Fundamentally, the Principia explains the phenomena described by Copernicus, Galileo and Kepler, by elucidating the universal laws underlying them. At the urging of Edmond Halley, secretary to the Royal Society, Newton set about to prove that Kepler's law of planetary motion would cause a planet to orbit elliptically around the sun. Newton established the mathematical basis for the law of inertia and the mechanics of fluids, including the effect of bodies moving through resistant fluids (friction). Further, Newton's law of universal gravitation proved the physical unity of the cosmos: he demonstrated that all of bodies - from dust particles to the moon in its orbit to tidal waves and the blaze of a comet - were subject to the universal law of gravitation, and could be explained, in mathematical terms, within a single physical theory.
"For the first time a single mathematical law could explain the motion of objects on earth as well as the phenomena of the heavens... It was this grand conception that produced a general revolution in human thought, equalled perhaps only by that following Darwin's Origin of the Species" (PMM).
The Principia explained a system of the universe that, once established, was unchallenged until the twentieth century ushered in quantum theory and the theories of relativity. The difficulty of its subject matter (Newton himself called it a "hard" book) and the influence of earlier theories somewhat delayed its general acceptance, but it's mathematical explanations of gravity and motion changed man's understaning of the universe. Going beyond even Horblit's assertion of the work as "the most influential of the seventeenth century" Principia essentially marks the beginning of modern physics.
Probably fewer than three hundred copies of the first edition of Principia were printed, under the supervision, and at the expense of, Edmond Halley. Newton and Halley undertook the distribution through various booksellers themselves, with perhaps 50 being given to Samuel Smith for sale on the Continent. The present copy contains the first issue of the title-page with the two-line imprint and the cancel P4. The variants described by Todd, the priority of which is indeterminate, correspond to those enumerated in the Norman bibliography as pertaining to the Norman copy with the following exceptions: page 209 signature is omitted, page 261 page number is correct, and page 267 signature is KK2.
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