Mathematics in Ancient and Medieval India c8.s3.63

c8.s3.63

The *Yuktibhāṣā* has given the complete rational of the eqns (1) and (2). Its author Jyeṣṭhadeva (c. 1500-1600) in an effort to find an expression for the difference between any arc and its sine chord, divided the circumference of the quarter of a circle into n equal divisions and considered the first and second sine differences. He then found the sum of the first n sine differences and cosine differences by considering all sine chords to be equal to corresponding arc and the small unit of the circumference to be equal to one unit, which evidently gives jīvā=s-(s³)/(3!r²) and śara=(s²r)/(2!r²).