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Alexis Fontaine's ‘Fluxio-differential method' and the origins of the calculus of several variables

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Alexis Fontaine des Bertins (1704–1771) was the first French mathematician to introduce what we would now regard as results in the calculus of several variables. One example is Fontaine's theorem nF = (∂̸ F /∂̸ x ) x + (∂̸ F /∂̸ y ) y of 1737 for homogeneous expressions F of degree n in x and y . Many years later Fontaine indicated this particular result to have been ‘a continuation of the method of solution' introduced by him in 1734 to solve the problem of the tautochrones. It is tempting to disregard this announcement, since the method applied to the tautochrones was a method of variations and not manifestly an exercise in the calculus of several variables. Do we have just another case of a mathematician's confusion about the origins of his earlier work? In this paper I describe Fontaine's possible intentions in his remarks.

Document Type: Research Article


Affiliations: Centre de Recherches Alexandre Koyré, 12, rue Colbert, 75.002, Paris, France

Publication date: May 1, 1981

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