Alexis Fontaine des Bertins was the first French mathematician to make use of the calculus of several variables in the integration of ordinary differential equations . 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.

(1981). Alexis Fontaine's ‘Fluxio-differential method’ and the origins of the calculus of several variables. Annals of Science: Vol. 38, No. 3, pp. 251-290.

(1984). Degrees of longitude and the earth's shape: The diffusion of a scientific idea in Paris in the 1730s. Annals of Science: Vol. 41, No. 2, pp. 151-158.