Introduction
The book, and this edition of it
A question asked in August 1684
The Principia began with a question. In August 1684 Edmond Halley rode to Cambridge to ask Isaac Newton what curve a planet would trace if the Sun pulled it with a force falling off as the inverse square of the distance. Hooke, Wren and Halley all suspected the inverse square. None of them could prove what orbit it gave. Newton said at once that it would be an ellipse, and that he had calculated it. He could not find the papers, so he promised to send a proof. That November a short tract, De motu corporum in gyrum, reached London. Over the next eighteen months it grew into three books.
The Royal Society licensed the work on 5 July 1686. The Imprimatur on the title page carries the name of its President, Samuel Pepys. The Society had no money left, so Halley paid for the printing himself, corrected the proofs, and wrote the Latin ode that stands before the text. The book appeared in July 1687.
What the three books do
Book I, De motu corporum, is pure mechanics. Bodies move under centripetal forces in empty space. Newton shows that equal areas in equal times means a force toward a fixed centre, that an ellipse with the force at a focus needs an inverse-square law, and that a uniform sphere attracts as if all its mass sat at its centre. He also takes up the two-body and three-body problems.
Book II is still about motion, now through air, water and other resisting media. It includes pendulum experiments, a theory of the speed of sound, and a demolition of the Cartesian vortices that were supposed to carry the planets.
Book III, De mundi systemate, applies all of this to the heavens. From the observed motions of Jupiter’s moons, the planets and our Moon, Newton argues that one gravitation, mutual and universal, falls off as the inverse square. He then uses it to explain the flattened Earth, the precession of the equinoxes, the tides, the irregularities of the Moon, and the paths of comets.
Which text is printed here
The Latin on these pages is the first edition (London, 1687), page for page. A small number in the left margin, with a ‖ in the line, marks where each page of the 1687 printing begins. The 1687 printing skips the page numbers 384–399; that gap is the printer’s, not ours. The figures are clean redrawings of the 1687 woodcuts.
Newton kept revising. The second edition (Cambridge, 1713, edited by Roger Cotes) and the third (London, 1726, edited by Henry Pemberton) recast Book III’s opening Hypotheses as Regulae philosophandi and Phaenomena, rewrote many arguments, and added the Scholium Generale at the end. Because the General Scholium is not in the first edition, it appears here in its 1726 form, clearly labelled. Where a note depends on a later change, it says so.
Spelling, punctuation, ligatures (æ, œ) and abbreviations are Newton’s printer’s. Two things will trip a modern reader at first: q; is short for -que (“and”), so atq; = atque; and Newton writes algebra in words, so SP quad. or SPq. is SP², cub. a cube, and in or × a product.
How the notes work
Every definition, law, lemma, proposition and scholium is a unit. Where a unit is annotated, the notes beside it have three layers:
- In plain English: a close paraphrase. It is not a translation to read instead of the Latin; it is there to get you through it.
- Words: Newton’s technical vocabulary and the Latin that is hard to look up.
- Commentary: first the concrete problem Newton is facing and why it was hard, then the idea, and only then the modern statement in symbols. These were hard-won results, and the notes try to show the difficulty rather than hide it.
Parts not yet annotated carry a short headnote and are marked annotation forthcoming. Their Latin is already complete.