, a celebrated mathematician of Alexandria, has been reputed to be the inventor of algebra; at least his is the earliest work extant on that science. It is not certain when he lived. Some have placed him before Christ, and some after, in the reigns of Nero and the Antonines; Saxius places him in the fourth century. He appears to be the same Diophantus who wrote the “Canon Astronomicus, which Suidas says was commented on by the celebrated Hypatia, daughter of Theon of Alexandria. His reputation must have been very high among the ancients, since they ranked him with Pythagoras and Euclid in mathematical learning. Bachet, in his notes upon the 5th book” De Arithmeticis," has collected, from Diophantus’s epitaph in the Anthologia, the following circumstances of his life; namely, that he was married when he was thirty-three years old, and had asonbornfive years after; that this son died when he was forty-two years of age, and that his father did not survive him above four years; from which it appears, that Diophantus was eighty-four years old when he died.

He wrote thirteen books of arithmetic, or algebra, which, Regiomontanus in his preface to Alfraganus tells us, are still preserved in manuscript in the Vatican library. Indeed Diophantus himself tells us that his work consisted of thirteen books, viz. at the end of his address to Dionysius, placed at the beginning of the work; and from hence Regiomontanus might be led to say the thirteen books were in that library. No more than six whole books, with part of a seventh, have ever been published; and it is probable | there are no more in being; indeed Bombelli, in the preface to his Algebra, written in 1572, says there were but six of the books then in the library, and that he and another were about a translation of them. Those six books, with the imperfect seventh, were first published at Basil by Xylander in 1575, but in a Latin version only, with the Greek scholia of Maximus Planudes upon the two first books, and observations of his own. The same books were afterwards published in Greek and Latin at Paris in 1G2I, by Bachet, an ingenious and learned Frenchman, who made a new Latin version of the work, and enriched it with very learned commentaries. Bachet did not entirely neglect the notes of Xylander in his edition, but he treated the scholiast Planudes with the utmost contempt. He seems to intimate, in what he says upon the 28th question of the second book, that the six books which we have of Diophantus may be nothing more than a collection made by some novice, of such propositions as he judged proper, out of the whole thirteen but Fabricius thinks there is no just ground for such a supposition. From him certain questions relating to square and cubic numbers, and to right-angled triangles, have been called Diophantine problems, because the nature of them was first and chiefly treated of by him in his arithmetic, or rather algebra. 1

1 Fabric. Bibl. Graec. —Hutton’s Dictionary. Montucla Hist. Math. Vs skis de Scieut. Math. —Moreri.