Proposition III. Theorem III.
Every body, that, by a radius drawn to the centre of another body howſover moved, deſcribed areas about that centre proportional to the times, is urged by a force compounded out of the centripetal force tending to that other body, and of all the accelerative force by which that other body is impelled.
Let L repreſent the one, and T the other body; and (by Cor. 6 of the laws) if both bodies are urged in the direction of parallel lines, by a new force equal and contrary to that by which the ſecond body T is urged, the firſt body L will go on to deſcribe about the other body T, the ſame areas as before: but the force, by which that other body T was urged, will be now deſtroyed by an equal and contrary force; and therefore (by Law 1.) that other body T, now left to it ſelf, will either reſt, or move uniformly forward in a right line: and the firſt body L impell'd by the difference of the forces, that is, by the force remaining, will go on to deſcribe about the other body T; areas proportional to the times. And therefore (by Theor. 2.) the difference of the forces is directed to the other body T as its centre. Q. E. D.
Cor. 1. Hence if the one body L, by a radius drawn to the other body T, deſcribes areas proportional to the times; and from the whole force, by which the firſt body L is urged (whether that force is
