Mechanics, Volume I

In a similar way, I then pursued other writings scattered here and there pertaining to this science referring to Mechanics, the science of motion, all of which I explained for my own use in a plain and uniform method, and arranged them into a suitable order. While occupied in this business, I not only came across many questions not yet treated before, which I have successfully solved; but I also attained several peculiar methods, by which both mechanics original: mechanica and analysis original: analysis; here Euler means the branch of mathematics we now call calculus themselves seem to have received no small increase. Hence, therefore, was born this treatise on motion original: de motu tractatus, in which I have set forth, in an analytical method and convenient order, both those things which I found in the writings of others concerning the motion of bodies, as well as those things which I myself have reflected upon.

Moreover, I sought the division of the work both from the distinction of the bodies themselves which are moved, and from their state, whether free or constrained original: vel libero vel non libero. The nature of the bodies itself supplied me with this division: first, I would investigate the motion of infinitely small bodies which are, as it were, points; then indeed I would proceed to bodies of finite magnitude, whether they be rigid, flexible, or composed of parts entirely disconnected from one another Euler is referring to the progression from point-masses to solid mechanics, and eventually to fluid mechanics. For just as in Geometry, in which the dimensions of bodies are taught, the treatment is accustomed to begin from points, so too the motion of bodies of finite magnitude cannot be explained unless the motion of the points from which the composite bodies must be conceived is first...