Chapter 2: True places of the planets

2.1-11 · descriptive (nothing to compute)

the beings at the apsis, conjunction and node that draw the planets (the directions they give are used in II.39-57)

1. adṛśyarūpāh kālasya mūrtayo bhagaṇāśritāh/
śīghramandoccapātākhyā grahāṇāṃ gatihetavah//

2. tadvātaraśmibhir *baddhās tais savyetarapāṇibhih/ (c naddhās)
prāk paścād apakṛṣyante yathāsannaṃ svadiṅmukham//

3. pravahākhyo marut tāṃs tu svoccābhimukham īrayet/
pūrvāparākṛṣṭās te *gatiṃ yānti pṛthagvidhāh//(c gatīr, pṛthagvidhām)

4. grahāt prāgbhagaṇārdhasthah prāṅmukhaṃ karṣati graham/
uccasaṃjño +aparārdhasthas tadvat paścānmukhaṃ graham//

5. svoccāpakṛṣṭā *bhagaṇaih prāṅmukhaṃ yānti yad grahāh/ (c bhagaṇāt)
tat teṣu dhanam ity uktam ṛṇaṃ paścānmukheṣu *ca// (tu)

6. *dakṣiṇottarato +apy evaṃ pāto *rāhuh svaraṃhasā/(c dakṣiṇottarayor, rāhuś ca raṃhasā)
vikṣipaty eṣa vikṣepaṃ candrādīnām apakramāt//

7. uttarābhimukhaṃ pāto vikṣipaty aparārdhagah/
grahaṃ prāgbhagaṇārdhastho yāmyāyām apakarṣati//

8. budhabhārgavayoh śīghrāt tadvat pāto *yadā sthitah/ (c yathāsthitah)
tacchīghrākarṣaṇāt tau tu vikṣipyete yathoktavat//

9. mahatvān maṇḍalasyārkah svalpam evāpakṛṣyate/
maṇḍalālpatayā candras tato bahv apakṛṣyate/

10. bhaumādayo +alpamūrtitvāc chīghramandoccasañjñakaih/ (c saṃjñitaih)
daivatair apakṛṣyante sudūram ativegitāh//

11. ato dhanarṇaṃ sumahat teṣāṃ gativaśād bhavet/
ākṛṣyamāṇās tair evaṃ vyomni yānty anilāhatāh//

2.12-13 · descriptive (nothing to compute)

eight kinds of motion, named without criteria and not used again except vakra (computed in II.51-55)

12. *vakrātivakrā vikalā mandā mandatarā samā/ (c vakrānuvakrā)
tathā śīghratarā śīghrā grahāṇām aṣṭadhā gatih//

13. tatrātiśīghrā śīghrākhyā mandā mandatarā samā/
ṛjvīti pañcadhā jñeyā *yā vakrā sātivakragā//(c +anyā vakrādikā matā)

2.14 · descriptive (nothing to compute)

the corrections bring the planets to their observed places

14. tattadgativaśān nityaṃ yathā dṛktulyatāṃ grahāh/
prayānti tat pravakṣyāmi sphuṭīkaraṇam ādarāt//

2.15-16 · computed

the rule said to generate the sines (gives the first six; the text computes with II.17-22)

15. rāśiliptāṣṭamo bhāgah prathamaṃ jyārdham ucyate/
tat tadvibhaktalabdhonamiśritaṃ tad dvitīyakam//

16. ādyenaivaṃ kramāt piṇḍān bhaktvā *labdhonasaṃyutāh/(c labdhonitair yutaih)
*khaṇḍakāh syuś caturviṃśajyārdhapiṇḍāh kramād amī//(c khaṇḍakais)

Computed by: sineTableByRule

2.17-22 · computed

the 24 tabular sines; versed sines as their complements

17. tattvāśvino +aṅkābdhikṛtā rūpabhūmidharartavah/(224, 449, 691)
khāṅkāṣṭau pañcaśūnyeśā bāṇarūpaguṇendavah//(890, 1105, 1315)

