Chapter 3: Direction, place and time

3.1 · descriptive (nothing to compute)

a level surface and a circle for the dial

1. śilātale +ambusaṃśuddhe vajralepe +api vā same/
tatra śaṅkvaṅgulair iṣṭaih samaṃ maṇḍalam ālikhet//

3.2-4 · computed

the north-south line bisecting equal forenoon and afternoon shadows; the other directions

2. tanmadhye sthāpayec chaṅkuṃ kalpanādvādaśāṅgulam/
tacchāyāgraṃ spṛśed yatra vṛtte pūrvāparārdhayoh//

3. tatra bindū vidhāyobhau vṛtte pūrvāparābhidhau/
tanmadhye timinā rekhā kartavyā dakṣiṇottarā//

4. yāmyottaradiśor madhye timinā pūrvapaścimā/
diṅmadhyamatsyaih saṃsādhyā vidiśas tadvad eva hi//

Computed by: meridianFromEqualShadows

3.5-7 · descriptive (nothing to compute)

the dial's square, the names of its lines, the line of the equinoctial shadow (the quantities measured on them are computed in III.22-28)

5. caturasraṃ bahih kuryāt sūtrair madhyād vinirgataih/
bhujasūtrāṅgulais tatra dattair iṣṭaprabhā smṛtā//

6. prākpaścimāśritā rekhā procyate samamaṇḍale/
unaṇḍale ca viṣuvanmaṇḍale parikīrtyate//

7. rekhā prācyaparā sādhyā viṣuvadbhāgragā tathā/
iṣṭacchāyāviṣuvator madhyam agrābhidhīyate//

3.8 · computed

hypotenuse from gnomon and shadow, and the converse

8. śaṅkucchāyākṛtiyuter mūlaṃ karṇo +asya vargatah/
projjhya śaṅkukṛtiṃ mūlaṃ chāyā śaṅkur viparyayāt//

Computed by: shadowTriangle

3.9-10 · computed

precession by libration

9. triṃśatkṛtyo yuge bhānāṃ cakraṃ prāk parilambate/
tadguṇād bhūdinair bhaktād dyugaṇād yad avāpyate//

10. taddos trighnā daśāptāṃśā vijñeyā ayanābhidhāh/
tatsaṃskṛtād grahāt krānticchāyācaradalādikam//

Computed by: ayanamsa

3.11-12 · computed

the motion of the equinox found from the shadow

11. sphuṭaṃ dṛktulyatāṃ gacched ayane viṣuvadvaye/
prāk cakraṃ calitaṃ hīne chāyārkāt karaṇāgate//

12. antarāṃśair athāvṛtya paścāc cheṣais tathādhike/
evaṃ viṣuvatī chāyā svadeśe yā dinārdhajā//

Computed by: precessionFromShadow

3.13-14 · computed

sines of latitude and co-latitude from the equinoctial shadow

13. dakṣiṇottararekhāyāṃ sā tatra viṣuvatprabhā//
śaṅkucchāyāhate trijye viṣuvatkarṇabhājite/

14. lambākṣajye tayoś cāpe lambākṣau dakṣiṇau sadā/
madhyacchāyā bhujas tena guṇitā tribhamaurvikā//

Computed by: latitudeFromEquinoctialShadow

3.15-17 · computed

latitude from the mid-day shadow and declination; the equinoctial shadow from the latitude

15. svakarṇāptā dhanurliptā natās tā dakṣiṇe bhuje/
uttarāś cottare yāmyās tāh sūryakrāntiliptikāh//

16. digbhede miśritāh sāmye viśliṣṭāś cākṣaliptikāh/
tābhyo +akṣajyā ca tadvargaṃ projjhya trijyākṛteh padam//

17. lambajyārkaguṇākṣajyā viṣuvadbhātha lambayā/
svākṣārkanatabhāgānāṃ dikṣāmye +antaram anyathā//

