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

113 equal to δθ³ / R = (225 × 225) / 3438 = 14' — 43" — 30". Here Ranganātha made a mistake in taking this to be 3438 / 222 = 15' — 16" — 48" — Even δθ³ / R is approximate and a more correct value of the second difference would be 14' — 47" approximately. Ranganātha then argues that taking this second difference to be 15 for the H sine 3438 ‘what will it be for the H sine 225' ?’ The answer would be (15 × 225) / 3438 = (15 × 25) / 382 = 375 / 382 = 1' approximately. So, the second difference in the beginning of the table happens to be 1' ie 225 / 225. This led the author of the Surya siddhānta to use the words “तद्विभक्तलब्धोन”. This being an approximate formulation, naturally necessitated a second formulation where the approximation led to an error of 1' through the verse “एकविंशाच्च विंशाच्च etc.” This second formulation intended to make a correction, was done in the wake of a correct calculation through the formulae I & II which were known even prior to Bhaskara. Verses 10, 11. To find the H sine of an intermediate angle. Suppose it is required to find the H sine of an angle θ° ie θ × 60'. Divide this by 225; the quotient gives the previous H sine. Then (R × D) / 225 where R is the remainder, and D the difference between the previous and next H sines, added to the previous H sine gives the H sine required. Comm. The formula is evidently based on an applica- tion of rule of three. Verse 11. To find the angle when the H sine is given Suppose the H sine of an angle is given to be x'. Subtract the greatest H sine that could be subtracted from this. 15