Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/322

 ame in that cae as if thoe attractions did not act at all. by cor. 6. of the laws of motion. And by a like reaoning if the attraction SN is les than the attraction SM, it will take away out of the attraction SM the part SN, o that there will remain only the part (of the attraction) MN, to diturb the proportionality of the area's and times, and the elliptical figure of the orbit. And in like manner if the attraction SN be greater than the attraction SM, the perturbation of the orbit and proportion will be produced by the difference MN alone. After this manner the attraction SN reduces always the attraction SM to the attraction MM the firt and econd attractions perfectly unchanged; and therefore the area's and times come then nearet to proportionality, and the orbit PAB to the above-mentioned elliptical figure, when the attraction MN is either none, or the leat that is poible; that is, when the accelerative attractions of the bodies P and T approach as near as poible to equality; that is, when the attraction SN is neither none at all, nor les than the leat of all the attractions SM, but is as it were a mean between the greatet and leat of all thoe attractions SM. that is, not much greater nor much les than the attraction SK. Q. E. D.

Let now the leer bodies P, S, revolve about a greater T in different planes; and the force LM acting in the direction of the line PT ituate in the plane of the orbit PAB, will have the ame effect as before; neither will it draw the body P from the plane of its orbit. But the other force NM acting in the direction of a line parallel to ST (and which therefore what the body S is without the line of the nodes in inclined