābhidhīyate ||

A line running east and west, passing through the tip of the equinoctial shadow, is likewise to be drawn. The interval between the given shadow ⟨-tip⟩ and the equinoctial ⟨line⟩ is called the agrā (amplitude).

शङ्कुच्छायाकृतियुतेर् मूलं कर्णोऽस्य वर्गतः । प्रोज्झ्य शङ्कुकृतिं मूलं छाया शङ्कुर् विपर्ययात् ॥

śaṅkucchāyākṛtiyuter mūlaṃ karṇo'sya vargataḥ | projjhya śaṅkukṛtiṃ mūlaṃ chāyā śaṅkur viparyayāt ||

The square root of the sum of the squares of the gnomon and the shadow is its hypotenuse (karṇa). From the square of that, casting out the square of the gnomon, the root is the shadow; and by the reverse ⟨process, casting out the square of the shadow, the root is⟩ the gnomon.

त्रिंशत्कृत्यो युगे भानां चक्रं प्राक् परिलम्बते । तद्गुणाद् भूदिनैर् भक्ताद् द्युगणाद् यद् अवाप्यते ॥

triṃśatkṛtyo yuge bhānāṃ cakraṃ prāk parilambate | tadguṇād bhūdinair bhaktād dyugaṇād yad avāpyate ||

Thirty times in a yuga the circle of the asterisms swings back eastward. From the ahargaṇa (dyugaṇa), multiplied by that ⟨thirty⟩ and divided by the terrestrial days ⟨in a yuga⟩, what is obtained —

तद्दोस् त्रिघ्ना दशाप्तांशा विज्ञेया अयनाभिधाः । तत्संस्कृताद् ग्रहात् क्रान्तिच्छायाचरदलादिकम् ॥

taddos trighnā daśāptāṃśā vijñeyā ayanābhidhāḥ | tatsaṃskṛtād grahāt krānticchāyācaradalādikam ||

— its bhuja ⟨in degrees⟩, multiplied by three and divided by ten, is to be known as the degrees called those of the ayana (precession). From the graha corrected by that ⟨follow⟩ the declination, the shadow, the ascensional difference (caradala) and the rest.

स्फुटं दृक्तुल्यतां गच्छेद् अयने विषुवद्वये । प्राक् चक्रं चलितं हीने छायार्कात् करणागते ॥

sphuṭaṃ dṛktulyatāṃ gacched ayane viṣuvadvaye | prāk cakraṃ calitaṃ hīne chāyārkāt karaṇāgate ||

⟨A place thus⟩ made true comes to agreement with observation (dṛk-tulyatā) at the solstice and at the two equinoxes. The circle has moved forward, eastward, when the ⟨sun⟩ arrived at by computation is less than the sun ⟨derived⟩ from the shadow —

अन्तरांशैर् अथावृत्य पश्चाच् छेषैस् तथाधिके । एवं विषुवती छाया स्वदेशे या दिनार्धजा ॥

antarāṃśair athāvṛtya paścāc cheṣais tathādhike | evaṃ viṣuvatī chāyā svadeśe yā dinārdhajā ||

— by the degrees of the difference; and turning back, ⟨it has moved⟩ westward by the remaining ⟨degrees⟩ likewise, when ⟨the computed sun⟩ is greater. Thus ⟨the precession is determined⟩. The equinoctial shadow is that which is produced at midday in one’s own place —

दक्षिणोत्तररेखायां सा तत्र विषुवत्प्रभा ॥ शङ्कुच्छायाहते त्रिज्ये विषुवत्कर्णभाजिते ।

dakṣiṇottararekhāyāṃ sā tatra viṣuvatprabhā || śaṅkucchāyāhate trijye viṣuvatkarṇabhājite |

— on the north–south line: that, there, is the equinoctial shadow (viṣuvat-prabhā). Two Radii, multiplied by the gnomon and by the ⟨equinoctial⟩ shadow ⟨respectively⟩ and divided by the equinoctial hypotenuse —

लम्बाक्षज्ये तयोश् चापे लम्बाक्षौ दक्षिणौ सदा । मध्यच्छाया भुजस् तेन गुणिता त्रिभमौर्विका ॥

lambākṣajye tayoś cāpe lambākṣau dakṣiṇau sadā | madhyacchāyā bhujas tena guṇitā tribhamaurvikā ||

— are the lambajyā (sine of the co-latitude) and the akṣajyā (sine of the latitude); the arcs of those two are the lamba and the akṣa, always south. The midday shadow is the bhuja; the sine of three signs (the Radius), multiplied by that —

स्वकर्णाप्ता धनुर्लिप्ता नतास् ता दक्षिणे भुजे । उत्तराश् चोत्तरे याम्यास् ताः सूर्यक्रान्तिलिप्तिकाः ॥

svakarṇāptā dhanurliptā natās tā dakṣiṇe bhuje | uttarāś cottare yāmyās tāḥ sūryakrāntiliptikāḥ ||

— and divided by its own hypotenuse: the minutes of that arc are the nata (zenith distance) — north when the bhuja is south, and south when ⟨the bhuja is⟩ north. Those, ⟨together with⟩ the minutes of the sun’s declination —

दिग्भेदे मिश्रिताः साम्ये विश्लिष्टाश् चाक्षलिप्तिकाः । ताभ्योऽक्षज्या च तद्वर्गं प्रोज्झ्य त्रिज्याकृतेः पदम् ॥

digbhede miśritāḥ sāmye viśliṣṭāś cākṣaliptikāḥ | tābhyo'kṣajyā ca tadvargaṃ projjhya trijyākṛteḥ padam ||

— when their directions differ, are mixed together ⟨added⟩; when the directions agree, are separated ⟨subtracted⟩ — ⟨and the result is⟩ the minutes of the akṣa (latitude). From these ⟨comes⟩ the akṣajyā; and, casting out the square of that from the square of the Radius, the root ⟨is⟩ —

लम्बज्यार्कगुणाक्षज्या विषुवद्भाथ लम्बया । स्वाक्षार्कनतभागानां दिक्साम्येऽन्तरम् अन्यथा ॥

lambajyārkaguṇākṣajyā viṣuvadbhātha lambayā | svākṣārkanatabhāgānāṃ diksāmye'ntaram anyathā ||

— the lambajyā. The akṣajyā, multiplied by twelve (arka) and divided by the lambajyā, is then the equinoctial shadow. Of the degrees of one’s own latitude and of the sun’s zenith distance: ⟨the sum⟩ when the directions are the same, the difference otherwise —

दिग्भेदेऽपक्रमः शेषस् तस्य ज्या त्रिज्यया हता । परमापक्रमज्याप्ता चापं मेषादिगो रविः ॥

digbhede'pakramaḥ śeṣas tasya jyā trijyayā hatā | paramāpakramajyāptā cāpaṃ meṣādigo raviḥ ||

— on difference of direction. The remainder is the declination (apakrama). Its sine, multiplied by the Radius and divided by the sine of the greatest declination, ⟨gives⟩ an arc: ⟨that is⟩ the sun, when it stands in the quadrant beginning with Aries.

कर्क्यादौ प्रोज्झ्य चक्रार्धात् तुलादौ भार्धसंयुतात् । मृगादौ प्रोज्झ्य भगणान् मध्याह्नेऽर्कः स्फुटो भवेत् ॥

karkyādau projjhya cakrārdhāt tulādau bhārdhasaṃyutāt | mṛgādau projjhya bhagaṇān madhyāhne'rkaḥ sphuṭo bhavet ||

In the quadrant beginning with Cancer, subtracting ⟨that arc⟩ from half a circle; in that beginning with Libra, ⟨the arc⟩ joined to half the circle of signs; in that beginning with Capricorn, subtracting from a whole revolution — ⟨thus⟩ the sun at midday becomes true.

तन्मान्दम् असकृद् वामं फलं मध्यो दिवाकरः । स्वाक्षार्कापक्रमयुतिर् दिक्साम्येऽन्तरम् अन्यथा ॥

tanmāndam asakṛd vāmaṃ phalaṃ madhyo divākaraḥ | svākṣārkāpakramayutir diksāmye'ntaram anyathā ||

Its manda equation, ⟨applied⟩ inversely and repeatedly, ⟨gives⟩ the mean sun. — The sum of one’s own latitude and of the sun’s declination when the directions are the same, the difference otherwise:

शेषं नतांशाः सूर्यस्य तद्बाहुज्या च कोटिजा । शङ्कुमानाङ्गुलाभ्यस्ते भुजत्रिज्ये यथाक्रमम् ॥

śeṣaṃ natāṃśāḥ sūryasya tadbāhujyā ca koṭijā | śaṅkumānāṅgulābhyaste bhujatrijye yathākramam ||

the remainder is the degrees of the sun’s zenith distance (nata). And ⟨take⟩ its sine (bāhujyā) and its cosine (koṭijā, i.e. koṭijyā); the bhuja-sine and the Radius, multiplied respectively by the measure of the gnomon in digits —

कोटिज्यया विभज्याप्ते छायाकर्णाव् अहर्दले । क्रान्तिज्या विषुवत्कर्णगुणाप्ता शङ्कुजीवया ॥

koṭijyayā vibhajyāpte chāyākarṇāv ahardale | krāntijyā viṣuvatkarṇaguṇāptā śaṅkujīvayā ||

— and divided by the koṭijyā, give the shadow and the hypotenuse at midday (ahardala). The krāntijyā, multiplied by the equinoctial hypotenuse and divided by the gnomon-sine (śaṅkujīvā) —

अर्काग्रा स्वेष्टकर्णघ्नी मध्यकर्णोद्धृता स्वका । विषुवद्भायुतार्काग्रा याम्ये स्याद् उत्तरो भुजः ॥

arkāgrā sveṣṭakarṇaghnī madhyakarṇoddhṛtā svakā | viṣuvadbhāyutārkāgrā yāmye syād uttaro bhujaḥ ||

— ⟨is⟩ the sun’s amplitude (arkāgrā). ⟨That⟩, multiplied by one’s own desired hypotenuse and divided by the midday hypotenuse, is one’s own ⟨amplitude⟩. The arkāgrā increased by the equinoctial shadow, when ⟨the declination is⟩ south, gives the northern bhuja.

विषुवत्याम् विशोध्योदग्गोले स्याद् बाहुर् उत्तरः । विपर्ययाद् भुजो याम्यो भवेत् प्राच्यपरान्तरे ॥

viṣuvatyām viśodhyodaggole syād bāhur uttaraḥ | viparyayād bhujo yāmyo bhavet prācyaparāntare ||

⟨The arkāgrā⟩ being subtracted from the equinoctial ⟨shadow⟩, when ⟨the sun is⟩ in the northern hemisphere, the base is north; from the contrary case the base becomes south — ⟨reckoned⟩ in the interval between east and west.

माध्याह्निको भुजो नित्यं छाया माध्याह्निकी स्मृता । लम्बाक्षजीवे विषुवच्छायाद्वादशसङ्गुणे ॥

mādhyāhniko bhujo nityaṃ chāyā mādhyāhnikī smṛtā | lambākṣajīve viṣuvacchāyādvādaśasaṅguṇe ||

That base is always the midday base, and ⟨the shadow got from it⟩ is known as the midday shadow. The lambajyā and the akṣajyā, multiplied by the equinoctial shadow and by twelve ⟨respectively⟩ —

क्रान्तिज्याप्ते तु तौ कर्णौ सममण्डलगे रवौ । सौम्याक्षोना यदा क्रान्तिः स्यात् तदा द्युदलश्रवः ॥

krāntijyāpte tu tau karṇau samamaṇḍalage ravau | saumyākṣonā yadā krāntiḥ syāt tadā dyudalaśravaḥ ||

— and divided by the krāntijyā, ⟨give⟩ those two hypotenuses when the sun stands on the prime vertical (sama-maṇḍala). When the declination is north and less than the latitude, then ⟨take⟩ the midday hypotenuse (dyudala-śravas) —

विषुवच्छाययाभ्यस्तः कर्णो मध्याग्रयोद्धृतः । स्वक्रान्तिज्या त्रिजीवाघ्नी लम्बज्याप्ताग्रमौर्विका ॥

viṣuvacchāyayābhyastaḥ karṇo madhyāgrayoddhṛtaḥ | svakrāntijyā trijīvāghnī lambajyāptāgramaurvikā ||

— which, multiplied by the equinoctial shadow and divided by the midday amplitude, ⟨gives the same⟩. One’s own krāntijyā, multiplied by the Radius and divided by the lambajyā, is the agrā-sine (agra-maurvikā).

स्वेष्टकर्णहता भक्ता त्रिज्ययाग्राङ्गुलादिका । त्रिज्यावर्गार्धतोऽग्रज्यावर्गोनाद् द्वादशाहतात् ॥

sveṣṭakarṇahatā bhaktā trijyayāgrāṅgulādikā | trijyāvargārdhato'grajyāvargonād dvādaśāhatāt ||

That, multiplied by one’s own desired hypotenuse and divided by the Radius, becomes the agrā in digits and the rest. From half the square of the Radius, diminished by the square of the agrā-sine, multiplied by twelve —

पुनर् द्वादशनिघ्नाच् च लभ्यते यत् फलं बुधैः । शङ्कुवर्गार्धसंयुक्तविषुवद्वर्गभाजितात् ॥

punar dvādaśanighnāc ca labhyate yat phalaṃ budhaiḥ | śaṅkuvargārdhasaṃyuktaviṣuvadvargabhājitāt ||

— and again multiplied by twelve, and divided by the square of the equinoctial ⟨shadow⟩ increased by half the square of the gnomon: the result which is thereby obtained by the wise —

तदेव करणी नाम तां पृथक् स्थापयेद् बुधः । अर्कघ्नी विषुवच्छायाग्रज्यया गुणिता तथा ॥

tadeva karaṇī nāma tāṃ pṛthak sthāpayed budhaḥ | arkaghnī viṣuvacchāyāgrajyayā guṇitā tathā ||

— that itself bears the name karaṇī; the wise ⟨calculator⟩ should set it down apart. Likewise the equinoctial shadow, multiplied by twelve (arka) and multiplied by the agrā-sine —

भक्ता फलाख्यं तद्वर्गसंयुक्तकरणीपदम् । फलेन हीनसंयुक्तं दक्षिणोत्तरगोलयोः ॥

bhaktā phalākhyaṃ tadvargasaṃyuktakaraṇīpadam | phalena hīnasaṃyuktaṃ dakṣiṇottaragolayoḥ ||

⟨The product,⟩ divided ⟨as before, gives what⟩ is called the phala (the “fruit”, the quotient). ⟨Take⟩ the root of the karaṇī (the surd) increased by the square of that ⟨phala⟩; ⟨that root,⟩ diminished by the phala and increased by it, for the southern and the northern hemisphere ⟨respectively⟩ —

याम्ययोर् विदिशोः शङ्कुर् एवं याम्योत्तरे रवौ । परिभ्रमति शङ्कोस् तु शङ्कुर् उत्तरयोस् तु सः ॥

yāmyayor vidiśoḥ śaṅkur evaṃ yāmyottare ravau | paribhramati śaṅkos tu śaṅkur uttarayos tu saḥ ||

— is the śaṅku (the sine of altitude) for the two southern intermediate directions ⟨south-east and south-west⟩; and equally so whether the sun revolves to the south or to the north of the gnomon (śaṅku) — but ⟨in the latter case⟩ that śaṅku is the one belonging to the two northern ⟨intermediate directions⟩.

तत्त्रिज्यावर्गविश्लेषान् मूलं दृग्ज्याभिधीयते । स्वशङ्कुना विभज्याप्ते दृक्त्रिज्ये द्वादशाहते ॥

tattrijyāvargaviśleṣān mūlaṃ dṛgjyābhidhīyate | svaśaṅkunā vibhajyāpte dṛktrijye dvādaśāhate ||

The root of the difference of the square of that ⟨śaṅku⟩ from the square of the Radius (trijyā) is called the dṛgjyā (the sine of zenith distance). The dṛgjyā and the Radius, each multiplied by twelve and divided by its own śaṅku, give —

छायाकर्णौ तु कोणेषु यथास्वं देशकालयोः । त्रिज्योदक्चरजायुक्ता याम्यायां तद्विवर्जिता ॥

chāyākarṇau tu koṇeṣu yathāsvaṃ deśakālayoḥ | trijyodakcarajāyuktā yāmyāyāṃ tadvivarjitā ||

— are the shadow and its hypotenuse in the intermediate directions (koṇa), each according to its own place and time. The Radius (trijyā), increased by the sine of the ascensional difference (carajyā) when ⟨the declination is⟩ north and diminished by it when south, ⟨is the antyā⟩.

अन्त्या नतोत्क्रमज्योना स्वाहोरात्रार्धसङ्गुणा । त्रिज्याभक्ता भवेच् छेदो लम्बज्याघ्नोऽथ भाजितः ॥

antyā natotkramajyonā svāhorātrārdhasaṅguṇā | trijyābhaktā bhavec chedo lambajyāghno'tha bhājitaḥ ||

The antyā, diminished by the versed sine (utkramajyā) of the nata (hour angle), multiplied by the semi-diameter of the sun's own diurnal circle (svāhorātrārdha) and divided by the Radius, becomes the cheda (the divisor). That, multiplied by the lambajyā (the sine of co-latitude) and then divided —

त्रिभज्यया भवेच् छङ्कुस् तद्वर्गं परिशोधयेत् । त्रिज्यावर्गात् पदं दृग्ज्या छायाकर्णौ तु पूर्ववत् ॥

tribhajyayā bhavec chaṅkus tadvargaṃ pariśodhayet | trijyāvargāt padaṃ dṛgjyā chāyākarṇau tu pūrvavat ||

— by the sine of three signs (tribhajyā, i.e. the Radius), gives the śaṅku. Its square is to be subtracted from the square of the Radius; the root ⟨of the remainder⟩ is the dṛgjyā; and the shadow and its hypotenuse ⟨are found⟩ as before.

अभीष्टच्छाययाभ्यस्ता त्रिज्या तत्कर्णभाजिता । दृग्ज्या तद्वर्गसंशुद्धात् त्रिज्यावर्गाच् च यत् पदम् ।

abhīṣṭacchāyayābhyastā trijyā tatkarṇabhājitā | dṛgjyā tadvargasaṃśuddhāt trijyāvargāc ca yat padam |

The Radius, multiplied by a given shadow and divided by that shadow's hypotenuse, is the dṛgjyā. And the root of the square of the Radius diminished by the square of that ⟨dṛgjyā⟩ —

शङ्कुः स त्रिभजीवाघ्नः स्वलम्बज्याविभाजितः । छेदः स त्रिज्ययाभ्यस्तः स्वाहोरात्रार्धभाजितः ॥

śaṅkuḥ sa tribhajīvāghnaḥ svalambajyāvibhājitaḥ | chedaḥ sa trijyayābhyastaḥ svāhorātrārdhabhājitaḥ ||

— that is the śaṅku. It, multiplied by the sine of three signs (tribhajīvā, the Radius) and divided by one's own lambajyā, is the cheda. That cheda, multiplied by the Radius and divided by the semi-diameter of one's own diurnal circle —

उन्नतज्या तया हीना स्वान्त्या शेषस्य कार्मुकम् । उत्क्रमज्याभिर् एवं स्युः प्राक्पश्चार्धनतासवः ॥

unnatajyā tayā hīnā svāntyā śeṣasya kārmukam | utkramajyābhir evaṃ syuḥ prākpaścārdhanatāsavaḥ ||

— is the unnatajyā ⟨the sine of the sun's elevation above the horizon⟩. One's own antyā being diminished by it, the arc of the remainder, ⟨taken⟩ by means of the versed sines, gives in this way the asus (respirations) of the nata of the eastern or of the western half ⟨of the day⟩.

इष्टाग्राघ्नी तु लम्बज्या स्वकर्णाङ्गुलभाजिता । क्रान्तिज्या सा त्रिजीवाघ्नी परमापक्रमोद्धृता ॥

iṣṭāgrāghnī tu lambajyā svakarṇāṅgulabhājitā | krāntijyā sā trijīvāghnī paramāpakramoddhṛtā ||

The lambajyā, multiplied by a given agrā (measure of amplitude) and divided by the corresponding hypotenuse in aṅgulas (digits), is the krāntijyā (the sine of declination). That, multiplied by the Radius (trijīvā) and divided by the sine of greatest declination (paramāpakrama) —

तच्चापं भादिकं क्षेत्रं पदैस् तत्र भवो रविः । इष्टेऽह्नि मध्ये प्राक्पश्चाद् धृते बाहुत्रयान्तरे ॥

taccāpaṃ bhādikaṃ kṣetraṃ padais tatra bhavo raviḥ | iṣṭe'hni madhye prākpaścād dhṛte bāhutrayāntare ||

— its arc is, in signs and the rest, the region ⟨of the sun⟩; by ⟨reference to⟩ the quadrants (pada) the sun is ⟨found to stand⟩ there. On a desired day, at midday and before and after ⟨it, the shadow being taken,⟩ the two intervals between the three bases ⟨of the shadow⟩ being laid off —

मत्स्यद्वयान्तरयुतेस् त्रिस्पृक्सूत्रेण भाभ्रमः । त्रिभद्युकर्णार्धगुणाः स्वाहोरात्रार्धभाजिताः ॥

matsyadvayāntarayutes trispṛksūtreṇa bhābhramaḥ | tribhadyukarṇārdhaguṇāḥ svāhorātrārdhabhājitāḥ ||

— from the junction ⟨of the lines drawn⟩ through the two fish-figures (matsya) in ⟨those⟩ intervals, and with a cord touching the three ⟨points⟩, ⟨is described⟩ the circuit of the shadow (bhābhrama). ⟨The sines,⟩ multiplied by half the diurnal diameter of three signs ⟨that is, by the day-radius of three signs⟩ and divided by their own diurnal semi-diameters —

क्रमाद् एकद्वित्रिभज्यास् तच्चापानि पृथक् पृथक् । स्वाधोऽधः परिशोध्याथ मेषाल् लङ्कोदयासवः ॥

kramād ekadvitribhajyās taccāpāni pṛthak pṛthak | svādho'dhaḥ pariśodhyātha meṣāl laṅkodayāsavaḥ ||

— in order, the sines of one, of two and of three signs: their arcs, taken each separately and each diminished by the one below it, are the asus of rising at Laṅkā ⟨of the signs⟩ beginning with Aries.

खागाष्टयोऽर्थगोऽगैकाः शरत्र्यङ्कहिमांशवः । स्वदेशचरखण्डोना भवन्तीष्टोदयासवः ॥

khāgāṣṭayo'rthago'gaikāḥ śaratryaṅkahimāṃśavaḥ | svadeśacarakhaṇḍonā bhavantīṣṭodayāsavaḥ ||

1,670; 1,795; and 1,935 ⟨respirations⟩. These, diminished by the cara-khaṇḍas (the portions of ascensional difference) of one's own country, become the asus of rising at the place desired.

व्यस्ता व्यस्तैर् युताः स्वैः स्वैः कर्कटाद्यास् ततस् त्रयः । उत्क्रमेण षडेवैते भवन्तीष्टास् तुलादयः ॥

vyastā vyastair yutāḥ svaiḥ svaiḥ karkaṭādyās tatas trayaḥ | utkrameṇa ṣaḍevaite bhavantīṣṭās tulādayaḥ ||

⟨These same numbers⟩ reversed, and increased by their own ⟨cara-khaṇḍas⟩ likewise reversed, are then the three ⟨signs⟩ beginning with Cancer; and these very six, in inverse order, become the desired ⟨rising times of the signs⟩ beginning with Libra.

गतभोग्यासवः कार्या भास्कराद् इष्टकालिकात् । स्वोदयासुहता भुक्तभोग्या भक्ताः खवह्निभिः ॥

gatabhogyāsavaḥ kāryā bhāskarād iṣṭakālikāt | svodayāsuhatā bhuktabhogyā bhaktāḥ khavahnibhiḥ ||

From the sun ⟨as computed⟩ for the desired time, the asus of the part elapsed and of the part to be traversed are to be made out: the degrees traversed and to be traversed, multiplied by the rising-asus of their own ⟨sign⟩ and divided by thirty.

अभीष्टघटिकासुभ्यो भोग्यासून् प्रविशोधयेत् । तद्वत् तदेष्यलग्नासून् एवं यातात् तथोत्क्रमात् ॥

abhīṣṭaghaṭikāsubhyo bhogyāsūn praviśodhayet | tadvat tadeṣyalagnāsūn evaṃ yātāt tathotkramāt ||

From the asus of the desired ghaṭikās subtract the asus of the part to be traversed; and likewise the asus of the lagnas (the signs) that are to come. Proceed so also from the elapsed ⟨time⟩, but in the reverse order.