18. śūnyalocanapañcaikāś chidrarūpamunīndavah/(1520, 1719)
viyaccandrātidhṛtayo guṇarandhrāmbarāśvinah//(1910, 2093)

19. muniṣaḍyamanetrāṇi candrāgnikṛtadasrakāh/(2267, 2431)
pañcāṣṭaviṣayākṣīṇi kuñjarāśvinagāśvinah//(2585, 2728)

20. randhrapañcāṣṭakayamā vasvadryaṅkayamās tathā/(2859, 2978)
kṛtāṣṭaśūnyajvalanā nagādriśaśivahnayah//(3084, 3179)

21. ṣaṭpañcalocanaguṇāś candranetrāgnivahnayah/(3256, 3321)
yamādrivahnijvalanā randhraśūnyārnavāgnayah//(3372), 3401)

22. rūpāgnisāgaraguṇā vasvagnikṛtavahnayah/(3431, 3438)
projjhyotkrameṇa vyāsārdhād utkramajyārdhapiṇḍikāh//

Computed by: jyaCONSTANTS.SINES

2.23-27 · computed

the 24 tabular versed sines

23. munayo randhrayamalā rasaṣaṭkā munīśvarāh/(7, 29, 66, 117)
dvyaṣṭaikā rūpaṣaḍdasrāh sāgarārthahutāśanāh/(182, 261, 354)

24. khartuvedā navādryarthā diṅnāgās tryarthakuñjarāh/(460, 710, 853)
nagāmbaraviyaccandrā rūpabhūdharaśaṅkarāh//(1007, 1171)

25. śarārṇavahutāśaikā bhujaṅgākṣiśarendavah/(1345, 1528)
navarūpamahīdhraikā gajaikāṅkaniśākarāh//1719, 1918)

26. guṇāśvirūpanetrāṇi pāvakāgniguṇāśvinah/(2123, 2333)
vasvarṇavārthayamalās turaṅgartunagāśvinah//(2548, 2767)

27. navāṣṭanavanetrāṇi pāvakaikayamāgnayah/(2989, 3293)
gajāgnisāgaraguṇā utkramajyārdhapiṇḍakāh//(3438)

Computed by: utkramaJyaCONSTANTS.VERSED_SINES

2.28 · computed

declination from the sine of greatest declination

28. paramāpakramajyā tu saptarandhraguṇendavah/(1397)
tadguṇā jyā trijīvāptā taccāpaṃ krāntir ucyate//(c iṣyate)

Computed by: latitudesCONSTANTS.SINE_OF_OBLIQUITY

2.29-33 · computed

anomaly and commutation; base- and perpendicular-sines; sines of any arc and arcs of any sine

29. grahaṃ saṃśodhya mandoccāt tathā śīghrād viśodhya ca/
śeṣaṃ kendrapadaṃ tasmād bhujajyā koṭir eva ca//(c kendraṃ padaṃ)

30. gatād bhujajyā viṣame gamyāt koṭih pade bhavet/
*yugme tu gamyād bāhujyā koṭijyā tu gatād bhavet//(c same)

31. liptās tattvayamair bhaktā *labdhaṃ jyāpiṇḍikaṃ gatām/(c labdhā jyāpiṇḍikā gatāh)
gatagamyāntarābhyastaṃ vibhajet tattvalocanaih//(225)

32. tadavāptaphalaṃ yojyaṃ jyāpiṇḍe *gatasaṃjñake/(c gatasaṃjñite)
syāt kramajyāvidhir ayaṃ utkramajyāsv api smṛtah//

33. jyāṃ *projjhya śeṣaṃ tattvāśvihataṃ tadvivaroddhṛtam/(c projjhyānyattattvayamair hatvā)(225)
saṃkhyātattvāśvisaṃvarge *saṃyojya dhanur ucyate//(c saṃyojyaṃ) (225)

