**Charles René Reyneau** was a French mathematician who published an influential textbook on the newly invented calculus.

- De Bérulle was a friend of Descartes and when Reyneau studied at the Oratory its teaching were strongly based on Descartes' philosophy.
- On 17 October 1676 Reyneau entered the Maison d'Institution of the Congregation of the Oratory in Paris where he met Nicolas Malebranche and Jean Prestet (1642-1691), who had just published his Élements des mathématiques Ⓣ(Elements of mathematics), the first edition appearing in 1675.
- Reyneau was sent to teach philosophy at Pezenas, then, in 1679, he moved to the Collège de Toulon and, in 1681, he was ordained a priest there.
- In 1682 Reyneau was appointed professor of mathematics at the University of Angers, replacing Jean Prestet.
- After giving up the struggle to continue his job in these difficult circumstances, Reyneau went to Paris and lived at the Oratorian house on rue Saint-Honorè for the rest of his life.
- For many years Reyneau was not really abreast of these new developments, even when Johann Bernoulli visited Paris in 1692, and Reyneau did not rush to keep up to date with the important new ideas.
- Malebranche asked Reyneau to undertake some editorial duties in 1694 but then, in 1698, he persuaded Reyneau to write a new textbook to provide instruction in the new mathematics.
- Reyneau did not work alone.
- The course that Johann Bernoulli gave to de l'Hôpital in 1692 gave rise to one or more copies, it served as a support for the personal works that Malebranche carried out to assimilate the methods of differential and integral calculus, but Reyneau also had this course in his hands.
- While he was still teaching at the University of Angers, Reyneau visited Paris in 1700 and spent from July to August there learning more mathematics from Pierre Varignon, someone whom he would naturally get to know since Varignon was a leading member of the group around Malebranche.
- Reyneau struggled to assimilate the differential and integral calculus participating in debates provoked by Michel Rolle on these topics.
- In 1705 Reyneau received Louis Byzance's papers and among them was a copy of Johann Bernoulli's "Leçons" that he had prepared for de l'Hôpital.
- Reyneau lent some of these papers to Pierre Rémond de Montmort who lost them.
- However Byzance's papers were helpful to Reyneau in working on getting his lecture notes into publishable form.
- Given the extract above where Reyneau is discussing what he learnt from Varignon about negative ratios, it is interesting to look at Reyneau's use of negative numbers in Analyse demontrée Ⓣ(Analysis demonstrated or How to solve mathematics problems and easily learn these sciences).
- In 1728, the year Reyneau died, Alexis Clairaut corrected errors in the book.

Born 11 June 1656, Brissac, Maine-et-Loire, France. Died 24 February 1728, Paris, France.

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**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive