nology and expression between the fuller text of Brahmagupta, XVIII, 3-5 and the more enigmatical text of Āryabhaṭīya, II, 32-33, in their statements of the famous Indian method (kuttaka) of solving indeterminate equations of the first degree. It seems probable to me that Brahmagupta had before him these two stanzas in their present form. It must be left to the mathematicians to decide which of the two rules is earlier.
The only serious internal discrepancy which I have been able to discover in the Āryabhaṭīya is the following. Indian astronomy, in general, maintains that the Earth is stationary and that the heavenly bodies revolve about it, but there is evidence in the Āryabhaṭīya itself and in the accounts of Āryabhaṭa given by later writers to prove that Āryabhaṭa maintained that the Earth, which is situated in the center of space, revolves on its axis, and that the asterisms are stationary. Later writers attack him bitterly on this point. Even most of his own followers, notably Lalla, refused to follow him in this matter and reverted to the common Indian tradition. Stanza IV, 9, in spite of Parameśvara, must be interpreted as maintaining that the asterisms are stationary and that the Earth revolves. And yet the very next stanza (IV, 10) seems to describe a stationary Earth around which the asterisms revolve. Quotations by Bhaṭṭotpala, the Vāsanāvārttika, and the Marīci indicate that this stanza was known in its present form from the eleventh century on. Is it capable of some different interpretation? Is it intended merely as a statement of the
