12. If motion be made by the concourse of two movents, whereof one is moved uniformly, the other beginning from rest in the angle of concourse with any acceleration whatsoever; the movent, which is moved uniformly, shall put forward the moved body in the several parallel spaces, less than if both the movents had uniform motion; and still less and less, as the motion of the other movent is more and more accelerated. Let the body be placed in A, (in the 7th figure) and be moved by two movents, by one with uniform motion from the strait line A B to the strait line C D parallel to it; and by the other with any acceleration, from the strait line A C to the strait line B D parallel to it; and in the parallelogram A B D C let a space be taken between any two parallels E F and G H. I say, that whilst the movent A C passes through the latitude which is between E F and G H, the body is less moved forwards from A B towards C D, than it would have been, if the motion from A C to B D had been uniform. For suppose that whilst the body is made to descend to the parallel E F by the power of the movent from A C towards B D, the same body in the same time is moved forwards to any point F in the line E F, by the power of the movent from A B towards C D; and let the strait line A F be drawn and produced indeterminately, cutting G H in H. Seeing therefore, it is as A E to A G, so E F to G H; if A C should descend towards B D with uniform motion, the body in the time G H, (for I make A C and its parallels the measure of time,) would be found in the point H. But because A C is supposed to be moved towards B D with motion continually accelerated, that is, in greater proportion of space to space, than of time to time, in the time G H the body will be in some parallel beyond it, as between G H and B D. Suppose now that in the end of the time G H it be in the parallel I K, and in I K let I L be taken equal to G H. When therefore the body is in the parallel I K, it will be in the point L. Wherefore when it was in the parallel G H, it was in some point between G and H, as in the point M; but if both the motions had been uniform, it had been in the point H; and therefore whilst the movent A C passes over the latitude which is between E F and G H, the body is less moved forwards from A B towards C D, than it would have been, if both the motions had been uniform; which was to be demonstrated. 13. Any length being given, which is passed through in a given time with uniform motion, to find out what length shall be passed through in the same time with motion uniformly accelerated, that is, with such motion that the proportion of the lengths passed through be continually duplicate to that of their times, and that the line of the impetus last acquired be equal to the line of the whole time of the motion.