Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/103

 II.

''The areas, which revolving bodies decribe by radii drawn to an immoveable centre of force, do lie in the ame immovable planes, and are proportional to the times in which they are decribed. Pl. 2. Fig. 5.''

OR uppoe the time to be divided into equal parts, and in the firt part of that time, let the body by its innate force decribe the right line AB. In the econd part of that time, the ame would, (by law 1.) if not hinder'd, proceed directly to c, along the line Bc equal to AB; o that by the radii AS, BS, cS drawn to the centre, the equal areas ASB, BSc, would be decribed. But when the body is arrived at B, uppoe that a centripetal force act at once with a great impule, and turning aide 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 econd part of the time, the body (by Cor. 1. of the laws) will be found in C, in the ame plane with the triangle ASB. Joyn SC, and, becaue SB and Cc are Rh