Page:English translation of the Surya Siddhanta and the Siddhanta Siromani by Sastri, 1861.djvu/280

 268 Appendix. enoe of them will be preceding sine (i. e., the sine of arc 8®^ degrees less than original arc). 20. But the first sine (or the sine of 3oi) is here equal to 224f (and not to 225 as it is usually stated to be). By this rule 24 sines may be successively found.* 21 and 22. If the sines of any two arcs of a quadrant be ■ Bole, for flndioi the eine. “nltdpKed by their cosines reciprooaUy of sum and difference of any (that is the sine of the first arc by the cosine of the 2d and the sine of the 2d by the cosine of the first aro) and the two produots divided by radius, then the quotients will, when added to¬ gether, be the sine of the sum of the two arcs, and the differ¬ ence of these quotients will be the sine of their difference.f This excellent rule called jTA-BHlvANi has been presOTibed for ascertaining the other sines. 23. This rule is of two sorts, the first of whioh is called SAMlsA-BHivANi (i. e., the rule for finding the sine of sum of two arcs) and the second antaea-bhIvanX (i. e., the rule to find the sine of difference of arcs). [If it be desired to reduce the sines to the value of any other radius than that above given of 3438.] Find the first sine by the aid of the above-mentioned rule peatibhIgajyakI- VIBHI. 24 and 25. And then reduce it to the value of any new radius by applying the proportion. After that apply the jyI- bhIvanI rule through the aid of the first sine and the cosine thns found, for as many sines as are required. The sines will thus be successively eliminated to the value of any new radius. The rule given in my Pat£ or LfLlvATf is not* sufficiently accurate (for nice calculations) I have not therefore repeated here that rough rule. • [These roles given in the verses from 16 to 20 are easily deduced from the roles given in the verses 21 and 22.—B. D.] , t BhaskabIohAbta lias given these rules in his work without any demon* stration.—B. D.] Digitized by Google