REYNEAU (Charles-Rene)

, commonly called Father Reyneau, a noted French mathematician, was born at Brissac in the province of Anjou, in the year 1656. At 20 years of age he entered himself among the Oratorians, a kind of religious order, in which the members lived in community without making any vows, and applied themselves chiefly to the education of youth. He was soon after sent, by his superiors, to teach philosophy at Pezenas, and then at Toulon. This requiring some acquaintance with geometry, he contracted a great affection for this science, which he cultivated and improved to a great extent; in consequence he was called to Angers in 1683, to fill the mathematical chair; and the Academy of Angers elected him a member in 1694.

In this occupation Father Reyneau, not content with making himself master of every thing worth knowing, which the modern analysis, so fruitful in sublime speculations and ingenious discoveries, had already produced, undertook to reduce into one body, for the use of his scholars, the principal theories scattered here and there in Newton, Descartes, Leibnitz, Bernoulli, the Leipsic Acts, the Memoirs of the Paris Academy, and in other works; treasures which by being so widely dispersed, proved much less useful than they otherwise might have been. The fruit of this undertaking, was his Analyse Demontrée, or Analysis Demonstrated, which he published in 2 volumes 4to, 1708.

Father Reyneau called this useful work, Analysis Demonstrated, because he demonstrates in it several methods which had not been demonstrated by the authors of them, or at least not with sufficient perspicuity and exactness; for it often happens that, in matters of this kind, a person is clear in a thing, without being able to demonstrate it. Some persons too have been so mistakingly fond of glory as to make a secret of their demonstrations, in order to perplex those, whom it would become them much better to instruct. This book of Reyneau's was so well approved, that it soon became a maxim, at least in France, that to follow him was the best, if not the only way, to make any extra- | ordinary progress in the mathematics. This was considering him as the first master, as the Euclid of the sublime geometry.

Reynean, aster thus giving lessons to those who undei stood something of geometry, thought proper to draw up some for such as were utterly unacquainted with that science. This was in some measure a condescension in him, but his passion to be useful made it easy and agreeable. In 1714 he published a volume in 4to on calculation, under the title of Science du Calcul des Grandeurs, of which the then Censor Royal, a most intelligent and impartial judge, says, in his approbation of it, that “though several books had already appeared upon the same subject, such a treatise as that before him was still wanting, as in it every thing was handled in a manner sufficiently extensive, and at the same time with all possible exactness and perspicuity.” In fact, though most branches of the mathematics had been well treated of before that period, there were yet no good elements, even of practical geometry. Those who knew no more than what precisely such a book ought to contain, knew too little to complete a good one; and those who knew more, thought themselves probably above the task; whereas Reyneau possessed at once all the learning and modesty necessary to undertake and execute such a work.

As soon as the Royal Academy of Sciences at Paris, in consequence of a regulation made in the year 1716, opened its doors to other learned men, under the title of Free Associates, Father Reynean was admitted of the number. The works however which we have already mentioned, besides a small piece upon Logic, are the only ones he ever published, or probably ever composed, except most of the materials for a second volume of his Science du Calcul, which he left behind him in manuscript. The last years of his life were attended with too much sickness to admit of any extraordinary application. He died in 1728, at 72 years of age, not more regretted on account of his great learning, than of his many virtues, which all conspired in an eminent degree to make that learning agreeable to those about him, and useful to the world. The first men in France deemed it an honour and a happiness to count him among their friends. Of this number were the chancellor of that kingdom, and Father Mallebranche, of whom Reyncau was a zealous and faithful disciple.