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

  • Bruce PourciauEmail author


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.



For help with translations from the French, Ed Sandifer and Rob Bradley; for translations from the Latin, feminist scholar Mary Ann Rossi; for helpful conversations on Newtonian mechanics, Michael Spivak and Scott Corry; for (temporarily) pulling Hermann’s Phoronomia out of a box addressed to the Huntington Library, Jessica Murphy at the (now departed) Burndy Library; and for editorial comments, intelligent and insightful, George Smith and an anonymous reader.


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Authors and Affiliations

  1. 1.Lawrence UniversityAppletonUSA

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