Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/320

 will be the accelerative attraction of the body P towards S at an ditance SP. Join PT and draw LM parallel to it meeting ST in M; and the attraction SL will be reolved (by cor. 2. of the laws of motion) into the attractions SM, LM. And o the body P will be urged with a threefold accelerative force. One of thee forces tends towards T; and aries from the mutual attraction of the bodies T and P. By this force alone the body P would decribe round the body T; by the radius PT, areas proportional to the times, and an ellipis whoe 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 becaue it tends from P to T will be uper-added to and coincide with the former force; and caue the area's to be till proportional to the times, by cor. 3. theor. 21. But becaue it is not reciprocally proportional to the quare of the ditance PT, it will compoe 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 ince by prop. 11. and by cor. 2. theor. 21. the force with which the ellipis is decribed about the focus T ought to be directed to that focus; and to be reciprocally proportional to the quare of the ditance PT; that compounded force varying from that proportion will make the orbit PAB vary from the figure of an ellipis that has its focus in the point T; and o much the more by how much the variation from that proportion is greater