Computed by: jyaarcJyamandaEquationsighraEquation

2.34-38 · computed

epicycles at the even and odd quadrants; the corrected epicycle

34. raver mandaparidhyaṃśā manavah śītago radāh/ (14, 32)
yugmānte viṣamānte tu nakhaliptonitās tayoh//

35. yugmānte +arthādrayah *khāgnisurāh sūryā navārṇavāh/(c khāgnih surās)(75, 30, 33, 12, 49)
oje dvyagā vasuyamā radā rudrā gajābdayah//

36. kujādīnāṃ *atah śīghrā yugmānte +arthāgnidasrakāh/(c tataś śaighryā)(235)
guṇāgnicandrāh *khanagā dvirasākṣīṇi go+agnayah//(c khāgāś ca)(133, 70, 262, 39)

37. ojānte *dvitriyamalā dviviśve yamaparvatāh/(c dvitrikayamāh)(132, 72)
khartudasrā viyadvedāh śīghrakarmaṇi kīrtitāh//(260,40)

38. ojayugmāntaraguṇā bhujajyā trijyayoddhṛtā/
*yugme vṛtte dhanarṇaṃ syād ojād ūnādhike sphuṭam// (c yugmavṛtte)

Computed by: CONSTANTS.MANDA_EPICYCLECONSTANTS.SIGHRA_EPICYCLEmandaEquation

2.39-42 · computed

the equations of the apsis and of the conjunction; the variable hypotenuse

39. tadguṇe bhujakoṭijye bhagaṇāṃśavibhājite/
tadbhujajyāphaladhanur māndaṃ liptādikaṃ phalam//

40. *śaighryaṃ koṭiphalaṃ kendre makarādau dhanaṃ smṛtam/(c śaighre)
saṃśodhyaṃ tu *trijīvāyāṃ karkyādau koṭijaṃ phalam//(c trijīvātah)

41. tadbāhuphalavargaikyān mūlaṃ karṇaś calābhidhah/
trijyābhyastaṃ bhujaphalaṃ calakarṇavibhājitam//

42. labdhasya cāpaṃ liptādiphalaṃ *śaighryam idaṃ smṛtam/ (c śaighram)
etad ādye kujādīnāṃ caturthe caiva karmaṇi//

Computed by: mandaEquationsighraEquation

2.43-45 · computed

the four successive corrections; the Sun and Moon by the apsis alone

43. māndaṃ karmaikam arkendor bhaumādīnām athocyate/
*śaighryaṃ māndaṃ punar māndaṃ śaighryaṃ catvāry anukramāt//(c śaighraṃ)

44. madhye śīghraphalasyārdhaṃ māndam ardhaphalaṃ tathā/
madhyagrahe *mandaphalaṃ sakalaṃ śaighryam eva ca//(c punar māndaṃ)

45. ajādikendre sarveṣāṃ *śaighrye mānde ca karmaṇi/(c mānde śaighre)
dhanaṃ grahāṇāṃ liptādi tulādāv rṇam eva ca//

Computed by: truePlaces

2.46 · computed

correction to places for apparent solar time

46. arkabāhuphalābhyastā grahabhuktir vibhājitā/
bhacakrakalikābhis tu liptāh karyā grahe +arkavat//

Computed by: apparentTimeCorrection

2.47-51 · computed

true daily motion

47. svamandabhuktisaṃśuddhā madhyabhuktir niśāpateh/
dorjyāntarādikaṃ kṛtvā bhuktāv ṛṇadhanaṃ bhavet//

48. grahabhukteh phalaṃ kāryaṃ grahavan mandakarmaṇi/
dorjyāntaraguṇā bhuktis tattvanetroddhṛtā punah// (225)

49. svamandaparidhikṣuṇṇā bhagaṇāṃśoddhṛtā kalāh/]
karkyādau tu dhanaṃ tatra makarādāv ṛṇaṃ smṛtam//

50. mandasphuṭīkṛtāṃ bhuktiṃ projjhya śīghroccabhuktitah/
taccheśaṃ vivareṇātha hanyāt trijyāntyakarṇayoh//

