Joseph-Louis Lagrange

Notes for scholars :

In examining the 2nd and subsequent posthumous editions of the Mécanique analytique several qualities are immediately striking.

Volume I closes with a detailed record of Lagrange's publications. Thus, scholars have a roadmap of his contributions. Lagrange, as a member of highly selective academies, had his complete life's work carefully annotated and preserved.
His introduction was in the style one often finds in 18th century mathematics publications. He begins by listing a "few" of those whose work he will apply. In Lagrange's case, the list of mathematicians is staggering: Archimedes, Galileo, Stevin, Huygens, Mersenne, Roberval, Descartes, Torricelli, Wallis, Nicomedes, Daniel Bernoulli, Jean Bernoulli, Aristotle . . . .
When Lagrange brought himself to write of his personal contributions, and ceased to elaborate on the accomplishments of others, he wrote in a style that was brief, clear and well organized. The "Mécanique analytique" must have been a very useful book for his contemporaries. Today's reader finds an almost handbook or College Outline Series quality to the writing.
There are absolutely no illustrations, diagrams or pictures, only equations and formulas with text. With Euler, Lagrange is considered a pioneer in the analysis of abstract non-geometrical mathematics. However, early in his career he investigated the tautochrone (1770).
With such an extensive list of publications, it is difficult to select those with the most lasting impact. We shall attempt to highlight a few. He ............

Proved Bachet's Conjecture that every integer is the sum of four squares.
Developed a method for continued fractions.
Developed several techniques and texts for solving algebraic equations.
Developed the coordinates and multipliers named for him.
Focused on the remainder in a Taylor series.
Formulated theories for power series.
Joined with Euler in founding Analysis.
Joined with Euler in founding the Calculus of Variations.
Explained and widened the standardization of calculus notation. Lagrange often explained his notation, showed its application and thereby educated his readers. After almost a century since Newton had published the Principia, calculus was still not understood and widely used among mathematicians.
Collaborated to establish the metric system in France.

References and Credits

*H. Goldstein, C. Poole and J.Safko, Classical Mechanics, 3rd ed., Addison Wesley, 2002, p. 21.

E. T. Bell, Men of Mathematics, Simon and Schuster, 1937.

J. L. Lagrange, Analytical mechanics, translated and edited by Auguste Boissonnade and J. L. Vagliente, Kluwer Academic Publishers, 1997.

J. L. Lagrange, Mécanique analytique, Paris, Mme. Ve Courcier, 1811, pp. 383-391.
J. L. Lagrange, Méchanique analytique, sic, Paris, Chez la Veuve Desaint, 1788.
The Huntington Library, San Marino, CA has several editions and translations of Lagrange's publications. We choose to cite only the second edition, volume 1, with an extensive "Liste des Ouvrages de Lagrange" as well as the errata to the first edition (1788). This particular volume is signed by Poisson, Legendre, Maurice de Prony and Lacroix (rapporteur) indicating support of the Académie Royale des Sciences.

George Sarton, "Lagrange's Personality (1736-1813)", Proceedings of the American Philosophical Society, Vol. 88, No.6, 1944, pp. 457-496.

The National Curve Bank thanks the Huntington Library for access to their materials.

The National Curve Bank especially thanks James T. Smith, Professor Emeritus of Mathematics, San Francisco State University, for the motivation to compose this web page. As a "mathematical tourist" he enjoyed taking the photos on a trip to Italy in 2008.

A large statue of Lagrange stands in the premises of the
Accademia delle Scienze di Torino of which he was a founder.
The Accademia is now on the upper floor of the Egyptian Museum. The Lagrange translation by Boissonnade and Vagliente has a picture showing this statue was once located at the center of a busy Turin intersection.