A Brief History of the Principia

1.1 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. WhenHalley 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 subject matter of book 2 of this early draft is much the same as that of book 3 of the Principia. In revising this text for the Principia, Newton limited book 1 to the subject of forces and motion in free spaces, that is, in spaces devoid of any resistance. Book 2 of the Principia contains an expanded version of the analysis of motion in resisting mediums, plus discussions of pendulums, of wave motion, and of the physics of vortices. In the Principia, the system of the world became the subject of what is there book 3, incorporating much that had been in the older book 2 but generally recast in a new form. As Newton explained in the final Principia, while introducing book 3, he had originally presented this subject in a popular manner, but then decided to recast it in a more mathematical form so that it would not be read by anyone who had not first mastered the principles of rational mechanics. Even so, whole paragraphs of the new book 3 were copied word for word from the old book 2.

1.2 Steps Leading to the Composition and Publication of the Principia

The history of the development of Newton's ideas concerning mechanics, more specifically dynamics, has been explored by many scholars and is still the subject of active research and study. The details of the early development of Newton's ideas about force and motion, however interesting in their own right, are not directly related to the present assignment, which is to provide a reader's guide to the Principia. Nevertheless, some aspects of this prehistory should be of interest to every prospective reader of the Principia. In thescholium to book 1, prop. 4, Newton refers to his independent discovery (in the 1660s) of the v2/r rule for the force in uniform circular motion (at speed v along a circle of radius r), a discovery usually attributed to Christiaan Huygens, who formally announced it to the world in his Horologium Oscillatorium of 1673. It requires only the minimum skill in algebraic manipulation to combine the rule v2/r with Kepler's third law in order to determine that in a system of bodies in uniform circular motion the force is proportional to 1/r2 or is inversely proportional to the square of the distance. Of course, this computation does not of itself specify anything about the nature of the force, whether it is a centripetal or a centrifugal force or whether it is a force in the sense of the later Newtonian dynamics or merely a Cartesian "conatus," or endeavor. In a manuscript note Newton later claimed that at an early date, in the 1660s, he had actually applied the v2/r rule to the moon's motion, much as he does later on in book 3, prop. 4, of the Principia, in order to confirm his idea of the force of "gravity extending to the Moon." In this way he could counter Hooke's allegation that he had learned the concept of aninverse-square force of gravity from Hooke.

A careful reading of the documents in question shows that sometime in the 1660s, Newton made a series of computations, one of which was aimed at proving that what was later known as the outward or centrifugal force arising from the earth's rotation is less than the earth's gravity, as it must be for the Copernican system to be possible. He then computed a series of forces. Cartesian vortical endeavors are not the...