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Reyneau, Charles René


(b.Brissac, Maine-et-Loire, 11 June 1656; d. Paris, France, 24 February 1728)


Reeyneau is important historically as the author of a textbook, written at the request of Malebrance, that was designed to provide instruction in the new mathematics developed at the beginning of the eighteenth century. The son of a surgeon, he studied at the Oratorian college in Angers. Attracted by the order, on 17 October 1676 he entered the Maison d’Institution in Paris, where, besides Malebranche, he met Jean Present, who had just published his Élements des mathématiques. In 1679 Reyneau was sent to the Collège de Toulon, and in March 1681 he was ordained a priest there. In October 1682 he went to the University of Angers to replace Present as professor of mathematics, a post he held for twenty-three years. Suffering from deafness, he had former students substitute for him for several years but was finally obliged to give up teaching in 1705. Reyneau spent the rest of his life in Paris, at the Oratorian house on rue Saint-Honorè, and published his textbooks there. He was named an associè libre of the Acadèmie Royal des Sciences on 12 February 1716.

Many surviving manuscripts reveal Reneau’s pedagogical ability and are valuable source for the study of mathematics in France at the end of the seventeenth century. Reyneau was only slightly aware of the projects of Malebranche and L’ Hospital in 1690–1691 and of the revolution resulting from Jahann Bernoulli’s stay in Paris in 1692. As late as 1694 all that Maleranche had for Reyneau to do was edit Present’s posthumous Géométric. But, after abadoing the last shred of Cartresion mathematics, textbook required by this turnabout (1698).

Reyneau worked with two other Oratorians, Louis Byzance and Claude Jaquement, who were better mathematics than he. Reyeanu had some difficulty in assimilating the differential and integral calculus and was very interested in the debates, beginning in 1700, provoked by Rolle on this subject. Reyeanu’s editorial efforts were frustrated in various ways, and the textbook was not published until 1708.

In 1705 Reyneau came into possession of Byzance’s papers, which included a copy of the “Lecons” that Bernoulli had prepared for ’Hospital. Unfortunately, Reyeanu lent some of the documents to Mont mort, who lost them. On the whole, however, he preserved as well as possible the manuscripts of the group around Malebranche; and from them he drew the inspiration for a second didactic work, published in 1714. This work, which attempted to preserve the central conceptions of the Oratorian mathematics of the end of the preceding century, was less successful than the first.

Reyneau’s most notable contribution to mathematical education was Analyze démontrée (1708). It was from the second edition of this work that d’Alembert learned the fundamentals of the subject.


I. Original Works. Ryeanu’s writings include Analyze démontrée ou la méthode résoudre les probléms des mathématiques et d’apprendre failemant ces science, expliquée et démontrée… et applique… à découvir les propriétés des figures de la géométrie simple et composée, à résodre les problémes… en employ ant le calcul oridinaire de l’algébra, le calcul différential et le calcul intégral…, 2vols. (Paris 1708; 2nd ed., enl., 1736–1738);La science du calcul des grandeur en général…, 2vols. (Paris, 1714–1735); La logique ou l’art de raissonner juste à l’usage des dames(Paris, 1744); and “Trité de la marine ou l’art de naviguer”. MS no. 3729, Bibilothéque Mazarine, Paris.

II. Secondary Literature. See an unsigned review of L’ analyse démontrée in Memories pour l’historic des sciences et des beaux-arts, 3 (708), 1438–1452; Bernard de Fontenelle, “Éloge du Pére Reyeanu”, in Historie de l’Acadème royale des sciences pour l’anneé 1728… avec les mémories… 112–116; and Pirer Costabel, “Deux in-edits de la correspondence indirect Leibinz-Reyeanu”, in Revue d’historie des sciences et de leurs applications, 2 (1949), 311–332; “Rectification et compliments…,” ibid., 19 (1966), 167–169; andOeuvres de Malebranche, XVII, pt. 2, Malebranche et la reforme a mthématique en France de 1689 à 1706 (Paris, 1968).

Pierre Costabel

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