Phoronomy is a doctrine of the composition of the motions of the same point according to its direction and velocity i.e., the presentation of a single motion as one that comprises within it two or perhaps several motions in one, at the same time, in the same point, so far as they together constitute one, that is, are one with this motion, but not in so far as they produce the latter as causes produce their effects. In order to find the motion arising from the composition of several—as many as one likes—one has only, as with the production of all quantities, first to seek out those that are compounded under given conditions, of two; and thereupon combine this with a third, etc. In consequence the doctrine of the composition of all motions is reducible to that of two. But two motions, of one and the same point that are present at the same point may be distinguished in a double manner, and as such be combined in a triple way therein. Firstly, they occur at the same time either in one and the same line, or in different lines; the latter are motions enclosing an angle. Those that occur in one and the same line are either contrary to one another in direction or maintain the same direction. As all these motions are contemplated as taking place alone, there results immediately from the relation of the lines, that is, of the spaces of motion described in equal time, the relation of velocity. Thus there are three cases:—1. As two motions (it matters not whether of equal or unequal velocities) combined in one body in the same direction, are to constitute a resultant compound motion; 2. As Two motions of the same point (of equal or unequal velocity), combined in contrary directions, are, through their composition, to constitute a third motion in the same line; 3. Two motions of a point, with equal or unequal velocities, but in different lines, enclosing an angle, are considered as compounded.
Proposition 1.
The composition of two motions of one and the same point, can only be conceived by one of them being presented in absolute space, but, instead of the other, a motion of an equal velocity in the contrary direction of the relative space [being presented] as identical with it.
