Page:Kant's Prolegomena etc (1883).djvu/289

 according to the rules of congmity, which is only possible, in all three cases, by means of the motion of the space that is congruous with one of the two given motions, whereby both are congruous with the compound [motion].

Observation 3.

Thus Phoronomy, not as pure doctrine of motion, but as pure doctrine of the quantity of motion, in which matter is conceived by no other quality but that of mere movability, contains nothing but this single proposition, carried out in the three cases adduced, of the composition of motion, and indeed of the possibility of rectilinear motion alone, not of curvilinear; for, because in the latter the motion is continuously changed in direction, a cause of this motion, which cannot be merely space, must be brought to bear. That only the single case in which the directions of the same enclose an angle, is usually understood by the designation compound motion, does some detriment to the principle of the division of a pure philosophical science generally, although not to physics: for, as concerns the latter, all the three cases treated in the above proposition admit of being adequately presented in the third alone. For when the angle enclosing the two given motions is conceived as infinitely small, it contains the first [case]; but if it be conceived as only divided in an infinitely small degree from a single straight line, it contains the second case; so that, in the proposition already stated respecting composite motion, all three cases mentioned by us, are capable of being given as in a universal formula. But in this way one could not learn to comprehend the qualitative doctrine of motion in its parts a priori, which in many respects is also useful.

If any one cares to connect the three parts in question of the universal Phoronomic proposition with the scheme of the subdivision of all pure conceptions of the understanding, here, especially with that of the conception of quantity, he will observe: that, as the conception of a quantity always contains that of the composition of the homogeneous, the doctrine of the composition of motions