Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/147

 which it will afterwards purue its coure. For by compounding the proper motion of the body with that motion, which the impule alone would rate, you'll have the motion with which the body will go off from a given place of impule, in the direction of a right line given in poition.

And if that body is continually diturbed by the action of ame foreign force, we may nearly know its coure, by collecting the changes which that force introduces in ome points, and elminating the continual changes it will undergo in the intermediate places, from the analogy that appears in the progres of the eries.

If a body P (Pl. 6. Fig. 4.) by means of a centripetal force tending to any given point R move in the perimeter of any given conic ection, whoe centre is C; and the law of the centripetal force is required: Draw C G parallel to the radius RP, and meeting the tangent PG of the orbit in G; and the force required (by cor. 1. & chol. prop, 10. & cor. 3. prop. 7.) will be as $$\textstyle \frac {CG^2}{RP^2}$$.