For theſe forces acting equally (with reſpect to the quantities of the bodies to be moved), and in the direction of parallel lines, will (by Law 2.) move all the bodies equally (as to velocity), and therefore will never produce any change in the poſitions or motions of the bodies among themſelves.
Hitherto I have laid down ſuch principles as have been received by mathematicians, and are confirmed by abundance of experiment. By the firſt two Laws and the firſt two Corollaries, Galileo diſcovered that the deſcent of bodies obſerved the duplicate ratio of the time, and that the motion of projectiles was in the curve of a parabola; experience agreeing with both, unleſs ſo far as theſe motions are a little retarded by the reſiſtance of the air. When a body is falling, the uniform force of its gravity acting equally, impreſſes, in equal particles of time, equal forces upon that body, and therefore generates equal velocities; and in the whole time impreſſes a whole force, and generates a whole velocity proportional to the time. And the ſpaces deſcribed in
