Reyneau, Charles-Rene

, commonly called Father Reyneau, a noted French mathematician, was born at Brissac, in the province of Anjou, in 1656. At twenty years of age he entered himself in the congregation of the Oratory at Paris, and was soon after sent, by his superiors, to teach philosophy at Pezenas, and then at Toulon. His employment requiring some acquaintance with geometry, he contracted a great affection for this science, which he cultivated and improved to so great an extent, that 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 Demontree,” or Analysis Demonstrated, which he published in 1708, 2 vols. 4to. He gave it the name of “Analysis Demonstrated,” because he demonstrates in it several methods which had not been handled by the authors of them, with sufficient perspicuity and exactness. The book 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 extraordinary progress in the mathematics; and he was considered as the first master, as the Euclid of the sublime geometry.

Reyneau, after thus giving lessons to those who understood something of geometry, thought proper to draw up some for such as were utterly unacquainted with that science. This produced in 1714, a volume in 4to, on calculation, under the title of “Science du Caicul des Grandeurs,” of which the then censor royal, a very 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 that knew more, thought themselves probably above the task, for which Reyneau was well qualified. In J 716 he was admitted into the royal academy of sciences of Paris, as what was then called a free associate. The works already mentioned are all he published except a small piece on “Logic.” He left, however, in ms. materials for a second volume of his “Science du Calcul.” He died much regretted, as he had always been highly respected, in 1728, at the age of seventy-two. ¹