Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/256

 to the velocity of the decribing line CP; that is, as the angle VCp to the angle VCP, therefore in a given ratio, and therefore proportional to the time. Since then the area decribed by the line Cp in an immovable plane is proportional to the time, it is manifet that a body, being acted upon by a jut quantity of centripetal force, may revolve with the point p in the curve line which the ame point p, by the method jut now explained, may be made to decribe in an immovable plane. Make the angle VCu equal to the angle PCp, and the line Cu equal to CV and the figure uCp equal to the figure VCP, and the body being always in the point p, will move in the perimeter of the revolving figure uCp, and will decribe its (revolving) arc up in the ame time that the other body P decribes the imilar and equal arc VP in the quiecent figure VPK. Find then by cor. 5. prop. 6. the centripetal force by which a body may be made to revolve in the curve line which the point p decribes in an immovable plane, and the problem will be olved. Q. E. F.

The difference of the forces, by which two bodies may be made to move equally, one in a quiecent, the other in the ame orbit revolving, is in a triplicate ratio of their common altitudes inverely.

Let the parts of the quiecent orbit VP, PK, (Pl. 18. Fig. 2.) be imilar and equal to the