Computed by: latitudeFromNoonShadowequinoctialShadowdeclinationFromNoonShadow

3.18-19 · computed

the Sun's longitude from its declination, by quadrants

18. digbhede +apakramah śeṣas tasya jyā trijyayā hatā/
paramāpakramajyāptā cāpaṃ meṣādigo ravih//

19. karkyādau projjhya cakrārdhāt tulādau bhārdhasaṃyutāt/
mṛgādau projjhya bhagaṇān madhyāhne +arkah sphuṭo bhavet//

Computed by: sunLongitudeFromDeclinationmeanSunFromDeclination

3.20 · computed

the mean Sun from the true; mid-day zenith-distance from latitude and declination

20. tanmāndam asakṛd vāmaṃ phalaṃ madhyo divākarah/
svākṣārkāpakramayutir dikṣāmye +antaram anyathā//

Computed by: meanSunFromTruenoonShadow

3.21-22 · computed

mid-day shadow and hypotenuse

21. śeṣaṃ natāṃśāh sūryasya tadbāhujyā ca koṭijyā/
śaṅkumānāṅgulābhyaste bhujatrijye yathākramam//

22. koṭijyayā vibhajyāpte chāyākarṇāv ahardale/
krāntijyā viṣuvatkarṇaguṇāptā śaṅkujīvayā//

Computed by: noonShadow

3.23-25 · computed

measure of amplitude; the base from it

23. arkāgrā sveṣṭakarṇaghnī madhyakarṇoddhṛtā svakā/
viṣuvadbhāyutārkāgrā yāmye syād uttaro bhujah//

24. viṣuvatyām viśodhyodaggole syād bāhur uttarah/
viparyayād bhujo yāmyo bhavet prācyaparāntare//

25. mādhyāhniko bhujo nityaṃ chāyā mādhyāhnikī smṛtā/
lambākṣajīve viṣuvacchāyādvādaśasaṅguṇe//

Computed by: amplitudeDigitsbaseFromAmplitude

3.26-27 · computed

hypotenuse on the prime vertical; the sine of amplitude

26. krāntijyāpte tu tau karṇau samamaṇḍalage ravau/
saumyākṣonā yadā kāntih syāt tadā dyudalaśravah//

27. viṣuvacchāyayābhyastah karṇo madhyāgrayoddhṛtah/
svakrāntijyā trijīvāghnī lambajyāptāgramaurvikā//

Computed by: primeVerticalHypotenusesineOfAmplitude

3.28 · computed

measure of amplitude in digits for any shadow

28. sveṣṭakarṇahatā bhaktā trijyayāgrāṅgulādikā/
trijyāvargārdhato +agrajyāvargonād dvādaśāhatāt//

Computed by: amplitudeDigits

3.29-33 · computed

shadow in the intermediate directions: surd and fruit

29. punar dvādaśanighnāc ca labhyate yat phalaṃ budhaih/
śaṅkuvargārdhasaṃyuktaviṣuvadvargabhājitāt//

30. tadeva karaṇī nāma tāṃ pṛthak sthāpayed budhah/
arkaghnī viṣuvacchāyāgrajyayā guṇitā tathā//

31. bhaktā phalākhyaṃ tadvargasaṃyuktakaraṇīpadam/
phalena hīnasaṃyuktaṃ dakṣiṇottaragolayoh//

32. yāmyayor vidiśoh śaṅkur evaṃ yāmyottare ravau/
paribhramati śaṅkos tu śaṅkur uttarayos tu sah//

33. tattrijyāvargaviśleṣān mūlaṃ dṛgjyābhidhīyate/
svaśaṅkunā vibhajyāpte dṛktrijye dvādaśāhate//

Computed by: cornerShadow

3.34-36 · computed

corner shadow and hypotenuse; altitude at any hour-angle

34. chāyākarṇau tu koṇeṣu yathāsvaṃ deśakālayoh/
trijyodakcarajāyuktā yāmyāyāṃ tadvivarjitā//

