portance in the history of Indian mathematics and astronomy. The second section, which deals with mathematics (the Ganitapāda), has been translated by Rodet in the Journal asiatique (1879), I, 393-434, and by Kaye in the Journal of the Asiatic Society of Bengal, 1908, pages 111-41. Of the rest of the work no translation has appeared, and only a few of the stanzas have been discussed. The aim of this work is to give a complete translation of the Āryabhātīya with references to some of the most important parallel passages which may be of assistance for further study. The edition of Kern makes no pretense of giving a really critical text of the Āryabhātīya. It gives merely the text which the sixteenth-century commentator Parameśvara had before him. There are several uncertainties about this text. Especially noteworthy is the considerable gap after IV, 44, which is discussed by Kern (pp. v-vi). The names of other commentators have been noticed by Bibhutibhusan Datta in the Bulletin of the Calcutta Mathematical Society, XVIII (1927), 12. All available manuscripts of the text should be consulted, all the other commentators should be studied, and a careful comparison of the Āryabhātīya with the abstracts from the old siddhāntas given by Varāhamihira, with the Sūryasiddhānta, with the Śisyadhīvrddhida of Lalla, and with the Brāhmasphutasiddhānta and the Khandakhādyaka of Brahmagupta should be made. All the later quotations from Āryabhata, especially those made by the commentators on Brahmagupta and Bhāskara, should be collected and verified. Some of those noted by Colebrooke do not seem to fit the published Ārya-
