Mathematics in Ancient and Medieval India c8.s1: Spherical Trigonometry
Mathematics in Ancient and Medieval India c8.s1
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Spherical Trigonometry
c8.s1.1
No problem of spherical trigonometry has been directly discussed by the ancient Indian astronomers. Nevertheless, we find in the *Sūryasiddhānta* and *Āryabhaṭīya* of Āryabhaṭa I certain expressions in connection with the solution of astronomical problems. The values of those expressions could not be deduced without the knowledge of spherical trigonometry.² This is demonstrated by the following formulae relating to sines and cosines of angles of a spherical triangle involving those expressions :
c8.s1.2
² Kaye, G. R. ‘Hindu Spherical Astronomy’, *Journal of the Asiatic Society of Bengal*, 15, new series, p. 153–55, 1919; vide also ‘Spherical Astronomy of Āryabhaṭa I’ by P. C. Sengupta. *The Cultural Heritage of India*, Ramkrishna Centenary Committee, 3, p. 369–73, Calcutta; Shukla, K. S. ‘Early Hindu Methods in Sperical Astronomy’, *Gaṇita*, 19, No. 2, p. 49–72, 1968.
c8.s1.3
i ) cos c=cos a cos b+sin a sin b cos C
ii ) sin A sin c=sin a sin C
and iii ) cos A sin c=cos a cos b-sin a cos b cos C
c8.s1.4
where A, B, C are the angles of a spherical triangle and a, b, c are the corresponding opposite sides. The Indian astronomers employed the sine function principally, and the versed sine occasionally. Sometimes they have used the sine of the complementary angle rather than the cosine function.
Linked texts (2)
- Sūryasiddhānta — Maya, Sanskrit
- Āryabhaṭīya — Āryabhaṭa, Sanskrit