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Author, then a Fellhw of Trinity-College$ Cambrigde + and
in the Year 1713, republished with confiderable Improve-
ments. Several other Authors have fince attempted to
make it plainer 5 by fetting afide many of the more
fublime MathematicalRefearches, and fubilituting either
more obvious Reafonings, or Experiments, in lieu thereof;
particularly Whiflon in his Prxeleh. Phyf. Mathemat. and
Gravefande in Element. e Infiit.
Notwithfianding the great Merit of this Philofophy, and
the univerfal Reception it has met with at home, it gains
ground very flowly abroad ; Newtonianifm has fcarce two
or three Adherents in a Nation; but Cartefianifm, Huyge-
flianifm, and Leibnitzianifm remain till in poffeflion.
The Philofopby itfelf is laid down chiefly in the third
Book of the Principia. The two preceding Books are
taken up in preparing the way, and laying down fuch Pr in-
ciples o Mathematicks as have the moit relation to Pbilo-
fopby: Such are the Laws and Conditionsof Powers. And
thefe, to render them lefs dry and geometrical, the Author
illuflrates by Scbolia in Tbilofoph.y, relating chiefly to the
Denfity and Refiflance of Bodies, the Motion of Light,
and Sounds, a Vacuum, Etc.
In the third Book he proceeds to the Philoropby itfelf;
and from the fame Principles deduces the Struaure of the
Univerfe; and the Powers of Gravity, whereby Bodies
tend towards the Sun and Planets; and from thefe Powers,
the Motions of the Planets and Comets, the Theory of the
Moon and the Tides.
This Book, which he calls de Mandi Siftemate, he tells us,
was firft wrote in the popular way: But confidering, that
fuch as are unacquainted with the faid Principles, would not
conceive the Force of the Confequences, nor be induced to
lay afide their antient Prejudices; for this Reafon, and to
prevent the thing from being in continual Difpute ; he di-
gefted the Sum of that Book into Propofitions, in the Ma-
thematical manner ; fo as it might only come to be read
by fuch as had firfi confider'd the Principles. Not that it
is necefary, a Man Ihould mailer them all. Many of them,
even the firft-rate Mathematicians, would find a Difficulty
in getting over. 'Tis enough to have read the Definitions,
Laws of Motion, and the three firft Sedions of the firft
Book; after which, the Author himfeif direas us to pafs
on to the Book de Syjfemate Mundi.
The feveral Articles of this Philtifopby, are deliver'd under
their refpeffive Heads in this Didionary ; as S'JN, MooN,
PLANET, COMET, EARTH, AIR, CENTRIPETAL Force,
RESISTANCE, MEDIUM, MATTER, SPAiCE, ELASTI-
CITY, Sc. A general Idea, or Abfiraa of the Whole,
we Ihall here gratify the Reader withal ; to lhew in what
Relation the feveral Parts Rand to each other.
The great Principle on which the whole Philofophy is
founded, is the Power of Gravity. This Principle is not
new: Kepler, long ago, hinted it in his Introdulf. ad Mot.
Martis. He even discovered fome of the Properties thereof,
and their EffehLs in the Motions of the primary Planets:
But the Glory of bringing it to a Phyfical Demonifration
was referved to the Engls Philofopber. SeeGRAVITY.
His Proof of the Principle from Phxnomena ; together
with the Application of the fame Principle to the various
other Appearances of Nature, or the deducing thofe Ap-
pearances from that Principle, conflitute the Newtonian
System ; which, drawn in Miniature, will fSand thus.
I. The Phxenomena are, I. That the Satellites of hqiter
do, by Radii drawn to the Center of the Planet, defcribe
Areas proportional to their Times; and that their Periodical
Times are in a fefquiplicate Ratio of their Difiances from
its Centre: in which all Obfervations of all Afironomers
agree. 2. The fame Phxnomenon holds of the Satellites of
Saturn, with regard to Saturn; and of the Moon with regard
to the Earth. 3. The periodical Times of the primary
Planets about the Sun, are in a fefquiplicate Ratio of their
mean distances from the Sun. But, 4. The primary Planets
do not defcribe Areas any way proportional to their periodi-
cal Times, about the Earth ; as being Sometimes feen Sta-
tionary, and Sometimes Retrograde with regard thereto, See
SATELLITES, PERIODS, USC.
1I. The Powers whereby the Satellites of 5hipiter are
conflantly drawn out of their retilinear Courfe, and re-
tain'd in their Orbits, do refpe& the Center of Ynpirer, and
sare reciprocally as the Squares of their ditlances from the
fame Centre. 2. The fume holds of the Satellites of Sa-
turn with regard to Saturn; of the Moon with regard to
the Earth: And of the primary Planets with regard to the
Sun. SeeCENTRIPETAL Force.
III. The Moon gravitates towards the Earth, and by
the Power of that Gravity is retain'd in her Orbit: And
the fame holds of the other Satellites with refpe& to their
primary Planets ; and of the Primaries with refpe&t to the
Sun. See MooN.
