Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/118



The ame things being uppoed the centripetal force is as the quare of the velocity directly. and that chord inverely. For the velocity is reciprocally as the perpendicular ST; by cor. 1. prop. 1.

Hence if any curvilinear figure APQ is given; and therein a point S is alo given to which a centripetal force is perpetually directed; that law of centripetal force may be found, by which the body P will be continually drawn back from a rectlinear coure, and being detained in the perimeter of that figure. will decribe the ame by a perpetual revolution. That is, we are to find by computation, either the olid $$\textstyle \frac {SP^2 \times QT^2}{QR}$$. of the olid $$\scriptstyle ST^2 \times PV$$, reciprocally proportional to this force. Examples of this we hall give in the following problems.

If a body revolves in the circumference of a circle; it is propoed to find the law of centripetal force directed to any given point. Pl. 3. Fig. 3.

Let VQPA be the circumference of the circle; S the given point to which as to a centre the force tends; P the body moving in the circumference; Q the next place into which it is to move; and PRZ the tangent of the circle at the preceding place. Through the point S draw the chord PV, and the diameter VA of the circle, join AP, and draw, QT perpendicular to SP, which produced, may meet the tangent