[A]fterwards it diffused it self thro' the Italic Philosophy, the followers of which taught, that each Star was a World in the infinite Æthereal Spac… - David Gregory

Mr Issac Newton in addition to the geometric figure in any orbit of a projectile sought also to find the measure of the (tending to a given centre) of the body borne in that orbit, from whatever cause that force may arise, be it from a deeper mechanical one or from a law imposed by the supreme creator of all things. He inquires geometrically into the law of centripetal force of a body moved in the circumference of a circle with the force tending to a given point either on the circumference or anywhere outside it or inside it, or even infinitely removed. By the same method he seeks the law of centripetal force tending to the centre of a plane nautical spiral (that is one that the radii cut in a given angle) which will drive a body in that spiral. Also the law of centripetal force that would make a body rotate in an ellipse when the centre of the ellipse coincides with the centre of forces. If the ellipse is changed into a hyperbola and the centripetal force into a centrifugal one the same things apply to the hyperbola. Also the resolution of the same problem when the centre of forces coincides with either focus of the ellipse shows that the law of centripetal force is reciprocally in the duplicate ratio of the distance [as the inverse square of the distance]; others had long before shown that this was the one and only law that would satisfy the other phenomenon observed by Kepler in the motion of the planets. These results also apply to the hyperbola and the parabola when the centre of forces is situated in a focus of the conic section.

For the Sun and Planets are separated from one another by so immense a distance, as renders them incapable of exerting most of those forces whereby all Bodies act upon one another; so that they have no other force left them whereby they can affect one another, but the single force of universal Gravity: Whereas in the production of several Phænomena, that are observ'd upon our Earth, innumerable other forces are exerted, such as are very hard to be distinguish'd from one another; which notwithstanding, if not accurately done, in vain do we attempt Nature, and make any inquiry into it.

Pythagoras... applied the proportion he had thus found by experiments, to the Heavens, and from thence learn'd the Harmony of the Spheres. And, by comparing these Weights with the Weights of the Planets, and the intervals of the Tones, produced by the Weights, with the interval of the Spheres; and lastly, the lengths of Strings with the Distances of the Planets from the Center of the Orbs; he understood, as it were by the Harmony of the Heavens, that the Gravity of the Planets towards the Sun (according to whose measures the Planets move) were reciprocally as the Squares of their Distances from the Sun.