Theoretical Constructions (II): Euler

Abstract

The general principles upon which Euler bases himself are the Newtonian laws expressed in differential form, the complete acceptance of the concept of force, the use of pressure as force per surface unit, and the use of clearly defined systems of Cartesian coordinates. All are expressed with an absolute conceptual clarity, and with admirable accuracy in the formulation of the equations, so much so that, although some of the concepts that Euler deploys had already been underlined or used by previous treatise writers, the redefining, concision and accuracy to which he submits them greatly surpasses all his predecessors. Just as in solid mechanics, many of his formulations come down to us almost without any alteration; and what is more, some of his discoveries have been attributed to other authors. In our attempts to follow the theoretical revolution of Euler, we begin with the ‘Principia motus fluidorum’, following with the other three works. As with d’Alembert, we shall limit ourselves only to the more relevant matters, as a detailed study would go significantly beyond the goals we have set ourselves. Finally, a note of a general nature: d’Alembert, as we have seen in the previous chapter, arrived at the constitutive equations of motion as a consequence of the study of a particular problem, which was the search for a new theory for resistance. Euler, by contrast, attacked the problems concerning fluids in a general and very pure way, without reference to any specific application.