one to the other in the duplicate ratio of the ſides AD, AE. Q.E.D.
Lemma X.
The ſpaces which a body deſcribes by any finite force urging it, whether that force is determined and immutable, or is continually augmented or continually diminiſhed, are in the very beginning of the motion one to the other in the duplicate ratio of the times.
Let the times be repreſented by the lines AD, AE, and the velocities generated in those times be ordinates DB, EC. The ſpaces described with these velocities will be as the areas ABD, ACE, deſcribed by thoſe ordinates, that is, at the very beginning of the motion (by Lem. 9.) in the duplicate ratio of the times AD, AE.
Cor 1. And hence one may eaſily infer, that the errors of the bodies deſcribing ſimilar parts of ſimilar figures in proportional times, are nearly in the duplicate ratio of the times in which they generated; if ſo be these errors are generated by any equal forces ſimilarly applied to the bodies, and meaſured by the diſtances of the bodies from those places of the ſimilar figures, at which, without the action of thoſe forces, the bodies would have arrived in thoſe proportional times.
