Philosophiæ Naturalis Principia Mathematica

Londini, 1687

In the summer of 1687 a Latin book of some five hundred pages came off a London press. It claimed to derive the motions of the planets, the comets, the Moon and the sea from three laws of motion and a single force that weakens as the square of the distance. This site prints that book in the language Newton wrote it in, and sets an English reader’s notebook beside it.

The Latin is complete: the title page, Newton’s preface, Halley’s ode, the Definitions and Laws of Motion, all three books, and, from the later editions, the famous Scholium Generale. Each page puts Newton on the left and the notes on the right: a plain English gloss, help with the hard words, and a commentary that starts from the concrete problem Newton is attacking before it gives the modern formula.

The opening of the work, from the preface and Halley’s ode through the Definitions, the Laws and the inverse-square law for an ellipse (Book I, Sections I–III), is fully annotated, and so is the General Scholium. Everything else has a headnote and is marked annotation forthcoming.

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Where to start

• Introduction: the book, its edition, and how to read these pages.
• Definitiones: mass, momentum, inertia, force, and the scholium on absolute space and time.
• Axiomata, sive Leges Motus: the three laws and their corollaries.
• Liber I, Sect. I: the method of first and last ratios (Newton’s calculus of limits).
• Liber I, Sect. II: equal areas in equal times, and the formula that turns orbits into force laws.
• Liber I, Sect. III: the ellipse, the focus, and the inverse square.
• Scholium Generale: hypotheses non fingo.
• Full contents