107 for finding the Rsines (i.e., Rsines and Rversed-sines) is being told in detail (below). FINDING THE RSINE OF AN ARC For example, if the Sun's mean anomaly is 140°, calculate the Rsine of 90° and the Rversed-sine of 50%; if the Sun's mean anomaly is 240⁰, calculate the Rsine of 90°, the Rversed-sine of 90°, and the Rsine of 600; and if the Sun's mean anomaly be 300°, calculate the Rsine of 90⁰, the Rversed-sine of 90°, again the Rsine of 90°, and the Rversed- sine of 30⁰. The above passage shows that in the time of Bhaskara I one of the methods used for finding the Rsine of an arc (>90°) was to apply the following formulae; Rsin (90°+0) = Rsin 90°- Rversin 0. Rsin (180⁰+0) = Rsin 90 Rversin 90°- Rsin 0 =Rsin 0. Rsin (270⁰ +0): = Rsin 90 Rversin 90°- Rsin 90⁰ + Rversin ( Rsin 90⁰ - Rversin 0, - where <90⁰. A rule for finding the Rsine (or Rversed-sine) of an arc (<90⁰): 3-4 (1). Reduce the arc to minutes and then divide by 225: the quotient denotes the number of (tabulated) Rsine- differences (or Rversed-sine-differences) to be taken com- pletely. Then multiply the remainder by the next (or current) Rsine-difference (or Rversed-sine-difference) and divide (the product) by 225. Add the quotient (thus obtained) to the sum of the (tabulated) Rsine-differences (or Rversed-sine-differences) obtained before. The sum thus obtained is the Rsine (or Rversed-sine) of the given arc.¹ This rule gives a method for calculating the Rsine or Rversed-sine of an arc by the help of the following table of Rsine-differences given by Aryabhata I in his Aryabhatiya². ¹ This rule occurs also in SuSi, ii. 31-32; BrSpSi, ii. 10; LBh, ii. 2 (ii)-3(i); ŠiDVṛ, I, ii. 12; Sise, iii. 15; Siśi, I, ii. 10(ii)-11. 2 i. 12. This table has been referred to in MBh, vii. 13,
