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 reduced to a more concise and practical form by Āryabhaṭa, born, as he tells us himself, at Pāṭaliputra in 476 A.D. He maintained the rotation of the earth round its axis (a doctrine not unknown to the Greeks), and explained the cause of eclipses of the sun and moon. Mathematics are treated in the third section of his work, the Āryabhaṭiya (ed. with comm. by Kern, Leyden, 1874; math. section trans. by Rodet, Journal Asiatique, 1879). Varāha Mihira, born near Ujjain, began his calculations about 505 A.D., and, according to one of his commentators, died in 587 A.D. He composed four works, written for the most part in the Aryā metre; three are astrological: the Bṛihat-saṃhitā (ed. Kern, Bibl. Ind., 1864, 1865, trans, in Journ. As. Soc., vol. iv.; new ed. with comm. of Bhaṭṭotpala by S. Dvivedī, Benares, 1895-97), the Bṛihaj-jātaka (or Horā-çāstra, trans. by C. Jyer, Madras, 1885), and the Laghu-jātaka (partly trans. by Weber, Ind. Stud., vol. ii., and by Jacobi, 1872). His Pancha-siddhāntikā (ed. and for the most part trans. by Thibaut and S. Dvivedī, Benares, 1889), based on five siddhāntas, is a karaṇa or practical astronomical treatise. Another distinguished astronomer was Brahmagupta, who, born in 598 A.D., wrote, besides a karaṇa, his Brāhma Sphuṭa-siddhānta when thirty years old (chaps. xii. and xviii. are mathematical). The last eminent Indian astronomer was Bhāskarāchārya, born in 1114 A.D. His Siddhānta-çiromaṇi has enjoyed more authority in India than any other astronomical work except the Sūrya-siddhānta.

Indian medical science must have begun to develop before the beginning of our era, for one of its chief authorities, Charaka, was, according to the Chinese