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Gaṇitānanda pp 333-343 | Cite as

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

  • K. RamasubramanianEmail author
Chapter

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.

Symbols

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.

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Cell for Indian Science and Technology in Sanskrit, Department of Humanities and Social SciencesIndian Institute of Technology BombayMumbaiIndia

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