Section II.
Of the invention of centripetal forces.
Proposition I. Theorem I.
The areas, which revolving bodies deſcribe by radii drawn to an immoveable centre of force, do lie in the ſame immovable planes, and are proportional to the times in which they are deſcribed. Pl. 2. Fig. 5.
OR ſuppoſe the time to be divided into
equal parts, and in the firſt part of that
time, let the body by its innate force deſcribe
the right line AB. In the ſecond
part of that time, the ſame would, (by law 1.) if not hinder'd, proceed directly to c, along the line Bc equal to AB; ſo that by the radii AS, BS, cS drawn to the centre, the equal areas ASB, BSc, would be deſcribed. But when the body is arrived at B,
ſuppoſe that a centripetal force act at once with a great impulſe, and turning aſide the body from the right line Bc, compells it afterwards to continue its
motion along the right line BC. Draw cC parallel to BS meeting BC in C; and at the end of the ſecond part of the time, the body (by Cor. 1. of the laws) will be found in C, in the ſame plane with the triangle ASB. Joyn SC, and, becauſe SB and Cc are
