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[1841]: “Mémoire sur les conditions d'intégrabilité des fonctions différentielles”, Journal de l'Ecole polytechnique 17 (1841) pp. 249–275.
[1974]: “Differentials, Higher-Order Differentials and the Derivative in the Leibnizian Calculus”, Archive for History of Exact Sciences 14 (1974) pp. 1–90.
[1739]: “Recherches générales sur le calcul intégral”, Histoire de l'Académie Royale des Sciences avec les Mémoires de Mathématique et de Physique 1739 pp. 425–436.
Condorcet, J. M. Marquis de [1765]: Du Calcul Intégral (Paris, 1765).
Courant, R. & Hilbert, D. [1953]: Methods of Mathematical Physics Volume 1 (Interscience, 1953).
Euler, Leonhard Leonhardi Euleri Opera Omnia Series I Opera Mathematica (Various cities, 1911–1956) Volumes 13 22 24 25. Series IVa Commercium Epistolicum (Basel, 1980) Volume 5. This volume of Series IVa is edited by A. P. Juškevič & R. Taton and contains selected French translations of Latin correspondence as well as valuable detailed notes of information.
[1734]: “De Infinitis Curvis Eiusdem Genesis Seu Methodus Inveniendi Aequationes Pro Infinitis Curvis Eiusdem Generis”, Commentarii academiae scientiarum Petropolitanae 7 (1734/35) 1740 pp. 174–189 = Opera S.I 22 (1936) pp. 36–56.
Euler, Leonhard [1744]: Methodus Inveniendi Lineas Curvas Maximi Minimive Proprietate Gaudentes Sive Solutio Problematis Isoperimetrici Latissimo Sensu Accepti (Lausanne, 1744) = Opera S.I 24 (1952), ed., Constantin Carathéodory
[1755]: Letter to Lagrange 6 September 1755 = Opera S.IVa 5 (1980) pp. 375–478 = Œuvres de Lagrange 14 pp. 144–146.
[1756]: Letter to Lagrange 24 April 1756 = Opera S.IVa 5 pp. 386–390 = Œuvres de Lagrange 14 pp. 152–154.
[1764a]: “Elementa Calculi Variationum”, Novi commentarii academiae scientiarum Petropolitanae 10 (1764), 1766 pp. 51–93. = Opera S.I 25 (1952) pp. 141–176.
[1764b]: “Analytica Explicatio Methodi Maximorum et Minimorum”, Novi ... Petropolitanae 10 (1764), 1766 pp. 94–134. = Opera S.I 25 pp. 177–207.
Euler, Leonhard [1770]: “Appendix de Calculo Variationum”, Institutiones Calculi Integralis, Volume 3 (1770) = Opera A.I 13 (1914) pp. 369–469.
[1771]: “Methodus Nova et Facilis Calculum Variationum Tractandi”, Novi ... Petropolitanae 16 (1771), 1772, pp. 35–70 = Opera S.I. 25 pp. 208–235.
[1983]: “J. L. Lagrange's Early Contributions to the Principles and Methods of Mechanics”, Archive for History of Exact Sciences 28 (1983) pp. 197–241.
Goldstein, Herbert [1950]: Classical Mechanics (Addison-Wesley, 1950).
Goldstine, Herman H. [1980]: A History of the Calculus of Variations from the 17th through the 19th Century (Springer-Verlag, 1980).
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[1981]: “The History of Differential Forms from Clairaut to Poincaré”, Historia Mathematica 8 (1981) pp. 161–188.
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Lagrange, Joseph Louis Œuvres de Lagrange J. A. Serret & G. Darboux, eds., 14 volumes (Paris, 1867–1892). The page references which I give in this article are, with one exception, to the edition of the particular work in question which appears in the Œuvres. (Thus, for example, [1806, 404] refers to page 404 of Œuvres 10.) The one exception is the Méchanique Analitique, for which I have included page numbers to the original edition of 1788 as well as to the edition in the Œuvres. See also the entry below under Méchanique Analitique.
[1754]: Letter to Euler 28 June 1754 = Œuvres 14 (1892) pp. 135–138 = Euler Opera Omnia S.IVa 5 pp. 361–366. (The correspondence between Euler and Lagrange before 1759 was conducted in Latin; after this date it was conducted in French.)
[1755a]: Letter to Euler 12 August 1755 = Œuvres 14 pp. 138–144 = Euler Opera S. IVa 5 pp. 366–375.
[1755b]: Letter to Euler 20 November 1755 = Œuvres 14 pp. 146–151 = Euler Opera S. IVa 5 pp. 378–386.
[1756]: Letter to Euler 5 October 1756 = Euler Opera S. IVa 5 p.p. 396–411. This letter is not in Lagrange's Œuvres 14.
Lagrange, Joseph Louis [1760a]: “Essai d'une nouvelle méthode pour déterminer les maxima et les minima des formules indéfinies”, Miscellanea Taurinensia 2 (1762) = Œuvres 1 (1867) pp. 335–362.
Lagrange, Joseph Louis [1760b]: “Application de la méthode exposée dans le mémoire précédent à la solution de différentes problèmes de dynamique”, Miscellanea Taurinensia 2 (1762) = Œuvres 1 pp. 365–468.
Lagrange, Joseph Louis [1764]: “Recherches sur la libration de la Lune dans lesquelles on tâche de résoudre la Question proposée par l'Académie Royale des Sciences, pour le Prix de l'année 1764”, Prix de l'Académie Royale des Sciences de Paris tome IX 1780 (1777) = Œuvres 6 (1878) pp. 5–61.
Lagrange, Joseph Louis [1780]: “Théorie de la libration de la lune, et des autres phénomènes qui dependent de la figure non sphérique de cette planète”, Nouveaux Memoires de l'Académie royale des Sciences de Berlin 1780 = Œuvres 5 (1870) pp. 5–122.
[1782]: Letter to Laplace 15 September 1782 = Œuvres 14 pp. 115–117.
Lagrange, Joseph Louis [1788]: Méchanique Analitique (Paris, 1788). The second edition of this work appeared in two volumes as the Mécanique Analytique, the first volume in 1811 and the second (posthumously) in 1815. The edition in the Œuvres 11 and 12 (1888) is based on the second edition. Although the second edition differs in many ways from the first, not only in details of presentation but also in scope, the passages of concern in this article remain unchanged except in notation.
Lagrange, Joseph Louis [1797]: Théorie des fonctions analytiques contenant les principles du calcul différentiel dégagés de toute consideration d'infiniment petits ou d'évanouissans de limites ou de fluxions et réduits à l'analyse algébrique des quantités finies, Journal de l'Ecole Polytechnique 3 (1797). Second edition published in 1813 = Œuvres 9 (1881) My references to numbered articles in the Théorie follow the edition of 1797.
Lagrange, Joseph Louis [1806]: Lećons sur le calcul des fonctions (Second edition, 1806) = Œuvres 10 (1884). The lessons on the calculus of variations did not appear in the first edition, published in 1801.
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Woodhouse, Robert [1810]: A Treatise on Isoperimetrical Problems and the Calculus of Variations (Cambridge, 1810).
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Fraser, C. J. L. Lagrange's changing approach to the foundations of the calculus of variations. Arch. Hist. Exact Sci. 32, 151–191 (1985). https://doi.org/10.1007/BF00329871
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DOI: https://doi.org/10.1007/BF00329871