A Brief History of the Principia

The Origins of the Principia

Isaac Newton's Principia was published in 1687. The full title is Philosophiae Naturalis Principia Mathematica, or Mathematical Principles of Natural Philosophy. A revised edition appeared in 1713, followed by a third edition in 1726, just one year before the author's death in 1727. The subject of this work, to use the name assigned by Newton in the first preface, is "rational mechanics." Later on, Leibniz introduced the name "dynamics." Although Newton objected to this name, "dynamics" provides an appropriate designation of the subject matter of the Principia, since "force" is a primary concept of that work. Indeed, the Principia can quite properly be described as a study of a variety of forces and the different kinds of motions they produce. Newton's eventual goal, achieved in the third of the three "books" of which the Principia is composed, was to apply the results of the prior study to the system of the world, to the motions of the heavenly bodies. This subject is generally known today by the name used a century or so later by Laplace, "celestial mechanics."

The history of how the Principia came into being has been told and retold. In the summer of 1684, the astronomer Edmond Halley visited Newton in order to find out whether he could solve a problem that had baffled Christopher Wren, Robert Hooke, and himself: to find the planetary orbit that would be produced by an inverse-square central force. Newton knew the answer to be an ellipse. He had solved the problem of elliptical orbits earlier, apparently in the period 1679–1680 during the course of an exchange of letters with Hooke. When Halley heard Newton's reply, he urged him to write up his results. With Halley's prodding and encouragement, Newton produced a short tract which exists in several versions and will be referred to as De Motu (On Motion), the common beginning of all the titles Newton gave to the several versions. Once started, Newton could not restrain the creative force of his genius, and the end product was the Principia. In his progress from the early versions of De Motu to the Principia, Newton's conception of what could be achieved by an empirically based mathematical science had become enlarged by several orders of magnitude.

As first conceived, the Principia consisted of two "books" and bore the simple title De Motu Corporum (On the Motion of Bodies). This manuscript begins, as does the Principia, with a series of Definitions and Laws of Motion, followed by a book 1 whose subject matter more or less corresponds to book 1 of the Principia. The subjec