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.