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Fractional Parts of Āryabhaṭa’s Sines and Certain Rules Found in Govindasvāmin’s Bhāṣya on the Mahābhāskarīya

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Abstract

The commentary of Govindasvāmin (circa \( {\textsc{ad}} \) 800-850) on the Mahābhāskarīya contains the sexagesimal fractional parts of the 24 tabular Sine-differences given by Āryabhaṭa I (born \( {\textsc{ad}} \) 476). These lead to a more accurate table of Sines for the interval of 225 min. Thus the last tabular Sine becomes.

Indian Journal of History of Science, Vol. 6, No. 1 (1971), pp. 51–59.

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Notes

  1. 1.

    It is now evident that the reading in the commentary by Parameśvara has also been skaki originally and not svaki as appears in the printed edition.

Abbreviations

a;b,c:

The usual notation for writing a number with whole part ‘a’ (say, in minutes) separated from its sexagesimal fractional parts (of various orders, ‘\( b \)’ (in second), ‘\( c \)’ (in thirds),…, by a semicolon.

\( D_{1} ,D_{2} \ldots \) :

Tabular Sine-differences such that \( D_{n} = R\,{ \sin }\,nh - R\,{ \sin }(n - 1)h;n = 1,2, \ldots \)

h :

Uniform tabular interval

L(h):

Last tabular Sine-difference when the tabular interval is \( h, \) so that \( L(h) = R - R\,{ \cos }\,h \).

m,n,p:

Positive integers.

R :

Radius, Sinus Totus, norm.

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Correspondence to K. Ramasubramanian .

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Ramasubramanian, K. (2019). Fractional Parts of Āryabhaṭa’s Sines and Certain Rules Found in Govindasvāmin’s Bhāṣya on the Mahābhāskarīya. In: Ramasubramanian, K. (eds) Gaṇitānanda. Springer, Singapore. https://doi.org/10.1007/978-981-13-1229-8_33

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