Euler's laws of motion each governed by Newton’s laws of motion, then Euler’s equations can be derived from Newton’s laws. Euler’s equations can, however, be taken as axioms describing the laws of motion for extended bodies, independently of any particle distribution. The total body force applied to a continuous body with mass , mass density , and volume , is the volume integral integrated over the volume of the body: where is the force acting on the body per unit mass (dimensions of acceleration, misleadingly called the "body force"), and is an infinitesimal mass element of the body. Body forces and contact forces acting
Elements of the Philosophy of Newton mutual Action of Bodies upon Light. Of the Resemblance between the seven Primitive Colours and the seven Notes in Musick. Introductory Ideas concerning Gravity and the Laws of Attraction: That the Opinion of a subtil Matter, Vortices, and a Plenitude, ought to be rejected (But not that subtile Aether which Sir Isaac makes the Cause of Attraction, Refraction, Animal Motion, &c. which pervades the Universe). That the Vortices and Plenitude of Descartes are impossible, and consequently that there is some other Cause of Gravity. What is meant by Vacuity and Space, without which there could be neither Gravity nor Motion.