ALGEBRA GOES TO EUROPE FROM INDIA 628. The grounds on which they proceeded are unfor- tunately not specified: but as they gave Bhaskara's age correctly, as well as several other dates right, which admit of being verified; it is presumed that they had grounds, though unexplained, for the information which they communicated.. 193 Mr. Bentley, who is little disposed to favour the anti- quity of an Indian astronomer, has given his reasons for considering the astronomical system which Brah- magupta teaches, to be between twelve and thirteen hundred years old (1263 years in A.D. 1799). Now as the system taught by this author is professedly one corrected and adapted by him to conform with the observed positions of the celestial objects when he wrote, the age, when their positions would be conform- able with the results of computations made as by him directed, is precisely the age of the author himself: and so far as Mr. Bentley's calculations may be consi- dered to approximate the truth, the date of Brahma- gupta's performance is determined with like approach to exactness, within a certain latitude however of uncertainty for allowance to be made on account of the inaccuracy of Hindu observations. The translator has assigned on former occasions the grounds upon which he sees reason to place the author's age, soon after the period when the vernal equinox coincided with the beginning of the lunar mansion and zodiacal asterism Avina, where the Hindu ecliptic now commences. He is supported in it by the senti- ments of Bhaskara and other Indian astronomers, who infer from Brahmagupta's doctrine concerning the solístitial points, of which he does not admit a periodi- cal motion, that he lived when the equinoxes did not, sensibly to him, deviate from the beginning of Asvin and middle of citra on the Hindu sphere. On these grounds it is maintained, that Brahmagupta is rightly placed in the sixth or beginning of the seventh century of the Christian era, as the subjoined calculations will more particularly show. The age when Brahmagupta
