The short form of the title of I. Newton’s treatise Philosophiae naturalis principia mathematica (‘Mathematical Principles of Natural Philosophy’, first edition 1687, second edition 1713). One of the most important scientific books ever written, it deals with the celestial mechanics of the Solar System and for the first time weaves together mathematical analysis and physical observation. It sets out Newton’s law of gravitation and Newton’s laws of motion, presents derivations of Kepler’s laws, and shows how the inverse-square law of gravitation produces motion in an ellipse. There are mathematical treatments of many other phenomena, including the tides and cometary orbits.