Page:Kant's Prolegomena etc (1883).djvu/279

 that from $$B$$ to $$A$$ being non-existent, and consequently there being in $$B$$ a lack of all motion, whereby, according to the usual explanation, rest would have to be assumed; but we may not assume it, because at a given velocity, no body may be conceived as at rest in any point of its uniform motion. Upon what, then, is the assumption of rest based in the second case, since this rising and falling is only separated by a moment? The ground lies in the latter motion not being conceived as uniform with the given velocity, but as being at first uniformly delayed, and afterwards uniformly accelerated, in suchwise that the velocity in point $$B$$ is not delayed, wholly, but only up to a certain degree, smaller than any velocity that can be given, by which, if instead of falling back, the line of its fall $$B \; A$$ were placed in the direction $$B \; a$$; in other words, the body were conceived as still rising, it would, as with a mere moment of velocity (the resistance of gravity being set aside), pass over, in any given time, however great, a space smaller than any space that could be given, and therefore its place (for any possible experience) would not change to all eternity. In consequence of this, it assumes a state of lasting presence in the same place, that is, of rest, although owing to the continuous action of gravity, that is, of the change of this state, the latter is immediately abolished. To be in a permanent state and to persist therein (if nothing else shifts it) are two distinct conceptions, of which one does no violence to the other. Thus rest cannot be explained through the lack of motion, which, as = o, does not admit of being constructed at all, but must be explained by permanent presence in the same place, and as this conception is constructed by the presentation of a motion with infinitely small velocity, throughout a finite time, it can be used for the subsequent application of mathematics to natural science.

To the conception of a composite motion means to present à priori in intuition a motion so far as it arises from two or more given [motions] united in one movable.