NEWTON, ISAAC (b. Woolsthorpe, England, 25 December 1642; d. London, England, 20 March 1727), mathematics, dynamics, celestial mechanics, astronomy, optics, natural philosophy.

    stated that in books I and II he had set forth principles of mathematical philosophy, which he would now apply to the system of the world. The preface refers to an earlier, more popular version,162 of which Newton had recast the substance “into the form of Propositions (in the mathematical way).”

A set of four “rules of reasoning in [natural] philosophy” follows the preface. Rule 1 is to admit no more causes than are “true and sufficient to explain” phenomena, while rule 2 is to “assign the same causes” insofar as possible to “the same natural effects.” In the first edition, rules 1 and 2 were called “hypotheses,” and they were followed by hypothesis 3, on the possibility of the transformation of every body “into a body of any other kind,” in the course of which it “can take on successively all the intermediate grades of qualities.” This “hypothesis” was deleted by the time of the second edition.163

A second group of the original “hypotheses” (5 through 9) were transformed into “phenomena” 1 and 3 through 6. The first states (with phenomenological evidence) the area law and Kepler's third law for the system of Jupiter's satellites (again Kepler is not named as the discoverer of the law). Phenomenon 2, which was introduced in the second edition, does the same for the satellites of Saturn (just discovered as the Principia was being written, and not mentioned in the first edition, where reference is made only to the first [Huygenian] satellite discovered). Phenomena 3 through 6 (originally hypotheses 6 through 9) assert, within the limits of observation: the validity of the Copernican system (phenomenon 3); the third law of Kepler for the five primary planets and the earth--here for the first time in the Principia mentioning Kepler by name and thus providing the only reference to him in relation to the laws or hypotheses of planetary motion (phenomenon 4); the area law for the “primary planets,” although without significant evidence (phenomenon 5); and the area law for the moon, again with only weak evidence and coupled with the statement that the law does not apply exactly since “the motion of the moon is a little disturbed by the action of the sun” (phenomenon 6).

It has been mentioned that Newton probably called these statements “phenomena” because he knew that they are valid only to the limits of observation. In this sense, Newton had originally conceived Kepler's laws as planetary “hypotheses,” as he had also done for the phenomena and laws of planetary satellites.164

The first six propositions given in book III display deductions from these “phenomena,” using the mathematical results that Newton had set out in book I. Thus, in proposition 1, the forces “by which the circumjovial planets are continually drawn off from rectilinear motions, and retained in their proper orbits” are shown (on the basis of the area law discussed in propositions 2 and 3, book I, and in phenomenon 1) to be directed toward Jupiter's center. On the basis of Kepler's third law (and corollary 6, proposition 4, book I) these forces must vary inversely as the square of the distance; propositions 2 and 3 deal similarly with the primary planets and our moon.

By proposition 5, Newton was able to conclude (in corollary 1) that there “is . . . a power of gravity tending to all the planets” and that the planets “gravitate” toward their satellites, and the sun “towards all the primary planets.” This “force of gravity” varies (corollary 2) as the inverse square of the distance; corollary 3 states that “all the planets do mutually gravitate towards one another.” Hence, “near their conjunction,” Jupiter and Saturn, since their masses are so great, “sensibly disturb each other's motions,” while the sun “disturbs” the motion of the moon and together both sun and moon “disturb our sea, as we shall hereafter explain.”

In a scholium, Newton said that the force keeping celestial bodies in their orbits “has been hitherto called centripetal force”; since it is now “plain” that it is “a gravitating force” he will “hereafter call it gravity.” In proposition 6 he asserted that “all bodies gravitate towards every planet”; while at equal distances from the center of any planet “the weight” of any body toward that planet is proportional to its “quantity of matter.” He provided experimental proof, using a pair of eleven-foot pendulums, each weighted with a round wooden box (for equal air resistance), into the center of which he placed seriatim equal weights of wood and gold, having experimented as well with silver, lead, glass, sand, common salt, water, and wheat. According to proposition 24, corollaries 1 and 6, book II, any variation in the ratio of mass to weight would have appeared as a variation in the period; Newton reported that through these experiments he could have discovered a difference as small as less than one part in a thousand in this ratio, had there been any.165

Newton was thus led to the law of universal gravitation, proposition 7: “That there is a power of gravity tending to all bodies, proportional to the several quantities of matter which they contain.” He had shown this power to vary inversely as the square of the distance; it is by this law that bodies (according to the third law of motion) act mutually upon one another.

From these general results, Newton turned to practical problems of astronomy. Proposition 8 deals with gravitating spheres and the relative masses and