As usually phrased, the law is this: That every particle of matter in the universe attracts every other particle with a force that varies directly with the mass of the particles and inversely as the squares of their mutual distance.
Newton did not vault at once to the full expression of this law, though he had formulated it fully before he gave the results of his investigations to the world.

We have now to follow the steps by which he reached this culminating achievement.
At the very beginning we must understand that the idea of universal gravitation was not absolutely original with Newton.

Away back in the old Greek days, as we have seen, Anaxagoras conceived and clearly expressed the idea that the force which holds the heavenly bodies in their orbits may be the same that operates upon substances at the surface of the earth.

With Anaxagoras this was scarcely more than a guess.

After his day the idea seems not to have been expressed by any one until the seventeenth century's awakening of science.