Eulers “Harmony” Between the Principles of “Rest” and “Least Action”

In 1751, LEONHARD EULER established “harmony” between two principles that had been stated by PIERRE-LOUIS-MOREAU DE MAUPERTUIS a few years earlier. These principles are intended to be the foundations of Mechanics; they are the principle of rest and the principle of least action. My claim is that the way in which “harmony” is achieved sets the foundations of so called Analytical Mechanics: it discloses the physical bases of the general ideas, concepts, and motivations of the formalism. My paper intends to show what those physical bases are, and how a picture of the formalism issues from them. This picture is shown to be recast in JOSEPH-LOUIS LAGRANGES justification of the formalism, which strengthens my claim.