Cor. 4. The ſame things being ſuppoſed the centripetal force is as the ſquare of the velocity directly. and that chord inverſely. For the velocity is reciprocally as the perpendicular ST; by cor. 1. prop. 1.
Cor. 5. Hence if any curvilinear figure APQ is given; and therein a point S is alſo 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 courſe, and being detained in the perimeter of that figure. will deſcribe the ſame by a perpetual revolution. That is, we are to find by computation, either the ſolid . of the ſolid , reciprocally proportional to this force. Examples of this we ſhall give in the following problems.
Proposition VII. Problem II.
If a body revolves in the circumference of a circle; it is propoſed 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
