  The first chapter of the Metaphysical Foundations, the Phoronomy, considers the quantity of motion of matter and how it is to be constructed in intuition a priori (so as to produce the kind of rules that are necessary for our experience of matter in motion). Since extension and impenetrability are not directly relevant to how different magnitudes (or degrees) of motion can be represented, Kant restricts his discussion in this chapter to matter considered as a point. Since the motion of a point in space can be represented straightforwardly, the main issue is how to represent the composition of two different motions. Kant's primary claim in this chapter is that due to the relativity of space (i.e., the fact that every motion can be viewed arbitrarily as either the motion of a body in a space at rest, or as a body in a state of rest in a space which is in motion in the opposite direction with the same velocity) “the composition of two motions of one and the same point can only be thought in such a way that one of them is represented in absolute space, and, instead of the other, a motion of the relative space with the same speed occurring in the opposite direction is represented as the same as the latter” (4:490). The proof of this Theorem considers the three possible cases for the composition of two motions: (i) The two motions are in the same direction; (ii) the two motions are in opposite directions; (iii) the two motions enclose an angle. Kant then shows how one can construct a priori in intuition a single motion out of the two motions described in cases (i)-(iii). The synthetic a priori outcome of this constructive procedure is a composition theorem that covers two fundamental results of classical physics: the parallelogram rule for velocity addition, and the Galilean kinematic transformations.  The theorem is needed for architectonic reasons too, not just as a foundation for science. Kant uses the composition theorem as a premise in his Dynamics, so as to infer a priori to forces from the composite motions they cause (e.g., 4:497). And, he invokes the theorem explicitly in his Mechanics, in the course of “constructing the communication of motion,” i.e. deriving the laws of impact (4:546).