शेषं चेत् त्रिंशताभ्यस्तम् अशुद्धेन विभाजितम् । भागैर् युक्तं च हीनं च तल्लग्नं क्षितिजे तदा ॥

śeṣaṃ cet triṃśatābhyastam aśuddhena vibhājitam | bhāgair yuktaṃ ca hīnaṃ ca tallagnaṃ kṣitije tadā ||

If there is a remainder, ⟨let it be⟩ multiplied by thirty and divided by the ⟨rising-asus of the sign⟩ that could not be subtracted; ⟨that sign,⟩ increased by the degrees ⟨so obtained⟩ or diminished by them, is then the lagna (the ascendant) on the horizon.

प्राक्पश्चान् नतनाडीभिस् तस्माल् लङ्कोदयासुभिः । भानौ क्षयधने कृत्वा मध्यलग्नं तदा भवेत् ॥

prākpaścān natanāḍībhis tasmāl laṅkodayāsubhiḥ | bhānau kṣayadhane kṛtvā madhyalagnaṃ tadā bhavet ||

⟨Then,⟩ by the nāḍīs of the nata (the hour angle) east or west, and thence by the asus of rising at Laṅkā, making subtraction from or addition to the sun, one obtains the madhya-lagna ⟨the point of the ecliptic then on the meridian⟩.

भोग्यासून् ऊनकस्याथ भुक्तासून् अधिकस्य च । सम्पिण्ड्यान्तरलग्नासून् एवं स्यात् कालसाधनम् ॥

bhogyāsūn ūnakasyātha bhuktāsūn adhikasya ca | sampiṇḍyāntaralagnāsūn evaṃ syāt kālasādhanam ||

The asus still to be traversed of the lesser ⟨longitude⟩, the asus already traversed of the greater, and the asus of the lagnas (signs) lying between — these being added together, the determination of the time (kāla-sādhana) is made in this way.

सूर्याद् ऊने निशाशेषे लग्नेऽर्काद् अधिके दिवा । भचक्रार्धयुताद् भानोर् अधिकेऽस्तमयात् परम् ॥

sūryād ūne niśāśeṣe lagne'rkād adhike divā | bhacakrārdhayutād bhānor adhike'stamayāt param ||

When the lagna is less than the sun, ⟨the time so found falls⟩ in the remainder of the night; when greater than the sun, in the daytime; when greater than the sun increased by half the circle of asterisms ⟨that is, by six signs⟩, after sunset.

सार्धानि षट्सहस्राणि योजनानि विवस्वतः । विष्कम्भो मण्डलस्येन्दोः सहाशीत्या चतुश्शतम् ॥

sārdhāni ṣaṭsahasrāṇi yojanāni vivasvataḥ | viṣkambho maṇḍalasyendoḥ sahāśītyā catuśśatam ||

Six thousand yojanas together with a half ⟨thousand more⟩ — ⟨such is⟩ the diameter of the disc of the Sun (vivasvat); of the Moon (indu), four hundred together with eighty.

स्फुटस्वभुक्त्या गुणितौ मध्यभुक्त्योद्धृतौ स्फुटौ । रवेः स्वभगणाभ्यस्तः शशाङ्कभगणोद्धृतः ॥

sphuṭasvabhuktyā guṇitau madhyabhuktyoddhṛtau sphuṭau | raveḥ svabhagaṇābhyastaḥ śaśāṅkabhagaṇoddhṛtaḥ ||

The two ⟨diameters⟩, each multiplied by its own true daily motion and divided by ⟨its⟩ mean daily motion, ⟨become⟩ the true ⟨diameters⟩. That of the Sun, multiplied by its own revolutions ⟨in an age⟩ and divided by the Moon's revolutions —

शशाङ्ककक्षागुणितो भाजितो वाऽर्ककक्षया । विष्कम्भश् चन्द्रकक्षायां तिथ्याप्ता मानलिप्तिका ॥

śaśāṅkakakṣāguṇito bhājito vā'rkakakṣayā | viṣkambhaś candrakakṣāyāṃ tithyāptā mānaliptikā ||

— or ⟨else⟩ multiplied by the Moon's orbit and divided by the Sun's orbit, ⟨gives⟩ the diameter ⟨as it stands⟩ on the Moon's orbit. Divided by fifteen (tithi), ⟨it becomes⟩ the measure in minutes.

स्फुटेन्दुभुक्तिर् भूव्यासगुणिता मध्ययोद्धृता । लब्धं सूची महीव्यासस्फुटार्कश्रवणान्तरम् ॥

sphuṭendubhuktir bhūvyāsaguṇitā madhyayoddhṛtā | labdhaṃ sūcī mahīvyāsasphuṭārkaśravaṇāntaram ||

The Moon's true daily motion, multiplied by the Earth's diameter and divided by ⟨her⟩ mean ⟨daily motion⟩ — what is obtained is the sūcī (the 'needle', the Earth's corrected diameter). The difference between the Earth's diameter and the true Sun's śravaṇa ⟨i.e. its disc reckoned at its own distance⟩ —

मध्येन्दुव्यासगुणितं मध्यार्कव्यासभाजितम् । विशोध्य लब्धं सूच्यां तु तमो लिप्तास् तु पूर्ववत् ॥

madhyenduvyāsaguṇitaṃ madhyārkavyāsabhājitam | viśodhya labdhaṃ sūcyāṃ tu tamo liptās tu pūrvavat ||

— multiplied by the Moon's mean diameter and divided by the Sun's mean diameter; subtracting what is obtained from the sūcī, ⟨the remainder is⟩ the shadow (tamas); and ⟨its⟩ minutes ⟨are found⟩ as before.

भानोर् भार्धे महीच्छाया तत्तुल्येऽर्कसमेऽपि वा । शशाङ्कपाते ग्रहणं कियद्भागाधिकोनके ॥

bhānor bhārdhe mahīcchāyā tattulye'rkasame'pi vā | śaśāṅkapāte grahaṇaṃ kiyadbhāgādhikonake ||

The Earth's shadow ⟨stands⟩ at half the circle of signs from the Sun. When the Moon's node coincides with that ⟨shadow⟩, or likewise with the Sun — or is greater or less ⟨than it⟩ by some degrees — ⟨there is⟩ an eclipse.

तुल्यौ राश्यादिभिः स्याताम् अमावास्यान्तकालिकौ । सूर्येन्दू पौर्णमास्यन्ते भार्धे भागादिकौ समौ ॥

tulyau rāśyādibhiḥ syātām amāvāsyāntakālikau | sūryendū paurṇamāsyante bhārdhe bhāgādikau samau ||

At the moment of the end of the new moon (amāvāsyā) the Sun and the Moon are equal in signs and the rest; at the end of the full moon (paurṇamāsī) they are equal in degrees and the rest ⟨when⟩ half the circle of signs ⟨is added⟩.

गतैष्यपर्वनाडीनां स्वफलेनोनसंयुतौ । समलिप्तौ भवेतां तौ पातस् तात्कालिकोऽन्यथा ॥

gataiṣyaparvanāḍīnāṃ svaphalenonasaṃyutau | samaliptau bhavetāṃ tau pātas tātkāliko'nyathā ||

Diminished or increased by the correction proper to the nāḍīs of the syzygy elapsed or still to come, those two become equal to the minute. The node ⟨too is taken⟩ for that same moment, ⟨but its correction is applied⟩ the other way about.

छादको भास्करस्येन्दुर् अधःस्थो घनवद् भवेत् । भूच्छायां प्राङ्मुखश् चन्द्रो विशत्य् अस्य भवेद् असौ ॥

chādako bhāskarasyendur adhaḥstho ghanavad bhavet | bhūcchāyāṃ prāṅmukhaś candro viśaty asya bhaved asau ||

The Moon, standing below, becomes the eclipser of the Sun, like a cloud. The Moon, moving eastward, enters the Earth's shadow; and that ⟨shadow⟩ becomes its ⟨eclipser⟩.

तात्कालिकेन्दुविक्षेपं छाद्यच्छादकमानयोः । योगार्धात् प्रोज्झ्य यच्छेषं तावच् छन्नं तद् उच्यते ॥

tātkālikenduvikṣepaṃ chādyacchādakamānayoḥ | yogārdhāt projjhya yaccheṣaṃ tāvac channaṃ tad ucyate ||

Subtract the Moon's latitude (vikṣepa) at that moment from half the sum of the measures of the eclipsed and the eclipsing ⟨bodies⟩; whatever remains — that much is called the obscured part (channa).

यद् ग्राह्यम् अधिके तस्मिन् सकलं न्यूनम् अन्यथा । योगार्धाद् अधिके न स्याद् विक्षेपे ग्राससम्भवः ॥

yad grāhyam adhike tasmin sakalaṃ nyūnam anyathā | yogārdhād adhike na syād vikṣepe grāsasambhavaḥ ||

If that ⟨remainder⟩ is greater than the eclipsed body, ⟨the eclipse is⟩ total; otherwise it falls short ⟨and is partial⟩. When the latitude is greater than half the sum, no obscuration (grāsa) can arise at all.

ग्राह्यग्राहकसंयोगवियोगौ दलितौ पृथक् । विक्षेपवर्गहीनाभ्यां तद्वर्गाभ्याम् उभे पदे ॥

grāhyagrāhakasaṃyogaviyogau dalitau pṛthak | vikṣepavargahīnābhyāṃ tadvargābhyām ubhe pade ||

The sum and the difference of the eclipsed and the eclipsing ⟨measures⟩, each halved separately; from those two squares, diminished by the square of the latitude, ⟨take⟩ the two square roots.

षष्ट्या संगुण्य सूर्येन्द्वोर् भुक्त्यन्तरविभाजिते । स्यातां स्थितिविमर्दार्धे नाडिकादिफले तयोः ॥

ṣaṣṭyā saṃguṇya sūryendvor bhuktyantaravibhājite | syātāṃ sthitivimardārdhe nāḍikādiphale tayoḥ ||

⟨Those two roots,⟩ multiplied by sixty and divided by the difference of the daily motions of the Sun and the Moon, become the half-duration (sthity-ardha) and the half-time of total obscuration (vimardārdha), the results of the two being in nāḍikās and the rest.

स्थित्यर्धनाडिकाभ्यस्ता गतयः षष्टिभाजिताः । लिप्तादि प्रग्रहे शोध्यं मोक्षे देयं पुनः पुनः ॥

sthityardhanāḍikābhyastā gatayaḥ ṣaṣṭibhājitāḥ | liptādi pragrahe śodhyaṃ mokṣe deyaṃ punaḥ punaḥ ||

The daily motions, multiplied by the nāḍikās of the half-duration and divided by sixty, ⟨give a result⟩ in minutes and the rest; it is to be subtracted ⟨from the longitudes⟩ for the first contact (pragraha) and added for the release (mokṣa) — again and again.

तद्विक्षेपैः स्थितिदलं विमर्दार्धं तथाऽसकृत् । संसाध्यम् अन्यथा पाते तल्लिप्तादिफलं स्वकम् ॥

tadvikṣepaiḥ sthitidalaṃ vimardārdhaṃ tathā'sakṛt | saṃsādhyam anyathā pāte talliptādiphalaṃ svakam ||

With the latitudes ⟨derived⟩ from those ⟨corrected places⟩, the half-duration and likewise the half-time of total obscuration are to be worked out repeatedly (asakṛt). In the case of the node, its own result in minutes and the rest ⟨is applied⟩ the other way about.

स्फुटतिथ्यवसाने तु मध्यग्रहणम् आदिशेत् । स्थित्यर्धनाडिकाहीने ग्रासो मोक्षस् तु संयुते ॥

sphuṭatithyavasāne tu madhyagrahaṇam ādiśet | sthityardhanāḍikāhīne grāso mokṣas tu saṃyute ||

At the end of the true tithi one should declare the middle of the eclipse; diminished by the nāḍikās of the half-duration ⟨it gives⟩ the first contact (grāsa), and increased ⟨by them⟩ the release (mokṣa).

तद्वद् एव विमर्दार्धनाडिकाहीनसंयुते । निमीलनोन्मीलनाख्ये भवेतां सकलग्रहे ॥

tadvad eva vimardārdhanāḍikāhīnasaṃyute | nimīlanonmīlanākhye bhavetāṃ sakalagrahe ||

In just the same way, ⟨that moment⟩ diminished and increased by the nāḍikās of the half-time of total obscuration gives the two ⟨moments⟩ named immersion (nimīlana) and emergence (unmīlana), in a total eclipse.

इष्टनाडीविहीनेन स्थित्यर्धेनार्कचन्द्रयोः । भुक्त्यन्तरं समाहन्यात् षष्ट्याप्ताः कोटिलिप्तिकाः ॥

iṣṭanāḍīvihīnena sthityardhenārkacandrayoḥ | bhuktyantaraṃ samāhanyāt ṣaṣṭyāptāḥ koṭiliptikāḥ ||

One should multiply the difference of the daily motions of the Sun and the Moon by the half-duration diminished by the desired nāḍīs; divided by sixty, ⟨the result gives⟩ the minutes of the koṭi (the upright).

भानोर् ग्रहे कोटिलिप्ता मध्यस्थित्यर्धसंगुणाः । स्फुटस्थित्यर्धसंभक्ताः स्फुटाः कोटिकलाः स्मृताः ॥

bhānor grahe koṭiliptā madhyasthityardhasaṃguṇāḥ | sphuṭasthityardhasaṃbhaktāḥ sphuṭāḥ koṭikalāḥ smṛtāḥ ||

In an eclipse of the Sun, the koṭi-minutes multiplied by the mean half-duration and divided by the true half-duration are held to be the true koṭi-minutes.

क्षेपो भुजस् तयोर् वर्गयुतेर् मूलं श्रवस् तु तत् । मानयोगार्धतः प्रोज्झ्य ग्रासस् तात्कालिको भवेत् ॥

kṣepo bhujas tayor vargayuter mūlaṃ śravas tu tat | mānayogārdhataḥ projjhya grāsas tātkāliko bhavet ||

The latitude (kṣepa) is the base (bhuja); the square root of the sum of the squares of those two is the hypotenuse (śravas). Subtracting that from half the sum of the ⟨two⟩ measures, the obscuration at that moment is obtained.

मध्यग्रहणतश् चोर्ध्वम् इष्टनाडीर् विशोधयेत् । स्थित्यर्धान् मौक्षिकाच् छेषं प्राग्वच् च्छेषं तु मौक्षिके ॥

madhyagrahaṇataś cordhvam iṣṭanāḍīr viśodhayet | sthityardhān maukṣikāc cheṣaṃ prāgvac ccheṣaṃ tu maukṣike ||

And for a time after the middle of the eclipse, one should subtract the desired nāḍīs from the half-duration on the side of release (maukṣika); the remainder ⟨is treated⟩ as before — and the remainder ⟨so found is the obscuration⟩ on the side of release.

ग्राह्यग्राहकयोगार्धाच् छोध्याः स्वच्छन्नलिप्तिकाः । तद्वर्गात् प्रोज्झ्य तत्कालविक्षेपस्य कृतिं पदम् ॥

grāhyagrāhakayogārdhāc chodhyāḥ svacchannaliptikāḥ | tadvargāt projjhya tatkālavikṣepasya kṛtiṃ padam ||

From half the sum of the eclipsed and the eclipsing ⟨measures⟩ the minutes of one's own ⟨given⟩ obscuration are to be subtracted; from the square of that ⟨remainder⟩, having taken away the square of the latitude for that time, ⟨take⟩ the square root.

कोटिलिप्ता रवेः स्पष्टस्थित्यर्धेनाहता हृताः । मध्येन लिप्तास् तन्नाड्यः स्थितिवद् ग्रासनाडिकाः ॥

koṭiliptā raveḥ spaṣṭasthityardhenāhatā hṛtāḥ | madhyena liptās tannāḍyaḥ sthitivad grāsanāḍikāḥ ||

⟨That root is⟩ the koṭi in minutes — in the case of the Sun, multiplied by the true half-duration and divided by the mean ⟨it gives the true⟩ minutes; the nāḍīs from those ⟨are found⟩ as in the case of the duration: ⟨they are⟩ the nāḍikās of the obscuration.

नतज्याऽक्षज्ययाभ्यस्ता त्रिज्याप्ता तस्य कार्मुकम् । वलनांशाः सौम्ययाम्याः पूर्वापरकपालयोः ॥

natajyā'kṣajyayābhyastā trijyāptā tasya kārmukam | valanāṃśāḥ saumyayāmyāḥ pūrvāparakapālayoḥ ||

The Sine of the hour-angle (nata), multiplied by the Sine of the terrestrial latitude (akṣa) and divided by the radius (trijyā) — the arc of that ⟨gives⟩ the degrees of deflection (valana), which are north and south in the eastern and the western hemisphere respectively.

राशित्रययुताद् ग्राह्यात् क्रान्त्यंशैर् दिक्षमैर् युताः । भेदेऽन्तराज् ज्या वलना सप्तत्यङ्गुलभाजिता ॥

rāśitrayayutād grāhyāt krāntyaṃśair dikṣamair yutāḥ | bhede'ntarāj jyā valanā saptatyaṅgulabhājitā ||

⟨Those degrees⟩ are increased by the degrees of declination ⟨reckoned⟩ from the eclipsed body increased by three signs, when the two are of like direction; when of different ⟨directions⟩, ⟨they are taken⟩ from their difference. The Sine ⟨of the result⟩ is the valana; divided by seventy, ⟨it stands⟩ in aṅgulas.

सोन्नतं दिनमध्यर्धं दिनार्धाप्तं फलेन तु । छिन्द्याद् विक्षेपमानानि तान्य् एषाम् अङ्गुलानि तु ॥

sonnataṃ dinamadhyardhaṃ dinārdhāptaṃ phalena tu | chindyād vikṣepamānāni tāny eṣām aṅgulāni tu ||

One and a half days together with the unnata ⟨the altitude reckoned in time⟩, divided by half the day — by that quotient one should divide the latitude and the ⟨disc-⟩measures: those ⟨results⟩ are their aṅgulas.

मध्यलग्नसमे भानौ हरिजस्य न सम्भवः । अक्षोदङ्मध्यभक्रान्तिसाम्ये नावनतेर् अपि ॥

madhyalagnasame bhānau harijasya na sambhavaḥ | akṣodaṅmadhyabhakrāntisāmye nāvanater api ||

When the Sun stands at the same ⟨point⟩ as the madhyalagna ⟨the meridian point of the ecliptic⟩, no harija ⟨parallax in longitude⟩ can arise; and when the ⟨terrestrial⟩ latitude (akṣa) and the northward declination of the meridian ⟨ecliptic point, madhyabha⟩ are equal, no avanati ⟨parallax in latitude⟩ either.

देशकालविशेषेण यथावनतिसम्भवः । लम्बनस्यापि पूर्वान्यदिग्वशाच् च तथोच्यते ॥

deśakālaviśeṣeṇa yathāvanatisambhavaḥ | lambanasyāpi pūrvānyadigvaśāc ca tathocyate ||

In what manner the avanati ⟨parallax in latitude⟩ arises through the particularity of place and time — and that of the lambana ⟨parallax in longitude⟩ too, by force of the direction, eastward or the other — is now told in like manner.

लग्नं पर्वान्तनाडीनां कुर्यात् स्वैर् उदयासुभिः । तज्ज्यान्त्यापक्रमज्याघ्नी लम्बज्याप्तोदयाभिधा ॥

lagnaṃ parvāntanāḍīnāṃ kuryāt svair udayāsubhiḥ | tajjyāntyāpakramajyāghnī lambajyāptodayābhidhā ||

One should compute the lagna ⟨the rising point of the ecliptic⟩ for the nāḍīs of the end of the parvan ⟨the moment of conjunction⟩ by the rising-times in asus of one's own ⟨place⟩. The sine of that, multiplied by the sine of the greatest declination and divided by the sine of the co-latitude (lambajyā), is what is called the udaya ⟨the orient-sine, udayajyā⟩.

तदा लङ्कोदयैर् लग्नं मध्यसंज्ञं यथोदितम् । तत्क्रान्त्यक्षांशसंयोगो दिक्षाम्येऽन्तरम् अन्यथा ॥

tadā laṅkodayair lagnaṃ madhyasaṃjñaṃ yathoditam | tatkrāntyakṣāṃśasaṃyogo dikṣāmye'ntaram anyathā ||

Then, by the rising-times at Laṅkā ⟨the right ascensions⟩, ⟨find⟩ the lagna named madhya ⟨the meridian ecliptic point⟩, as has been stated. The sum of its declination and the degrees of latitude ⟨is taken⟩ when the direction is the same; otherwise the difference.

शेषं नतांशास् तन्मौर्वी मध्यज्या साभिधीयते । मध्योदयज्ययाभ्यस्ता त्रिज्याप्ता वर्गितं फलम् ॥

śeṣaṃ natāṃśās tanmaurvī madhyajyā sābhidhīyate | madhyodayajyayābhyastā trijyāptā vargitaṃ phalam ||

The remainder is the degrees of ⟨meridian⟩ zenith-distance (natāṃśa); its sine is what is called the madhyajyā. That ⟨madhyajyā⟩, multiplied by the udayajyā and divided by the radius (trijyā) — the result is squared.

मध्यज्यावर्गविश्लिष्टं दृक्क्षेपः शेषतः पदम् । तत्त्रिज्यावर्गविश्लेषान् मूलं शङ्कुः स दृग्गतिः ॥

madhyajyāvargaviśliṣṭaṃ dṛkkṣepaḥ śeṣataḥ padam | tattrijyāvargaviśleṣān mūlaṃ śaṅkuḥ sa dṛggatiḥ ||

⟨That squared result⟩ being subtracted from the square of the madhyajyā, the root of the remainder is the dṛkkṣepa. From the difference of the square of that and the square of the radius, the root is the śaṅku ⟨the gnomon-sine⟩; that is the dṛggati.

नतांशबाहुकोटिज्येऽस्फुटे दृक्क्षेपदृग्गती । एकज्यावर्गतश् छेदो लब्धं दृग्गतिजीवया ॥

natāṃśabāhukoṭijye'sphuṭe dṛkkṣepadṛggatī | ekajyāvargataś chedo labdhaṃ dṛggatijīvayā ||

The sines of the bhuja and the koṭi of the natāṃśa ⟨the degrees of meridian zenith-distance⟩ are the rough (asphuṭa) dṛkkṣepa and dṛggati. The divisor (cheda) proceeds from the square of the sine of one sign ⟨rāśi⟩: it is what is obtained ⟨when that square is divided⟩ by the dṛggatijīvā.

मध्यलग्नार्कविश्लेषज्या छेदेन विभाजिता । रवीन्द्वोर् लम्बनं ज्ञेयं प्राक्पश्चाद् घटिकादिकम् ॥

madhyalagnārkaviśleṣajyā chedena vibhājitā | ravīndvor lambanaṃ jñeyaṃ prākpaścād ghaṭikādikam ||

The sine of the interval between the madhyalagna and the Sun, divided by the cheda ⟨the divisor⟩ — that is to be known as the lambana ⟨parallax in longitude⟩ of the Sun and Moon, east or west, in ghaṭikās and the rest.

मध्यलग्नाधिके भानौ तिथ्यन्तात् प्रविशोधयेत् । धनम् ऊनेऽसकृत् कर्म यावत् सर्वं स्थिरीभवेत् ॥

madhyalagnādhike bhānau tithyantāt praviśodhayet | dhanam ūne'sakṛt karma yāvat sarvaṃ sthirībhavet ||

When the Sun is greater than the madhyalagna, ⟨the lambana⟩ is to be subtracted from the end of the tithi; when less, it is additive. The operation ⟨is to be repeated⟩ again and again until the whole becomes fixed.

दृक्क्षेपः शीततिग्मांश्वोर् मध्यभुक्त्यन्तराहतः । तिथिघ्नत्रिज्यया भक्तो लब्धं सावनतिर् भवेत् ॥

dṛkkṣepaḥ śītatigmāṃśvor madhyabhuktyantarāhataḥ | tithighnatrijyayā bhakto labdhaṃ sāvanatir bhavet ||

The dṛkkṣepa, multiplied by the difference of the mean daily motions of the Moon and the Sun ⟨the cold-rayed and the hot-rayed⟩ and divided by the radius multiplied by the tithi ⟨fifteen⟩ — the quotient is the avanati ⟨parallax in latitude⟩.

दृक्क्षेपात् सप्ततिहृताद् भवेद् वावनतिः फलम् । अथवा त्रिज्यया भक्तात् सप्तसप्तकसङ्गुणात् ॥

dṛkkṣepāt saptatihṛtād bhaved vāvanatiḥ phalam | athavā trijyayā bhaktāt saptasaptakasaṅguṇāt ||

Or the avanati is the result from the dṛkkṣepa divided by seventy. Or from ⟨the dṛkkṣepa⟩ divided by the radius and multiplied by seven sevens ⟨forty-nine⟩.

मध्यज्यादिग्वशात् सा च विज्ञेया दक्षिणोत्तरा । सेन्दुविक्षेपदिक्षाम्ये युक्ता विश्लेषितान्यथा ॥

madhyajyādigvaśāt sā ca vijñeyā dakṣiṇottarā | senduvikṣepadikṣāmye yuktā viśleṣitānyathā ||

And that ⟨avanati⟩ is to be known as south or north according to the direction of the madhyajyā. When its direction is the same as that of the Moon's latitude (vikṣepa) it is added ⟨to it⟩; otherwise it is subtracted.

