Abstract
To deduce the maxima and the minima of the function u from the method that we have indicated, we should begin by eliminating from this function m different variables with the help of the formulas in (2). After this elimination, the variables which remain, to number \(n-m, \, \) should be considered as independent; and, the systems of values of these variables should be sought which render the function u or the function du discontinuous, as well as those which satisfy, whatever the differentials of these same variables, the equation.
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Notes
- 1.
Cauchy uses the term développe here which is literally translated as developed. However, the term also conveys the idea of growth or expansion. This latter meaning has been used here and throughout the text to significantly improve the readability of his work and to more accurately convey Cauchy’s true message.
- 2.
Cauchy describes the situation well enough to avoid the use of a diagram here. Following a tradition set out by Lagrange, Cauchy purposefully omits diagrams of any type from both his Calcul infinitésimal and Cours d’analyse books.
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Cates, D.M. (2019). USE OF INDETERMINATE FACTORS IN THE STUDY OF MAXIMA AND MINIMA.. In: Cauchy's Calcul Infinitésimal. Springer, Cham. https://doi.org/10.1007/978-3-030-11036-9_11
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DOI: https://doi.org/10.1007/978-3-030-11036-9_11
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