The maths of India

ARYABHATTA was author of the Arykshiasata (800 couplets) and Dasagi-tica (ten stanzas), known by the numerous quotations of BRAHMEGUPTA, BHAT'TATPALA, and others, who cite both under these respective titles. The laghu Arya-sidd''hanta, as a work of the same author, and, perhaps, one of those above-mentioned, is several times quoted by BHA'SCARA'S commentator MUNIS'WARA. He likewise treated of Algebra, &c. under the distinct heads of Cuttaca, a problem serving for the resolution of indeterminate ones, and Vija principle of computation, or analysis in general.

From the quotations of writers on astronomy, and particularly of BRAHMEGUPTA, who in many instances cites ARYABHAT'TA to controvert his positions, (and is in general contradicted in his censure by his own scholiast PBIT'HUDACA, either correcting his quotations, or vindicating the doctrine of the earlier author), it appears, that ARYABHAT'TA affirmed the diurnal revolution of the earth on its axis; and that he accounted for it by a wind or current of aerial fluid, the extent of which, according to the orbit assigned to it by him, corresponds to an elevation of little more than a hundred miles from the surface of the earth ; that he possessed the true theory of the causes of lunar and solar eclipses, and disregarded the imaginary dark planets of the mythologists and astrologers; affirming the moon and primary planets (and even the stars) to be essentially dark, and only illumined by the sun : that he noticed the motion of the solstitial and equinoctial points, but restricted it to a regular oscillation, of which he assigned the limit and the period : that he ascribed to the epicycles, by which the motion of a planet is represented, a form varying from the circle and nearly elliptic : that he recognised a motion of the nodes and asides of all the primary planets, as well as of the moon; though in this instance, as in some others, his censurer imputes to him variance of doctrine.

The magnitude of the earth, and extent of the encompassing wind, is among the instances wherein he is reproached by BRAHMEGUPTA with versatility, as not having adhered to the same position throughout his writings; but he is vindicated on this, as on most occasions, by the scholiast of his censurer. Particulars of this question, leading to rather curious matter, deserve notice.

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