सिद्धान्तशिरोमणि: गणिताध्याय (भास्कराचार्य - ग्रहगणित, मध्यमाधिकार व स्पष्टाधिकार सटीक)

104 Verse 1. In as much as true positions of the planets alone are required to decide auspicious moment; for journeys, marriages, celebrations pertaining to temples, astrology and the like, we shall now give the methods of rectifying the mean positions of the planets so as to accord with their observed positions. Comm. Clear. Verse 2-9. Obtaining the sines of the angles and tabulation of the sines. The planet deflected to the true position from the mean lies at the end of a half-chord (which is the Hindu sine of an angle) so that many processes pertaining to a planet are carried through Sines of angles; hence the word half-chord alone is connoted in this work wherever the word Jyā meaning a chord is used. The lengths of these half-chords (or the Hindu Sines) for angles increasing from 0° to 90° at intervals of 3¾° are as follows—225', 449', 671, 890, 1105, 1315, 1520, 1719, 1910, 2093, 2267, 2431, 2585, 2728, 2859, 2977, 3084, 3177, 3256, 3321, 3372, 3409, 3431, 3438. The ut-kramajyāis or the Hindu versed-sines are respectively 7, 29, 66, 117, 182, 261, 354, 461, 579, 710, 853, 1007, 1171, 1345, 1528, 1719, 1918, 2123, 2333, 2548, 2767, 2989, 3213, 3438. The word Tribhajyā or Trijyā is half-diameter. The word jyā khandas used by pandits connote the differences between successive sines. Comm. There is a difference between modern trigono- metrical sines and the Hindu sines as detailed below (Ref.