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Bharatiya Jyotihshastra (History of Indian Astronomy), translated by R. V. Vaidya v2.c12.s7: (3) The Adhikāra on Three Problems

Bhāratīya Jyotiḥśāstra (History of Indian Astronomy), translated by R. V. Vaidya v2.c12.s7

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(3) The Adhikāra on Three Problems

v2.c12.s7.1

The Adhikāra on three problems is so called in our astronomical works because it deals with the questions of direction, region and time. The method of determining directions is given in it in different ways. It is explained how to find the ascendant for a given moment or conversely the unknown moment from the given ascendant. The calculation by other methods is also possible, e.g. four shadows, etc. The question of ‘deśāntara’ (longitude) from Ujjain is usually dealt with in the chapter on mean motions and therefore omitted in this chapter. It, however, contains methods for finding the distance of a place from the equator, that is, latitude. The question of shadow is dealt with at considerable length. For calculation, a gnomon 12 ‘aṅgulas’ long, is taken as the unit while determining the length of the shadow. What will be the length of the shadow cast by a gnomon at a given moment and in what direction it would fall, and what would be the length and direction of the shadow cast by the Sun (or a planet) posited on any side of the gnomon, and such other questions are included under “determination of shadow”. The authors preceding *Bhāskarācārya* have given only the method of calculating the shadow cast by the gnomon in an East-West, North-South, and the (four) intermediate directions. *Bhāskarācārya* alone has described the method of finding the shadow cast by the gnomon when the sun stands in any direction with regard to it. And on this point he proudly remarks :

v2.c12.s7.2

Sanskrit

v2.c12.s7.3

याम्योदक्समकोणभाः किल कृताः पूर्वैः पृथक्साधने- र्दिग्भागेष्विव रातरांतरगता याः प्रच्छके च्छावशात् ।। ता एकानयने न चानयति यो मन्ये तमन्यं भुवि ज्योतिर्विद्वदनार्णवदभिमकुलप्रौल्लासने भास्करं ।। ४४ ।। सिद्धांतशिरोमणि, त्रिप्रश्नाधिकार.

v2.c12.s7.4

∗ Kulkarni has compiled works entitled Karaṇa Śiromaṇi and Graha Jyotsnā. I have not seen them and hence more information about them cannot be given. These works are not printed. I understand that Keropant Nana had a high opinion about these works. Kulkarni was born in Malvan in Saka 1767 and died in Saka 1815. He was in service in the Education Department in Ratnagiri District from 1865 to 1875 AD.. and, later on in the Revenue Department till the end. He had also written a book showing the positions of stars which was printed in 1886 A.D.

v2.c12.s7.5

Time is determined from (the length and direction of) shadow cast by the gnomon. The shadow is, however, mainly useful in setting up the ‘Nalikā’ sighting tube before observation. Following is the main method of setting up the ‘Nalikā’ for observation :—To determine, beforehand, by calculation from the astronomical works the length and direction of the shadow likely to be cast by the gnomon when set up in the light of the sun or any planet at a particular moment and then to set the sighting tube in that position for observing the planet. If the planet be observed in that position, then the position calculated from the book would be considered correct.

v2.c12.s7.6

Palabhā is the name given to the length of the shadow cast by the twelve-angula gnomon at any place on the equinoctial day. Palabhā forms the base, gnomon the perpendicular and the line joining the extremities of the gnomon and the shadow, the ‘akṣa-karṇa’ (hypotenuse). The area bounded by this right angled triangle is termed ‘akṣa-kṣetra’. This region of ‘akṣa-kṣetra’ has much importance in our astronomy. At many places, the measures of different items are calculated by drawing another figure similar to this ‘akṣa-kṣetra’; and the Adhikāra on three problems devotes much space to problems associated with such figures.

v2.c12.s7.7

A list of latitudes and longitudes of some cities given in the Siddhānta-Tatva-Viveka has been given (page 163)

v2.c12.s7.8

Malayendu Suri, a commentator of the Yantrarāja, has given latitudes of 75 cities. The work has been printed and the latitudes are of some cities that have been engraved on the instrument devised by Sakharam* Joshi, referred to before (in the footnote on page 233) :—

v2.c12.s7.9

| City | O | ' | City | O | ' | City | O |
| Srirangapattan | 15 | 27 | Janasthan (Nasik) | 20 | 12 | Mathura | 26 | 36 |
| Bijapur | 16 | 42 | Bradhnapur (Burhanpur) | 21 | 0 | Madava | 27 | 0 |
| Karavir | 17 | 21 | Ujjain | 22 | 37 | Indra-Prastha | 28 | 40 |
| Saptarsi (Satara) | 17 | 42 | Ahmedabad | 23 | 0 | Kuruksetra | 30 | 0 |
| Nandigram | 18 | 26 | Varanasi | 25 | 36 | Kashmir | 35 | 0 |

v2.c12.s7.10

Lists like the above are now of no use, since the British Government has determined very accurate latitudes and longitudes of thousands of places in this country. It will, however, be seen that our people had made efforts in that direction and one can also judge how accurate it was.

v2.c12.s7.11

∗ There is a commentary on the Pratod Yantra by Sakharam, wherein latitude 17° 41' 50" has been taken for working out examples. And Sakharam Joshi of Kodoli has also given 17° 41' 50" as the latitude of Satara. A copy of the commentary was obtained at Ashta in the Satara District. This indicates that the commentary definitely belongs to him.

Cites (4)