rapidity. He restated the laws of motion in such clear and simple terms that for two and a half centuries no word or line has been changed. Bringing to bear his new calculus he readily solved the problem of falling bodies, and in 1666 discovered the laws of circular motion, seven years before they were published by Huygens in 1673.
To such a wide reader and deep thinker as Newton, the problem of "gravity" would appeal with keen interest. It would have been but natural that he should have gathered together all that was available of the literature of the subject. Thus he was familiar with Kepler's views expressed in the following citation:
The true theory of gravity is founded on the following axioms. Gravity is a mutual affection between cognate bodies toward union or conjunction, similar to the magnetic virtue. . . . If the moon and the earth were not retained in their orbits by their animal force or some other equivalent, the earth would mount to the moon by a fifty-fourth part of their distance from each other, and the moon would fall toward the earth through the other fifty-three parts, that is, assuming that the substance of the earth is of the same density. . ., The sphere of the attractive virtue which is in the moon extends to the earth and entices up the waters, but as the moon flies rapidly across the zenith and the waters can not follow so quickly, a flow of the ocean is occasioned toward the westward. If the attractive virtue of the moon extends to the earth, it follows, with greater reason, that the attractive virtue of the earth extends to the moon and much farther, and, in short, nothing which consists of earthy substance, however constituted, although thrown up to any height, can ever escape the powerful operation of this attractive virtue.
Borelli (1608-1679) also expresses views no less explicit, and, in his work, "On the Satellites of Jupiter," distinctly attributes the revolutions of the heavenly bodies to the force of gravity. So also Bullialdus wrote "that all force respecting the sun as its center, and depending upon matter, must be in a reciprocally duplicate ratio of the distance from the center." This last sentence is quoted from one of Newton's letters, and shows how carefully he had read on the subject.
Of Newton's immediate contemporaries, Robert Hooke and Edmund Halley were actively working in this field. Hooke (1635-1702) especially is ambitious to secure the honor of the solution of the problem the answer to which he reads almost exactly right, but the proof of which—poor man—he can not give. Failing in the demonstration himself, he talks on the subject, about the subject, and all over the subject, in the meetings of the Royal Society, in his papers and in his letters. So full of it is he that he imagines that whatever any one else does is stolen from him. Finally Sir Cristopher Wren offers him a prize if in two months he will produce the boasted of solution. None is forthcoming and history must write Hooke down as a most ardent worker and ingenious man, but as totally unequal to the great task imposed upon Newton.
Halley is more modest; he applies the laws of circular motion published by Huygens in 1671, sees clearly that the Inw of inverse squares
