Article ID: CBB715090012

The Principia’s second law (as Newton understood it) from Galileo to Laplace (2020)


Newton certainly regarded his second law of motion in the Principia as a fundamental axiom of mechanics. Yet the works that came after the Principia, the major treatises on the foundations of mechanics in the eighteenth century—by Varignon, Hermann, Euler, Maclaurin, d’Alembert, Euler (again), Lagrange, and Laplace—do not record, cite, discuss, or even mention the Principia’s statement of the second law. Nevertheless, the present study shows that all of these scientists do in fact assume the principle that the Principia’s second law asserts as a fundamental axiom in their mechanics. (For what that second law asserts, we rely on Newton’s own testimony.) Some, like Varignon and Hermann, assume the axiom implicitly, apparently unaware that any assumption is being made, while others, like Maclaurin and Euler, assume the axiom explicitly, apparently unaware that the assertion assumed is the second law as Newton himself understood it. But in every case these scientists employ the principle asserted by the Principia’s second law fundamentally, unaware that they should be citing Neutonus, Prin., Phil. Nat. Math., Lex II.

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Authors & Contributors
Capecchi, Danilo
Maltese, Giulio
Belkind, Ori
Borgato, Maria Teresa
Darrigol, Olivier
Dijck, Maarten Van
Archive for History of Exact Sciences
Foundations of Science
Studies in History and Philosophy of Science
Bollettino di Storia delle Scienze Matematiche
科学史研究 Kagakusi Kenkyu (History of Science)
Motion (physical)
Philosophy of science
Newton, Isaac
Galilei, Galileo
Descartes, René
Euler, Leonhard
Kepler, Johannes
Leibniz, Gottfried Wilhelm von
Time Periods
18th century
17th century
16th century
Early modern
19th century
Accademia delle Scienze dell'Istituto di Bologna
Cambridge University

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