पृष्ठम्:महाभास्करीयम्.djvu/२००

TRUE DISTANCE OF THE SUN OR MOON 115 A. D.) under the name of udayantara-saṁskāra.¹ It reappears in the works of Bhaskara II (1150 A. D.) and Nilakantha (1500 A. D.). Definitions of the bahu and koti (due to a planet's mean anomaly): 8. The portions (of the mean anomalistic quadrant) traversed and to be traversed (by a planet) are called bahu and koti or koti and bahu, according as the mean anomalistic quadrant (occupied by the planet) is odd or even. The bahuphala and kotiphala are obtained as before for the determination of the hypotenuse (i.e., the distance of the planet). A rule for the determination of the true distance in minutes of the Sun or Moon: 9-12. (When the Sun or Moon is) in the first or fourth (mean anomalistic) quadrant, add the kotiphala to the radius; (when) in the remaining (quadrants), subtract that from the radius: the resulting sum or difference is the upright. The square root of the sum of the squares of that and the bahuphala is called the hypotenuse. Multiply that hypotenuse (severally) by the bahuphala and kotiphala and divide (each product) by the radius: the results are (again) the bahuphala and kotiphala. From them obtain the hypotenuse (again) as before. Again multiply this hypotenuse (severally) by the initial bahuphala and kotiphala and divide (each product) by the radius. In this way, proceeding as above, obtain the hypotenuse again and again until two successive values of the hypotenuse agree (to minutes). (Thus is obtained the nearest approximation to the true distance in minutes of the Sun or Moon)." 1 Sise, xi. 1, 2 SiSi, 1, ii. 62-63. 3 TS, ii. 30. This definition is found also in SuSi, ii. 30; BrSpSi, ii. 12(ii); ŚiDVṛ, I, ii. 10-11; SiŚe, iii. 13(i); SiŚi, 1, ii. 19. 5 Cf. LBh, ii. 6-7.