तया स्थितिविमर्दार्धग्रासाद्यं तु यथोदितम् । प्रमाणं वलनाभीष्टग्रासादि हिमरश्मिवत् ॥

tayā sthitivimardārdhagrāsādyaṃ tu yathoditam | pramāṇaṃ valanābhīṣṭagrāsādi himaraśmivat ||

By that ⟨apparent latitude⟩ the half-duration (sthityardha), the half-totality (vimardārdha), the obscuration (grāsa) and the rest ⟨are found⟩ as has been stated; and the measure (pramāṇa), the deflection (valana), the obscuration at a desired ⟨moment⟩ and so on, as in the case of the cold-rayed one ⟨the Moon⟩.

स्थित्यर्धोनाधिकात् प्राग्वत् तिथ्यन्ताल् लम्बनं पुनः । ग्रासमोक्षोद्भवं साध्यं तन्मध्यहरिजान्तरम् ॥

sthityardhonādhikāt prāgvat tithyantāl lambanaṃ punaḥ | grāsamokṣodbhavaṃ sādhyaṃ tanmadhyaharijāntaram ||

From the ⟨moment of the⟩ end of the tithi diminished and increased by the half-duration, the lambana is ⟨to be found⟩ again, as before; that arising at first contact (grāsa) and at release (mokṣa) is to be computed, ⟨and⟩ its interval from the harija ⟨parallax in longitude⟩ of the middle ⟨of the eclipse⟩.

प्राक्कपालेऽधिकं मध्याद् भवेत् प्राग्रहणं यदि । मौक्षिकं लम्बनं हीनं पश्चार्धे तु विपर्ययः ॥

prākkapāle'dhikaṃ madhyād bhavet prāgrahaṇaṃ yadi | maukṣikaṃ lambanaṃ hīnaṃ paścārdhe tu viparyayaḥ ||

If, in the eastern hemisphere (prākkapāla), the lambana of the first contact should be greater than that of the middle and the lambana of the release less — but in the western half the reverse —

तदा मोक्षस्थितिदले देयं प्रग्रहणे तथा । हरिजान्तरकं शोध्यं यत्रैतत् स्याद् विपर्ययः ॥

tadā mokṣasthitidale deyaṃ pragrahaṇe tathā | harijāntarakaṃ śodhyaṃ yatraitat syād viparyayaḥ ||

then the harijāntara ⟨the difference of the parallaxes in longitude⟩ is to be added to the half-duration of the release, and likewise to that of the first contact (pragrahaṇa); where this is reversed, it is to be subtracted.

एतद् उक्तं कपालैक्ये तद्भेदे लम्बनैकता । स्वे स्वे स्थितिदले योज्या विमर्दार्धेऽपि चोक्तवत् ॥

etad uktaṃ kapālaikye tadbhede lambanaikatā | sve sve sthitidale yojyā vimardārdhe'pi coktavat ||

This has been stated for the case where the hemisphere (kapāla) is one and the same; when they differ, the lambanas are made one ⟨their sum is taken⟩. It is to be applied to each half-duration respectively, and to the half-totality (vimardārdha) too, just as has been stated.

न छेद्यकम् ऋते यस्माद् भेदा ग्रहणयोः स्फुटाः । ज्ञायन्ते तत् प्रवक्ष्यामि छेद्यकज्ञानम् उत्तमम् ॥

na chedyakam ṛte yasmād bhedā grahaṇayoḥ sphuṭāḥ | jñāyante tat pravakṣyāmi chedyakajñānam uttamam ||

Since without the ⟨graphical⟩ projection (chedyaka) the exact particulars of the two eclipses are not known, I shall declare that excellent science of projection.

सुसाधितायाम् अवनौ बिन्दुं कृत्वा ततो लिखेत् । सप्तवर्गाङ्गुलेनादौ मण्डलं वलनाश्रितम् ॥

susādhitāyām avanau binduṃ kṛtvā tato likhet | saptavargāṅgulenādau maṇḍalaṃ valanāśritam ||

Upon a well-prepared ⟨and levelled⟩ ground, having made a point, one should then draw first, with forty-nine digits ⟨as radius⟩, the circle that serves for the deflection (valana).

ग्राह्यग्राहकयोगार्धसम्मितेन द्वितीयकम् । मण्डलं तत् समासाख्यं ग्राह्यार्धेन तृतीयकम् ॥

grāhyagrāhakayogārdhasammitena dvitīyakam | maṇḍalaṃ tat samāsākhyaṃ grāhyārdhena tṛtīyakam ||

⟨Then⟩ a second circle, measured by half the sum of the eclipsed and the eclipsing ⟨bodies⟩; that circle is named samāsa ⟨‘the sum’⟩; and a third with half the eclipsed body ⟨as radius⟩.

याम्योत्तराप्राच्यपरासाधनं पूर्ववद् दिशाम् । प्राग् इन्दोर् ग्रहणं पश्चान् मोक्षोऽर्कस्य विपर्ययात् ॥

yāmyottarāprācyaparāsādhanaṃ pūrvavad diśām | prāg indor grahaṇaṃ paścān mokṣo'rkasya viparyayāt ||

The determining of the directions — south and north, east and west — ⟨is⟩ as before. The Moon's eclipse ⟨begins⟩ on the east and the release ⟨falls⟩ on the west; for the Sun, by the reverse.

यथादिशं प्राग्रहणं वलनं हिमदीधितेः । मौक्षिकं तु विपर्यस्तं विपरीतम् इदं रवेः ॥

yathādiśaṃ prāgrahaṇaṃ valanaṃ himadīdhiteḥ | maukṣikaṃ tu viparyastaṃ viparītam idaṃ raveḥ ||

The deflection at the Moon's first contact ⟨is laid off⟩ according to its own direction, but that at the release reversed; for the Sun this ⟨rule⟩ is the contrary.

वलनाग्रान् नयेन् मध्यं सूत्रं यद्य् अत्र संस्पृशेत् । तत्समासे ततो देयौ विक्षेपौ ग्रासमौक्षिकौ ॥

valanāgrān nayen madhyaṃ sūtraṃ yady atra saṃspṛśet | tatsamāse tato deyau vikṣepau grāsamaukṣikau ||

From the tip of the deflection one should draw a line to the centre; where it touches ⟨the samāsa circle⟩, from that ⟨point⟩ upon the samāsa are then to be laid off the two latitudes, that of the first contact and that of the release.

विक्षेपाग्रात् पुनः सूत्रं मध्यबिन्दुं प्रवेशयेत् । तद्ग्राह्यबिन्दुसंस्पर्शाद् ग्रासमोक्षौ विनिर्दिशेत् ॥

vikṣepāgrāt punaḥ sūtraṃ madhyabinduṃ praveśayet | tadgrāhyabindusaṃsparśād grāsamokṣau vinirdiśet ||

From the tip of the latitude one should again carry a line into the centre point; by its touching of the point on the eclipsed body's ⟨circle⟩, one should declare the ⟨places of⟩ first contact and of release.

नित्यशोऽर्कस्य विक्षेपाः परिलेखे यथादिशम् । विपरीताः शशाङ्कस्य तद्वशाद् अथ मध्यमम् ॥

nityaśo'rkasya vikṣepāḥ parilekhe yathādiśam | viparītāḥ śaśāṅkasya tadvaśād atha madhyamam ||

In the projection, the latitudes ⟨in an eclipse⟩ of the Sun are always ⟨laid off⟩ according to their own direction, those ⟨in an eclipse⟩ of the Moon reversed; and in accordance with that, the middle ⟨latitude⟩ next.

वलनं प्राङ्मुखं देयं तद्विक्षेपैकता यदि । भेदे पश्चान् मुखं देयम् इन्दोर् भानोर् विपर्ययात् ॥

valanaṃ prāṅmukhaṃ deyaṃ tadvikṣepaikatā yadi | bhede paścān mukhaṃ deyam indor bhānor viparyayāt ||

The deflection is to be laid off facing east if it is of one direction with that latitude; if they differ, facing west — ⟨so⟩ for the Moon; for the Sun by the reverse.

वलनाग्रात् पुनः सूत्रं मध्यबिन्दुं प्रवेशयेत् । मध्यसूत्रेण विक्षेपं वलनाभिमुखं नयेत् ॥

valanāgrāt punaḥ sūtraṃ madhyabinduṃ praveśayet | madhyasūtreṇa vikṣepaṃ valanābhimukhaṃ nayet ||

From the tip of the deflection one should again carry a line into the centre point; by that central line one should draw the latitude, facing toward the deflection.

विक्षेपाग्राल् लिखेद् वृत्तं ग्राहकार्धेन तेन यत् । ग्राह्यवृत्तं समाक्रान्तं तद्ग्रस्तं तमसा भवेत् ॥

vikṣepāgrāl likhed vṛttaṃ grāhakārdhena tena yat | grāhyavṛttaṃ samākrāntaṃ tadgrastaṃ tamasā bhavet ||

From the tip of the latitude one should draw a circle with half the eclipsing body ⟨as radius⟩; whatever of the eclipsed body's circle is overspread by it, that is seized by the darkness.

छेद्यकं लिखता भूमौ फलके वा विपश्चिता । विपर्ययो दिशां कार्यः पूर्वापरकपालयोः ॥

chedyakaṃ likhatā bhūmau phalake vā vipaścitā | viparyayo diśāṃ kāryaḥ pūrvāparakapālayoḥ ||

By the learned man who draws the projection upon the ground or upon a board, a reversal of the directions is to be made as regards the eastern and the western halves ⟨of the sky⟩.

स्वच्छत्वाद् द्वादशांशोऽपि ग्रस्तश् चन्द्रस्य दृश्यते । लिप्तात्रयम् अपि ग्रस्तं तीक्ष्णत्वान् न विवस्वतः ॥

svacchatvād dvādaśāṃśo'pi grastaś candrasya dṛśyate | liptātrayam api grastaṃ tīkṣṇatvān na vivasvataḥ ||

Because of ⟨the Moon's⟩ clearness, even a twelfth part of the Moon obscured is seen; but of the Sun, even three minutes obscured are not ⟨seen⟩, on account of its fierce brightness.

स्वसंज्ञितास् त्रयः कार्या विक्षेपाग्रेषु बिन्दवः । तत्र प्राङ्मध्ययोर् मध्ये तथा मौक्षिकमध्ययोः ॥

svasaṃjñitās trayaḥ kāryā vikṣepāgreṣu bindavaḥ | tatra prāṅmadhyayor madhye tathā maukṣikamadhyayoḥ ||

Three points, each named by its own ⟨designation⟩, are to be made at the tips of the latitudes; then, between the first-contact ⟨point⟩ and the middle, and likewise between the release ⟨point⟩ and the middle —

लिखेन् मत्स्यौ तयोर् मध्यान् मुखपुच्छविनिःसृतम् । प्रसार्य सूत्रद्वितयं तयोर् यत्र युतिर् भवेत् ॥

likhen matsyau tayor madhyān mukhapucchaviniḥsṛtam | prasārya sūtradvitayaṃ tayor yatra yutir bhavet ||

— one should draw two 'fish-figures' (matsya); extending from the middle of the two a pair of lines issuing out of mouth and tail, ⟨see⟩ where their meeting falls —

तत्र सूत्रेण विलिखेच् चापं बिन्दुत्रयस्पृशा । स पन्था ग्राहकस्योक्तो येनासौ सम्प्रयास्यति ॥

tatra sūtreṇa vilikhec cāpaṃ bindutrayaspṛśā | sa panthā grāhakasyokto yenāsau samprayāsyati ||

— there, with a line ⟨as radius⟩ touching the three points, one should draw an arc; that is declared to be the path of the eclipsing body, along which it will travel.

ग्राह्यग्राहकयोगार्धात् प्रोज्झ्येष्टग्रासम् आगतम् । अवशिष्टाङ्गुलसमां शलाकां मध्यबिन्दुतः ॥

grāhyagrāhakayogārdhāt projjhyeṣṭagrāsam āgatam | avaśiṣṭāṅgulasamāṃ śalākāṃ madhyabindutaḥ ||

From half the sum of the eclipsed and the eclipsing ⟨bodies⟩, having cast out the desired ⟨amount of⟩ obscuration, ⟨take⟩ what results; a rod (śalākā) equal to the remaining digits, ⟨measured⟩ from the centre point —

तयोर् मार्गोन्मुखीं दद्याद् ग्रासतः प्राग्ग्रहाश्रिताम् । विमुञ्चतो मोक्षदिशि ग्राहकाध्वानम् एव सा ॥

tayor mārgonmukhīṃ dadyād grāsataḥ prāggrahāśritām | vimuñcato mokṣadiśi grāhakādhvānam eva sā ||

— one should lay ⟨it⟩ off facing the path of those two: from the ⟨time of⟩ obscuration, resting on the side of the first contact; and for the ⟨body⟩ releasing, in the direction of the release. That ⟨rod reaches⟩ the very path of the eclipsing body.

स्पृशेद् यत्र ततो वृत्तं ग्राहकार्धेन संलिखेत् । तेन ग्राह्यं यदाक्रान्तं तत् तमोग्रस्तम् आदिशेत् ॥

spṛśed yatra tato vṛttaṃ grāhakārdhena saṃlikhet | tena grāhyaṃ yadākrāntaṃ tat tamograstam ādiśet ||

Where it touches ⟨that path⟩, from that ⟨point⟩ one should draw a circle with half the eclipsing body ⟨as radius⟩; whatever of the eclipsed body is overspread by it, that one should declare seized by the darkness.

मानान्तरार्धेन मितां शलाकां ग्रासदिङ्मुखीम् । निमीलनाख्यां दद्यात् सा तन्मार्गे यत्र संस्पृशेत् ॥

mānāntarārdhena mitāṃ śalākāṃ grāsadiṅmukhīm | nimīlanākhyāṃ dadyāt sā tanmārge yatra saṃspṛśet ||

A rod measured by half the difference of the ⟨two⟩ diameters, facing the direction of the first contact and named 'immersion' (nimīlana), one should lay off; where it touches upon that path —

ततो ग्राहकखण्डेन प्राग्वन् मण्डलम् आलिखेत् । तद्ग्राह्यमण्डलयुतिर् यत्र तत्र निमीलनम् ॥

tato grāhakakhaṇḍena prāgvan maṇḍalam ālikhet | tadgrāhyamaṇḍalayutir yatra tatra nimīlanam ||

— from there, with the eclipsing body's portion ⟨half-diameter⟩, one should draw a circle as before; where that meets the circle of the eclipsed body, there is the immersion.

एवम् उन्मीलने मोक्षदिङ्मुखीं सम्प्रसारयेत् । विलिखेन् मण्डलं प्राग्वद् उन्मीलनम् अथोक्तवत् ॥

evam unmīlane mokṣadiṅmukhīṃ samprasārayet | vilikhen maṇḍalaṃ prāgvad unmīlanam athoktavat ||

So too in the case of the emergence (unmīlana): one should extend ⟨the rod⟩ facing the direction of the release, and draw a circle as before; the emergence ⟨is then found⟩ as has been stated.

अर्धाद् ऊने सधूम्रं स्यात् कृष्णम् अर्धाधिकं भवेत् । विमुञ्चतः कृष्णताम्रं कपिलं सकलग्रहे ॥

ardhād ūne sadhūmraṃ syāt kṛṣṇam ardhādhikaṃ bhavet | vimuñcataḥ kṛṣṇatāmraṃ kapilaṃ sakalagrahe ||

When less than half ⟨is obscured, the colour⟩ is smoky; when more than half, it becomes black; of the ⟨body⟩ releasing, black-coppery; at a total eclipse, tawny.

रहस्यम् एतद् देवानां न देयं यस्य कस्यचित् । सुपरीक्षितशिष्याय देयं वत्सरवासिने ॥

rahasyam etad devānāṃ na deyaṃ yasya kasyacit | suparīkṣitaśiṣyāya deyaṃ vatsaravāsine ||

This is a secret of the gods; it is not to be given to just anyone. It is to be given to a well-tested pupil, one who has dwelt ⟨with the teacher⟩ a year.

ताराग्रहाणाम् अन्योन्यं स्यातां युद्धसमागमौ । समागमः शशाङ्केन सूर्येणास्तमनं सह ॥

tārāgrahāṇām anyonyaṃ syātāṃ yuddhasamāgamau | samāgamaḥ śaśāṅkena sūryeṇāstamanaṃ saha ||

Among the star-grahas (tārāgraha) there occur, one with another, war (yuddha) and conjunction (samāgama); with the Moon (śaśāṅka) ⟨the meeting is called⟩ conjunction, and with the Sun, setting (astamana).

शीघ्रे मन्दाधिकेऽतीतः संयोगो भवितान्यथा । द्वयोः प्राग्यायिनोर् एवं वक्रिणोस् तु विपर्ययात् ॥

śīghre mandādhike'tītaḥ saṃyogo bhavitānyathā | dvayoḥ prāgyāyinor evaṃ vakriṇos tu viparyayāt ||

If the swift ⟨graha⟩ is in advance of the slow one, the conjunction is past; otherwise it is still to come. So it is for two ⟨grahas⟩ moving eastward; but for two retrograde ⟨grahas⟩, by reversal.

प्राग्यायिन्य् अधिकेऽतीतो वक्रिण्य् एष्यः समागमः । ग्रहान्तरकलाः स्वस्वभुक्तिलिप्ताः समाहताः ॥

prāgyāyiny adhike'tīto vakriṇy eṣyaḥ samāgamaḥ | grahāntarakalāḥ svasvabhuktiliptāḥ samāhatāḥ ||

⟨When one is direct and one retrograde:⟩ if the eastward-moving one is in advance, the conjunction is past; if the retrograde one ⟨is in advance⟩, the conjunction is to come. The minutes of the interval between the two grahas are multiplied by the minutes of the daily motion of each severally,

भुक्त्यन्तरेण विभजेद् अनुलोमविलोमयोः । द्वयोर् वक्रिण्य् अथैकस्मिन् भुक्तियोगेन भाजयेत् ॥

bhuktyantareṇa vibhajed anulomavilomayoḥ | dvayor vakriṇy athaikasmin bhuktiyogena bhājayet ||

and one should divide by the difference of the daily motions when ⟨the two move⟩ alike, forward or backward; but when one of the two is retrograde, one should divide by the sum of the daily motions.

लब्धं लिप्तादिकं शोध्यं गते देयं भविष्यति । विपर्ययाद् वक्रगत्योर् एकस्मिंस् तु धनव्ययौ ॥

labdhaṃ liptādikaṃ śodhyaṃ gate deyaṃ bhaviṣyati | viparyayād vakragatyor ekasmiṃs tu dhanavyayau ||

The quotient, in minutes and the rest, is to be subtracted ⟨from each graha⟩ when ⟨the conjunction⟩ is past, and to be added when it is to come. For two of retrograde motion, the reverse; but when one alone ⟨is retrograde⟩, ⟨there are⟩ addition and subtraction ⟨respectively⟩.

समलिप्तौ भवेतां तौ ग्रहौ भगणसंस्थितौ । विवरं तद्वद् उद्धृत्य दिनादिफलम् इष्यते ॥

samaliptau bhavetāṃ tau grahau bhagaṇasaṃsthitau | vivaraṃ tadvad uddhṛtya dinādiphalam iṣyate ||

⟨Thus⟩ those two grahas, standing in the circle of asterisms (bhagaṇa), come to have the same minutes. Dividing the interval in the same way, the result in days and the rest ⟨the time of the conjunction⟩ is obtained.

कृत्वा दिनक्षपामानं तथा विक्षेपलिप्तिकाः । नतोन्नतं साधयित्वा स्वकाल् लग्नवशात् तयोः ॥

kṛtvā dinakṣapāmānaṃ tathā vikṣepaliptikāḥ | natonnataṃ sādhayitvā svakāl lagnavaśāt tayoḥ ||

Having computed the measure of the day and of the night, and likewise the minutes of latitude (vikṣepa), and having determined, by means of the lagna, the meridian-distance (natonnata) of the two ⟨grahas⟩ from their own ⟨places⟩ —

विषुवच्छाययाभ्यस्ताद् विक्षेपाद् द्वादशोद्धृतात् । फलं स्वनतनाडीघ्नं स्वदिनार्धविभाजितम् ॥

viṣuvacchāyayābhyastād vikṣepād dvādaśoddhṛtāt | phalaṃ svanatanāḍīghnaṃ svadinārdhavibhājitam ||

From the latitude multiplied by the equinoctial shadow (viṣuvacchāyā) and divided by twelve, the result ⟨is then⟩ multiplied by one's own nata nāḍīs and divided by one's own half-day.

लब्धं प्राच्याम् ऋणं सौम्याद् विक्षेपात् पश्चिमे धनम् । दक्षिणे प्राक्कपाले स्वं पश्चिमे तु तथा क्षयः ॥

labdhaṃ prācyām ṛṇaṃ saumyād vikṣepāt paścime dhanam | dakṣiṇe prākkapāle svaṃ paścime tu tathā kṣayaḥ ||

The quotient, ⟨arising⟩ from a northern (saumya) latitude, is subtractive in the east and additive in the west; from a southern ⟨latitude⟩ it is additive in the eastern hemisphere, and in the western it is subtractive (kṣaya).

सत्रिभग्रहजक्रान्तिभागघ्नाः क्षेपलिप्तिकाः । विकलाः स्वम् ऋणं क्रान्तिक्षेपयोर् भिन्नतुल्ययोः ॥

satribhagrahajakrāntibhāgaghnāḥ kṣepaliptikāḥ | vikalāḥ svam ṛṇaṃ krāntikṣepayor bhinnatulyayoḥ ||

The minutes of latitude (kṣepa), multiplied by the degrees of the declination (krānti) derived from the graha increased by three signs, ⟨become⟩ seconds; ⟨they are⟩ additive or subtractive according as the declination and the latitude are of different or of the same ⟨direction⟩.

नक्षत्रग्रहयोगेषु ग्रहास्तोदयसाधने । शृङ्गोन्नतौ तु चन्द्रस्य दृक्कर्मादाव् इदं स्मृतम् ॥

nakṣatragrahayogeṣu grahāstodayasādhane | śṛṅgonnatau tu candrasya dṛkkarmādāv idaṃ smṛtam ||

In the conjunctions of grahas with nakṣatras, in the determination of the setting and rising of grahas, and in ⟨the computation of⟩ the elevation of the Moon's horns — in the dṛkkarma and the rest — this ⟨process⟩ is prescribed.

तात्कालिकौ पुनः कार्यौ विक्षेपौ च तयोस् ततः । दिक्तुल्ये त्व् अन्तरं भेदे योगः शिष्टं ग्रहान्तरम् ॥

tātkālikau punaḥ kāryau vikṣepau ca tayos tataḥ | diktulye tv antaraṃ bhede yogaḥ śiṣṭaṃ grahāntaram ||

Again, the latitudes of those two ⟨grahas⟩ are to be computed for the given moment; then, if they are of the same direction, ⟨take⟩ the difference, if of different directions, the sum: what remains is the interval between the grahas.

कुजार्किज्ञामरेज्यानां त्रिंशदर्धार्धवर्धिताः । विष्कम्भाश् चन्द्रकक्षायां भृगोः षष्टिर् उदाहृता ॥

kujārkijñāmarejyānāṃ triṃśadardhārdhavardhitāḥ | viṣkambhāś candrakakṣāyāṃ bhṛgoḥ ṣaṣṭir udāhṛtā ||

Of Mars (kuja), Saturn (arki), Mercury (jña) and Jupiter (amarejya) the diameters (viṣkambha), in the Moon's orbit, are thirty, increased ⟨successively⟩ by half of a half; of Venus (bhṛgu) sixty is declared.

त्रिचतुः कर्णयुत्याप्तास् ते द्विघ्नास् त्रिज्यया हताः । स्फुटाः स्वकर्णास् तिथ्याप्ता भवेयुर् मानलिप्तिकाः ॥

tricatuḥ karṇayutyāptās te dvighnās trijyayā hatāḥ | sphuṭāḥ svakarṇās tithyāptā bhaveyur mānaliptikāḥ ||

These, doubled and multiplied by the radius (trijyā), are divided by the sum of the third and fourth hypotenuses (karṇa); ⟨thus made⟩ true by their own hypotenuses, and divided by fifteen, they become the minutes of ⟨apparent⟩ size.

छायाभूमौ विपर्यस्ते स्वच्छायाग्रे तु दर्शयेत् । ग्रहः स्वदर्पणान्तःस्थः शङ्क्वग्रे सम्प्रदिश्यते ॥

chāyābhūmau viparyaste svacchāyāgre tu darśayet | grahaḥ svadarpaṇāntaḥsthaḥ śaṅkvagre sampradiśyate ||

On the shadow-ground, ⟨the whole being⟩ reversed, one should exhibit ⟨the graha⟩ at the tip of its own shadow; for the graha, standing within its own mirror-image, is pointed out ⟨as lying⟩ at the top of the gnomon (śaṅku).

