Philosophiæ Naturalis Principia Mathematica

Philosophiæ Naturalis Principia Mathematica (English: The Mathematical Principles of Natural Philosophy), often called simply the Principia (/prɪnˈsɪpiə, -ˈkɪp-/), is a book by Sir Isaac Newton that expounds Newton's laws of motion and his law of universal gravitation.

The Principia is written in Latin and comprises three volumes, and was authorized (imprimatur) by Samuel Pepys, then-President of the Royal Society on 5 July 1686 and first published in 1687. After annotating and correcting his personal copy of the first edition, Newton published two further editions, during 1713 with errors of the 1687 corrected, and an improved version of 1726.

The Principia forms a mathematical foundation for the theory of classical mechanics, and is generally considered to be one of the most important works in the history of science. It has been referred to as "the greatest scientific work in history" and "the supreme expression in human thought of the mind's ability to hold the universe fixed as an object of contemplation".

In formulating his physical laws, Newton developed and used mathematical methods now included in the field of calculus, expressing them in the form of geometric propositions about "vanishingly small" shapes. In a revised conclusion to the Principia (see § General Scholium), Newton emphasized the empirical nature of the work with the expression Hypotheses non fingo ("I frame/feign no hypotheses"). Among other achievements, Newton provides an explanation for Johannes Kepler's laws of planetary motion, which Kepler had obtained empirically.