The Diophantinc arithmetic was almost entirely ne glected after the work of M. Fermat, till it was again taken up by Euler; but the numerous and beautiful dis coveries of that great man, sufficiently compensate for the little attention which has been given to it by other mathematicians. La Grange has also rendered the highest services to the indeterminate analysis, and de monstrated several problems concerning integers which Fermat had left unsolved. Nor must we omit to men tion, that Mr Leslie, to whom geometry and physics arc alike indebted, has published a most valuable paper on the same subject in the 2d vol. of the Transactions of the Royal Society of Edinburgh.
It has often been alleged, but certainly without justice, that the levity of the female character is unfit for the severer exercises of the understanding. It may be af firmed, with more truth, that the mental superiority of the other sex is not so much the effect of any original endowments of mind, as of a more extended education, assisted by other accidental causes. Italy, in modern times, has given birth to many illustrious women, who have distinguished themselves in the most difficult de partments of science; and the school of Alexandria, at a more early period, furnished an example of the same kind in Hypatia, the daughter of Them. This cele brated young lady, who was equally remarkable for her beauty and accomplishments, modestly declined the pro posals of many suitors, and resolved to sacrifice the charms of love to the higher and more exquisite de lights of philosophy. She wrote a commentary on Apol lonius, and another on Diophantus, besides some astro nomical tables; but none of her writings have come down to us except the third book of her commentary on the Ahnagest of Ptolomy. The unhappy fate of this accomplished woman presents one of those disgraceful enormities, which, under the mask of religious zeal, have too often polluted the pages of ecclesiastical his tory. After being stripped naked, she was dragged to a church, probably to give an air of piety to the transac tion, and cruelly put to death by a band of misguided fanatics, because she was suspected to be the cause of a misunderstanding which subsisted at that time between the archbishop and the prefect of Alexandria.
From this shameful event we may reckon the decline of mathematics at that celebrated seat of learning. Af ter languishing a short time, their downfal was com pleted by the Arabs, about the middle of the seventh century. Fortunately, before this took place, they had been transferred by Proclus to Greece, where, for some time, they continued to be cultivated ; but the days of Euclid and Apollonius were now no more, and the re searches of the later Greek mathematicians are mere puerilities compared with the manly investigations of their predecessors. Magic squares were the most bril
liant of their discoveries! The sciences never made much progress among the Romans. The warlike habits of that people were un friendly to the mild arts of peace, and to all the refine ments which promote domestic happiness. They not only neglected mathematical learning, but often sub jected it to the severest persecution. Various decrees of the senate were passed during the republic, against those who should introduce the sciences of Greece into Rome; and in the times of the emperors, the term pia ihematieue was so much degraded, as to be nearly of the same import with magician or astrologer.* We need not wonder, therefore, why the Romans cannot produce a single name in the history of mathematics, whicli rises even to mediocrity. The celebrated Varro, who, on account of his extensive information, obtained the honourable title of "the most learned of the Ro mans," (doctissimus Romanorum,) wrote on arithmetic and geometry; but his treatises on these subjects were probably far from profound, and more in the style of the orator than the mathematician. His book on arithmetic existed towards the close of the sixteenth century ; at feast, Vertranius Maurus asserts, that about that time a copy of it was in the library of cardinal Ridolfi ; hitherto it has not been given to the public.
Perhaps we ought to except from the censure we have passed on the Roman mathematicians the respect able but unfortunate Boethius, had this amiable philoso pher been indebted to his own countrymen for his great erudition; but he employed eighteen years of laborious study in the schools of Athens, which had then acquired some celebrity by the learning of Proclus, and his dis ciples. He submitted, for the benefit of his Latin read ers, to teach the first elements of the arts and sciences of Greece. The geometry of Euclid, and the arithmetic of Nicomachus, were translated by his pen; and his commentaries furnish us with many interesting facts relative to the history of both. His writings were trans lated, in their turn, by the most glorious of the English monarchs ; and contributed to diffuse a solitary ray of knowledge through the dark ages of ignorance and bar barism, which so long overspread Europe.