Page:English translation of the Surya Siddhanta and the Siddhanta Siromani by Sastri, 1861.djvu/27

 the given arc which falls in the quadrant where it terminates, but the sine of the (of that arc) is the sine of that arc which it wants to complete the quadrant where the given arc ends; and the sine of the  (of the arc) which ends in an even quadrant (i. e. 2nd and 4th) is the sine of that arc which it wants to complete the quadrant where the given arc ends; but the sine of the  (of that arc) is the sine of that part of the given arc which falls in that quadrant where it terminates.

. (Reduce the given degrees &c., to minutes.) Divide the minutes by 225: and the sine (in 17—22) corresponding to the quotient is called the  (the past) sine, (and the next sine is called the  to be past sine): multiply (the remainder in the said division) by the difference between the  and sine and divide the product by 225,

. Add the quotient to the sine past: (the sum will be the sine required). This is the Rule for finding the right sines (of the given degrees &c.) In the same way, the versed sines (of the given degrees &c.) can be found.

. Subtract the (next less) sine (from the given sine); multiply the remainder by 225 and divide the product by the difference (between the next less and greater sines): add the quotient to the product of 225, and that number (which corresponds to the next less sine); the sum will be (the number of minutes contained in) the arc (required).

. There are fourteen degrees (of the concentric) in the periphery of the or first epicycle of the Sun, and thirty-two degrees (in the periphery of the 1st epicycle) of the Moon, when these epicycles are described at the end of an even quadrant (of the concentric or on the Line of the Apsides.) But when they are described at the end of an odd quadrant (of the concentric, or on the diameter of the concentric perpendicular to the Line of the Apsides) the degrees in both are