PREFACE

Just as in the first Volume I explained the free motions of bodies acted upon by any forces whatsoever, so in this second Volume I have decided to treat motions that are not free; this difference in the explanation of motion is of such great importance that the division of the entire work has been deservedly based upon it. For in free motion original: "motu libero", the path described by a body is determined both by the motion already inherent in it and by the forces—both absolute forces and resistance—by which the body is affected, because it is assumed that nothing is present besides these forces and resistance to determine the body's motion. And therefore, this is the primary property of free motion: that the path described by the body is not pressed upon at all; that is to say, a channel Euler uses the "canal" or "channel" as a conceptual model for a constrained path curved exactly according to the path which the body ought to describe will sustain no pressure at all from the passing body, but the body passes through it freely. In motion that is not free, however, we assume that besides the forces and resistance by which the body is stirred, a path has been prescribed, so that the body is compelled to move along this path. This prescribed path, therefore, can be conveniently considered in the likeness of a channel in which the body moves and from which it cannot break out. Since, therefore, in motions of this kind the path in which the body must move is given, it must be investigated,