From the first law of Kepler, namely, the proportionality of the areas to the times of their description, Newton inferred that the force which retained the planet in its orbit was always directed to the sun. From the second, namely, that every planet moves in an ellipse with the sun as one of foci, he drew the more general inference that the force by which the planet moves round that focus varies inversely as the square of its distance therefrom. He demonstrated that a planet acted upon by such a force could not move in any other curve than a conic section; and he showed when the moving body would describe a circular, an elliptical, a parabolic, or hyperbolic orbit. He demonstrated, too, that this force or attracting, gravitating power resided in even the least particle; but that in spherical masses it operates as if confined to their centres, so that one sphere or body will act upon another sphere or body with a force directly proportional to the quantity of matter and inversely as the square of the distance between their centres, and that their velocities of mutual approach will be in the inverse ratio of their quantities of matter. Thus he outlined the universal law. _The System of the World_ It was the ancient opinion of not a few (writes Newton in Book III.) in the earliest ages of philosophy that the fixed stars stood immovable in the highest parts of the world; that under the fixed stars the planets were carried about the sun; that the earth, as one of the planets, described an annual course about the sun, while, by a diurnal motion, it was in the meantime revolved about its own axis; and that the sun, as the common fire which served to warm the whole, was fixed in the centre of the universe. It was from the Egyptians that the Greeks derived their first, as well as their soundest notions of philosophy. It is not to be denied that Anaxagoras, Democritus and others would have it that the earth possessed the centre of the world, but it was agreed on both sides that the motions of the celestial bodies were performed in spaces altogether free and void of resistance. The whim of solid orbs was[1] of later date, introduced by Endoxus, Calippus and Aristotle, when the ancient philosophy began to decline. As it was the unavoidable consequence of the hypothesis of solid orbs while it prevailed that the comets must be thrust down below the moon, so no sooner had the late observations of astronomers restored the comets to their ancient places in the higher heavens than these celestial spaces were at once cleared of the encumbrance of solid orbs, which by these observations were broken to pieces and discarded for ever.