पृष्ठम्:महाभास्करीयम्.djvu/२०४

119 which is Bhaskara II's approximation for the true distance of the Sun or Moon.¹ TRUB DAILY MOTION OF THE SUN OR MOON It may be pointed out here that the method of successive approxi- mations, which has been used for finding the true distance of the Sun or Moon in the stanzas under consideration, was used by Lalla for determi- ning the radii of the true epicycles of the Sun and Moon.² A rule for finding the true daily motion (called karnabhukti) of the Sun or Moon: 13. Always multiply the (mean) daily motion of the Sun or Moon by the radius and (then) divide (the product) by the hypotenuse (i.e., the true distance) determined by the method of successive approximations; the result is the true daily motion (of the Sun or Moon). That is Sun's true daily motion Sun's mean daily motion xR Sun's true distance in minutes Moon's mean daily motion X R Moon's true distance in minutes' and Moon's true daily motion= where R is the standard radius (-3438').³ ¹ See Si Si, I, v. 4. 2 See Ś¡DVṛ, I, ii. 44. 3 The object here is to obtain the angular velocity expressed in minutes, which will correspond also to the linear velocity in a circle of radius R. Parameśvara in his comm. on LBh, ii. 8 writes that, in place of the true distance in the above formulae, certain astronomers make use of the expression (kotiphala )² R RF kotiphala F (1) where - or + sign is taken according as the planet is in the half-orbit beginning with the anomalistic sign Cancer or in that beginning with the anomalistic sign Capricorn. t may be pointed out that the expression (1) is an approximate ue of H,, the second approximation to the pe distance.