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Extra info for The Aryabhatiya of Aryabhata: An Ancient Indian Work on Mathematics and Astronomy
Sample text
9. The area of any plane figure is found by determining two sides and then multiplying them together. The chord of the sixth part of the circumference is equal to rhe nidiiLs, •See ibid, and Bibl. , IX, 19G, for discussion of the inacn n ’ e value given in the second part of the rule. W ill (1927), 10. 20, 000. skara, Goladhydya, Bhuvanakosa (stanza 52), Vasandbhdsya, refers to this rule of Aryabhata. 11. One should divide a quarter of the circumference of ;i circle (into as many equal parts as are desired).
Then in accordance with the rule 34X 29 = 9SG and 956+15 = 1001 This number 1001 is the smallest number which will satisfy both equations. Strictly speaking, the rule applies only to the third process given above. The solution of the single inde terminate equation is taken for granted and is not given in full. There is nothing to indicate how far the reciprocal division was to be carried. Must it be carried to the point where the last remainder is 1? Must the number of quotients taken to make the chain be even in number?
But if the intention was that of stating that the product of the quotient and an assumed number, and the difference between the remainders, are to be added below the quotients to form a chain the thought is expressed in a very curious way. Ganguly finds justification for this interpretation (p. 172) in his formulas, but I cannot help feeling that the San skrit is stretched in order to make it fit the formula. The general method of solution by reciprocal division and formation of a chain is clear, but some of the details are uncertain and we do not know to what sort of problems Aryabhata applied it.
