196 BRAHMAGUPTA AS AN ALGEBRAISI written algebra, as well as to the circumstance of his being named by numerous writers as the founder of a sect, or author of a system in astronomy, and being quoted at the head of algebraists, when the commen- tators of extant treatises have occasion to mention early and original writers on this branch of science, it is not necessary to seek further for a mathematician qualified to have been the great improver of the ana- lytic art, and likely to have been the person by whom it was carried to the pitch to which it is found to have attained among the Hindus, and at which it is observ ed to be nearly stationary through the long lapse of ages which have since passed the later additions being few and unessential in the writings of Brahmagupta, of Bhaskara and of Jñanaraja, though they lived at intervals of centuries from each other. Aryabhata, Colebrooke rightly says then being the earliest author known to have treated of Algebra among the Hindus, and being likely to be, if not the inventor, the improver of that analysis, by whom too it was pushed nearly to the whole degree of excellence which it is found to have attained among them; it becomes in an especial manner interesting to investigate any discoverable trace in the absence of better and more direct evidence, which may tend to fix the date of his labours; or to indicate the time which elapsed between him and Brahmagupta, whose age is more accurately determined. Taking Aryabhata, for reasons given, to have preceded Brahmagupta and Varahamihira by several centuries; and Brahmagupta to have flourished more than twelve hundred years ago, and Varahamihira, concerning whose works and age. Colebrooke has given a few notes, and has placed him at the beginning of the sixth century after Christ, it appears probable that this earliest of known Hindu algebraists wrote as far back as the fifth century of the Christian era; and perhaps in an earlier age. Hence it is concluded that he is nearly as ancient as the Greecian algebraist Diophantus, sup