As to the Moon, the Propofition is thus proved: The
Moon's mean diflance is 6o Semidiameters of the Earth ;
her Pericd, with regard to the fix'd Stars, is 2? Days, 7


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Hours, 43 Minutes;    and the Earth's Circumference
1 23 249600 Paris Feet. . Now, fuppofing the Moon to have
lott all its Motion, and to be let drop to the Earth, with
the Power which retains her irt her Orbit ; in the fpace of
one Minute fhe will fall 15 t Paris Feet.X the Arch the
describes in her mean Motion at the difiance of 6o Semi-
dianieters of the Earth being the verfed Sine of 15 -, Paris
Feet. Hence, as the Power as it approaches the Earth, in-
creafes in a duplicate Ratio of the diflance inverly ; fo, as
at the Surface of the Earth, 'tis 6o X 60 greater than the
Moon : A Body falling with that Force in our Region
muff, in a Minute's time, defcribe the fpace of 6o x 6o X
1 i s12 Paris Feet ; and 1 5 x Paris Feet in the fpace of one
Se cond.
But this is the Rate at which Bodies fall, by their Gra-
vity, at the Surface of our Earth , as Huygens has demon-
ilrated, by Experiments with Pendulums. Confequently,
the Power whereby the Moon is retain'd in her Orbit, is the
very fame we call Gravity : Forif they were different, a
Body failing with both Powers together, would defcend
with double the Velocity, and in a Second of Time de-
fcribe 30 i Feet. See DESCENT of Bodies.
As to the other fecundary Planets, their Phlenomena with
refpea to their primary ones, being of the fame kind with
thofe of the Moon about the Earth; 'tis argued, by Ana-
logy, they depend on the fame Caufes: It being a Rule-
or Axiom all Philofophers agree to, That Effeds of the
fame kind, have the fame Caufes. Again, Attra&ion is
always mutual, i. e. the Reaction is equal to the Adion.
Confequently, the primary Planets gravitate towards their
fecundary ones; the Earth towards the Moon, and the Sun
towards 'cm all. And this Gravity, with regard to each fe-
veral Planet, is reciprocally as the Square of its diflance friom
its CentreofGravity. See ATTRACTION, REACTION, SC.
IV. All Bodies gravitate towards all the Planets; and
their Weights towards any one PL net, at equal difrances
from the Centre of the Planet, are proportional to the
Quantity of Matter in each.
For the Law of the Defcent of heavy Bodies towards
the Earth, fetting afide their unequal Retardation from the
Refiflance of the Air, is this ; that all Bodies fall equal
fpacesin equal times: But the nature of Gravity orWeight,
no doubt, is the fame on the other Planets, as on the
Earth. See WEIGHT.
Suppofe, e. gr. fuch Bodies raifed to the Surface of the
Moon, and together with the Moon deprived at once of all
Progreffive Motion, and drop'd towards the Earth: 'Tis
fhewn, that in equal Times they will defcribe equal Spaces
with the Moon; and, therefore, that their Quantity of
Matter is to that of the Moon, as their Weights to its
Weight.
Adti, that fince fupirer's Satellites revolve in times that
are in a fefquiplicate Ratio of their diflances from the Centre
of 5upier, and consequently at equal diflances from Yupiter
their accelerating Gravities are equal ; therefore, falling
equal Altitudes in equal Times, they will defcribe equal
Spaces: juil as in heavy Bodies on our Earth. And the
fame Argument will hold of the primary Planets with re-
gard to the Sun. And the Powers whereby unequal Bodies
are equally accelerated, are as the Bodies; i. e. theWeights
are as the Quantities of Mlatrer in the Planets. And the
Weights of the primary and fecundary Planets towards the
Sun, are as the Quantities of Matter in the Planets and Sa-
tellites.
And hence are feveral Corollaries drawn relating to the
Weitghs of Bodieson the Surface of the Earth, Magnetifm,
and the Exi/ence of a Vacuum. Which fee under the
Articles VACUUM, WEIGHT, and MAGNETISM.
V. Gravity extends itfelf towards all Bodies, and is in
proportion to the Quantity of Matter in each.
That all the Planets gravitate towards each other, has
been already fIhewn ; likewife, that the Gravity towards
any one confider'd apart, is reciprocally as the Squares of
its Diflance from the Centre of the Planet : Confequently,
Gravity is proportional to the Matter therein. Further, As
all the Parts of any Planet, A, gravitatq towards another
Planet, B 5 and the Gravity of any part is to the Gravity
of the whole, as the Matter of the part to the Matter of
the whole; and Reaaion equal to A61ion: The Planet B
will gravitate towards al the Parts of the Planet A  ; and
its Gravity towards any part, will be to its Gravity towards
the whole, as the Matter of the part to the Matter of the
whole.
Hence, we derive Methods of finding and comparing the
Weights of Bodies towards different Planets; of finding the
Quantity of Matter in the feveral Planets; and their Den
ities: Since the Weights of equal Bodies revolving about
Pl anets, are as the Diameters of their Orbits direffly, an4
as the Squares of the Periodical Times, inverly; and the
Weights at any diflance from the Centre of the Planet
are greater or lefs in a duplicate Ratio of their di-
flances, inverfly: And fince the Quantities of Matter
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