Mechanics, Volume I

...rest, especially since there would be an opportunity for bringing forward specimens of the calculus calculi: the mathematical system of differentials and integrals Euler was pioneerng. Finally, in the two last chapters, I have contemplated the curvilinear motions motion along a curved path, rather than a straight line of bodies, which arise when the direction of the soliciting powers potentiarum sollicitantium: the external forces "urging" or acting upon a body does not coincide with the direction of the projected body. For in this case, the body is perpetually drawn away from a straight path and is compelled to move in a curved line. In the fifth chapter, indeed, I have explained this kind of curvilinear motion in a vacuum original: in vacuo; in the sixth chapter, however, I have simultaneously considered the resistance of the medium.

The primary problems, therefore, which are contained in these chapters, are concerned with this: that for a body projected in any way and acted upon by any powers, the curve in which it moves may be determined, and at the same time the speed of the body at individual points of the curve may be indicated—and this both in a vacuum and in a resisting medium. From these primary propositions, others then arose, in which either from a given curve described by a body, or from a given nature of the motion, both the soliciting powers and the resistance are sought.

In this undertaking, I have applied myself primarily to encompassing all problems treated by Newton as well as by others pertaining to this matter, and to delivering genuine solutions through the analytical method methodo analytica: a system of solving physics problems using algebraic symbols and equations rather than the traditional geometric diagrams used by Newton. With these topics, therefore, this first Volume is finished. I have written it, as well as the following one, in such a way that anyone who is sufficiently practiced in the analysis of both finites and infinites what we now call algebra and calculus will be able to understand everything with wonderful ease, and read through this entire work without any further guidance.