plane, P a body iſſuing from the place P in the direction of the right line PZ, Q the ſame body revolving in its trajectory, and PQR the trajectory it ſelf which is required to be found, deſcribed in that given plane. join CQ, QS, and if in QS we take SV proportional to the centripetal force with which the body is attracted towards the centre S, and draw VT parallel to CQ and meeting SC in T; then will the force SV be reſolved into two, (by cor. 2. of the laws of motion) the force ST, and the force TV; of which ST attracting the body in the direction of a line perpendicular to that plane, does not at all change its motion in that plane. But the action of the other force TV coinciding with the poſition of the plane it ſelf, attracts the body directly towards the given point C in that plane; and therefore cauſes the body to move in this plane in the ſame manner as if the force ST were taken away, and the body were to revolve in free ſpace about the centre C by means of the Force TV alone. But there being given the centripetal force TV with which the body Q revolves in free ſpace about the given centre C, there is given (by pro. 42.) the trajectory PQR which the body deſcribes; the place Q in which the body will be found at any given time; and laſtly, the velocity of the body in that place Q. And ſo è contra. Q. E. I.
