Mathematics in Ancient and Medieval India c8.219

c8.219

Ptolemy ( c. 150 A. D. ) first gave a table of chords within a circle of diameter 60 unit and expressed it in sexagesimal unit. The arc ranges from ½ degrees to 180 degrees at intervals of ½ degrees. With the help of this table, when the length of the arc is known, the corresponding length of the chord can be calculated and vice versa¹. The chord lengths were given by Ptolemy in terms of its diameter where as in India they were given in terms of its radius. Depending on the similarity of the Greek and Hindu methods, M. Biot² opined that this Indian table of *Jyā* was probably obtained from the chords of Ptolemy. Burgess expressed the view "it is rather difficult to calculate the sines given in the *Sūryasiddhānta* from Ptolemy's table of chords. Further Hindu sines differ considerably from that of Ptolemy in few instances"³. Burgess is quite justified in his observation the two methods are more or less identical. More light on the subject is likely to clarify further the question under issue. Needham⁴ is of the opinion that the Indian work was taken over by the Arabs and by them transmitted to Europe. Since Indian system of place value notation and many elements of the Indian mathematical works were adopted by the Arabs, it is quite plausible that the first impulse of preparing a sine table came to the Arabs from India. Ibn Jābir ibn Sinān al Battāni (c. 858–927 A. D.) used sines and introduced concepts from which the tangent and cotangent can be derived⁵.