पृष्ठम्:महाभास्करीयम्.djvu/२२२

TRUB LONGITUDE OF MARS, BETC., BY EPICYCLIC THEORY 137 (Then calculate the sighrakendraphala). Multiply the ra- dius by the sighrakendraphala and divide (the product) by the (planet's) sighrakarna; then reduce that to arc. Apply half of that are to the longitude obtained above, reversely (i.e., add when the sighrakendra is in the half orbit beginning with the sign Aries and subtract when the sighrakendra is in the half orbit beginning with Libra). Therefrom calculate (the arc corresponding to) the manda- (kendra)phala and apply the whole of that to the mean longitude of the planet. Thus are obtained the true-mean longitudes of Mars, Saturn, and Jupiter. The true-mean longitude corrected for the are derived from the sighrakendraphala (literally, the arc corresponding to the result derived from the longitude of the sighrocca minus the true- mean longitude of the planet) is to be known as the true longi- tude. The method (to be used) for the remaining planets (i.e., Mercury and Venus) is now being told. The longitude of the (planet's) mandocca (i.e., apogee) reversely increased or decreased by half the arc derived from the sighrakendraphala determines the true-mean longitude (of the planet). And that (true-mean longitude) corrected for the arc derived from the sighra(kendraphala) is known as the true longitude. ¹ 'The arc derived from the sighrakendraphala' is obtained by first multiplying the radius by the sighrakendraphala and dividing by the sighrakarna and then reducing that to arc. See stanza 41. The rule given in stanzas 40-43 is found also in A, iii. 23; LBh, ii. 32- 35; ŚiDV, I, ii. 30-34; TS, ii. 55-65, 66(1). 2 What is meant here may be explained as follows: Subtract the mean longitude of the planet from the longitude of the planet's sighrocca. Multiply the Rsine of that by the planet's corrected sighra epicycle and divide by 80: the result is the planet's sighrakendraphala. Multiply that by the radius and divide by the planet's sighrakarna, and reduce the resul- ting Rsine to the corresponding arc. Add half of it to or subtract that from the longitude of the planet's mandocca according as the sighrakendra of the planet is in the half orbit beginning with the sign Libra or Aries. Treat this