Page:Kant's Prolegomena etc (1883).djvu/278

 latter, one will say; for, only in so far as it moves is it present in this point. But let us assume the motion in this way:

that the body describes the line $$A \; B$$ forwards and backwards, from $$B$$ to $$A$$, with uniform velocity in suchwise that, since the moment it is in $$B$$ is common to both motions, the motion from $$A$$ to $$B$$ is described in half a second, that from $$B$$ to $$A$$ also in half a second, but both together in a whole second, so that not the smallest portion of time has been expended on the presence of the body in $$B$$; in this way, without the least increase of these motions, the latter, which took place in the direction $$B \; A$$, can be changed into that in the direction $$B \; a$$, which lies in a straight line with $$A \; B$$, and hence the body, while it is in $$B$$, must be regarded not as at rest, but as moved. It would have therefore also to be considered as moved in the first motion, returning in upon itself in the point $$B$$, which is impossible; because, in accordance with what has been assumed, it is only a moment that belongs to the motion $$A \; B$$, and at the same time to the equal motion $$B \; A$$, which is opposed to the former one and conjoined with it in one and the same moment of complete lack of motion; consequently if this constitutes the conception of rest, in the uniform motion $$A \; a$$, rest of the body must also be proved in every point (e.g., in $$B$$), which contradicts the above assertion. Again, let the line $$A \; B$$ be represented as over the point $$A$$ perpendicularly, so that a body rising from $$A$$ to $$B$$, after having lost its motion through gravity in the point $$B$$, would fill back again from $$B$$ to $$A$$. Now I ask whether the body in $$B$$ is to be considered as moved or at rest? Without doubt, it will be said, at rest; because all previous motion has been taken from it, after it has reached this point, and a uniform motion back is as yet to follow, consequently is not present, and the lack of motion, it will be added, is rest. In the first case, however, of an assumed uniform motion, the motion $$B \; A$$ could not commence otherwise, than by the motion $$A \; B$$ having previously ceased, and