51. calakarṇahṛtaṃ bhuktau karṇe trijyādhike dhanam/
ṛṇam ūne +adhike projjhya śeṣaṃ vakragatir bhavet//

Computed by: dailyMotions

2.52 · descriptive (nothing to compute)

why a planet far from its conjunction retrogrades

52. dūrasthitah svaśīghroccād grahah śithilaraśmibhih/
savyetarākṛṣtatanur bhavet vakragatis tadā//

2.53-55 · computed

commutations at which retrogradation begins and ends

53. kṛtartucandrair vedendraih śūnyatryekair guṇāṣṭabhih/(164, 144, 130, 83)
śararudraiś caturtheṣu kendrāṃśair bhūsutādayah//(115)

54. bhavanti vakriṇas tais tu svaih svaiś cakrād viśodhitaih/
avaśiṣṭāṃśatulyaih svaih kendrair ujjhanti vakratām//

55. mahattvāc chīghraparidheh saptame bhṛgubhūsutau/
aṣṭame jīvaśaśaijau navame tu śanaiścarah//

Computed by: dailyMotionsCONSTANTS.RETROGRADE_COMMUTATION

2.56-58 · computed

equated nodes, latitude, true declination

56. kujārkigurupātānāṃ grahavac chīghrajaṃ phalam/
vāmaṃ tṛtīyakaṃ māndaṃ budhabhārgavayoh phalam//

57. svapātonād grahāj jīvā śīghrād bhṛgujasaumyayoh/
vikṣepaghny antyakarṇāptā vikṣepas trijyayā vidhoh//

58. vikṣepāpakramaikatve krāntir vikṣepasaṃyutā/
digbhede viyutā spaṣṭā bhāskarasya yathāgatā//

Computed by: latitudes

2.59-63 · computed

a planet's day; ascensional difference; day and night at a latitude

59. grahodayaprāṇahatā khakhāṣṭaikoddhṛtā gatih/
cakrāsavo labdhayutā svāhorātrāsavah smṛtāh//

60. krānteh kramotkrammajye dve kṛtvā tatrotkramajyayā/
hīnā trijyā dinavyāsadalaṃ taddakṣiṇottaram//

61. krāntijyā viṣuvadbhāghnī kṣitijyā dvādaśoddhṛtā/
trijyāguṇāhorātrārdhakarṇāptā carajāsavah//

62. tatkārmukam udakkrāntau *dhanaśanī pṛthakṣthite/(c dhanahānī)
svāhorātracaturbhāge dinarātridale smṛte//

63. yāmyakrāntau viparyaste dviguṇe tu dinakṣape/
vikṣepayuktonitayā krāntyā bhānām api svake//

Computed by: dayAndNight

2.64-69 · computed

asterisms, yogas, lunar days, karanas, with time elapsed and to come

64. bhabhogo +aṣṭaśatīliptāh khāśviśailās tathā titheh/
grahaliptābhabhogāptā bhāni bhuktyā dinādikam//

65. ravīnduyogaliptābhyo yogā bhabhogabhājitāh/
gatā gamyāś ca ṣaṣṭighnyo bhuktiyogāptanāḍikāh//

66. arkonacandraliptābhyas tithayo bhogabhājitāh/
gatā gamyāś ca ṣaṣṭighnyo nāḍyo bhuktyantaroddhṛtāh//

67. dhruvāṇi śakunir nāgaṃ tṛtīyaṃ tu catuṣpadam/
kiṃstughnaṃ tu caturdaśyāh kṛṣṇāyāś cāparārdhatah//

68. bavādīni tatah sapta carākhyakaraṇāni ca/
māse +aṣṭakṛtva ekaikaṃ karaṇānāṃ pravartate//

69. tithyardhabhogaṃ sarveṣāṃ karaṇānāṃ prakalpayet/
eṣā sphutagatih proktā sūryādīnāṃ khacāriṇām//

Computed by: pancangakaranaName