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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- 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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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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