Page:Aryabhatiya of Aryabhata, English translation.djvu/80

50 ksiptam. In the first method it is necessary to supply much to fill out the meaning, but the translation of these words themselves is a more natural one. In the second method it is not necessary to supply anything except "quotient" with matigunam (in the first method it is necessary to supply "remainder"). 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 Sanskrit 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.