Abstract
The well-known property that the second order differences of sines are proportional to the sines themselves was known even to Āryabhaṭa I (born ad 476) whose Āryabhaṭīya is the earliest extant historical work (of the dated type) containing a sine table.
Indian Journal of History Science, Vol. 7, No. 2 (1972), pp. 81–86.
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Notes
- 1.
The Sanskrit text (
), as quoted in the NAB, states the Lemmas as two Rules of Three. See Gupta R.C., Some Important Indian Mathematical Methods as conceived in Sanskrit Language, paper presented at the International Sanskrit Conference, New Delhi, March 1972, p. 3. For a nice statement of the Lemmas, see Gupta R. C., Second-Order Interpolation in Indian Mathematics etc., I.J.H.S., Vol.4 (1969), p. 95, verses 7–8.
), as quoted in the NAB, states the Lemmas as two Rules of Three. See Gupta R.C., Some Important Indian Mathematical Methods as conceived in Sanskrit Language, paper presented at the International Sanskrit Conference, New Delhi, March 1972, p. 3. For a nice statement of the Lemmas, see Gupta R. C., Second-Order Interpolation in Indian Mathematics etc., I.J.H.S., Vol.4 (1969), p. 95, verses 7–8.Author information
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Ramasubramanian, K. (2019). Early Indians on Second-Order Sine-Differences. In: Ramasubramanian, K. (eds) Gaṇitānanda. Springer, Singapore. https://doi.org/10.1007/978-981-13-1229-8_34
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