both ways, it will paſs through the centre of force.
Cor. 3. If the chords AB, BC, and DE, EF, of arcs deſcrib'd in equal times, in ſpaces void of reſiſtance, are compleated into the parallelograms ABCD, DEFZ; the forces in B and E are one to the other in the ultimate ratio of the diagonals BV, EZ, when thoſe arcs are diminiſhed in infinitum. For the motions B; and EF of the body (by cor. 1. of the laws) are compounded of the motions Bc, BV and Ef, EZ: but BV and EZ, which are equal to Cc and Ff in the demonſtration of this propoſition, were generated by the impulſes of the centripetal force in B and E, and are therefore proportional to thoſe impulſes.
Cor. 4. The forces by which bodies, in ſpaces void of reſiſtance, are drawn back from rectilinear motions, and turned into curvilinear orbits, are one to another as the vers'd ſines of arcs deſcribed in equal times; which verſed ſines tend to the centre of force, and biſect the chords when thoſe arcs are diminiſhed to infinity. For ſuch vers'd ſines are the halfs of the diagonals mentioned in cor. 3.
Cor. 5. And therefore thoſe forces are to the force of gravity, as the ſaid vers'd ſines to the vers'd ſines perpendicular to the horizon of thoſe parabolic arcs which projectiles deſcribe in the ſame time.
Cor. 6. And the ſame things do all hold good (by cor. 5. of the laws) when the planes in which the bodies are mov'd, together with the centres of force which are placed in thoſe planes, are not at reſt but move uniformly forward in right lines.
