The centrifugal force of a body is proportional to _r^3/T^2_, but by Kepler's third law _r^3/T^2_ is constant for all the planets, reckoning _r_ from the sun. Hence the centripetal force needed to hold in all the planets will be a single force emanating from the sun and varying inversely with the square of the distance from that body. Such a force is at once necessary and sufficient. Such a force would explain the motion of the planets. But then all this proceeds on a wrong assumption--that the planetary motion is circular. Will it hold for elliptic orbits? Will an inverse square law of force keep a body moving in an elliptic orbit about the sun in one focus? This is a far more difficult question. Newton solved it, but I do not believe that even he could have solved it, except that he had at his disposal two mathematical engines of great power--the Cartesian method of treating geometry, and his own method of Fluxions. One can explain the elliptic motion now mathematically, but hardly otherwise; and I must be content to state that the double fact is true--viz., that an inverse square law will move the body in an ellipse or other conic section with the sun in one focus, and that if a body so moves it _must_ be acted on by an inverse square law. [Illustration: FIG. 59.] This then is the meaning of the first and third laws of Kepler. What about the second? What is the meaning of the equable description of areas? Well, that rigorously proves that a planet is acted on by a force directed to the centre about which the rate of description of areas is equable. It proves, in fact, that the sun is the attracting body, and that no other force acts. For first of all if the first law of motion is obeyed, _i.e._ if no force acts, and if the path be equally subdivided to represent equal times, and straight lines be drawn from the divisions to any point whatever, all these areas thus enclosed will be equal, because they are triangles on equal base and of the same height (Euclid, I). See Fig. 59; _S_ being any point whatever, and _A_, _B_, _C_, successive positions of a body.