Perspectives on Science 19 (4):426-452 (2011)

Abstract
One of the most influential scientific treatises in Cauchy's era was J.-L. Lagrange's Mécanique Analytique, the second edition of which came out in 1811, when Cauchy was barely out of his teens. Lagrange opens his treatise with an unequivocal endorsement of infinitesimals. Referring to the system of infinitesimal calculus, Lagrange writes:Lorsqu'on a bien conçu l'esprit de ce système, et qu'on s'est convaincu de l'exactitude de ses résultats par la méthode géométrique des premières et dernières raisons, ou par la méthode analytique des fonctions dérivées, on peut employer les infiniment petits comme un instrument sûr et commode pour abréger et simplifier les demonstrations.Lagrange's renewed enthusiasm for ..
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DOI 10.1162/POSC_a_00047
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Mècanique Analytique (Analytical Mechanics).J. L. Lagrange - forthcoming - Boston Studies in the Philosophy of Science.
Non-Standard Analysis.Abraham Robinson - 1961 - North-Holland Publishing Co..

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