This edition presents Andrew Motte’s 1729 English translation of Newton’s Philosophiæ Naturalis Principia Mathematica, thoroughly revised and annotated by historian Florian Cajori (with R. T. Crawford stewarding the final publication after Cajori’s death in 1930). It opens with a portrait and Halley’s celebratory ode, then the prefaces to the first three Latin editions, where Newton defines “rational mechanics” as the mathematical study of motion and forces, and declares his program: from phenomena infer forces, then from forces deduce further phenomena. Book I develops the mathematical tools (limits, conics, central forces, apsidal motion, pendula), proving that orbits with equal-areas law imply centripetal attraction. Book II treats motion in resisting media—drag proportional to velocity or its square, hydrostatics, pendular resistance, and waves—bridging ideal dynamics and real fluids. Book III applies the theory to the heavens, stating “Rules of Reasoning,” listing “Phenomena,” and deriving universal gravitation, lunar nodes, tides, precession, cometary paths, and the *General Scholium*. A separate “System of the World” offers a more synthetic exposition. Cajori’s extensive appendix supplies historical and explanatory notes throughout. Cotes’s preface to the second edition champions Newton’s experimental philosophy against scholastic “occult qualities” and Cartesian vortices. He argues from terrestrial gravitation and pendulum experiments to mutual attraction, then by Keplerian area and period–distance laws to centripetal forces inversely as the square of distance, unifying moon, planets, and comets under a single gravitational principle. The prefaces chronicle Newton’s method (analysis from phenomena; synthesis to prediction), Halley’s role in pressing publication, and later refinements to lunar theory, precession, comet orbits, and fluid resistance. Altogether, the volume frames the *Principia* as both a mathematical edifice and a philosophical watershed: geometry and experiment joined to reveal a world governed not by speculative mechanisms but by demonstrable universal laws. This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1934.