पञ्चहस्तोच्छ्रितौ शङ्कू यथादिग् भ्रमसंस्थितौ । ग्रहान्तरेण विक्षिप्ताव् अधो हस्तनिखातगौ ॥

pañcahastocchritau śaṅkū yathādig bhramasaṃsthitau | grahāntareṇa vikṣiptāv adho hastanikhātagau ||

Two gnomons five cubits (hasta) high, set up in their proper directions upon the circle (bhrama), separated ⟨from one another⟩ by the interval of the two grahas, and sunk a cubit below ⟨into the ground⟩ —

छायाकर्णौ ततो दद्याच् छायाग्राच् छङ्कुमूर्धगौ । छायाकर्णाग्रसंयोगे संस्थितस्य प्रदर्शयेत् ॥

chāyākarṇau tato dadyāc chāyāgrāc chaṅkumūrdhagau | chāyākarṇāgrasaṃyoge saṃsthitasya pradarśayet ||

then one should lay down the two shadow-hypotenuses (chāyākarṇa), running from the tip of the shadow to the head of the gnomon; at the meeting of the tips of the shadow-hypotenuses one should exhibit ⟨the place⟩ of the ⟨graha⟩ so situated.

स्वशङ्कुमूर्धगौ व्योम्नि ग्रहौ दृक्तुल्यताम् इतौ । उल्लेखं तारकास्पर्शाद् भेदे भेदः प्रकीर्त्यते ॥

svaśaṅkumūrdhagau vyomni grahau dṛktulyatām itau | ullekhaṃ tārakāsparśād bhede bhedaḥ prakīrtyate ||

The two grahas, ⟨set thus⟩ at the heads of their own gnomons, have come in the sky to equality of sight (dṛktulyatā). From the touching of the discs (tārakā) ⟨the war is called⟩ ullekha, ⟨and⟩ when there is cleaving, bheda is declared.

युद्धम् अंशुविमर्दाख्यम् अंशुयोगे परस्परम् । अंशाद् ऊनेऽपसव्याख्यं युद्धम् एकोऽत्र चेद् अणुः ॥

yuddham aṃśuvimardākhyam aṃśuyoge parasparam | aṃśād ūne'pasavyākhyaṃ yuddham eko'tra ced aṇuḥ ||

When the rays ⟨of the two⟩ meet one another, the war is named aṃśuvimarda (the crushing of rays). When ⟨the interval is⟩ less than a degree, the war is called apasavya, if one of the two here is minute (aṇu).

समागमोऽंशाद् अधिके भवतश् चेद् वलान्वितौ । अपसव्ये जितो युद्धे पिहितोऽणुर् अदीप्तिमान् ॥

samāgamo'ṃśād adhike bhavataś ced valānvitau | apasavye jito yuddhe pihito'ṇur adīptimān ||

It is ⟨mere⟩ conjunction (samāgama) when ⟨the interval is⟩ more than a degree, if the two are possessed of strength (vala). In the apasavya war the one conquered is the minute one, obscured and lacking brightness (adīptimān).

रूक्षो विवर्णो विध्वस्तो विजितो दक्षिणाश्रितः । उदक्स्थो दीप्तिमान् स्थूलो जयी याम्येऽपि यो बली ॥

rūkṣo vivarṇo vidhvasto vijito dakṣiṇāśritaḥ | udakstho dīptimān sthūlo jayī yāmye'pi yo balī ||

⟨The graha that is⟩ rough, discoloured, shattered, ⟨and⟩ stationed to the south is the vanquished; ⟨the one⟩ stationed to the north, bright and large, is the victor — and so also is one in the south, if it be the stronger.

आसन्नाव् अप्य् उभौ दीप्तौ भवतश् चेत् समागमः । स्वल्पौ द्वाव् अपि विध्वस्तौ भवेतां कूटविग्रहौ ॥

āsannāv apy ubhau dīptau bhavataś cet samāgamaḥ | svalpau dvāv api vidhvastau bhavetāṃ kūṭavigrahau ||

If both, though close together, are bright, it is ⟨mere⟩ conjunction. If both are small and shattered, they become ⟨a case of⟩ feigned fight (kūṭavigraha).

उदक्स्थो दक्षिणस्थो वा भार्गवः प्रायशो जयी । शशाङ्केनैवम् एतेषां कुर्यात् संयोगसाधनम् ॥

udakstho dakṣiṇastho vā bhārgavaḥ prāyaśo jayī | śaśāṅkenaivam eteṣāṃ kuryāt saṃyogasādhanam ||

Whether stationed to the north or to the south, Venus (bhārgava) is for the most part the victor. In this same way one should make the computation of the conjunction of these ⟨grahas⟩ with the Moon (śaśāṅka).

भावाभावाय लोकानां कल्पनेयं प्रदर्शिता । स्वमार्गगाः प्रयान्त्य् एते दूरम् अन्योन्यम् आश्रिताः ॥

bhāvābhāvāya lokānāṃ kalpaneyaṃ pradarśitā | svamārgagāḥ prayānty ete dūram anyonyam āśritāḥ ||

This scheme (kalpanā) has been set forth for ⟨the sake of⟩ the being and the non-being of the peoples. ⟨In fact⟩ these ⟨grahas⟩, going each in its own path, travel far apart from one another, ⟨only seeming⟩ to rest upon one another.

प्रोच्यन्ते लिप्तिका भानां स्वभोगोऽथ दशाहतः । भवन्त्य् अतीतधिष्ण्यानां भोगलिप्तायुता ध्रुवाः ॥

procyante liptikā bhānāṃ svabhogo'tha daśāhataḥ | bhavanty atītadhiṣṇyānāṃ bhogaliptāyutā dhruvāḥ ||

The minutes ⟨of longitude⟩ of the nakṣatras are now declared. Each star's own portion (svabhoga), multiplied by ten and joined to the portion-minutes of the nakṣatras already elapsed, becomes the dhruvakas ⟨polar longitudes⟩.

अष्टार्णवाः शून्यकृताः पञ्चषष्टिर् नगेषवः । अष्टार्था अब्धयोऽष्टागा अङ्गागा मनवस् तथा ॥

aṣṭārṇavāḥ śūnyakṛtāḥ pañcaṣaṣṭir nageṣavaḥ | aṣṭārthā abdhayo'ṣṭāgā aṅgāgā manavas tathā ||

Forty-eight, forty, sixty-five, fifty-seven, fifty-eight, four, seventy-eight, seventy-six, and likewise fourteen.

कृतेषवो युगरसाः शून्यवाणा वियद्रसाः । खवेदाः सागरनगा गजागाः सागरर्तवः ॥

kṛteṣavo yugarasāḥ śūnyavāṇā viyadrasāḥ | khavedāḥ sāgaranagā gajāgāḥ sāgarartavaḥ ||

Fifty-four, sixty-four, fifty, sixty, forty, seventy-four, seventy-eight, sixty-four.

मनवोऽथ रसा वेदा वैश्वम् आप्यार्धभोगगम् । आप्यस्यैवाभिजित् प्रान्ते वैश्वान्ते श्रवणस्थितिः ।

manavo'tha rasā vedā vaiśvam āpyārdhabhogagam | āpyasyaivābhijit prānte vaiśvānte śravaṇasthitiḥ |

Then fourteen, six, four. The Vaiśva ⟨Uttarāṣāḍhā⟩ falls at half the portion of the Āpya ⟨Pūrvāṣāḍhā⟩; Abhijit is at the very end of that same Āpya, and at the end of the Vaiśva stands Śravaṇa.

त्रिचतुः पादयोः सन्धौ श्रविष्ठा श्रवणस्य तु । स्वभोगतो वियन् नागाः षट्कृतिर् यमलाश्विनः ॥

tricatuḥ pādayoḥ sandhau śraviṣṭhā śravaṇasya tu | svabhogato viyan nāgāḥ ṣaṭkṛtir yamalāśvinaḥ ||

Śraviṣṭhā ⟨Dhaniṣṭhā⟩ is at the junction of the third and fourth quarters (pāda) of Śravaṇa. ⟨For the rest, reckoned⟩ from their own portion: eighty, thirty-six, twenty-two.

रन्ध्राद्रयः क्रमाद् एषां विक्षेपाः स्वाद् अपक्रमात् । दिङ्मासविषयाः सौम्ये याम्ये पञ्च दिशो नव ॥

randhrādrayaḥ kramād eṣāṃ vikṣepāḥ svād apakramāt | diṅmāsaviṣayāḥ saumye yāmye pañca diśo nava ||

Seventy-nine. In order, the latitudes (vikṣepa) of these ⟨are now stated⟩, ⟨reckoned⟩ from their own point of declination ⟨on the ecliptic⟩: ten, twelve, five in the north; in the south, five, ten, nine.

सौम्ये रसाः खं याम्येऽगाः सौम्ये खार्कास् त्रयोदश । दक्षिणे रुद्रयमलाः सप्तत्रिंशद् अथोत्तरे ॥

saumye rasāḥ khaṃ yāmye'gāḥ saumye khārkās trayodaśa | dakṣiṇe rudrayamalāḥ saptatriṃśad athottare ||

In the north six, nought; in the south seven; in the north nought, twelve, thirteen. In the south eleven and two; then thirty-seven in the north.

याम्येऽध्यर्धत्रिककृता नव सार्धशरेषवः । उत्तरस्यां तथा षष्टिस् त्रिंशत् षट्त्रिंशद् एव हि ॥

yāmye'dhyardhatrikakṛtā nava sārdhaśareṣavaḥ | uttarasyāṃ tathā ṣaṣṭis triṃśat ṣaṭtriṃśad eva hi ||

In the south, one and a half, three, four, nine, five and a half; in the north five, and likewise sixty, thirty, and thirty-six indeed.

दक्षिणे त्व् अर्धभागस् तु चतुर्विंशतिर् उत्तरे । भागाः षड्विंशतिः खं च दास्रादीनां यथाक्रमम् ॥

dakṣiṇe tv ardhabhāgas tu caturviṃśatir uttare | bhāgāḥ ṣaḍviṃśatiḥ khaṃ ca dāsrādīnāṃ yathākramam ||

In the south, half a degree; in the north twenty-four degrees, twenty-six, and nought — of ⟨the nakṣatras⟩ beginning with the Dāsra ⟨Aśvinī⟩, in due order.

अशीतिभागैर् याम्यायाम् अगस्त्यो मिथुनान्तगः । विंशे च मिथुनस्यांशे मृगव्याधो व्यवस्थितः ॥

aśītibhāgair yāmyāyām agastyo mithunāntagaḥ | viṃśe ca mithunasyāṃśe mṛgavyādho vyavasthitaḥ ||

Agastya ⟨Canopus⟩, at eighty degrees in the south, is at the end of Mithuna ⟨Gemini⟩. And in the twentieth degree of Mithuna is stationed Mṛgavyādha ⟨Sirius⟩.

विक्षेपो दक्षिणे भागैः खार्णवैः स्वाद् अपक्रमात् । हुतभुग्ब्रह्महृदयौ वृषे द्वाविंशभागगौ ॥

vikṣepo dakṣiṇe bhāgaiḥ khārṇavaiḥ svād apakramāt | hutabhugbrahmahṛdayau vṛṣe dvāviṃśabhāgagau ||

⟨Its⟩ latitude is forty degrees in the south, from its own point of declination. Hutabhuj ⟨Agni⟩ and Brahmahṛdaya are in Vṛṣa ⟨Taurus⟩, gone to the twenty-second degree.

अष्टाभिस् त्रिंशता चैव विक्षिप्ताव् उत्तरेण तौ । गोलं बद्ध्वा परीक्षेत विक्षेपं ध्रुवकं स्फुटम् ॥

aṣṭābhis triṃśatā caiva vikṣiptāv uttareṇa tau | golaṃ baddhvā parīkṣeta vikṣepaṃ dhruvakaṃ sphuṭam ||

Those two are deflected to the north by eight and by thirty ⟨degrees⟩ respectively. Having constructed a sphere ⟨an armillary globe⟩, one should verify the latitude and the polar longitude exactly.

वृषे सप्तदशे भागे यस्य याम्योऽंशकद्वयात् । विक्षेपोऽभ्यधिको भिन्द्याद् रोहिण्याः शकटं तु सः ॥

vṛṣe saptadaśe bhāge yasya yāmyo'ṃśakadvayāt | vikṣepo'bhyadhiko bhindyād rohiṇyāḥ śakaṭaṃ tu saḥ ||

Whichever ⟨graha⟩, in the seventeenth degree of Vṛṣa ⟨Taurus⟩, has a southern latitude exceeding two degrees — that one will split the cart (śakaṭa) of Rohiṇī.

ग्रहवद् द्युनिशे भानां कुर्याद् दृक्कर्म पूर्ववत् । ग्रहमेलकवच् छेषं ग्रहभुक्त्या दिनानि च ॥

grahavad dyuniśe bhānāṃ kuryād dṛkkarma pūrvavat | grahamelakavac cheṣaṃ grahabhuktyā dināni ca ||

For the nakṣatras one should compute day and night ⟨their diurnal and nocturnal arcs⟩ as for a graha, and perform the dṛkkarma ⟨reduction to the visible place⟩ as before. The rest is as in the conjunction of grahas; and the days ⟨are found⟩ by the graha's daily motion.

एष्यो हीने ग्रहे योगो ध्रुवकाद् अधिके गतः । विपर्ययाद् वक्रगते ग्रहे ज्ञेयः समागमः ॥

eṣyo hīne grahe yogo dhruvakād adhike gataḥ | viparyayād vakragate grahe jñeyaḥ samāgamaḥ ||

When the graha is less ⟨than the dhruvaka⟩, the conjunction (yoga) is yet to come; when greater than the dhruvaka, it is past. The reverse when the graha is retrograde (vakra) — thus is the meeting to be known.

फाल्गुन्योर् भाद्रपदयोस् तथैवाषाढयोर् द्वयोः । विशाखाश्विनिसौम्यानां योगतारोत्तरा स्मृता ॥

phālgunyor bhādrapadayos tathaivāṣāḍhayor dvayoḥ | viśākhāśvinisaumyānāṃ yogatārottarā smṛtā ||

Of the two Phalgunīs, of the two Bhādrapadās, likewise of the two Āṣāḍhās, and of Viśākhā, Aśvinī and the Saumya ⟨Mṛgaśiras⟩ — the junction-star (yogatārā) is declared to be the northern one.

पश्चिमोत्तरताराया द्वितीया पश्चिमे स्थिता । हस्तस्य योगतारा सा श्रविष्ठायाश् च पश्चिमा ॥

paścimottaratārāyā dvitīyā paścime sthitā | hastasya yogatārā sā śraviṣṭhāyāś ca paścimā ||

That one which stands to the west, second from the north-western star, is the junction-star of Hasta; and of Śraviṣṭhā, the western one.

ज्येष्ठाश्रवणमैत्राणां बार्हस्पत्यस्य मध्यमा । भरण्याग्नेयपित्र्याणां रेवत्याश् चैव दक्षिणा ॥

jyeṣṭhāśravaṇamaitrāṇāṃ bārhaspatyasya madhyamā | bharaṇyāgneyapitryāṇāṃ revatyāś caiva dakṣiṇā ||

Of Jyeṣṭhā, Śravaṇa and the Maitra ⟨Anurādhā⟩, and of the Bārhaspatya ⟨Puṣya⟩ — the middle one. Of Bharaṇī, the Āgneya ⟨Kṛttikā⟩, the Pitrya ⟨Maghā⟩ and Revatī — the southern one.

रोहिण्यादित्यमूलानां प्राची सार्पस्य चैव हि । यथा प्रत्यवशेषाणां स्थूला स्याद् योगतारका ॥

rohiṇyādityamūlānāṃ prācī sārpasya caiva hi | yathā pratyavaśeṣāṇāṃ sthūlā syād yogatārakā ||

Of Rohiṇī, the Āditya ⟨Punarvasu⟩ and Mūla, and of the Sārpa ⟨Āśleṣā⟩ too — the eastern one. Of all that remain, whichever star is the large ⟨bright⟩ one is the junction-star.

पूर्वस्यां ब्रह्महृदयाद् अंशकैः पञ्चभिः स्थितः । प्रजापतिर् वृषान्तेऽसौ सौम्येऽष्टत्रिंशदंशकैः ॥

pūrvasyāṃ brahmahṛdayād aṃśakaiḥ pañcabhiḥ sthitaḥ | prajāpatir vṛṣānte'sau saumye'ṣṭatriṃśadaṃśakaiḥ ||

Prajāpati stands five degrees to the east of Brahmahṛdaya; he is at the end of Vṛṣa ⟨Taurus⟩, thirty-eight degrees to the north.

अपांवत्सस् तु चित्राया उत्तरेऽंशैस् तु पञ्चभिः । बृहत् किञ्चिद् अतो भागैर् आपः षड्भिस् तथोत्तरे ॥

apāṃvatsas tu citrāyā uttare'ṃśais tu pañcabhiḥ | bṛhat kiñcid ato bhāgair āpaḥ ṣaḍbhis tathottare ||

Apāṃvatsa is five degrees to the north of Citrā. Somewhat larger ⟨brighter⟩ than it, Āpaḥ is six degrees further north.

अथोदयास्तमययोः परिज्ञानं प्रकीर्त्यते । दिवाकरकराक्रान्तमूर्तीनाम् अल्पतेजसाम् ॥

athodayāstamayayoḥ parijñānaṃ prakīrtyate | divākarakarākrāntamūrtīnām alpatejasām ||

Now is proclaimed the ascertainment of the risings and settings of those ⟨grahas⟩ whose disks are overpowered by the rays of the day-maker ⟨the Sun⟩, and whose brilliance is faint.

सूर्याद् अभ्यधिकाः पश्चाद् अस्तं जीवकुजार्कजाः । ऊनाः प्रागुदयं यान्ति शुक्रज्ञौ वक्रिणौ तथा ॥

sūryād abhyadhikāḥ paścād astaṃ jīvakujārkajāḥ | ūnāḥ prāgudayaṃ yānti śukrajñau vakriṇau tathā ||

Jupiter, Mars and Saturn, when ⟨their longitudes are⟩ greater than the Sun's, go to setting in the west; when less, they go to rising in the east. So too Venus and Mercury when retrograde.

ऊना विवस्वतः प्राच्याम् अस्तं चन्द्रज्ञभार्गवाः । व्रजन्त्य् अभ्यधिकाः पश्चाद् उदयं शीघ्रयायिनः ॥

ūnā vivasvataḥ prācyām astaṃ candrajñabhārgavāḥ | vrajanty abhyadhikāḥ paścād udayaṃ śīghrayāyinaḥ ||

The Moon, Mercury and Venus, when less than the Sun, go to setting in the east; when greater, ⟨they go⟩ to rising in the west — ⟨these being⟩ the swift-moving ones.

सूर्यास्तकालिकौ पश्चात् प्राच्याम् उदयकालिकौ । दिवा चार्कग्रहौ कुर्याद् दृक्कर्माथ ग्रहस्य तु ॥

sūryāstakālikau paścāt prācyām udayakālikau | divā cārkagrahau kuryād dṛkkarmātha grahasya tu ||

For the west ⟨the positions are taken⟩ as at the time of sunset, for the east as at the time of sunrise; one should compute the two — the Sun and the graha — for the ⟨civil⟩ day; and then the dṛkkarma (the correction to visible position) of the graha.

ततो लग्नान्तरप्राणाः कालांशाः षष्टिभाजिताः । प्रतीच्यां षड्भयुतयोस् तद्वल् लग्नान्तरासवः ॥

tato lagnāntaraprāṇāḥ kālāṃśāḥ ṣaṣṭibhājitāḥ | pratīcyāṃ ṣaḍbhayutayos tadval lagnāntarāsavaḥ ||

Then the prāṇas of the difference of the two lagnas ⟨rising points⟩, divided by sixty, are the time-degrees (kālāṃśa). In the west, ⟨the lagnas are taken⟩ of the two ⟨bodies⟩ each increased by six signs; the asus of the lagna-difference ⟨are found⟩ in the same way.

एकादशामरेज्यस्य तिथिसङ्ख्यार्कजस्य च । अस्तांशा भूमिपुत्रस्य दश सप्ताधिकास् ततः ॥

ekādaśāmarejyasya tithisaṅkhyārkajasya ca | astāṃśā bhūmiputrasya daśa saptādhikās tataḥ ||

Eleven ⟨time-degrees⟩ for Jupiter, and the number of the tithis ⟨fifteen⟩ for Saturn; the setting-degrees of Mars are, beyond that, ten increased by seven ⟨seventeen⟩.

पश्चाद् अस्तमयोऽष्टाभिर् उदयः प्राङ्महत्तया । प्राग् अस्तम् उदयः पश्चाद् अल्पत्वाद् दशभिर् भृगोः ॥

paścād astamayo'ṣṭābhir udayaḥ prāṅmahattayā | prāg astam udayaḥ paścād alpatvād daśabhir bhṛgoḥ ||

Venus's setting in the west and rising in the east ⟨occur⟩ at eight ⟨degrees⟩, by reason of ⟨her⟩ greatness; ⟨her⟩ setting in the east and rising in the west, by reason of ⟨her⟩ smallness, at ten.

एवं बुधो द्वादशभिश् चतुर्दशभिर् अंशकैः । वक्री शीघ्रगतिश् चार्कात् करोत्य् अस्तमयोदयौ ॥

evaṃ budho dvādaśabhiś caturdaśabhir aṃśakaiḥ | vakrī śīghragatiś cārkāt karoty astamayodayau ||

So too Mercury, at twelve and at fourteen degrees — ⟨when⟩ retrograde and ⟨when⟩ of swift motion respectively — makes his setting and rising from the Sun.

एभ्योऽधिकैः कालभागैर् दृश्या न्यूनैर् अदर्शनाः । भवन्ति लोके खचरा भानुभाग्रस्तमूर्तयः ॥

ebhyo'dhikaiḥ kālabhāgair dṛśyā nyūnair adarśanāḥ | bhavanti loke khacarā bhānubhāgrastamūrtayaḥ ||

With time-degrees greater than these they are visible; with less, invisible. So do the sky-goers ⟨the grahas⟩ become in the world, their disks devoured by the Sun's light.

तत्कालांशान्तरकला भुक्त्यन्तरविभाजिताः । दिनादि तत्फलं लब्धं भुक्तियोगेन वक्रिणः ॥

tatkālāṃśāntarakalā bhuktyantaravibhājitāḥ | dinādi tatphalaṃ labdhaṃ bhuktiyogena vakriṇaḥ ||

The minutes of the difference of those time-degrees ⟨from the present distance⟩, divided by the difference of the two daily motions — the result obtained is in days and the rest; for a retrograde ⟨graha⟩, by the sum of the daily motions.

तल्लग्नासुहते भुक्ती अष्टादशशतोद्धृते । स्यातां कालगती ताभ्यां दिनादि गतगम्ययोः ॥

tallagnāsuhate bhuktī aṣṭādaśaśatoddhṛte | syātāṃ kālagatī tābhyāṃ dinādi gatagamyayoḥ ||

The two daily motions, multiplied by the asus of that lagna-⟨difference⟩ and divided by eighteen hundred, become the motions in time; by these two ⟨is obtained⟩, in days and the rest, ⟨the interval⟩ elapsed and to come.

स्वात्यगस्त्यमृगव्याधचित्राज्येष्ठाः पुनर्वसुः । अभिजिद् ब्रह्महृदयं त्रयोदशभिर् अंशकैः ॥

svātyagastyamṛgavyādhacitrājyeṣṭhāḥ punarvasuḥ | abhijid brahmahṛdayaṃ trayodaśabhir aṃśakaiḥ ||

Svāti, Agastya ⟨Canopus⟩, Mṛgavyādha ⟨Sirius⟩, Citrā, Jyeṣṭhā, Punarvasu, Abhijit, Brahmahṛdaya ⟨become visible⟩ at thirteen degrees.

हस्तश्रवणफाल्गुन्यः श्रविष्ठा रोहिणीमघाः । चतुर्दशांशकैर् दृश्या विशाखाश्विनिदैवतम् ॥

hastaśravaṇaphālgunyaḥ śraviṣṭhā rohiṇīmaghāḥ | caturdaśāṃśakair dṛśyā viśākhāśvinidaivatam ||

Hasta, Śravaṇa, the Phālgunīs ⟨both⟩, Śraviṣṭhā, Rohiṇī, Maghā, Viśākhā, and that whose deity is the Aśvins ⟨Aśvinī⟩ are visible at fourteen degrees.

