Chapter 1

Motion Which In Is Not Free

Motion is the translation of a body from the place it occupies to another place. True rest is a body remaining at the same place.

Euler
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Table of Contents

DEFINITION 1.

  1. A body is said not to move freely, [i.e. to be constrained ] when external obstacles impede its progress, and in a like manner its motion in that direction is less than it should be moving, by reason of the absolute forces acting on it.

Scholium 1.

  1. In the motion of free points that we set out in the first part, the space in which we assume the body moves is a vacuum free from all obstacles; now truly we put in place a space for comparison, so that it is not permitted for the body to progress in any direction because of solid walls across which it is not allowed to pass.

Corollary 1.

  1. Therefore when a body finds an obstacle to its own motion it is not able to keep moving in that direction which it held, then either it comes to rest or the motion must continue in another direction.

Corollary 2.

  1. Moreover, in what direction the body progresses after meeting the obstacle must be determined from the circumstances both of the motion and of the position of the obstacle.

Scholium 2

  1. It seems that this is relevant to the theory of the collisions of bodies, in which the body is not yet free to move in this way or that. Truly in this book we assume obstacles of other kinds, which do not require that acquaintance. These are continuous obstacles that restrict the motion of points and neither do they allow any turning back; and a pipe or channel which is either straight or curved is an obstacle of this kind, along which the motion of a small body must continue. In this case the path inside is prescribed in which the body is to progress, and it is not able to escape because of the firmness of the pipe [or tube]. Whereby, since here in place of a body we consider a point, a point on a given line must be moving from this position, and it is unable to leave this line.

Scholium 3.

  1. Moreover in this book we deal with the two motions of the impeded or restricted kind, [p. 3] of which the first we have made mention includes the motion of points on a given line or curve. The other kind restricts the freedom of the motion less ; for it only prescribes a surface on which the body must always be moving. And we are to explain these two kinds of impediments to the motion in this book.

Corollary 3. 7. Therefore these properties are sought for the first kind of motion which are : the speed of the body or rather of a point in the position of any prescribed line; the force on this line; and the time in which a given point traverses a portion of the path.

Corollary 4. 8. Concerning the motion of the other kind, more than the motion on this line has to be found, as the body describes the motion upon a given surface. Concerning which we uncover the principles in this first chapter.

Scholium 4.

  1. Truly in this first chapter we investigate both kinds of motions, for which the body is acted on by no forces, where we show with what speed it should be progressing, and what force is must exert everywhere not only on a given line but also on a given surface. But if only a surface is given, then in addition we must determine the path along which the body moves when acted on by no forces. Then we set out the principles, by which it can be determined, what changes in the path arise with forces acting, both absolute and relative, [p. 4] and from which in the following chapters we can deduce particular individual cases.

Scholium 5.

  1. Moreover, for both motion on a given line as for motion on a given surface, we imagine that all friction has been removed and we put no retardation to the motion in place. On this account the lines and the surfaces upon which the points are placed to be moved, are considered to be the smoothest and free of all asperities, least the motion should be liable to be slowed down on that account. All rotational motion also we imagine to be removed everywhere, which is to be explain at length later. Because of this, a point is considered to be moving as if by creeping along, in order that any part of this, if in this manner a point can be considered as made up of parts of points [this is an idea introduced in Ch. I of Book I and not yet used], then they have the same motion.

Scholium 6.

  1. Therefore what has been treated in the preceding book, and what is to be treated concerning the motion of points in this book, can be adapted to bodies of finite size also, but only if the movement of these is always parallel to themselves, and all the parts of the body are provided with equal motion. This indeed will become clearer from the following books, for which there is no disagreements between the case of the motion of finite bodies from the motion of points. On which account therefore in these books we consider only points since, as they do not have different parts, thus also they are unable to have parts with different motions.

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