Page:Aryabhatiya of Aryabhata, English translation.djvu/33

Rh Brockhaus, by Kern, by Barth, by Rodet, by Kaye, by Fleet, by Sarada Kanta Ganguly, and by Sukumar Ranjan Das. I have not had access to the Prthivir Itihasa of Durgadas Lahiri.

The words varga and avarga seem to refer to the Indian method of extracting the square root, which is described in detail by Rodet and by Avadhesh Narayan Singh. I cannot agree with Kaye's statement that the rules given by Aryabhata for the extraction of square and cube roots (II, 4-5) "are perfectly general (i.e., algebraical)" and apply to all arithmetical notations, nor with his criticism of the foregoing stanza: "Usually the texts give a verse explaining this notation, but this explanatory' verse is not Aryabhata's." Sufficient evidence has not been adduced by him to prove either assertion.

The varga or "square" places are the first, third, fifth, etc., counting from the right. The avarga or "non-square" places are the second, fourth, sixth, etc., counting from the right. The words varga and avarga seem to be used in this sense in II, 4. There is no good reason for refusing to take them in the same sense here. As applied to the Sanskrit alphabet the varga letters referred to here are those from k to m,