कृत्तिकामैत्रमूलानि सार्पं रौद्रर्क्षम् एव च । दृश्यन्ते पञ्चदशभिर् आषाढाद् द्वितयं तथा ॥

kṛttikāmaitramūlāni sārpaṃ raudrarkṣam eva ca | dṛśyante pañcadaśabhir āṣāḍhād dvitayaṃ tathā ||

Kṛttikā, the Maitra ⟨asterism, Anurādhā⟩, Mūla, the Sārpa ⟨asterism, Āśleṣā⟩, and the Raudra asterism ⟨Ārdrā⟩, and likewise the pair beginning with Āṣāḍhā ⟨Pūrva- and Uttarāṣāḍhā⟩, are seen at fifteen ⟨degrees⟩.

भरणीतिष्यसौम्यानि सौक्ष्म्यात् त्रिःसप्तकांशकैः । शेषाणि सप्तदशभिर् दृश्यादृश्यानि भानि तु ॥

bharaṇītiṣyasaumyāni saukṣmyāt triḥsaptakāṃśakaiḥ | śeṣāṇi saptadaśabhir dṛśyādṛśyāni bhāni tu ||

Bharaṇī, Tiṣya ⟨Puṣya⟩, and the Saumya ⟨asterism, Mṛgaśiras⟩, by reason of their minuteness, at thrice seven ⟨twenty-one⟩ degrees; the rest at seventeen — thus are the asterisms visible and invisible.

अष्टादशशताभ्यस्ता दृश्यांशाः स्वोदयासुभिः । विभज्य लब्धाः क्षेत्रांशास् तैर् दृश्यादृश्यताथवा ॥

aṣṭādaśaśatābhyastā dṛśyāṃśāḥ svodayāsubhiḥ | vibhajya labdhāḥ kṣetrāṃśās tair dṛśyādṛśyatāthavā ||

Or else: the degrees of visibility, multiplied by eighteen hundred and divided by the asus of the ⟨asterism's⟩ own rising, give as quotient the degrees of arc (kṣetrāṃśa); by these too ⟨are determined⟩ visibility and invisibility.

प्राग् एषाम् उदयः पश्चाद् अस्तो दृक्कर्म पूर्ववत् । गतैष्यदिवसप्राप्तिर् भानुभुक्त्या सदैव हि ॥

prāg eṣām udayaḥ paścād asto dṛkkarma pūrvavat | gataiṣyadivasaprāptir bhānubhuktyā sadaiva hi ||

Their rising is in the east and their setting in the west; the dṛkkarma is as before. The finding of the days elapsed and to come is always by the Sun's daily motion alone.

अभिजिद् ब्रह्महृदयं स्वातीवैष्णववासवाः । अहिर्बुध्न्यम् उदक्स्थत्वान् न लुप्यन्तेऽर्करश्मिभिः ॥

abhijid brahmahṛdayaṃ svātīvaiṣṇavavāsavāḥ | ahirbudhnyam udaksthatvān na lupyante'rkaraśmibhiḥ ||

Abhijit, Brahmahṛdaya, Svāti, the Vaiṣṇava ⟨asterism, Śravaṇa⟩, the Vāsava ⟨asterism, Śraviṣṭhā⟩, and Ahirbudhnya ⟨Uttarabhādrapadā⟩ — because they stand to the north, are not blotted out by the Sun's rays.

उदयास्तविधिः प्राग्वत् कर्तव्यः शीतगोर् अपि । भागैर् द्वादशभिः पश्चाद् दृश्यः प्राग् यात्य् अदृश्यताम् ॥

udayāstavidhiḥ prāgvat kartavyaḥ śītagor api | bhāgair dvādaśabhiḥ paścād dṛśyaḥ prāg yāty adṛśyatām ||

The method of ⟨computing⟩ rising and setting is to be applied to the cold-rayed one ⟨the Moon⟩ also, just as before. At twelve degrees ⟨of distance from the Sun⟩ it is visible in the west; in the east it passes into invisibility.

रवीन्द्वोः षड्भयुतयोः प्राग्वल् लग्नान्तरासवः । एकराशौ रवीन्द्वोश् च कार्या विवरलिप्तिकाः ॥

ravīndvoḥ ṣaḍbhayutayoḥ prāgval lagnāntarāsavaḥ | ekarāśau ravīndvoś ca kāryā vivaraliptikāḥ ||

For the Sun and the Moon, each increased by six signs, ⟨find⟩ as before the asus of the interval between their rising-points ⟨lagna⟩; and when the Sun and the Moon stand in one and the same rāśi, the minutes of their difference are to be taken ⟨instead⟩.

तन्नाडिकाहते भुक्ती रवीन्द्वोः षष्टिभाजिते । तत्फलान्वितयोर् भूयः कर्तव्या विवरासवः ॥

tannāḍikāhate bhuktī ravīndvoḥ ṣaṣṭibhājite | tatphalānvitayor bhūyaḥ kartavyā vivarāsavaḥ ||

The daily motions ⟨bhukti⟩ of the Sun and the Moon, multiplied by those nāḍikās and divided by sixty ⟨give the corrections⟩; and with the two ⟨bodies⟩ increased by those results, the asus of the interval are to be computed again.

एवं यावत् स्थिरीभूता रवीन्द्वोर् अन्तरासवः । तैः प्राणैर् अस्तमेतीन्दुः शुक्लेऽर्कास्तमयात् परम् ॥

evaṃ yāvat sthirībhūtā ravīndvor antarāsavaḥ | taiḥ prāṇair astametīnduḥ śukle'rkāstamayāt param ||

⟨Repeat⟩ thus until the asus of the interval between the Sun and the Moon become fixed. By that number of prāṇas the Moon sets, in the bright fortnight, after sunset.

भगणार्धं रवेर् दत्त्वा कार्यास् तद्विवरासवः । तैः प्राणैः कृष्णपक्षे तु शीतांशुर् उदयं व्रजेत् ॥

bhagaṇārdhaṃ raver dattvā kāryās tadvivarāsavaḥ | taiḥ prāṇaiḥ kṛṣṇapakṣe tu śītāṃśur udayaṃ vrajet ||

Having added half a revolution ⟨six signs⟩ to the Sun, the asus of that interval are to be computed; by that number of prāṇas, in the dark fortnight, the cold-rayed one comes to its rising.

अर्केन्द्वोः क्रान्तिविश्लेषो दिक्साम्ये युतिर् अन्यथा । तज्ज्येन्दुर् अर्काद् यत्रासौ विज्ञेया दक्षिणोत्तरा ॥

arkendvoḥ krāntiviśleṣo diksāmye yutir anyathā | tajjyendur arkād yatrāsau vijñeyā dakṣiṇottarā ||

The difference of the declinations of the Sun and the Moon ⟨is to be taken⟩ when the two directions are the same, their sum otherwise. The Sine of that ⟨gives the distance of⟩ the Moon from the Sun; it is to be known as south or north according to where that ⟨Moon⟩ stands.

मध्याह्नेन्दुप्रभाकर्णसङ्गुणा यदि सोत्तरा । तदार्कघ्नाक्षजीवायां शोध्या योज्या च दक्षिणा ॥

madhyāhnenduprabhākarṇasaṅguṇā yadi sottarā | tadārkaghnākṣajīvāyāṃ śodhyā yojyā ca dakṣiṇā ||

⟨That Sine,⟩ multiplied by the hypotenuse of the Moon's midday shadow — if it is north, it is then to be subtracted from the Sine of latitude ⟨akṣajyā⟩ multiplied by twelve; and if south, added.

शेषं लम्बज्यया भक्तं लब्धो बाहुः स्वदिङ्मुखः । कोटिः शङ्कुस् तयोर् वर्गयुतेर् मूलं श्रुतिर् भवेत् ॥

śeṣaṃ lambajyayā bhaktaṃ labdho bāhuḥ svadiṅmukhaḥ | koṭiḥ śaṅkus tayor vargayuter mūlaṃ śrutir bhavet ||

The remainder, divided by the Sine of co-latitude ⟨lambajyā⟩, gives the base ⟨bāhu⟩, lying toward its own direction. The upright ⟨koṭi⟩ is the gnomon; the square root of the sum of the squares of those two becomes the hypotenuse.

सूर्योनशीतगोर् लिप्ताः शुक्लं नवशतोद्धृताः । चन्द्रबिम्बाङ्गुलाभ्यस्तं हृतं द्वादशभिः स्फुटम् ॥

sūryonaśītagor liptāḥ śuklaṃ navaśatoddhṛtāḥ | candrabimbāṅgulābhyastaṃ hṛtaṃ dvādaśabhiḥ sphuṭam ||

The minutes of the Moon diminished by the Sun, divided by nine hundred, ⟨give⟩ the illuminated part ⟨śukla⟩; multiplied by the aṅgulas of the Moon's disc and divided by twelve, it is exact.

दत्त्वार्कसंज्ञितं बिन्दुं ततो बाहुं स्वदिङ्मुखम् । ततः पश्चान् मुखीं कोटिं कर्णं कोट्यग्रमध्यगम् ॥

dattvārkasaṃjñitaṃ binduṃ tato bāhuṃ svadiṅmukham | tataḥ paścān mukhīṃ koṭiṃ karṇaṃ koṭyagramadhyagam ||

Having set down a point named 'the Sun', ⟨draw⟩ from it the base toward its own direction; then from that ⟨draw⟩ the upright facing west, ⟨and⟩ the hypotenuse running from the centre to the tip of the upright.

कोटिकर्णयुताद् बिन्दोर् बिम्बं तात्कालिकं लिखेत् । कर्णसूत्रेण दिक्सिद्धिं प्रथमं परिकल्पयेत् ॥

koṭikarṇayutād bindor bimbaṃ tātkālikaṃ likhet | karṇasūtreṇa diksiddhiṃ prathamaṃ parikalpayet ||

From the point where the upright and the hypotenuse meet, one should draw the disc ⟨of the Moon⟩ for that moment. By the hypotenuse-line one should first establish the directions.

शुक्लं कर्णेन तद्बिम्बयोगाद् अन्तर्मुखं नयेत् । शुक्लाग्रयाम्योत्तरयोर् मध्ये मत्स्यौ प्रसाधयेत् ॥

śuklaṃ karṇena tadbimbayogād antarmukhaṃ nayet | śuklāgrayāmyottarayor madhye matsyau prasādhayet ||

The illuminated part one should carry inward along the hypotenuse from where it meets that disc. Between the tip of the illuminated part and the south and north ⟨points⟩ one should construct two fish-figures ⟨matsya⟩.

तन्मध्यसूत्रसंयोगाद् बिन्दुत्रिस्पृग् लिखेद् धनुः । प्राग्बिम्बं यादृग् एव स्यात् तादृक् तत्र दिने शशी ॥

tanmadhyasūtrasaṃyogād bindutrispṛg likhed dhanuḥ | prāgbimbaṃ yādṛg eva syāt tādṛk tatra dine śaśī ||

From the meeting of their median lines one should draw an arc touching the three points. Whatever the disc drawn before turns out to be, such is the Moon on that day.

कोट्या दिक् साधनात् तिर्यक्सूत्रान्ते शृङ्गम् उन्नतम् । दर्शयेद् उन्नतां कोटिं कृत्वा चन्द्रस्य साकृतिः ॥

koṭyā dik sādhanāt tiryaksūtrānte śṛṅgam unnatam | darśayed unnatāṃ koṭiṃ kṛtvā candrasya sākṛtiḥ ||

By the upright, through the determination of the directions, the horn at the end of the transverse line is the elevated one. One should exhibit ⟨the figure⟩, having made the upright erect — such is the shape of the Moon.

कृष्णे षड्भयुतं सूर्यं विशोध्येन्दोस् तथासितम् । दद्याद् वामं भुजं तत्र पश्चिमं मण्डलं विधोः ॥

kṛṣṇe ṣaḍbhayutaṃ sūryaṃ viśodhyendos tathāsitam | dadyād vāmaṃ bhujaṃ tatra paścimaṃ maṇḍalaṃ vidhoḥ ||

In the dark ⟨fortnight⟩, having subtracted from the Moon the Sun increased by six signs, ⟨find⟩ in the same way the dark part ⟨asita⟩. There one should lay off the base in the contrary ⟨direction⟩, and the disc of the Moon to the west.

एकायनगतौ स्यातां सूर्यचन्द्रमसौ यदा । तद्युतौ मण्डले क्रान्त्योस् तुल्यत्वे वैधृताभिधः ॥

ekāyanagatau syātāṃ sūryacandramasau yadā | tadyutau maṇḍale krāntyos tulyatve vaidhṛtābhidhaḥ ||

When the Sun and the Moon are found to be moving in one and the same ayana, and their sum amounts to a full circle, ⟨and⟩ their declinations are equal, ⟨that conjunction⟩ bears the name Vaidhṛta.

विपरीतायनगतौ चन्द्रार्कौ क्रान्तिलिप्तिकाः । समास् तदा व्यतीपातो भगणार्धे तयोर् युतौ ॥

viparītāyanagatau candrārkau krāntiliptikāḥ | samās tadā vyatīpāto bhagaṇārdhe tayor yutau ||

When the Moon and the Sun are moving in opposite ayanas and the minutes of their declination are equal, then it is Vyatīpāta, their sum ⟨being⟩ half a revolution.

तुल्यांशुजालसम्पर्कात् तयोस् तु प्रवहाहतः । तद्दृक्क्रोधभवो वह्निर् लोकाभावाय जायते ॥

tulyāṃśujālasamparkāt tayos tu pravahāhataḥ | taddṛkkrodhabhavo vahnir lokābhāvāya jāyate ||

From the contact of their equal nets of rays, smitten by the pravaha ⟨wind⟩, a fire, born of the wrath of their gaze, arises for the annihilation of the worlds.

विनाशयति पातोऽस्मिन् लोकानाम् असकृद् यतः । व्यतीपातः प्रसिद्धोऽयं सञ्ज्ञाभेदेन वैधृतः ॥

vināśayati pāto'smin lokānām asakṛd yataḥ | vyatīpātaḥ prasiddho'yaṃ sañjñābhedena vaidhṛtaḥ ||

Since in this ⟨conjunction⟩ the pāta destroys the worlds again and again, it is well known as Vyatīpāta; by a difference of name, ⟨it is⟩ Vaidhṛta.

स कृष्णो दारुणवपुर् लोहिताक्षो महोदरः । सर्वानिष्टकरो रौद्रो भूयो भूयः प्रजायते ॥

sa kṛṣṇo dāruṇavapur lohitākṣo mahodaraḥ | sarvāniṣṭakaro raudro bhūyo bhūyaḥ prajāyate ||

He is black, of terrible body, red-eyed, huge-bellied; doer of every kind of harm, fierce — he comes to birth again and again.

भास्करेन्द्वोर् भचक्रान्तश् चक्रार्धावधिसंस्थयोः । दृक्तुल्यसाधितांशादियुक्तयोः स्वाव् अपक्रमौ ॥

bhāskarendvor bhacakrāntaś cakrārdhāvadhisaṃsthayoḥ | dṛktulyasādhitāṃśādiyuktayoḥ svāv apakramau ||

Of the Sun and the Moon standing at the end of the zodiacal circle ⟨for Vaidhṛta⟩ or at the limit of half the circle ⟨for Vyatīpāta⟩, and furnished with the degrees and the rest worked out to agree with observation, ⟨find⟩ their respective declinations.

अथौजपदगस्येन्दोः क्रान्तिर् विक्षेपसंस्कृता । यदि स्याद् अधिका भानोः क्रान्तेः पातो गतस् तदा ॥

athaujapadagasyendoḥ krāntir vikṣepasaṃskṛtā | yadi syād adhikā bhānoḥ krānteḥ pāto gatas tadā ||

Now, if the Moon standing in an odd quadrant has its declination, corrected by the latitude, greater than the declination of the Sun, then the pāta is past.

ऊना चेत् स्यात् तदा भावी वामं युग्मपदस्य च । पदान्यत्वं विधोः क्रान्तिर् विक्षेपाच् चेद् विशुध्यति ॥

ūnā cet syāt tadā bhāvī vāmaṃ yugmapadasya ca | padānyatvaṃ vidhoḥ krāntir vikṣepāc ced viśudhyati ||

If it is less, then ⟨the pāta⟩ is to come; and for ⟨the Moon⟩ in an even quadrant, the contrary. The Moon's quadrant is a different one if the declination is cleared away by the latitude.

क्रान्त्योर् ज्ये त्रिज्ययाभ्यस्ते परक्रान्तिज्ययोद्धृते । तच्चापान्तरम् अर्धं वा योज्यं भाविनि शीतगौ ॥

krāntyor jye trijyayābhyaste parakrāntijyayoddhṛte | taccāpāntaram ardhaṃ vā yojyaṃ bhāvini śītagau ||

The Sines of the two declinations, multiplied by the radius and divided by the Sine of the greatest declination — the difference of their arcs, or half of it, is to be added to the Moon when ⟨the pāta⟩ is to come;

शोध्यं चन्द्राद् गते पाते तत्सूर्यगतिताडितम् । चन्द्रभुक्त्या हृतं भानौ लिप्तादि शशिवत् फलम् ॥

śodhyaṃ candrād gate pāte tatsūryagatitāḍitam | candrabhuktyā hṛtaṃ bhānau liptādi śaśivat phalam ||

— and is to be subtracted from the Moon when the pāta is past. That ⟨same difference⟩, multiplied by the Sun's motion and divided by the Moon's daily motion, gives the result in minutes and the rest for the Sun, ⟨to be applied⟩ as with the Moon.

तद्वच्छशाङ्कपातस्य फलं देयं विपर्ययात् । कर्मैतद् असकृत् तावद् यावत् क्रान्ती समे तयोः ॥

tadvacchaśāṅkapātasya phalaṃ deyaṃ viparyayāt | karmaitad asakṛt tāvad yāvat krāntī same tayoḥ ||

In the same way the result for the Moon's node is to be applied, ⟨but⟩ in the reverse manner. This operation ⟨is repeated⟩ over and over, so long as until the declinations of the two are equal.

क्रान्त्योः समत्वे पातोऽथ प्रक्षिप्तांशोनिते विधौ । हीनेऽर्धरात्रिकाद् यातो भावी तात्कालिकेऽधिके ॥

krāntyoḥ samatve pāto'tha prakṣiptāṃśonite vidhau | hīne'rdharātrikād yāto bhāvī tātkālike'dhike ||

When the declinations are equal, then ⟨is⟩ the pāta. Now, the Moon being increased or diminished by the degrees: if it is less than the midnight ⟨Moon⟩, ⟨the pāta⟩ is past; if greater than the ⟨Moon⟩ for the given moment, it is to come.

स्थिरीकृतार्धरात्रेन्द्वोर् द्वयोर् विवरलिप्तिकाः । षष्टिघ्न्यश् चन्द्रभुक्त्याप्ताः पातकालस्य नाडिकाः ॥

sthirīkṛtārdharātrendvor dvayor vivaraliptikāḥ | ṣaṣṭighnyaś candrabhuktyāptāḥ pātakālasya nāḍikāḥ ||

The minutes of the interval between the two — the Moon made fixed ⟨by that correction⟩ and the midnight Moon — multiplied by sixty and divided by the Moon's daily motion, are the nāḍīs of the time of the pāta.

रवीन्दुमानयोगार्धं षष्ट्या सङ्गुण्य भाजयेत् । तयोर् भुक्त्यन्तरेणाप्तं स्थित्यर्धं नाडिकादि तत् ॥

ravīndumānayogārdhaṃ ṣaṣṭyā saṅguṇya bhājayet | tayor bhuktyantareṇāptaṃ sthityardhaṃ nāḍikādi tat ||

Half the sum of the measures ⟨of the discs⟩ of the Sun and the Moon one should multiply by sixty and divide by the difference of their daily motions; what is obtained is the half-duration, in nāḍīs and the rest.

पातकालः स्फुटो मध्यः सोऽपि स्थित्यर्धवर्जितः । तस्य सम्भवकालः स्यात् तत् संयुक्तोऽन्त्यसञ्ज्ञितः ॥

pātakālaḥ sphuṭo madhyaḥ so'pi sthityardhavarjitaḥ | tasya sambhavakālaḥ syāt tat saṃyukto'ntyasañjñitaḥ ||

The true time of the pāta is the middle; that same, lessened by the half-duration, is the time of its coming into being ⟨its beginning⟩; joined with it, it is called the end.

आद्यन्तकालयोर् मध्यः कालो ज्ञेयोऽतिदारुणः । प्रज्वलज् ज्वलनाकारः सर्वकर्मसु गर्हितः ॥

ādyantakālayor madhyaḥ kālo jñeyo'tidāruṇaḥ | prajvalaj jvalanākāraḥ sarvakarmasu garhitaḥ ||

The time midway between the times of beginning and end is to be known as exceedingly terrible, having the form of a blazing fire, condemned in all rites.

एकायनगतं यावद् अर्केन्द्वोर् मण्डलान्तरम् । सम्भवस् तावद् एवास्य सर्वकर्मविनाशकृत् ॥

ekāyanagataṃ yāvad arkendvor maṇḍalāntaram | sambhavas tāvad evāsya sarvakarmavināśakṛt ||

So long as the interval of the discs of the Sun and the Moon lies within one and the same ayana, just so long is the occurrence of this ⟨pāta⟩, which works the destruction of all rites.

स्नानदानजपश्राद्धव्रतहोमादिकर्मभिः । प्राप्यते सुमहच्छ्रेयस् तत्कालज्ञानतस् तथा ॥

snānadānajapaśrāddhavratahomādikarmabhiḥ | prāpyate sumahacchreyas tatkālajñānatas tathā ||

By the acts of bathing, giving, japa, śrāddha, vows, homa and the rest, and likewise from the knowledge of that time, very great blessing is obtained.

रवीन्द्वोस् तुल्यता क्रान्त्योर् विषुवत्सन्निधौ यदा । द्विर् भवेद् धि तदा पातः स्याद् अभावो विपर्ययात् ॥

ravīndvos tulyatā krāntyor viṣuvatsannidhau yadā | dvir bhaved dhi tadā pātaḥ syād abhāvo viparyayāt ||

When the equality of the declinations of the Sun and the Moon occurs in the neighbourhood of the equinox, then indeed the pāta happens twice; in the contrary case there is none at all.

शशाङ्कार्कयुतेर् लिप्ता भभोगेन विभाजिताः । लब्धं सप्तदशान्तोऽन्यो व्यतीपातस् तृतीयकः ॥

śaśāṅkārkayuter liptā bhabhogena vibhājitāḥ | labdhaṃ saptadaśānto'nyo vyatīpātas tṛtīyakaḥ ||

The minutes of the sum of the Moon and the Sun, divided by the extent of an asterism — of the quotient, the end of the seventeenth is another, a third Vyatīpāta.

सार्पेन्द्रपौष्ण्यधिष्ण्यानाम् अन्त्याः पादा भसन्धयः । तदग्रभेष्व् आद्यपादो गण्डान्तं नाम कीर्त्यते ॥

sārpendrapauṣṇyadhiṣṇyānām antyāḥ pādā bhasandhayaḥ | tadagrabheṣv ādyapādo gaṇḍāntaṃ nāma kīrtyate ||

The last quarters of the asterisms of the Serpents ⟨Āśleṣā⟩, of Indra ⟨Jyeṣṭhā⟩ and of Pūṣan ⟨Revatī⟩ are the junctures of the asterisms; and in the asterisms next in front of them, the first quarter — that is proclaimed by the name Gaṇḍānta.

व्यतीपातत्रयं घोरं गण्डान्तत्रितयं तथा । एतद् भसन्धित्रितयं सर्वकर्मसु वर्जयेत् ॥

vyatīpātatrayaṃ ghoraṃ gaṇḍāntatritayaṃ tathā | etad bhasandhitritayaṃ sarvakarmasu varjayet ||

The triad of Vyatīpātas is dreadful, and likewise the triad of Gaṇḍāntas; this triad of asterism-junctures one should shun in all rites.

इत्य् एतत् परमं पुण्यं ज्योतिषां चरितं हितम् । रहस्यं महद् आख्यातं किम् अन्यच्छ्रोतुम् इच्छसि ॥

ity etat paramaṃ puṇyaṃ jyotiṣāṃ caritaṃ hitam | rahasyaṃ mahad ākhyātaṃ kim anyacchrotum icchasi ||

Thus has this been declared — the supremely holy and beneficial course of the heavenly bodies, the great mystery. What else do you wish to hear?

अथार्कांशसमुद्भूतं प्रणिपत्य कृताञ्जलिः । भक्त्या परमयाभ्यर्च्य पप्रच्छेदं मयासुरः ॥

athārkāṃśasamudbhūtaṃ praṇipatya kṛtāñjaliḥ | bhaktyā paramayābhyarcya papracchedaṃ mayāsuraḥ ||

Then, bowing down with joined palms to him who had arisen from a portion of the Sun (arka-aṃśa), and worshipping ⟨him⟩ with the highest devotion, Maya the Asura asked this:

भगवन् किम्प्रमाणा भूः किम् आकारा किम् आश्रया । किंविभागा कथं चात्र सप्तपातालभूमयः ॥

bhagavan kimpramāṇā bhūḥ kim ākārā kim āśrayā | kiṃvibhāgā kathaṃ cātra saptapātālabhūmayaḥ ||

O Lord, of what measure is the earth, of what shape, on what support? What are its divisions, and how do the seven pātāla-earths stand here?

