**Charles René Reyneau**'s father was a surgeon. He studied at the Oratorian College in Angers. In October 1676 he entered the Maison d'Institution in Paris where he met Malebranche. 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. However, in 1705, he had to give up teaching as be became deaf. He had been going deaf for a number of years but he managed to keep his post by having former students give his lectures for him. After giving up the struggle to continue his job in these difficult circumstances, Reyneau went to Paris and lived at the Oratorian house there for the rest of his life.

This was a time when there were major new mathematical ideas coming through the work of Johann Bernoulli and being brought into France through de L'Hôpital and others. 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 struggled to assimilate the differential and integral calculus participating in debates provoked by Rolle on these topics. He worked with other mathematicians but, mainly due to his having to learn revolutionary new ideas as he went along, the book took a long time to complete. The two volume work *Analyse démontrée* was published in 1708 and a second enlarged edition was produced which was the text from which d'Alembert learnt mathematics.

In 1705 Reyneau obtained a copy of *Leçons* prepared by Johann Bernoulli for de L'Hôpital. Reyneau lent some documents to Montmort who lost them. Reyneau wrote a second work in 1714 which [1]:-

... attempted to preserve the central conceptions of the Oratorian mathematics of the end of the preceding century,[but]was less successful than the first.

**Article by:** *J J O'Connor* and *E F Robertson*