will be the accelerative attraction of the body P towards S at an diſtance SP. Join PT and draw LM parallel to it meeting ST in M; and the attraction SL will be reſolved (by cor. 2. of the laws of motion) into the attractions SM, LM. And ſo the body P will be urged with a threefold accelerative force. One of theſe forces tends towards T; and ariſes from the mutual attraction of the bodies T and P. By this force alone the body P would deſcribe round the body T; by the radius PT, areas proportional to the times, and an ellipſis whoſe focus is in the centre of the body T; and this it would do whether the body T remained unmoved, or whether it were agitated by that attraction. This appears from prop. 11. and cor. 2 & 3 of theor. 21. The other force is that of the attraction LM, which becauſe it tends from P to T will be ſuper-added to and coincide with the former force; and cauſe the area's to be ſtill proportional to the times, by cor. 3. theor. 21. But becauſe it is not reciprocally proportional to the ſquare of the diſtance PT, it will compoſe when added to the former, a force varying from proportion; which variation will be the greater, by how much the proportion of this force to the former is greater, cæteris paribus. Therefore ſince by prop. 11. and by cor. 2. theor. 21. the force with which the ellipſis is deſcribed about the focus T ought to be directed to that focus; and to be reciprocally proportional to the ſquare of the diſtance PT; that compounded force varying from that proportion will make the orbit PAB vary from the figure of an ellipſis that has its focus in the point T; and ſo much the more by how much the variation from that proportion is greater