35. antyā natotkramajyonā svahorātrārdhasaṅguṇā/
trijyābhaktā bhavec chedo lambajyāghno +atha bhājitah//

36. tribhajyayā bhavec chaṅkus tadvargaṃ pariśodhayet/
trijyāvargāt padaṃ dṛgjyā chāyākarṇau tu pūrvavat//

Computed by: cornerShadowaltitudeAtHourAngle

3.37-39 · computed

hour-angle from a given shadow

37. abhīṣṭacchāyayābhyastā trijyā tatkarṇabhājitā/
dṛgjyā tadvargasaṃśuddhāt trijyāvargāc ca yat padam/

38. śaṅkuh sa tribhajīvāghnah svalambajyāvibhājitah/
chedah sa trijyayābhyastah svāhorātrārdhabhājitah//

39. unnatajyā tayā hīnā svāntyā śeṣasya kārmukam/
utkramajyābhir evaṃ syuh prākpaścārdhanatāsavah//

Computed by: hourAngleFromShadow

3.40-41 · computed

declination and longitude from a measure of amplitude; three shadow tips laid off

40. iṣṭāgrāghnī tu lambajyā svakarṇāṅgulabhājitā/
krāntijyā sā trijīvāghnī paramāpakramoddhṛtā//

41. taccāpaṃ bhādikaṃ kṣetraṃ padais tatra bhavo ravih/
iṣṭe +ahni madhye prākpaścād dhṛte bāhutrayāntare//

Computed by: sunFromAmplitudeshadowPathCircle

3.42-43 · computed

the path of the shadow; rising times at Lanka derived from the sines

42. matsyadvayāntarayutes trispṛkṣūtreṇa bhābhramah/
tribhadyukarṇārdhaguṇāh svāhorātrārdhabhājitāh//

43. kramād ekadvitribhajyās taccāpāni pṛthak pṛthak/
svādho +adhah pariśodhyātha meṣāl laṅkodayāsavah//

Computed by: shadowPathCirclerisingTimesAtLankaDerived

3.44-45 · computed

rising times; ascensional difference by signs

44. khāgāṣṭayo +arthago +agaikāh śaratryaṅkahimāṃśavah/
svadeśacarakhaṇḍonā bhavantīṣṭodayāsavah//

45. vyastā vyastair yutāh svaih svaih karkaṭādyās tatas trayah/
utkrameṇa ṣaḍevaite bhavantīṣṭās tulādayah//

Computed by: risingTimesCONSTANTS.RISING_AT_LANKA

3.46-48 · computed

the ascendant from the time since sunrise

46. gatabhogyāsavah kāryā bhāskarād iṣṭakālikāt/
svodayāsuhatā bhuktabhogyā bhaktāh khavahnibhih//

47. abhīṣṭaghaṭikāsubhyo bhogyāsūn praviśodhayet/
tadvat tadeṣyalagnāsūn evaṃ yātāt tathotkramāt//

48. śeṣaṃ cet triṃśatābhyastam aśuddhena vibhājitam/
bhāgair yuktaṃ ca hīnaṃ ca tallagnaṃ kṣitije tadā// (c bhāgahīnaṃ ca yuktaṃ ca)

Computed by: lagnaFromTimelongitudeAfterAscensionascendant

3.49 · computed

the point of the ecliptic on the meridian

49. prākpaścān natanāḍībhis tasmāl laṅkodayāsubhih/
bhānau kṣayadhane kṛtvā madhyalagnaṃ tadā bhavet//

Computed by: meridianPoint

3.50 · computed

the time between two points of the ecliptic

50. bhogyāsūn ūnakasyātha bhuktāsūn adhikasya ca/
sampīṇḍyāntaralagnāsūn evaṃ syāt kālasādhanam//

Computed by: timeBetween

3.51 · computed

whether the time is in the day or the night

51. sūryād ūne niśāśeṣe lagne +arkād adhike divā/
bhacakrārdhayutād bhānor adhikke +astamayāt param// [candragrahaṇa]

Computed by: partOfDay