Mathematical Principles of Natural Philosophy

is ordinarily referred to motion. In this sense, rational mechanics will be the science of motions that result from any forces, and of the forces required for any motions, accurately proposed and demonstrated. This part of mechanics was cultivated by the ancients in the five powers These are the "simple machines" of classical antiquity: the lever, pulley, wheel and axle, wedge, and screw. relating to the manual arts, who considered gravity (since it is not a manual power) hardly otherwise than in the moving of weights by those powers. But we, considering not the arts but philosophy original: "philosophiae." In Newton's time, "natural philosophy" was the study of the physical world, what we now call science., and writing not about manual but natural powers, treat those things primarily which relate to gravity, levity original: "levitatem." In older physics, levity was the supposed inherent quality of "lightness" that caused things like smoke to rise, the opposite of gravity., elastic force, the resistance of fluids, and suchlike forces, whether attractive or impulsive: And for that reason, we propose these as our Mathematical Principles of Natural Philosophy. For the whole difficulty of philosophy seems to consist in this: that from the phenomena of motions we investigate the forces of nature, and then from these forces we demonstrate the remaining phenomena. And to this end relate the general propositions which we have treated in the first and second books. In the third book, however, we have proposed an example of this matter through the explanation of the system of the world. For there, from celestial phenomena, through the propositions mathematically demonstrated in the prior books, the forces of gravity are derived by which bodies tend toward the sun and the individual planets. Then from these forces, also through mathematical propositions, the motions of the planets, comets, the moon, and the sea are deduced. I wish it were possible to derive the rest of the phenomena of nature from mechanical principles by the same kind of reasoning. For many things move me to suspect somewhat that they may all depend upon certain forces by which the particles of bodies, through causes not yet known, are either mutually impelled toward one another and cohere according to regular figures, or are repelled and recede from one another; being ignorant of these forces, philosophers have hitherto attempted to understand nature in vain. I hope, however, that either to this mode of philosophizing, or to some truer one, the principles set down here will afford some light.

In publishing these things, the most keen and, in every branch of literature, most learned man Edmond Halley Halley was a renowned astronomer who not only encouraged Newton to write the Principia but also paid for its publication. has labored with great diligence; he not only corrected the errors of the typesetters and saw to the engraving of the diagrams, but he was also the primary mover behind my undertaking this edition. Indeed, when he had obtained from me the demonstration of the figure of the celestial orbits, he did not cease to request that I communicate the same to the Royal Society, which thereafter, by its encouragements and kind auspices, caused me to begin thinking about publishing the same. But after I had entered upon the inequalities of the lunar motions,