In January 1684, Edmond Halley, Christopher Wren and Robert Hooke had a conversation in which Hooke claimed to not only have derived the inverse-square law, but also all the laws of planetary motion. Wren was unconvinced, Hooke did not produce the claimed derivation although the others gave him time to do it, and Halley, who could derive the inverse-square law for the restricted circular case (by substituting Kepler’s relation into Huygens’ formula for the centrifugal force) but failed to derive the relation generally, resolved to ask Isaac Newton.
Halley’s visits to Newton in 1684 thus resulted from his debates about planetary motion with Wren and Hooke, and they seem to have provided Newton with the incentive and spur to develop and write what became Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy). Halley was at that time a Fellow and Council member of the Royal Society in London. Halley’s visit to Newton in Cambridge in 1684 probably occurred in August. When Halley asked Newton’s opinion on the problem of planetary motions discussed earlier that year between Halley, Hooke and Wren, Newton surprised Halley by saying that he had already made the derivations some time ago; but that he could not find the papers. Halley then had to wait for Newton to ‘find’ the results, but in November 1684 Newton sent Halley an amplified version of whatever previous work Newton had done on the subject. This took the form of a 9-page manuscript, “De motu corporum in gyrum” (“Of the motion of bodies in an orbit”): the title is shown on some surviving copies, although the (lost) original may have been without title.
Newton’s sent his tract to Halley in late 1684, it derived what are now known as the three laws of Kepler, assuming an inverse square law of force, and generalized the result to conic sections. It also extended the methodology by adding the solution of a problem on the motion of a body through a resisting medium. The contents of so excited Halley by their mathematical and physical originality and far-reaching implications for astronomical theory, that he immediately went to visit Newton again, in November 1684, asking to let the Royal Society have more of such work. The results of their meetings clearly helped to stimulate Newton with the enthusiasm needed to take his investigations of mathematical problems much further in this area of physical science, and he did so in a period of highly concentrated work that lasted at least until mid-1686.
Newton’s single-minded attention to his work generally, and to his project during this time, is shown by later reminiscences from his secretary and copyist of the period, Humphrey Newton. His account tells of Isaac Newton’s absorption in his studies, how he sometimes forgot his food, or his sleep, or the state of his clothes, and how when he took a walk in his garden he would sometimes rush back to his room with some new thought, not even waiting to sit before beginning to write it down. Other evidence also shows Newton’s absorption in the Principia: Newton for years kept up a regular programme of chemical or alchemical experiments, and he normally kept dated notes of them, but for a period from May 1684 to April 1686, Newton’s chemical notebooks have no entries at all. So it seems that Newton abandoned pursuits to which he was normally dedicated, and did very little else for well over a year and a half, but concentrated on developing and writing what became his great work.
The first of the three constituent books was sent to Halley for the printer in spring 1686, and the other two books somewhat later. The complete work, Philosophiae Naturalis Principia Mathematica, published by Halley at his own financial risk, appeared in July 1687.
Edited from Wikipedia by Deskarati