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

Book III, “The System of the World.”

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