Mechanics, Volume I

[I] subject [them], and I investigate what alteration of motion the various soliciting forces potentiae sollicitantes: external forces acting upon a body to change its state produce in them. However, I consider a body to be free when nothing prevents it from advancing with that speed and in that direction which it ought to have, both by reason of its inherent motion motus insitus: the motion already belonging to the body; inertia and by reason of the soliciting forces. Thus, the planets, as well as bodies on Earth that are either falling or projected, are said to move freely, because in their motion they follow both their inherent force and the effect of the soliciting force. But a body descending on an inclined plane, or a pendulum undergoing oscillations, does not move freely; for the underlying plane, or the pendulum being fixed at one end, prevents the body from descending directly as the force of gravity original: vis gravitatis requires.

Therefore, in the first Chapter, I set forth the general properties of motion and what is usually taught concerning speed, space, and time; and I demonstrate the universal laws of nature which a free body, solicited by no forces, observes. Namely, that if such a body is once at rest, it must persevere in rest forever; but if it has motion, it must advance forever with the same speed in a straight line. Both of these laws can be most conveniently understood under the name of the conservation of state Euler’s term for the Law of Inertia, or Newton's First Law. From this, it follows that the conservation of state is an essential property of all bodies, and