अहोरात्रव्यवस्थां च विदधाति कथं रविः । कथं पर्येति वसुधां भुवनानि विभावयन् ॥

ahorātravyavasthāṃ ca vidadhāti kathaṃ raviḥ | kathaṃ paryeti vasudhāṃ bhuvanāni vibhāvayan ||

And how does the Sun (ravi) establish the ordering of day and night? How does he go around the earth, illuminating the worlds?

देवासुराणाम् अन्योन्यम् अहोरात्रं विपर्ययात् । किमर्थं तत् कथं वा स्याद् भानोर् भगणपूरणात् ॥

devāsurāṇām anyonyam ahorātraṃ viparyayāt | kimarthaṃ tat kathaṃ vā syād bhānor bhagaṇapūraṇāt ||

The day and night of the gods and of the asuras are mutually reversed — for what reason is that, and how does it come about from the Sun's completing his revolution through the circle of asterisms (bhagaṇa)?

पित्र्यं मासेन भवति नाडीषष्ट्या तु मानुषम् । तद् एव किल सर्वत्र न भवेत् केन हेतुना ॥

pitryaṃ māsena bhavati nāḍīṣaṣṭyā tu mānuṣam | tad eva kila sarvatra na bhavet kena hetunā ||

⟨The day and night⟩ of the fathers comes about by a month, but that of men by sixty nāḍīs. That same ⟨measure⟩, surely, does not hold everywhere — from what cause?

दिनाब्दमासहोराणाम् अधिपा न समाः कुतः । कथं पर्येति भगणः सग्रहोऽयं किम् आश्रयः ॥

dinābdamāsahorāṇām adhipā na samāḥ kutaḥ | kathaṃ paryeti bhagaṇaḥ sagraho'yaṃ kim āśrayaḥ ||

Why are the lords of the day, the year, the month and the horā (the hour) not alike ⟨in their order⟩? How does this circle of asterisms with its grahas revolve, and what is its support?

भूमेर् उपर्युपर्यूर्ध्वाः किम् उत्सेधाः किम् अन्तराः । ग्रहर्क्षकक्षाः किंमात्राः स्थिताः केन क्रमेण ताः ॥

bhūmer uparyuparyūrdhvāḥ kim utsedhāḥ kim antarāḥ | graharkṣakakṣāḥ kiṃmātrāḥ sthitāḥ kena krameṇa tāḥ ||

Above the earth, one above another, what are their elevations, what their intervals? Of what measure are the orbits (kakṣā) of the grahas and the asterisms, and in what order do they stand?

ग्रीष्मे तीव्रकरो भानुर् न हेमन्ते तथाविधः । कियती तत्करप्राप्तिर् मानानि कति किं च तैः ॥

grīṣme tīvrakaro bhānur na hemante tathāvidhaḥ | kiyatī tatkaraprāptir mānāni kati kiṃ ca taiḥ ||

In summer the Sun is fierce-rayed; in winter he is not so. How far does the reach of his rays extend? How many are the measures ⟨of time⟩, and what ⟨is accomplished⟩ by them?

एवं मे संशयं छिन्धि भगवन् भूतभावन । अन्यो न त्वाम् ऋते छेत्ता विद्यते सर्वदर्शिवान् ॥

evaṃ me saṃśayaṃ chindhi bhagavan bhūtabhāvana | anyo na tvām ṛte chettā vidyate sarvadarśivān ||

Thus cut away my doubt, O Lord, quickener of beings. There is no other cutter ⟨of it⟩ but you, who see all.

इति भक्त्योदितं श्रुत्वा मयोक्तं वाक्यम् अस्य हि । रहस्यं परम् अध्यायं ततः प्राह पुनः स तम् ॥

iti bhaktyoditaṃ śrutvā mayoktaṃ vākyam asya hi | rahasyaṃ param adhyāyaṃ tataḥ prāha punaḥ sa tam ||

Having heard this speech uttered to him by Maya out of devotion, he then again spoke to him this supremely secret chapter.

शृणुष्वैकमना भूत्वा गुह्यम् अध्यात्म संज्ञितम् । प्रवक्ष्याम्य् अतिभक्तानां नादेयं विद्यते मम ॥

śṛṇuṣvaikamanā bhūtvā guhyam adhyātma saṃjñitam | pravakṣyāmy atibhaktānāṃ nādeyaṃ vidyate mama ||

Listen, becoming single-minded, to the secret named adhyātma. I shall declare it: to those of great devotion nothing of mine is withheld.

वासुदेवः परं ब्रह्म तन्मूर्तिः पुरुषः परः । अव्यक्तो निर्गुणः शान्तः पञ्चविंशात् परोऽव्ययः ॥

vāsudevaḥ paraṃ brahma tanmūrtiḥ puruṣaḥ paraḥ | avyakto nirguṇaḥ śāntaḥ pañcaviṃśāt paro'vyayaḥ ||

Vāsudeva is the supreme brahman; his embodiment is the supreme puruṣa — unmanifest, without guṇas, tranquil, beyond the twenty-fifth, imperishable.

प्रकृत्यन्तर्गतो देवो बहिर् अन्तश् च सर्वगः । सङ्कर्षणोऽपः सृष्ट्वादौ तासु वीर्यम् अवासृजत् ॥

prakṛtyantargato devo bahir antaś ca sarvagaḥ | saṅkarṣaṇo'paḥ sṛṣṭvādau tāsu vīryam avāsṛjat ||

The god who has entered within prakṛti, pervading all without and within — as Saṅkarṣaṇa, having created the waters in the beginning, he cast his seed (vīrya) into them.

तदण्डम् अभवद् धैमं सर्वत्र तमसावृतम् । तत्रानिरुद्धः प्रथमं व्यक्तीभूतः सनातनः ॥

tadaṇḍam abhavad dhaimaṃ sarvatra tamasāvṛtam | tatrāniruddhaḥ prathamaṃ vyaktībhūtaḥ sanātanaḥ ||

That became a golden egg, everywhere enveloped in darkness. Therein Aniruddha, the eternal, first became manifest.

हिरण्यगर्भो भगवान् एष छन्दसि पठ्यते । आदित्यो ह्य् आदिभूतत्वात् प्रसूत्या सूर्य उच्यते ॥

hiraṇyagarbho bhagavān eṣa chandasi paṭhyate | ādityo hy ādibhūtatvāt prasūtyā sūrya ucyate ||

This Lord is recited in the Veda as Hiraṇyagarbha. He is Āditya because he is the first of beings, and from his bringing-forth (prasūti) he is called Sūrya.

परं ज्योतिस् तमः पारे सूर्योऽयं सवितेति च । पर्येति भुवनान्य् एष भावयन् भूतभावनः ॥

paraṃ jyotis tamaḥ pāre sūryo'yaṃ saviteti ca | paryeti bhuvanāny eṣa bhāvayan bhūtabhāvanaḥ ||

The supreme light beyond darkness — this is Sūrya, and Savitṛ too. He, the quickener of beings, goes round the worlds, quickening them.

प्रकाशात्मा तमोहन्ता महान् इत्य् एष विश्रुतः । ऋचोऽस्य मण्डलं सामान्युस्रामूर्तिर् यजूंषि च ॥

prakāśātmā tamohantā mahān ity eṣa viśrutaḥ | ṛco'sya maṇḍalaṃ sāmānyusrāmūrtir yajūṃṣi ca ||

Whose very self is light, slayer of darkness, he is renowned as 'the Great'. The Ṛc verses are his disk, the Sāmans his rays, and the Yajus his body.

त्रयीमयोऽयं भगवान् कालात्मा कालकृद् विभुः । सर्वात्मा सर्वगः सूक्ष्मः सर्वम् अस्मिन् प्रतिष्ठितम् ॥

trayīmayo'yaṃ bhagavān kālātmā kālakṛd vibhuḥ | sarvātmā sarvagaḥ sūkṣmaḥ sarvam asmin pratiṣṭhitam ||

This Lord is made of the triple Veda, whose self is Time, the maker of Time, all-pervading; the self of all, going everywhere, subtle. All is established in him.

रथे विश्वमये चक्रं कृत्वा संवत्सरात्मकम् । छन्दांस्य् अश्वाः सप्त युक्ताः पर्यटत्य् एष सर्वदा ॥

rathe viśvamaye cakraṃ kṛtvā saṃvatsarātmakam | chandāṃsy aśvāḥ sapta yuktāḥ paryaṭaty eṣa sarvadā ||

Having made upon a chariot consisting of the universe a wheel whose essence is the year, with the metres as his seven yoked horses, he travels round for ever.

त्रिपादम् अमृतं गुह्यं पादोऽयं प्रकटोऽभवत् । सोऽहङ्कारं जगत्सृष्ट्यै ब्रह्माणम् असृजत् प्रभुः ॥

tripādam amṛtaṃ guhyaṃ pādo'yaṃ prakaṭo'bhavat | so'haṅkāraṃ jagatsṛṣṭyai brahmāṇam asṛjat prabhuḥ ||

Three quarters of him are the hidden immortal; this one quarter became manifest. That Lord, for the creation of the world, brought forth Brahmā, who bears the form of ahaṅkāra.

तस्मै वेदान् वरान् दत्त्वा सर्वलोकपितामहम् । प्रतिष्ठाप्याण्डमध्येऽथ स्वयं पर्येति भावयन् ॥

tasmai vedān varān dattvā sarvalokapitāmaham | pratiṣṭhāpyāṇḍamadhye'tha svayaṃ paryeti bhāvayan ||

Having given him the Vedas as boons, and having established him, the grandfather of all worlds, in the middle of the egg, he himself then goes round, quickening ⟨all⟩.

अथ सृष्ट्यां मनश् चक्रे ब्रह्माहङ्कारमूर्तिभृत् । मनसश् चन्द्रमा जज्ञे सूर्योऽक्ष्णोस् तेजसां निधिः ॥

atha sṛṣṭyāṃ manaś cakre brahmāhaṅkāramūrtibhṛt | manasaś candramā jajñe sūryo'kṣṇos tejasāṃ nidhiḥ ||

Then Brahmā, bearing the form of ahaṅkāra, set his mind upon creation. From his mind the Moon was born; from his eyes the Sun, the treasury of light.

मनसः खं ततो वायुर् अग्निर् आपो धरा क्रमात् । गुणैकवृद्ध्या पञ्चैव महाभूतानि जज्ञिरे ॥

manasaḥ khaṃ tato vāyur agnir āpo dharā kramāt | guṇaikavṛddhyā pañcaiva mahābhūtāni jajñire ||

From mind ⟨came⟩ ether, then wind, fire, water, earth in order. By the increase of one quality ⟨at each step⟩, the five great elements were born.

अग्नीषोमौ भानुचन्द्रौ ततस् त्व् अङ्गारकादयः । तेजोभूखाम्बुवातेभ्यः क्रमशः पञ्च जज्ञिरे ॥

agnīṣomau bhānucandrau tatas tv aṅgārakādayaḥ | tejobhūkhāmbuvātebhyaḥ kramaśaḥ pañca jajñire ||

Fire and Soma are the Sun and Moon; then Aṅgāraka (Mars) and the rest — five were born in order from fire, earth, ether, water and wind.

पुनर् द्वादशधात्मानं व्यभजद् राशिसञ्ज्ञकम् । नक्षत्ररूपिणं भूयः सप्तविंशात्मकं वशी ॥

punar dvādaśadhātmānaṃ vyabhajad rāśisañjñakam | nakṣatrarūpiṇaṃ bhūyaḥ saptaviṃśātmakaṃ vaśī ||

Again the Master divided himself twelvefold, called the rāśis; and further into the form of the nakṣatras, consisting of twenty-seven.

ततश् चराचरं विश्वं निर्ममे देवपूर्वकम् । ऊर्ध्वमध्याधरेभ्योऽथ स्रोतोभ्यः प्रकृतीः सृजन् ॥

tataś carācaraṃ viśvaṃ nirmame devapūrvakam | ūrdhvamadhyādharebhyo'tha srotobhyaḥ prakṛtīḥ sṛjan ||

Then he fashioned the universe, moving and unmoving, beginning with the gods, creating the natural kinds (prakṛti) from the upward, middle and downward streams.

गुणकर्मविभागेन सृष्ट्वा प्राग्वद् अनुक्रमात् । विभागं कल्पयामास यथास्वं वेददर्शनात् ॥

guṇakarmavibhāgena sṛṣṭvā prāgvad anukramāt | vibhāgaṃ kalpayāmāsa yathāsvaṃ vedadarśanāt ||

Having created ⟨them⟩ by the distinction of guṇa and karma, in due sequence as before, he arranged their division, each according to its own, out of the vision of the Veda —

ग्रहनक्षत्रताराणां भूमेर् विश्वस्य वा विभुः । देवासुरमनुष्याणां सिद्धानां च यथाक्रमम् ॥

grahanakṣatratārāṇāṃ bhūmer viśvasya vā vibhuḥ | devāsuramanuṣyāṇāṃ siddhānāṃ ca yathākramam ||

— of the grahas, the nakṣatras and the stars, of the earth, indeed of the universe, of gods, asuras, men and siddhas, each in its order, ⟨he⟩ the all-pervading.

ब्रह्माण्डम् एतत् सुषिरं तत्रेदं भूर्भुवादिकम् । कटाहद्वितयस्येव सम्पुटं गोलकाकृति ॥

brahmāṇḍam etat suṣiraṃ tatredaṃ bhūrbhuvādikam | kaṭāhadvitayasyeva sampuṭaṃ golakākṛti ||

This egg of Brahmā is hollow; within it is this ⟨world⟩ beginning with bhūḥ and bhuvaḥ — like the closed hollow of a pair of pans, globular in shape.

ब्रह्माण्डमध्ये परिधिर् व्योमकक्षाभिधीयते । तन्मध्ये भ्रमणं भानाम् अधोऽधः क्रमशस् तथा ॥

brahmāṇḍamadhye paridhir vyomakakṣābhidhīyate | tanmadhye bhramaṇaṃ bhānām adho'dhaḥ kramaśas tathā ||

In the middle of the egg of Brahmā, the circumference is called the orbit of the sky (vyoma-kakṣā). Within it is the revolution of the luminaries, lower and lower in succession.

मन्दामरेज्यभूपुत्रसूर्यशुक्रेन्दुजेन्दवः । परिभ्रमन्त्य् अधोऽधःस्थाः सिद्धविद्याधरा घनाः ॥

mandāmarejyabhūputrasūryaśukrendujendavaḥ | paribhramanty adho'dhaḥsthāḥ siddhavidyādharā ghanāḥ ||

Manda ⟨Saturn⟩, Amarejya ⟨Jupiter⟩, Bhūputra ⟨Mars⟩, the Sun, Śukra ⟨Venus⟩, Induja ⟨Mercury⟩ and Indu ⟨the Moon⟩ — these revolve, each set lower than the one before; ⟨and below them⟩ the siddhas, the vidyādharas, and the clouds.

मध्ये समन्ताद् अण्डस्य भूगोलो व्योम्नि तिष्ठति । बिभ्राणः परमां शक्तिं ब्रह्मणो धारणात्मिकाम् ॥

madhye samantād aṇḍasya bhūgolo vyomni tiṣṭhati | bibhrāṇaḥ paramāṃ śaktiṃ brahmaṇo dhāraṇātmikām ||

In the middle of the egg ⟨of Brahmā⟩, ⟨enclosed⟩ on all sides, the globe of the earth stands in space, bearing the supreme power of Brahmā, whose very nature is to hold ⟨all things in place⟩.

तदन्तरपुटाः सप्त नागासुरसमाश्रयाः । दिव्यौषधिरसोपेता रम्याः पातालभूमयः ॥

tadantarapuṭāḥ sapta nāgāsurasamāśrayāḥ | divyauṣadhirasopetā ramyāḥ pātālabhūmayaḥ ||

Within it are seven shells, refuges of nāgas and asuras, supplied with the saps of divine herbs, delightful — the nether lands (pātāla).

अनेकरत्ननिचयो जाम्बूनदमयो गिरिः । भूगोलमध्यगो मेरुर् उभयत्र विनिर्गतः ॥

anekaratnanicayo jāmbūnadamayo giriḥ | bhūgolamadhyago merur ubhayatra vinirgataḥ ||

A mass of many jewels, made of jāmbūnada gold, is the mountain Meru, which stands at the centre of the earth-globe and protrudes at both ends ⟨north and south⟩.

उपरिष्टात् स्थितास् तस्य सेन्द्रा देवा महर्षयः । अधस्ताद् असुरास् तद्वद् द्विषन्तोऽन्योन्यम् आश्रिताः ॥

upariṣṭāt sthitās tasya sendrā devā maharṣayaḥ | adhastād asurās tadvad dviṣanto'nyonyam āśritāḥ ||

Above it are stationed the gods together with Indra, and the great ṛṣis; below, in like manner, the asuras — hating one another, ⟨each⟩ established ⟨at his own end⟩.

ततः समन्तात् परिधिः क्रमेणायं महार्णवः । मेखलेव स्थितो धात्र्या देवासुरविभागकृत् ॥

tataḥ samantāt paridhiḥ krameṇāyaṃ mahārṇavaḥ | mekhaleva sthito dhātryā devāsuravibhāgakṛt ||

Then all around, in due order, is this encircling belt, the great ocean, standing like a girdle of the earth, and making the division between gods and asuras.

समन्तान् मेरुमध्यात् तु तुल्यभागेषु तोयधेः । द्वीपेषु दिक्षु पूर्वादिनगर्यो देवनिर्मिताः ॥

samantān merumadhyāt tu tulyabhāgeṣu toyadheḥ | dvīpeṣu dikṣu pūrvādinagaryo devanirmitāḥ ||

All around, at equal divisions from the middle of Meru, upon the ocean, on the dvīpas, in the directions beginning with the east, are cities built by the gods.

भूवृत्तपादे पूर्वस्यां यमकोटीति विश्रुता । भद्राश्ववर्षे नगरी स्वर्णप्राकारतोरणा ॥

bhūvṛttapāde pūrvasyāṃ yamakoṭīti viśrutā | bhadrāśvavarṣe nagarī svarṇaprākāratoraṇā ||

At a quarter of the earth's circumference to the east, in the Bhadrāśva varṣa, is the city renowned as Yamakoṭi, with rampart and gateway of gold.

याम्यायां भारते वर्षे लङ्का तद्वन् महापुरी । पश्चिमे केतुमालाख्ये रोमकाख्या प्रकीर्तिता ॥

yāmyāyāṃ bhārate varṣe laṅkā tadvan mahāpurī | paścime ketumālākhye romakākhyā prakīrtitā ||

To the south, in the Bhārata varṣa, is likewise the great city Laṅkā; to the west, in ⟨the varṣa⟩ named Ketumāla, ⟨the city⟩ called Romaka is famed.

उदक् सिद्धपुरी नाम कुरुवर्षे प्रकीर्तिता । तस्यां सिद्धा महात्मानो निवसन्ति गतव्यथाः ॥

udak siddhapurī nāma kuruvarṣe prakīrtitā | tasyāṃ siddhā mahātmāno nivasanti gatavyathāḥ ||

To the north, in the Kuru varṣa, is famed ⟨the city⟩ named Siddhapurī; in it dwell the siddhas, great souls, freed from affliction.

भूवृत्तपादविवरास् ताश् चान्योन्यं प्रतिष्ठिताः । ताभ्यश् चोत्तरगो मेरुस् तावान् एव सुराश्रयः ॥

bhūvṛttapādavivarās tāś cānyonyaṃ pratiṣṭhitāḥ | tābhyaś cottarago merus tāvān eva surāśrayaḥ ||

These ⟨four cities⟩ stand a quarter of the earth's circumference apart from one another; and north of them, at just that same distance, is Meru, the abode of the gods.

तासाम् उपरिगो याति विषुवस्थो दिवाकरः । न तासु विषुवच्छाया नाक्षस्योन्नतिर् इष्यते ॥

tāsām uparigo yāti viṣuvastho divākaraḥ | na tāsu viṣuvacchāyā nākṣasyonnatir iṣyate ||

The Sun, when standing at the equinox, passes directly overhead of them. In them neither an equinoctial shadow nor any elevation of the pole (akṣa) is admitted.

मेरोर् उभयतो मध्ये ध्रुवतारे नभः स्थिते । निरक्षदेशसंस्थानाम् उभये क्षितिजाश्रये ॥

meror ubhayato madhye dhruvatāre nabhaḥ sthite | nirakṣadeśasaṃsthānām ubhaye kṣitijāśraye ||

On both sides of Meru, at the middle ⟨of the heavens⟩, the two pole-stars are set in the sky; for those who live in the region without latitude, the two rest upon the horizon.

अतो नाक्षोच्छ्रयस् तासु ध्रुवयोः क्षितिजस्थयोः । नवतिर् लम्बकांशास् तु मेरावक्षांशकास् तथा ।

ato nākṣocchrayas tāsu dhruvayoḥ kṣitijasthayoḥ | navatir lambakāṃśās tu merāvakṣāṃśakās tathā |

Hence in them there is no elevation of the ⟨celestial⟩ pole, the two pole-stars standing on the horizon; ⟨there⟩ the degrees of the co-latitude (lambaka) are ninety, and at Meru the degrees of latitude (akṣa) are likewise ⟨ninety⟩.

मेषादौ देवभागस्थे देवानां याति दर्शनम् । असुराणां तुलादौ तु सूर्यस् तद्भागसञ्चरः ॥

meṣādau devabhāgasthe devānāṃ yāti darśanam | asurāṇāṃ tulādau tu sūryas tadbhāgasañcaraḥ ||

At the beginning of Meṣa, standing in the gods' half, ⟨the Sun⟩ comes into the sight of the gods; but at the beginning of Tulā the Sun, travelling in their half, ⟨comes into the sight⟩ of the asuras.

अत्यासन्नतया तेन ग्रीष्मे तीव्रकरा रवेः । देवभागे सुराणां तु हेमन्ते मन्दतान्यथा ॥

atyāsannatayā tena grīṣme tīvrakarā raveḥ | devabhāge surāṇāṃ tu hemante mandatānyathā ||

Because of ⟨the Sun's⟩ extreme nearness, its rays are fierce in summer for the gods in the gods' region; but in winter, contrariwise, ⟨they are⟩ feeble.

देवासुरा विषुवति क्षितिजस्थं दिवाकरम् । पश्यन्त्य् अन्योन्यम् एतेषां वामसव्ये दिनक्षपे ॥

devāsurā viṣuvati kṣitijasthaṃ divākaram | paśyanty anyonyam eteṣāṃ vāmasavye dinakṣape ||

At the equinox gods and asuras see the Sun standing upon the horizon, and see one another; for these two, day and night are as left and right ⟨— each the reverse of the other's⟩.

मेषादाव् उदितः सूर्यस् त्रीन् राशीन् उदगुत्तरम् । सञ्चरन् प्रागहर्मध्यं पूरयेन् मेरुवासिनाम् ॥

meṣādāv uditaḥ sūryas trīn rāśīn udaguttaram | sañcaran prāgaharmadhyaṃ pūrayen meruvāsinām ||

The Sun, risen at the beginning of Meṣa, travelling three rāśis northward, fills out the first half of the day for the dwellers on Meru.

कर्क्यादीन् सञ्चरंस् तद्वद् अह्नः पश्चार्धम् एव सः । तुलादींस् त्रीन् मृगादींश् च तद्वद् एव सुरद्विषाम् ॥

karkyādīn sañcaraṃs tadvad ahnaḥ paścārdham eva saḥ | tulādīṃs trīn mṛgādīṃś ca tadvad eva suradviṣām ||

Travelling ⟨the three rāśis⟩ beginning with Karka, he in like manner ⟨fills out⟩ the latter half of the day. And ⟨travelling⟩ the three beginning with Tulā and ⟨the three⟩ beginning with Mṛga, just so for the enemies of the gods.

अतो दिनक्षपे तेषाम् अन्योन्यं हि विपर्ययात् । अहोरात्रप्रमाणं च भानोर् भगणपूरणात् ॥

ato dinakṣape teṣām anyonyaṃ hi viparyayāt | ahorātrapramāṇaṃ ca bhānor bhagaṇapūraṇāt ||

Hence the day and night of those two are mutually reversed; and the measure of a day-and-night comes from the Sun's completing a revolution of the zodiac (bhagaṇa).

दिनक्षपार्धम् एतेषाम् अयनान्ते विपर्ययात् । उपर्यात्मानम् अन्योन्यं कल्पयन्ति सुरासुराः ॥

dinakṣapārdham eteṣām ayanānte viparyayāt | uparyātmānam anyonyaṃ kalpayanti surāsurāḥ ||

For these, half of the day and of the night ⟨falls⟩ at the end of an ayana, by reason of the reversal; and gods and asuras each reckon themselves to be above the other.

