ON CONSTRAINED MOTION IN GENERAL.

...we just made mention, and which encompasses the motion of points upon a given line, whether straight or curved. The other species restricts the freedom of motion less, for it prescribes only a surface in which the body must perpetually remain. And these two species of hindered motion original: "motus impediti"; refers to motion restricted by physical boundaries like tracks or walls we are about to explain in this book.

Corollary 3.

7. What must therefore be investigated in the first species are the speed original: "celeritas" of the body, or rather the point, at any location on the prescribed line; the pressure exerted upon this line; and the time in which the point traverses a given portion of the path.

Corollary 4.

8. Concerning the motion of the second species, however, in addition to these factors, the line itself which the body describes upon the given surface must be found. We shall reveal the sources of these matters in this first chapter.

Scholion 4.

9. In this chapter, we will first investigate the motion of both species if the body is urged by no forces original: "a nullis potentiis sollicitetur"; this refers to "free" movement under constraint where no gravity or external pushing is involved; here we will show with what speed it must proceed, and with how much force it presses everywhere against both the given line and the given surface. But if only the surface is given, we shall furthermore determine the path in which the body will move when urged by no forces. Then, we will explain the principles from which it will be possible to judge what changes are produced by urging forces, both absolute and rela-