The Principia: Mathematical Principles of Natural Philosophy

The Mathematical Principles of Natural Philosophy is often referred to as simply the Principia. It is a work in three books by Isaac Newton, in Latin, first published 5 July 1687. After annotating and correcting his personal copy of the first edition, Newton published two further editions. The Principia states Newton's laws of motion, forming the foundation of classical mechanics; Newton's law of universal gravitation; and a derivation of Kepler's laws of planetary motion.

The Principia is considered one of the most important works in the history of science. The French mathematical physicist Alexis Clairaut declared in 1747: "The famous book of Mathematical Principles of Natural Philosophy marked an age of a great revolution in physics. The method followed by its illustrious author Sir Newton and has spread the light of mathematics on a science which up to then had remained in the darkness of conjectures."

A more recent assessment has been that while acceptance of Newton's theories was not immediate, by the end of a century after publication in 1687, "no one could deny that" (out of the Principia) "a science had emerged that, at least in certain respects, so far exceeded anything that had ever gone before that it stood alone as the ultimate exemplar of science generally."

In formulating his theories, Newton developed and used mathematical methods which are now included in the field of calculus. But the language of calculus as we know it today is absent from the Principia. Newton gave many of his proofs in a geometric form of infinitesimal calculus, based on limits of ratios of vanishing small geometric quantities.