अन्येऽपि समसूत्रस्था मन्यन्तेऽधः परस्परम् । भद्राश्वकेतुमालस्था लङ्कासिद्धपुराश्रिताः ॥

anye'pi samasūtrasthā manyante'dhaḥ parasparam | bhadrāśvaketumālasthā laṅkāsiddhapurāśritāḥ ||

Others too, standing on the same diameter, think each other to be below — those in Bhadrāśva and Ketumāla, those who dwell in Laṅkā and Siddhapura.

सर्वत्रैव महीगोले स्वस्थानम् उपरि स्थितम् । मन्यन्ते खे यतो गोलस् तस्य क्वोर्ध्वं क्व वाप्य् अधः ॥

sarvatraiva mahīgole svasthānam upari sthitam | manyante khe yato golas tasya kvordhvaṃ kva vāpy adhaḥ ||

Everywhere on the earth-globe men reckon their own place to be uppermost. But since the globe ⟨stands⟩ in space, where is its up and where its down?

अल्पकायतया लोकाः स्वस्थानात् सर्वतो मुखम् । पश्यन्ति वृत्ताम् अप्य् एतां चक्राकारां वसुन्धराम् ॥

alpakāyatayā lokāḥ svasthānāt sarvato mukham | paśyanti vṛttām apy etāṃ cakrākārāṃ vasundharām ||

Because their own bodies are small, men, looking out on every side from where they stand, see this earth — round though it is — as having the shape of a disc.

सव्यं भ्रमति देवानाम् अपसव्यं सुरद्विषाम् । उपरिष्टाद् भगोलोऽयं व्यक्षे पश्चान् मुखः सदा ॥

savyaṃ bhramati devānām apasavyaṃ suradviṣām | upariṣṭād bhagolo'yaṃ vyakṣe paścān mukhaḥ sadā ||

This sphere of the asterisms (bhagola) revolves above ⟨them⟩ leftward (savya) for the gods and rightward (apasavya) for the enemies of the gods; in the region without latitude it always faces west.

अतस् तत्र दिनं त्रिंशन्नाडिकं शर्वरी तथा । हानिवृद्धी सदा वामं सुरासुरविभागयोः ॥

atas tatra dinaṃ triṃśannāḍikaṃ śarvarī tathā | hānivṛddhī sadā vāmaṃ surāsuravibhāgayoḥ ||

Hence there the day is thirty nāḍikās and the night likewise. Decrease and increase are always contrary in the two divisions, of gods and of asuras.

मेषादौ तु सदा वृद्धिर् उदगुत्तरतोऽधिका । देवांशे च क्षपाहानिर् विपरीतं तथासुरे ॥

meṣādau tu sadā vṛddhir udaguttarato'dhikā | devāṃśe ca kṣapāhānir viparītaṃ tathāsure ||

From the beginning of Meṣa there is always increase ⟨of the day⟩, greater the further north; and in the gods' portion a decrease of the night — contrariwise in the asuras'.

तुलादौ द्युनिशोर् वामं क्षयवृद्धी तयोर् उभे । देशक्रान्तिवशान् नित्यं तद्विज्ञानं पुरोदितम् ॥

tulādau dyuniśor vāmaṃ kṣayavṛddhī tayor ubhe | deśakrāntivaśān nityaṃ tadvijñānaṃ puroditam ||

From the beginning of Tulā it is contrary for day and night: for those two, both the waning and the waxing ⟨are reversed⟩. This ⟨holds⟩ always according to the latitude of the place and the declination; the knowledge of it has been stated before.

भूवृत्तं क्रान्तिभागघ्नं भगणांशविभाजितम् । अवाप्तयोजनैर् अर्को व्यक्षाद् यात्य् उपरिस्थितः ॥

bhūvṛttaṃ krāntibhāgaghnaṃ bhagaṇāṃśavibhājitam | avāptayojanair arko vyakṣād yāty uparisthitaḥ ||

The earth's circumference, multiplied by the degrees of declination and divided by the degrees of a revolution ⟨of the zodiac⟩ — by the yojanas thus obtained ⟨is measured the distance⟩ from the region without latitude at which the Sun passes overhead.

परमापक्रमाद् एवं योजनानि विशोधयेत् । भूवृत्तपादाच् छेषाणि यानि स्युर् योजनानि तैः ॥

paramāpakramād evaṃ yojanāni viśodhayet | bhūvṛttapādāc cheṣāṇi yāni syur yojanāni taiḥ ||

In this same way, from the greatest declination one should subtract the yojanas ⟨so found⟩ from a quarter of the earth's circumference; whatever yojanas then remain, by those ⟨the next step is made⟩.

अयनान्ते विलोमेन देवासुरविभागयोः । नाडीषष्ट्या सकृद् अहर्निशाप्य् अस्मिन् सकृत् तथा ॥

ayanānte vilomena devāsuravibhāgayoḥ | nāḍīṣaṣṭyā sakṛd aharniśāpy asmin sakṛt tathā ||

At the end of the ayana ⟨the solstice⟩, in reverse order in the two divisions of the gods and of the asuras, ⟨there occurs⟩ but once a day of sixty nāḍīs; and in this ⟨same place⟩, likewise, but once a ⟨such⟩ night.

तदन्तरेऽपि षष्ट्यन्ते क्षयवृद्धी अहर्निशोः । परतो विपरीतोऽयं भगोलः परिवर्तते ॥

tadantare'pi ṣaṣṭyante kṣayavṛddhī aharniśoḥ | parato viparīto'yaṃ bhagolaḥ parivartate ||

In the interval between those ⟨two⟩ as well, at the end of sixty ⟨nāḍīs⟩ ⟨come⟩ the decrease and the increase of day and night; beyond ⟨that point⟩ this sphere of the asterisms (bhagola) revolves inverted.

ऊने भूवृत्तपादे तु द्विज्यापक्रमयोजनैः । धनुर् मृगस्थः सविता देवभागे न दृश्यते ॥

ūne bhūvṛttapāde tu dvijyāpakramayojanaiḥ | dhanur mṛgasthaḥ savitā devabhāge na dṛśyate ||

But at ⟨the distance of⟩ a quarter of the earth's circumference diminished by the yojanas ⟨answering to⟩ the declination of the Sine of two ⟨signs⟩, the Sun standing in Dhanus or Mṛga ⟨Makara⟩ is not seen in the division of the gods.

तथा चासुरभागे तु मिथुने कर्कटे स्थितः । नष्टच्छाया महीवृत्तपादे दर्शनम् आदिशेत् ॥

tathā cāsurabhāge tu mithune karkaṭe sthitaḥ | naṣṭacchāyā mahīvṛttapāde darśanam ādiśet ||

And so too in the division of the asuras, ⟨the Sun⟩ standing in Mithuna or Karkaṭa ⟨is not seen⟩. At ⟨such⟩ a quarter of the earth's circle ⟨reckoned⟩ from the shadowless ⟨equator⟩ one should declare ⟨his⟩ visibility.

एकज्यापक्रमानीतैर् योजनैः परिवर्जिते । भूमिकक्षाचतुर्थांशे व्यक्षाच् छेषैस् तु योजनैः ॥

ekajyāpakramānītair yojanaiḥ parivarjite | bhūmikakṣācaturthāṃśe vyakṣāc cheṣais tu yojanaiḥ ||

In the fourth part of the earth's orbit ⟨circumference⟩ when it has been diminished by the yojanas brought out from the declination of the Sine of one ⟨sign⟩ — that is, by the yojanas remaining, ⟨reckoned⟩ from the equator (vyakṣa) —

धनुर् मृगालिकुम्भेषु संस्थितोऽर्को न दृश्यते । देवभागेऽसुराणां तु वृषाद्ये भचतुष्टये ॥

dhanur mṛgālikumbheṣu saṃsthito'rko na dṛśyate | devabhāge'surāṇāṃ tu vṛṣādye bhacatuṣṭaye ||

the Sun stationed in Dhanus, Mṛga ⟨Makara⟩, Ali ⟨Vṛścika⟩ and Kumbha is not seen in the division of the gods; but for the asuras ⟨he is not seen⟩ in the tetrad of signs beginning with Vṛṣa.

मेरौ मेषादिचक्रार्धे देवाः पश्यन्ति भास्करम् । सकृद् एवोदितं तद्वद् असुराश् च तुलादिगम् ॥

merau meṣādicakrārdhe devāḥ paśyanti bhāskaram | sakṛd evoditaṃ tadvad asurāś ca tulādigam ||

At Meru the gods see the Sun, risen but once, throughout the half of the circle beginning with Meṣa; and in the same way the asuras ⟨see him⟩ when he is in ⟨the half⟩ beginning with Tulā.

भूमण्डलात् पञ्चदशे भागे देवेऽथ वासुरे । उपरिष्टाद् व्रजत्य् अर्कः सौम्ययाम्यायनान्तगः ॥

bhūmaṇḍalāt pañcadaśe bhāge deve'tha vāsure | upariṣṭād vrajaty arkaḥ saumyayāmyāyanāntagaḥ ||

At the fifteenth part ⟨of the circle, measured⟩ from the earth's ⟨equatorial⟩ circle, whether in the gods' ⟨division⟩ or in the asuras', the Sun passes overhead when he has reached the end of his northern or of his southern ayana.

तदन्तरालयोश् च्छाया याम्योदक् सम्भवत्य् अपि । मेरोर् अभिमुखं याति परतः स्वविभागयोः ॥

tadantarālayoś cchāyā yāmyodak sambhavaty api | meror abhimukhaṃ yāti parataḥ svavibhāgayoḥ ||

In the two intervals between those, the shadow arises both southward and northward; beyond ⟨them⟩, in each of its own two divisions, it goes facing Meru.

भद्राश्वोपरिगः कुर्याद् भारते तूदयं रविः । रात्र्यर्धं केतुमाले तु कुराव् अस्तमयं तदा ॥

bhadrāśvoparigaḥ kuryād bhārate tūdayaṃ raviḥ | rātryardhaṃ ketumāle tu kurāv astamayaṃ tadā ||

The Sun, passing above Bhadrāśva, makes sunrise in Bhārata, midnight in Ketumāla, and at that time setting in Kuru.

भारतादिषु वर्षेषु तद्वद् एव परिभ्रमन् । मध्योदयार्धरात्र्यस्तकालान् कुर्यात् प्रदक्षिणम् ॥

bhāratādiṣu varṣeṣu tadvad eva paribhraman | madhyodayārdharātryastakālān kuryāt pradakṣiṇam ||

Revolving in just that manner over the varṣas beginning with Bhārata, he makes, in clockwise course (pradakṣiṇam), the times of midday, of sunrise, of midnight and of setting.

ध्रुवोन्नतिर् भचक्रस्य नतिर् मेरुं प्रयास्यतः । निरक्षाभिमुखं यातुर् विपरीते नतोन्नते ॥

dhruvonnatir bhacakrasya natir meruṃ prayāsyataḥ | nirakṣābhimukhaṃ yātur viparīte natonnate ||

For one who is going to Meru ⟨there is⟩ elevation of the pole star and depression of the circle of asterisms; for one going toward the equator (nirakṣa), the depression and the elevation are reversed.

भचक्रं ध्रुवयोर् बद्धम् आक्षिप्तं प्रवहानिलैः । पर्येत्य् अजस्रं तन्नद्धा ग्रहकक्षा यथाक्रमम् ॥

bhacakraṃ dhruvayor baddham ākṣiptaṃ pravahānilaiḥ | paryety ajasraṃ tannaddhā grahakakṣā yathākramam ||

The circle of asterisms, bound at the two poles and driven on by the pravaha winds, revolves unceasingly; and the orbits of the grahas, fastened to it, ⟨revolve⟩ in their due order.

सकृद् उद्गतम् अब्दार्धं पश्यन्त्य् अर्कं सुरासुराः । पितरः शशिगाः पक्षं स्वदिनं च नरा भुवि ॥

sakṛd udgatam abdārdhaṃ paśyanty arkaṃ surāsurāḥ | pitaraḥ śaśigāḥ pakṣaṃ svadinaṃ ca narā bhuvi ||

The gods and the asuras see the Sun, risen but once, for half a year; the pitṛs, who are on the Moon, for a fortnight (pakṣa); and men on the earth ⟨see him⟩ for their own day.

उपरिष्ठस्य महती कक्षाल्पाधःस्थितस्य च । महत्या कक्षया भागा महान्तोऽल्पास् तथाल्पया ॥

upariṣṭhasya mahatī kakṣālpādhaḥsthitasya ca | mahatyā kakṣayā bhāgā mahānto'lpās tathālpayā ||

Of ⟨a body⟩ placed above, the orbit is great; and of one placed below, small. With a great orbit the degrees are large, and so with a small ⟨orbit⟩ they are small.

कालेनाल्पेन भगणं भुङ्क्तेऽल्पभ्रमणाश्रितः । ग्रहः कालेन महता मण्डले महति भ्रमन् ॥

kālenālpena bhagaṇaṃ bhuṅkte'lpabhramaṇāśritaḥ | grahaḥ kālena mahatā maṇḍale mahati bhraman ||

A graha that keeps to a small revolution-⟨path⟩ traverses a revolution ⟨of the asterisms⟩ in a small time; ⟨and⟩ in a great time when it moves in a great circle.

स्वल्पयातो बहून् भुङ्क्ते भगणान् शीतदीधितिः । महत्या कक्षया गच्छन् ततः स्वल्पं शनैश्चरः ॥

svalpayāto bahūn bhuṅkte bhagaṇān śītadīdhitiḥ | mahatyā kakṣayā gacchan tataḥ svalpaṃ śanaiścaraḥ ||

The cold-rayed ⟨Moon⟩, moving in a very small ⟨orbit⟩, traverses many revolutions; Saturn (śanaiścara), going with a great orbit, ⟨traverses⟩ therefore very few.

मन्दाद् अधः क्रमेण स्युश् चतुर्था दिवसाधिपाः । वर्षाधिपतयस् तद्वत् तृतीयाश् च प्रकीर्तिताः ॥

mandād adhaḥ krameṇa syuś caturthā divasādhipāḥ | varṣādhipatayas tadvat tṛtīyāś ca prakīrtitāḥ ||

Downward from Saturn (manda), in order, every fourth ⟨graha⟩ is lord of the days; and in like manner every third is declared lord of the years.

ऊर्ध्वक्रमेण शशिनो मासानाम् अधिपाः स्मृताः । होरेशाः सूर्यतनयाद् अधोऽधः क्रमशस् तथा ॥

ūrdhvakrameṇa śaśino māsānām adhipāḥ smṛtāḥ | horeśāḥ sūryatanayād adho'dhaḥ kramaśas tathā ||

In the upward order from the Moon are held to be the lords of the months; and the lords of the horās ⟨hours⟩ ⟨are reckoned⟩ successively downward from the son of the Sun ⟨Saturn⟩.

भवेद् भकक्षा तीक्ष्णांशोर् भ्रमणं षष्टिताडितम् । सर्वोपरिष्टाद् भ्रमति योजनैस् तैर् भमण्डलम् ॥

bhaved bhakakṣā tīkṣṇāṃśor bhramaṇaṃ ṣaṣṭitāḍitam | sarvopariṣṭād bhramati yojanais tair bhamaṇḍalam ||

The orbit of the asterisms (bhakakṣā) would be the revolution-⟨circuit⟩ of the sharp-rayed ⟨Sun⟩ multiplied by sixty; above all ⟨the rest⟩ the sphere of the asterisms revolves through those yojanas.

कल्पोक्तचन्द्रभगणा गुणिताः शशिकक्षया । आकाशकक्षा सा ज्ञेया करव्याप्तिस् तथा रवेः ॥

kalpoktacandrabhagaṇā guṇitāḥ śaśikakṣayā | ākāśakakṣā sā jñeyā karavyāptis tathā raveḥ ||

The Moon's revolutions declared for a kalpa, multiplied by the Moon's orbit — that is to be known as the orbit of the sky (ākāśakakṣā), and likewise as the reach of the Sun's rays.

सैव यत्कल्पभगणैर् भक्ता तद्भ्रमणं भवेत् । कुवासरैर् विभज्याह्नः सर्वेषां प्राग्गतिः स्मृता ॥

saiva yatkalpabhagaṇair bhaktā tadbhramaṇaṃ bhavet | kuvāsarair vibhajyāhnaḥ sarveṣāṃ prāggatiḥ smṛtā ||

That same ⟨sky-orbit⟩, divided by the kalpa-revolutions of whatever ⟨body⟩, becomes that body's revolution-⟨orbit⟩; and divided by the terrestrial days, it is declared to be the eastward motion of them all for a day.

भुक्तियोजनजा सङ्ख्या सेन्दोर् भ्रमणसङ्गुणा । स्वकक्षाप्ता तु सा तस्य तिथ्याप्ता गतिलिप्तिका ॥

bhuktiyojanajā saṅkhyā sendor bhramaṇasaṅguṇā | svakakṣāptā tu sā tasya tithyāptā gatiliptikā ||

The number produced from the yojanas of ⟨daily⟩ travel, multiplied by the Moon's orbit and divided by ⟨the body's⟩ own orbit — that belongs to that body; divided by the tithis ⟨fifteen⟩, it is the minutes of its motion.

कक्षा भूकर्णगुणिता महीमण्डलभाजिता । तत्कर्णा भूमिकर्णोना ग्रहौच्च्यं स्वं दलीकृताः ॥

kakṣā bhūkarṇaguṇitā mahīmaṇḍalabhājitā | tatkarṇā bhūmikarṇonā grahauccyaṃ svaṃ dalīkṛtāḥ ||

The orbit multiplied by the earth's diameter and divided by the earth's circumference ⟨gives⟩ the diameter of that ⟨orbit⟩; ⟨those diameters,⟩ diminished by the earth's diameter and halved, ⟨give⟩ the graha's own elevation.

खत्रयाब्धिद्विदहनाः कक्षा तु हिमदीधितेः । ज्ञशीघ्रस्याङ्कखद्वित्रिकृतशून्येन्दवस् तथा ॥

khatrayābdhidvidahanāḥ kakṣā tu himadīdhiteḥ | jñaśīghrasyāṅkakhadvitrikṛtaśūnyendavas tathā ||

The orbit of the frost-rayed ⟨Moon⟩ is 324,000 ⟨yojanas⟩; and that of Mercury's śīghra is 1,043,209.

शुक्रशीघ्रस्य सप्ताग्निरसाब्धिरसषड्यमाः । ततोऽर्कबुधशुक्राणां खखार्थैकसुरार्णवाः ॥

śukraśīghrasya saptāgnirasābdhirasaṣaḍyamāḥ | tato'rkabudhaśukrāṇāṃ khakhārthaikasurārṇavāḥ ||

Of Venus's śīghra, 2,664,637; then of the Sun, Mercury and Venus, 4,331,500.

कुजस्याप्य् अङ्कशून्याङ्कषड्वेदैकभुजङ्गमाः । चन्द्रोच्चस्य कृताष्टाब्धिवसुद्वित्र्यष्टवह्नयः ॥

kujasyāpy aṅkaśūnyāṅkaṣaḍvedaikabhujaṅgamāḥ | candroccasya kṛtāṣṭābdhivasudvitryaṣṭavahnayaḥ ||

Of Mars also, 8,146,909; of the Moon's apogee (candrocca), 38,328,484.

कृतर्तुमुनिपञ्चाद्रिगुणेन्दुविषया गुरोः । स्वर्भानोर् वेदतर्काष्टद्विशैलार्थखकुञ्जराः ॥

kṛtartumunipañcādriguṇenduviṣayā guroḥ | svarbhānor vedatarkāṣṭadviśailārthakhakuñjarāḥ ||

Of Jupiter, 51,375,764; of Rāhu (svarbhānu), 80,572,864.

पञ्चवाणाक्षिनागर्तुरसाद्र्यर्काः शनेस् ततः । भानां रविखशून्याङ्कवसुरन्ध्रशराश्विनः ॥

pañcavāṇākṣināgarturasādryarkāḥ śanes tataḥ | bhānāṃ ravikhaśūnyāṅkavasurandhraśarāśvinaḥ ||

Then of Saturn, 127,668,255; and of the asterisms, 259,890,012.

खव्योमखत्रयखसागरषट्कनागव्योमाष्टशून्ययमरूपनगाष्टचन्द्राः । ब्रह्माण्डसम्पुटपरिभ्रमणं समन्ताद् अभ्यन्तरे दिनकरस्य करप्रसारः ॥

khavyomakhatrayakhasāgaraṣaṭkanāgavyomāṣṭaśūnyayamarūpanagāṣṭacandrāḥ | brahmāṇḍasampuṭaparibhramaṇaṃ samantād abhyantare dinakarasya karaprasāraḥ ||

18,712,080,864,000,000 ⟨yojanas is⟩ the circuit, on every side, of the shell of the Brahma-egg (brahmāṇḍa); within it ⟨lies⟩ the spreading of the day-maker's rays.

अथ गुप्ते शुचौ देशे स्नातः शुचिर् अलङ्कृतः । सम्पूज्य भास्करं भक्त्या ग्रहान् भान्य् अथ गुह्यकान् ॥

atha gupte śucau deśe snātaḥ śucir alaṅkṛtaḥ | sampūjya bhāskaraṃ bhaktyā grahān bhāny atha guhyakān ||

Now, in a hidden and clean place, having bathed, purified and adorned, ⟨the teacher⟩ worships with devotion the Sun (bhāskara), the grahas, the asterisks (bhāni, the nakṣatras), and then the Guhyakas —

पारम्पर्योपदेशेन यथाज्ञानं गुरोर् मुखात् । आचार्यः शिष्यबोधार्थं सर्वं प्रत्यक्षदर्शिवान् ॥

pāramparyopadeśena yathājñānaṃ guror mukhāt | ācāryaḥ śiṣyabodhārthaṃ sarvaṃ pratyakṣadarśivān ||

— the teacher (ācārya), who has seen the whole of it with his own eyes, ⟨teaching⟩ by instruction handed down in succession, according to the knowledge ⟨received⟩ from his guru's mouth, for the instruction of pupils —

भूभगोलस्य रचनां कुर्याद् आश्चर्यकारिणीम् । अभीष्टं पृथिवीगोलं कारयित्वा तु दारवम् ॥

bhūbhagolasya racanāṃ kuryād āścaryakāriṇīm | abhīṣṭaṃ pṛthivīgolaṃ kārayitvā tu dāravam ||

— should make the construction of the sphere of the earth and the asterisms (bhū-bha-gola), a wonder-working thing. Having had a wooden globe of the earth made, of the desired size, ⟨he should set in it⟩ —

दण्डं तन्मध्यगं मेरोर् उभयत्र विनिर्गतम् । आधारकक्षाद्वितयं कक्षा वैषुवती तथा ॥

daṇḍaṃ tanmadhyagaṃ meror ubhayatra vinirgatam | ādhārakakṣādvitayaṃ kakṣā vaiṣuvatī tathā ||

— a rod passing through its centre, issuing out on both sides of Meru; a pair of supporting circles (ādhāra-kakṣā), and likewise the equinoctial circle (vaiṣuvatī kakṣā).

भगणांशाङ्गुलैः कार्या दलितैस् तिस्र एव ताः । स्वाहोरात्रार्धकर्णैश् च तत्प्रमाणानुमानतः ॥

bhagaṇāṃśāṅgulaiḥ kāryā dalitais tisra eva tāḥ | svāhorātrārdhakarṇaiś ca tatpramāṇānumānataḥ ||

Those three ⟨circles⟩ are to be made with aṅgulas equal to the degrees of a revolution halved ⟨that is, 180⟩; and ⟨the rest⟩ with the half-diameters of their own diurnal circles (ahorātra), reckoned in proportion to that measure.

क्रान्तिविक्षेपभागैश् च दलितैर् दक्षिणोत्तरैः । स्वैः स्वैर् अपक्रमैस् तिस्रो मेषादीनाम् अपक्रमात् ॥

krāntivikṣepabhāgaiś ca dalitair dakṣiṇottaraiḥ | svaiḥ svair apakramais tisro meṣādīnām apakramāt ||

And by the degrees of declination and of celestial latitude, halved, southern and northern; three ⟨circles⟩ of Aries and the rest by their own respective declinations, ⟨measured⟩ from the ecliptic —

कक्षाः प्रकल्पयेत् ताश् च कर्क्यादीनां विपर्ययात् । तद्वत् तिस्रस् तुलादीनां मृगादीनां विलोमतः ॥

kakṣāḥ prakalpayet tāś ca karkyādīnāṃ viparyayāt | tadvat tisras tulādīnāṃ mṛgādīnāṃ vilomataḥ ||

— those circles he should lay out; and those of Cancer and the rest in the reverse order. Likewise three of Libra and the rest, and of Capricorn and the rest in inverted order.

