Leonhard Euler's "principle of mechanics" (an essay on the foundations of the equations of motion)

Abstract

Leonhard Euler derived equations of motion for both (in modern terminology) point mass mechanics and analytic mechanics. In order to derive the equations, some dynamic premise has to be introduced; this is the "principle of mechanics". It stems from the recognition that infinitesimal motions are uniformly accelerated. Then, using Galileo Galilei's theorem on the fall, mathematical relations among differentials acquire physical meaning, and become the "principle of mechanics".