AN APPROXIMATE FORMULA FOR RSIN 207 The Rsine-differences (corresponding to the twenty-four elements of a quadrant) are 225 (makhi), etc. (as stated by Āryabhata I).² The dimensions of the epicycles have been stated after dividing them by 4. They are the same as given by Aryabhata I. In fact all the astro- nomical constants stated in the above stanzas are the same as found in the Āryabhatiya. It must be pointed out that, according to Bhāskara I, the manda and sighra epicycles stated above from the Aryabhațiya of Aryabhaṭa I, correspond to the beginnings of the respective quadrants as is evident from the rule stated in MBh, iv. 38-39(i) and LBh, ii. 31-32 and explained in Bhaskara I's commentary on A, iii. 22. Govinda Svāmi, however, is of opinion that the sighra epicycles stated by Aryabhata I correspond to the beginnings of the respective quadrants, but the manda epicycles stated by Aryabhata I, correspond to the endings of the respective quadrants.³ Consequently, he has replaced the rule referred to above by another rule which has been quoted by Udaya-divākara in his commentary on LBh, ii. 31-32. This controversy is due to the fact that Aryabhata I himself does not say whether the epicycles given by him correspond to the begin- nings or endings of the quadrants. A rule for finding the bahuphala and kotiphala, etc., without the use of the Rsine-difference table: 17-19. (Now) I briefly state the rule (for finding the bhujaphala and kotiphala etc.) without making use of the Rsine-differences, 225, etc. Subtract the degrees of the bhuja (or koti) from the deg- rees of half a circle (i.e., 180°). Then multiply the remainder by the degrees of the bhuja (or koti) and put down the result at two places. At one place subtract the result from 40500. By one-fourth of the remainder (thus obtained) divide the result 2 For the table of Rsine-differences referred to here, see supra, p. 108. 8 See Govinda Svāmi's comm, on MBh, iv. 38-39(i).
