Abstract
Mathematical analysis has many beginnings, and in the 19th century its history has a lot to do with the reformulations of the calculus that gradually led to the creation of adequate foundations and standards of rigorous argument. This does not mean that these were the only issues occupying the minds of mathematicians, or that they succeeded completely, but in important ways the subject was greatly transformed as the century progressed.
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Notes
- 1.
For a rich and stimulating account of rigour in 18th-century mathematics, and of what was involved in the transition to the 19th century, I particularly recommend Schubring (2005).
- 2.
For a growing and invaluable guide, consult the Euler Archive on the web.
- 3.
The translation is taken from Struik (1969, 384).
- 4.
On d’Alembert’s life and times see Hankins (1970). A vigorous new edition of all of d’Alembert’s papers is also underway.
- 5.
See Whiteside, The Mathematical Papers of Isaac Newton, Vol. 6, p. 108.
- 6.
See ‘Limite’, Encyclopédie, vol. 9, 1765. There is an extract from d’Alembert’s essay on differentials, Encyclopédie, vol. 4, (1754) in Struik (1969, 342–345) and also in Fauvel and Gray (1987, 18.A3).
- 7.
See the letter to D. Bernoulli , quoted in Euler , Opera Omnia, IV, A5, p. 330, n. 2.
- 8.
It was originally called the École Centrale des Travaux Publics (the Central School for Public Works) thus for civil and military engineering, and given its present name the in the following year.
- 9.
The prize was awarded to Simon Antoine Jean L’Huillier for his Exposition élémentaire (1787).
- 10.
See the extract in Fauvel and Gray (1987, 18.A4) and below.
- 11.
In Lagrange (1826, 182) quoted in Sørensen (2005, 470).
- 12.
See Struik Sourcebook, 272–280, F&G 13.A3. I have removed some repetitions from the text.
- 13.
See Jesseph (2015, 194–195); the volume contains a number of important articles on Leibniz’s mathematics and philosophy.
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Gray, J. (2015). Lagrange and Foundations for the Calculus. In: The Real and the Complex: A History of Analysis in the 19th Century. Springer Undergraduate Mathematics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-23715-2_1
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