Article ID: CBB715090012

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

unapi

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
Maltese, Giulio
Reichenberger, Andrea
Brading, Katherine
Verelst, Karin
Takahashi, Ken'ichi
Suisky, Dieter
Concepts
Motion (physical)
Physics
Mechanics
Mathematics
Philosophy of science
Forces
Time Periods
18th century
17th century
Renaissance
16th century
Early modern
19th century
Places
Europe
Italy
France
Institutions
Cambridge University
Accademia delle Scienze dell'Istituto di Bologna
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