Brahmagupta refers to Āryabhaṭa some sixty times. Most of these passages contain very general criticism of Āryabhaṭa as departing from smṛti or being ignorant of astronomy, but for some 30 stanzas it can be shown that the identical stanzas or stanzas of identical content were known to Brahmagupta and ascribed to Āryabhaṭa. In XI, 8 Brahmagupta names the Aryāṣṭaśata as the work of Āryabhaṭa, and XI, 43, jānāty ekam api yato nāryabhaṭo gaṇitakālagolānām, seems to refer to the three sections of our Aryāṣṭaśata. These three sections contain exactly 108 stanzas. No stanza from the section on mathematics has been quoted or criticized by Brahmagupta, but it is hazardous to deduce from that, as Kaye does,[1] that this section on mathematics is spurious and is a much later addition.[2] To satisfy the conditions demanded by Brahmagupta's name Aryāṣṭaśata there must have been in the work of Āryabhaṭa known to him exactly 33 other stanzas forming a more primitive and less developed mathematics, or these 33 other stanzas must have been astronomical in character, either forming a separate chapter or scattered through the present third and fourth sections. This seems to be most unlikely. I doubt the validity of Kaye's contention that the Gaṇitapāda was later than Brahmagupta. His suggestion that it is by the later Āryabhaṭa who was the author of the Mahāsiddhānta (published in the "Benares Sanskrit
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PREFACE
