Alexis Fontaine's integration of ordinary differential equations and the origins of the calculus of several variables

Summary

Alexis Fontaine des Bertins (1704–1771) was the first French mathematician to make use of the calculus of several variables in the integration of ordinary differential equations (1738). In this paper I argue that this usage evolved from Fontaine's ‘fluxio-differential method’ of the early 1730s. In this way I extend the thesis enunciated in an earlier paper in this journal.