याम्यगोलाश्रिताः कार्याः कक्षाधाराद् द्वयोर् अपि । याम्योदग्गोलसंस्थानां भानाम् अभिजितस् तथा ॥

yāmyagolāśritāḥ kāryāḥ kakṣādhārād dvayor api | yāmyodaggolasaṃsthānāṃ bhānām abhijitas tathā ||

⟨Those of Libra and of Capricorn⟩ are to be made resting in the southern hemisphere, ⟨reckoned⟩ from the supporting circle, for both ⟨sets⟩ alike. Likewise ⟨circles⟩ of the asterisms standing in the southern and northern hemispheres, and of Abhijit,

सप्तर्षीणाम् अगस्त्यस्य ब्रह्मादीनां च कल्पयेत् । मध्ये वैषुवती कक्षा सर्वेषाम् एव संस्थिता ॥

saptarṣīṇām agastyasya brahmādīnāṃ ca kalpayet | madhye vaiṣuvatī kakṣā sarveṣām eva saṃsthitā ||

of the Seven Sages (saptarṣi), of Agastya, and of Brahmā and the rest, he should lay out. In the middle of all of them stands the equinoctial circle.

तदाधारयुतेर् ऊर्ध्वम् अयने विषुवद्वयम् । विषुवत्स्थानतो भागैः स्फुटैर् भगणसञ्चरात् ॥

tadādhārayuter ūrdhvam ayane viṣuvadvayam | viṣuvatsthānato bhāgaiḥ sphuṭair bhagaṇasañcarāt ||

Above the junction of that ⟨equinoctial circle⟩ with the supports are the two solstices and the two equinoxes. From the equinoctial point, by exact degrees, according to the progress of the revolution ⟨of the signs⟩,

क्षेत्राण्य् एवम् अजादीनां तिर्यग्ज्याभिः प्रकल्पयेत् । अयनाद् अयनं चैव कक्षा तिर्यक् तथापरा ॥

kṣetrāṇy evam ajādīnāṃ tiryagjyābhiḥ prakalpayet | ayanād ayanaṃ caiva kakṣā tiryak tathāparā ||

— thus should he lay out the fields (kṣetra) of Aries and the rest by transverse chords (jyā); and another circle ⟨is to be drawn⟩ crosswise, from solstice to solstice.

क्रान्तिसञ्ज्ञा तया सूर्यः सदा पर्येति भासयन् । चन्द्राद्याश् च स्वकैः पातैर् अपमण्डलम् आश्रितैः ॥

krāntisañjñā tayā sūryaḥ sadā paryeti bhāsayan | candrādyāś ca svakaiḥ pātair apamaṇḍalam āśritaiḥ ||

That is named the ecliptic (krānti). Along it the Sun always travels round, giving light. And the Moon and the rest ⟨travel⟩ by their own nodes, which rest upon the ecliptic (apamaṇḍala);

ततोऽपकृष्टा दृश्यन्ते विक्षेपान्तेष्व् अपक्रमात् । उदयक्षितिजे लग्नम् अस्तं गच्छच् च तद्वशात् ॥

tato'pakṛṣṭā dṛśyante vikṣepānteṣv apakramāt | udayakṣitije lagnam astaṃ gacchac ca tadvaśāt ||

thence they are seen drawn away from the ecliptic at the limits of their latitude. And by that same ⟨deflection⟩ ⟨are determined⟩ the ascendant (lagna) on the eastern horizon, and the point going to setting.

लङ्कोदयैर् यथासिद्धं खमध्योपरि मध्यमम् । मध्यक्षितिजयोर् मध्ये या ज्या सान्त्याभिधीयते ॥

laṅkodayair yathāsiddhaṃ khamadhyopari madhyamam | madhyakṣitijayor madhye yā jyā sāntyābhidhīyate ||

By the risings at Laṅkā (right ascensions), as established, ⟨is found⟩ the mid-heaven point above the zenith. The chord (jyā) that lies between the meridian and the horizon is called antyā.

ज्ञेया चरदलज्या च विषुवत् क्षितिजान्तरम् । कृत्वोपरि स्वकं स्थानं मध्ये क्षितिजमण्डलम् ॥

jñeyā caradalajyā ca viṣuvat kṣitijāntaram | kṛtvopari svakaṃ sthānaṃ madhye kṣitijamaṇḍalam ||

And the chord of half the ascensional difference (cara-dala-jyā) is to be known as the interval between the equinoctial ⟨circle⟩ and the horizon. Having set one's own place above and the horizon-circle in the middle,

वस्त्रच्छन्नं बहिश् चापि लोकालोकेन वेष्टितम् । अमृतस्रावयोगेन कालभ्रमणसाधनम् ॥

vastracchannaṃ bahiś cāpi lokālokena veṣṭitam | amṛtasrāvayogena kālabhramaṇasādhanam ||

⟨the sphere⟩ covered with cloth outside, and encircled by the Lokāloka ⟨mountain⟩ — by the application of a flow of amṛta ⟨quicksilver⟩ it becomes an instrument for the revolution of time.

तुङ्गबीजसमायुक्तं गोलयन्त्रं प्रसाधयेत् । गोप्यम् एतत् प्रकाशोक्तं सर्वगम्यं भवेद् इह ॥

tuṅgabījasamāyuktaṃ golayantraṃ prasādhayet | gopyam etat prakāśoktaṃ sarvagamyaṃ bhaved iha ||

One should perfect the sphere-instrument (gola-yantra) fitted with its tuṅga-bīja ⟨the driving contrivance at the apex⟩. This is to be kept secret; declared openly, it would here become accessible to everyone.

तस्माद् गुरूपदेशेन रचयेद् गोलम् उत्तमम् । युगे युगे समुच्छिन्ना रचनेयं विवस्वतः ॥

tasmād gurūpadeśena racayed golam uttamam | yuge yuge samucchinnā racaneyaṃ vivasvataḥ ||

Therefore let him construct the excellent sphere by a guru's instruction. In age after age this construction of Vivasvat ⟨the Sun⟩ is wholly lost,

प्रसादात् कस्यचिद् भूयः प्रादुर् भवति कामतः । कालसंसाधनार्थाय तथा यन्त्राणि साधयेत् ॥

prasādāt kasyacid bhūyaḥ prādur bhavati kāmataḥ | kālasaṃsādhanārthāya tathā yantrāṇi sādhayet ||

and by ⟨his⟩ grace it again becomes manifest to some one ⟨person⟩, at will. For the exact determination of time one should likewise perfect instruments.

एकाकी योजयेद् बीजं यन्त्रे विस्मयकारिणि । शङ्कुयष्टिधनुश्चक्रैश् छायायन्त्रैर् अनेकधा ॥

ekākī yojayed bījaṃ yantre vismayakāriṇi | śaṅkuyaṣṭidhanuścakraiś chāyāyantrair anekadhā ||

Alone should one fit the bīja ⟨driving contrivance⟩ into the wonder-working instrument. By gnomon, staff, arc and circle, and by shadow-instruments of many kinds,

गुरूपदेशाद् विज्ञेयं कालज्ञानम् अतन्द्रितैः । तोययन्त्रकपालाद्यैर् मयूरनरवानरैः ॥ ससूत्ररेणुगर्भैश् च सम्यक् कालं प्रसाधयेत् ॥

gurūpadeśād vijñeyaṃ kālajñānam atandritaiḥ | toyayantrakapālādyair mayūranaravānaraiḥ || sasūtrareṇugarbhaiś ca samyak kālaṃ prasādhayet ||

the knowledge of time is to be learnt from a guru's instruction by the unwearying. By water-instruments, the bowl (kapāla) and the rest, by ⟨figures of⟩ peacocks, men and monkeys, and by ⟨vessels⟩ holding cords and sand within, one should determine time accurately.

पारदाराम्बुसूत्राणि शुल्वतैलजलानि च । बीजानि पांसवस् तेषु प्रयोगास् तेऽपि दुर्लभाः ॥

pāradārāmbusūtrāṇi śulvatailajalāni ca | bījāni pāṃsavas teṣu prayogās te'pi durlabhāḥ ||

Mercury, ārā, water and cords; and copper, oil and water — these ⟨and⟩ sands are the bījas ⟨the driving agents⟩; but the ways of applying them too are hard to come by.

ताम्रपात्रम् अधश्छिद्रं न्यस्तं कुण्डेऽमलाम्भसि । षष्टिर् मज्जत्य् अहोरात्रे स्फुटं यन्त्रं कपालकम् ॥

tāmrapātram adhaśchidraṃ nyastaṃ kuṇḍe'malāmbhasi | ṣaṣṭir majjaty ahorātre sphuṭaṃ yantraṃ kapālakam ||

A copper vessel, pierced below, set in a basin of clear water, sinks sixty times in a day and night: that is the accurate instrument, the bowl (kapālaka).

नरयन्त्रं तथा साधु दिवा च विमले रवौ । छायासंसाधनैः प्रोक्तं कालसाधनम् उत्तमम् ॥

narayantraṃ tathā sādhu divā ca vimale ravau | chāyāsaṃsādhanaiḥ proktaṃ kālasādhanam uttamam ||

Likewise the man-instrument (nara-yantra) is good, by day and when the Sun is clear. By the working out of shadows it is declared an excellent means of determining time.

ग्रहनक्षत्रचरितं ज्ञात्वा गोलं च तत्त्वतः । ग्रहलोकम् अवाप्नोति पर्यायेणात्मवान् नरः ॥

grahanakṣatracaritaṃ jñātvā golaṃ ca tattvataḥ | grahalokam avāpnoti paryāyeṇātmavān naraḥ ||

Having known the courses of the grahas and the nakṣatras, and the sphere, in their true nature, the self-possessed man attains in due course to the world of the grahas.

ब्राह्मं दिव्यं तथा पित्र्यं प्राजापत्यं गुरोस् तथा । सौरं च सावनं चान्द्रम् आर्क्षं मानानि वै नव ॥

brāhmaṃ divyaṃ tathā pitryaṃ prājāpatyaṃ guros tathā | sauraṃ ca sāvanaṃ cāndram ārkṣaṃ mānāni vai nava ||

The Brāhma, the divine (divya), likewise the ancestral (pitrya), the Prājāpatya, and likewise that of Jupiter (guru), the solar (saura), the civil (sāvana), the lunar (cāndra), and the sidereal (ārkṣa) — the measures ⟨of time⟩ are indeed nine.

चतुर्भिर् व्यवहारोऽत्र सौरचान्द्रार्क्षसावनैः । बार्हस्पत्येन षष्ट्यब्दं ज्ञेयं नान्यैस् तु नित्यशः ॥

caturbhir vyavahāro'tra sauracāndrārkṣasāvanaiḥ | bārhaspatyena ṣaṣṭyabdaṃ jñeyaṃ nānyais tu nityaśaḥ ||

Here practical usage ⟨proceeds⟩ by four — by the solar, the lunar, the sidereal and the civil. By the Bārhaspatya ⟨measure⟩ the sixty-year ⟨cycle⟩ is to be known; but by the others there is no everyday ⟨use⟩.

सौरेण द्युनिशोर् मानं षडशीतिमुखानि च । अयनं विषुवच्चैव संक्रान्तेः पुण्यकालता ॥

saureṇa dyuniśor mānaṃ ṣaḍaśītimukhāni ca | ayanaṃ viṣuvaccaiva saṃkrānteḥ puṇyakālatā ||

By the solar ⟨are reckoned⟩ the measure of day and night, the ṣaḍaśīti-mukhas, the ayana ⟨solstitial course⟩ and the equinox (viṣuvat), and the holiness of the time of a saṃkrānti ⟨the Sun's transit into a rāśi⟩.

तुलादि षडशीत्यह्नां षडशीतिमुखं क्रमात् । तच्चतुष्टयम् एव स्याद् द्विस्वभावेषु राशिषु ॥

tulādi ṣaḍaśītyahnāṃ ṣaḍaśītimukhaṃ kramāt | taccatuṣṭayam eva syād dvisvabhāveṣu rāśiṣu ||

Beginning from Tulā ⟨Libra⟩, at ⟨intervals⟩ of eighty-six days, a ṣaḍaśīti-mukha ⟨occurs⟩ in order; and that set of four falls precisely in the dual-natured (dvisvabhāva) rāśis.

षड्विंशे धनुषो भागे द्वाविंशेऽनिमिषस्य च । मिथुनाष्टादशे भागे कन्यायास् तु चतुर्दश ॥

ṣaḍviṃśe dhanuṣo bhāge dvāviṃśe'nimiṣasya ca | mithunāṣṭādaśe bhāge kanyāyās tu caturdaśa ||

In the twenty-sixth degree of Dhanus ⟨Sagittarius⟩, and in the twenty-second of the Unblinking One ⟨Mīna, Pisces⟩, in the eighteenth degree of Mithuna ⟨Gemini⟩, and in the fourteenth of Kanyā ⟨Virgo⟩.

ततः शेषाणि कन्याया यान्य् अहानि तु षोडश । क्रतुभिस् तानि तुल्यानि पितॄणां दत्तम् अक्षयम् ॥

tataḥ śeṣāṇi kanyāyā yāny ahāni tu ṣoḍaśa | kratubhis tāni tulyāni pitṝṇāṃ dattam akṣayam ||

Then those sixteen days that remain of Kanyā ⟨Virgo⟩ — those are equal to sacrifices (kratu); what is given to the ancestors ⟨in them⟩ is imperishable.

भचक्रनाभौ विषुवद्द्वितयं समसूत्रगम् । अयनद्वितयं चैव चतस्रः प्रथितास् तु ताः ॥

bhacakranābhau viṣuvaddvitayaṃ samasūtragam | ayanadvitayaṃ caiva catasraḥ prathitās tu tāḥ ||

At the nave of the wheel of asterisms (bhacakra), the pair of equinoctial ⟨points⟩ lying on one and the same diameter, and likewise the pair of solstitial (ayana) ⟨points⟩ — these four are the celebrated ones.

तदन्तरेषु संक्रान्तिद्वितयं द्वितयं पुनः । नैरन्तर्यात् तु संक्रान्तेर् ज्ञेयं विष्णुपदीद्वयम् ॥

tadantareṣu saṃkrāntidvitayaṃ dvitayaṃ punaḥ | nairantaryāt tu saṃkrānter jñeyaṃ viṣṇupadīdvayam ||

In the intervals between them ⟨come⟩ a pair of saṃkrāntis, and again a pair; but from ⟨their⟩ immediately following upon a saṃkrānti, the pair of Viṣṇupadīs is to be known.

भानोर् मकरसङ्क्रान्तेः षण्मासा उत्तरायणम् । कर्क्यादेस् तु तथैव स्यात् षण्मासा दक्षिणायनम् ॥

bhānor makarasaṅkrānteḥ ṣaṇmāsā uttarāyaṇam | karkyādes tu tathaiva syāt ṣaṇmāsā dakṣiṇāyanam ||

From the Sun's transit into Makara ⟨Capricorn⟩, six months are the northern course (uttarāyaṇa); and from the beginning of Karka ⟨Cancer⟩, just so, six months are the southern course (dakṣiṇāyana).

द्विराशिनाथा ऋतवस् ततोऽपि शिशिरादयः । मेषादयो द्वादशैते मासास् तैर् एव वत्सरः ॥

dvirāśināthā ṛtavas tato'pi śiśirādayaḥ | meṣādayo dvādaśaite māsās tair eva vatsaraḥ ||

The seasons (ṛtu) have two rāśis each, and they too ⟨run⟩ from that ⟨same point⟩, beginning with Śiśira. These twelve, beginning with Meṣa ⟨Aries⟩, are the months, and by these very ⟨months⟩ ⟨is⟩ the year.

अर्कमानकलाः षष्ट्या गुणिता भुक्तिभाजिताः । तदर्धनाड्यः सङ्क्रान्तेर् अर्वाक् पुण्यं तथा परे ॥

arkamānakalāḥ ṣaṣṭyā guṇitā bhuktibhājitāḥ | tadardhanāḍyaḥ saṅkrānter arvāk puṇyaṃ tathā pare ||

The minutes of the Sun's measure ⟨the diameter of his disc⟩, multiplied by sixty and divided by ⟨his daily⟩ motion (bhukti), ⟨give nāḍīs⟩; half those nāḍīs before the saṃkrānti are holy ⟨time⟩, and so many after.

अर्काद् विनिःसृतः प्राचीं यद् यात्य् अहरहः शशी । तच् चान्द्रमानम् अंशैस् तु ज्ञेया द्वादशभिस् तिथिः ॥

arkād viniḥsṛtaḥ prācīṃ yad yāty aharahaḥ śaśī | tac cāndramānam aṃśais tu jñeyā dvādaśabhis tithiḥ ||

That which the Moon (śaśī), having gone forth from the Sun, travels eastward day by day — that is the lunar measure; and a tithi is to be known by twelve degrees.

तिथिः करणम् उद्वाहः क्षौरं सर्वक्रियास् तथा । व्रतोपवासयात्राणां क्रिया चान्द्रेण गृह्यते ॥

tithiḥ karaṇam udvāhaḥ kṣauraṃ sarvakriyās tathā | vratopavāsayātrāṇāṃ kriyā cāndreṇa gṛhyate ||

The tithi, the karaṇa, marriage, tonsure, and likewise all ⟨such⟩ rites, and the performance of vows, fasts and journeys — ⟨these⟩ are taken by the lunar ⟨measure⟩.

त्रिंशता तिथिभिर् मासश् चान्द्रः पित्र्यम् अहः स्मृतम् । निशा च मासपक्षान्तौ तयोर् मध्ये विभागतः ॥

triṃśatā tithibhir māsaś cāndraḥ pitryam ahaḥ smṛtam | niśā ca māsapakṣāntau tayor madhye vibhāgataḥ ||

By thirty tithis ⟨is⟩ the lunar month; it is remembered as a day of the ancestors (pitṛs) — and a night ⟨as well⟩; the end of the month and the end of the fortnight are, by division, in the middle of those two.

भचक्रभ्रमणं नित्यं नाक्षत्रं दिनम् उच्यते । नक्षत्रनाम्ना मासास् तु ज्ञेयाः पर्वान्तयोगतः ॥

bhacakrabhramaṇaṃ nityaṃ nākṣatraṃ dinam ucyate | nakṣatranāmnā māsās tu jñeyāḥ parvāntayogataḥ ||

The constant revolution of the wheel of asterisms (bhacakra) is called the sidereal (nākṣatra) day. But the months, ⟨named⟩ by the name of a nakṣatra, are to be known from the conjunction ⟨of the Moon with it⟩ at the end of the parvan.

कार्तिक्यादिषु संयोगे कृत्तिकादि द्वयं द्वयम् । अन्त्योपान्त्यौ पञ्चमश् च त्रिधा मासत्रयं स्मृतम् ॥

kārtikyādiṣu saṃyoge kṛttikādi dvayaṃ dvayam | antyopāntyau pañcamaś ca tridhā māsatrayaṃ smṛtam ||

At the conjunction ⟨of the Moon⟩ at ⟨the full moons⟩ beginning with Kārttikī, ⟨the nakṣatras⟩ beginning with Kṛttikā ⟨are assigned⟩ two and two; but the last, the last but one, and the fifth — ⟨thus⟩ three months are remembered as being of three each.

वैशाखादिषु कृष्णे च योगः पञ्चदशे तिथौ । कार्त्तिकादीनि वर्षाणि गुरोर् अस्तोदयात् तथा ॥

vaiśākhādiṣu kṛṣṇe ca yogaḥ pañcadaśe tithau | kārttikādīni varṣāṇi guror astodayāt tathā ||

And in ⟨the months⟩ beginning with Vaiśākha the conjunction ⟨falls⟩ on the fifteenth tithi in the dark ⟨fortnight⟩. The years beginning with Kārttika ⟨are reckoned⟩ likewise, from the setting and rising of Jupiter (guru).

उदयाद् उदयं भानोः सावनं तत् प्रकीर्तितम् । सावनानि स्युर् एतेन यज्ञकालविधिस् तु तैः ॥

udayād udayaṃ bhānoḥ sāvanaṃ tat prakīrtitam | sāvanāni syur etena yajñakālavidhis tu taiḥ ||

From the Sun's rising to ⟨his⟩ rising — that is proclaimed to be the civil (sāvana) ⟨day⟩. By this ⟨reckoning⟩ the civil ⟨days, months and years⟩ come to be; and by them ⟨is⟩ the rule for the times of sacrifice.

सूतकादिपरिच्छेदो दिनमासाब्दपास् तथा । मध्यमा ग्रहभुक्तिस् तु सावनेनैव गृह्यते ॥

sūtakādiparicchedo dinamāsābdapās tathā | madhyamā grahabhuktis tu sāvanenaiva gṛhyate ||

The determination of ⟨the periods of⟩ birth-impurity (sūtaka) and the like, and likewise the lords of the day, of the month and of the year, and the mean daily motion of the grahas — ⟨these⟩ are taken by the civil ⟨measure⟩ alone.

सुरासुराणाम् अन्योन्यम् अहोरात्रं विपर्ययात् । यत्प्रोक्तं तद् भवेद् दिव्यं भानोर् भगणपूरणात् ॥

surāsurāṇām anyonyam ahorātraṃ viparyayāt | yatproktaṃ tad bhaved divyaṃ bhānor bhagaṇapūraṇāt ||

The day and night of the gods and the asuras, mutually reversed, which has been declared ⟨earlier⟩ — that is the divine ⟨measure⟩, ⟨completed⟩ by the Sun's filling out a revolution of the zodiac.

मन्वन्तरव्यवस्था च प्राजापत्यम् उदाहृतम् । न तत्र द्युनिशोर् भेदो ब्राह्मं कल्पः प्रकीर्तितम् ॥

manvantaravyavasthā ca prājāpatyam udāhṛtam | na tatra dyuniśor bhedo brāhmaṃ kalpaḥ prakīrtitam ||

And the arrangement of the manvantaras is declared to be the Prājāpatya ⟨measure⟩; therein there is no distinction of day and night. The Brāhma ⟨measure⟩ is proclaimed to be the kalpa.

एतत् ते परमाख्यातं रहस्यं परमाद्भुतम् । ब्रह्मैतत् परमं पुण्यं सर्वपापप्रणाशनम् ॥

etat te paramākhyātaṃ rahasyaṃ paramādbhutam | brahmaitat paramaṃ puṇyaṃ sarvapāpapraṇāśanam ||

This supremely wondrous mystery has been declared to thee in the highest ⟨manner⟩; this is Brahman, supremely holy, the destroyer of all sin.

दिव्यं चार्क्षं ग्रहाणां च दर्शितं ज्ञानम् उत्तमम् । विज्ञायार्कादिलोकेषु स्थानं प्राप्नोति शाश्वतम् ॥

divyaṃ cārkṣaṃ grahāṇāṃ ca darśitaṃ jñānam uttamam | vijñāyārkādilokeṣu sthānaṃ prāpnoti śāśvatam ||

The divine and the sidereal ⟨measures⟩, and the excellent knowledge of the grahas, have been shown ⟨to thee⟩; having understood ⟨it⟩, one attains an everlasting station in the worlds of the Sun and the rest.

इत्य् उक्त्वा मयम् आमन्त्र्य सम्यक् तेनाभिपूजितः । दिवम् आचक्रमेऽर्कांशः प्रविवेश स्वमण्डलम् ॥

ity uktvā mayam āmantrya samyak tenābhipūjitaḥ | divam ācakrame'rkāṃśaḥ praviveśa svamaṇḍalam ||

Having spoken thus, and having taken leave of Maya, duly honoured by him, the portion of the Sun (arkāṃśa) went up to heaven and entered his own orb.

मयोऽथ दिव्यं तज्ज्ञानं ज्ञात्वा साक्षाद् विवस्वतः । कृतकृत्यम् इवात्मानं मेने निर्धूतकल्मषम् ॥

mayo'tha divyaṃ tajjñānaṃ jñātvā sākṣād vivasvataḥ | kṛtakṛtyam ivātmānaṃ mene nirdhūtakalmaṣam ||

Then Maya, having learnt that divine knowledge directly from Vivasvat ⟨the Sun⟩, deemed himself as one whose task was accomplished, his defilement shaken off.

ज्ञात्वा तम् ऋषयश् चाथ सूर्यलब्धवरं मयम् । परिबब्रुर् उपेत्याथो ज्ञानं पप्रच्छुर् आदरात् ॥

jñātvā tam ṛṣayaś cātha sūryalabdhavaraṃ mayam | paribabrur upetyātho jñānaṃ papracchur ādarāt ||

And then the ṛṣis, knowing him — Maya, who had obtained the boon from the Sun — approached and surrounded ⟨him⟩, and asked him for the knowledge with reverence.

स तेभ्यः प्रददौ प्रीतो ग्रहाणां चरितं महत् । अत्यद्भुततमं लोके रहस्यं ब्रह्मसम्मितम् ॥

sa tebhyaḥ pradadau prīto grahāṇāṃ caritaṃ mahat | atyadbhutatamaṃ loke rahasyaṃ brahmasammitam ||

He, well pleased, gave to them the great ⟨science of the⟩ course of the grahas — most exceedingly wondrous in the world, a mystery commensurate with the Veda (brahma-sammita).