Mechanics, Volume I

[their] motion has been diligently examined. For the motion of a body having a finite magnitude finite magnitude: a physical object with measurable size, as opposed to a mathematical point cannot be considered or determined in any other way, unless it is first defined what kind of motion each of its individual particles or points punctum: an infinitely small piece of matter with no dimensions, often called a "point-mass" possesses. Therefore, this treatment concerning the motion of points is the foundation and the principal part of the whole of Mechanics original: Mechanica; the science of how forces affect the motion of bodies, upon which all the remaining parts rely.

Therefore, I have dedicated these first two volumes to this inquiry on the motion of points; in the first of these, I have contemplated free points points moving without constraints, like a ball thrown in the air, and in the second, those that are not free points whose motion is restricted, such as a bead on a wire. Moreover, most of the principles I have set forth in these books apply more broadly than to points alone; from them, the motion of finite bodies can frequently be determined—specifically the total motion the motion of the object's center of mass, but not the motion by which individual parts move relative to one another.

For from the fact that a point projected in a vacuum describes a parabola parabola: the specific U-shaped curve followed by a projectile under the influence of gravity, it is also understood that any finite bodies, if projected, must move in parabolas; however, the motion of the individual parts such as the rotation or vibration of the object as it flies does not follow from this. That investigation is proper to the subsequent Books, in which the motion of finite bodies will be defined. In a similar way also, those things which Newton Sir Isaac Newton (1642–1727), whose Principia established the laws of motion demonstrated concerning the motion of bodies acted upon by centripetal forces vires centripetae: forces that pull an object toward a center, like gravity pulling a planet toward the sun are valid only for points; nevertheless, in the meantime, he correctly transferred those principles to the motion of the planets. In this first Volume, therefore, [I subject] free points to examination