Abstract
On 12 August 1755 a 19-year-old, one Ludovico de la Grange Tournier of Turin, wrote Euler a brief letter to which was attached an appendix containing mathematical details of a very beautiful and revolutionary idea (see Lagrange [1755] and Euler [1755]). He saw how to eliminate from Euler’s methods of 1744 the tedium and need for geometrical insight and to reduce the entire process to a quite analytic machine or apparatus, which could turn out the necessary condition of Euler and more, almost automatically. This basic idea of Lagrange ushered in a new epoch in the calculus of variations. Indeed after seeing Lagrange’s work, Euler dropped his own method, espoused that of Lagrange, and renamed the subject the calculus of variations.1
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References
See Euler [1764], p. 145. This volume (I, XXV) contains a number of papers written by Euler both before and after his Methodus… of 1744. After Lagrange’s publication Euler wrote several papers on our subject, the first of which appeared in 1764. It, and two others as well, are largely expositions of Lagrange’s elegant method.
Lagrange [ 1760 ]. It is also of interest to see [1760’], pp. 365–468, where he disucsses the principle of least action and its relation to the calculus of variations.
Lagrange [1760]. In the Memoirs of the Turin Academy he published not only the 1760/61 paper but a second one that appeared in Vol. IV, 1766/69. The reader may also wish to consult his paper on pp. 4–20 of Vol. I, which he wrote in 1759 (Lagrange [1759]) on maxima and minima of real functions, especially his discussion of the second differential.
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Goldstine, H.H. (1980). Lagrange and Legendre. In: A History of the Calculus of Variations from the 17th through the 19th Century. Studies in the History of Mathematics and Physical Sciences, vol 5. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8106-8_3
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DOI: https://doi.org/10.1007/978-1-4613-8106-8_3
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