the common centre of gravi-
ty of the Earth, Sun, and
all the Planets is at rest II,
232; confirmed by Cor. 2.
Prop. 14. Book 3.
the common centre of gravi-
ty of the Earth and Moon
goes round the orbis mag-
nus II, 235; its distance
from the Earth and from
the Moon II, 311
Centre of the forces by which
revolving bodies are retain-
ed in their orbits, how in-
dicated by the description
of areas I, 63; how found
by the given velocities of
the revolving bodies I, 67
Circle, by what law of centri-
petal force tending to any
given point, its circumfe-
rence may be defcribed I,
64, 70, 73
Conic fections, by what law of
centripetal force tending to
any given point they may be
defcribed by revolving bo-
dies I, 93

the geometrical defcription of
them when the foci are
given I, Sect. 4.
when the foci are not given I,
Sect. 5.

when the centres or asymp-
totes are given I, 132

Comets

a fort of Planets, not meteors
II, 331, 360
higher than the Moon, and
in the planetary regions II,
323

their diftance how collected
very nearly by obfervations
II, 324

more of them obferved in the
hemifphere towards the
Sun, than in the oppofite
hemifphere; and how this
comes to pass II, 330
fhine by the Sun's light re-
flected from them II, 330
furrounded with vaft atmo-
fpheres II, 327, 331
thofe which come neareft to
the Sun probably the leaft,
II, 374
why they are not compre-
hended within a zodiack,
like the Planets, but move
differently into all parts of
the Heavens II, 385
may fometimes fall into the
Sun, and afford a new fup-
ply of fire II, 385.
the use of them hinted II,
371

move in conic fections, having

their foci in the Sun's cen-
tre, and by radij drawn to
the Sun defcribe areas pro-
portional to the times.
Move in ellipfes if they
come round again in their
orbits, but thefe ellipfes
will be near to parabolas

II, 332
Comet's parabolic trajectory
found from three obferva-
tions given II, 340; cor-
rected when found II, 375
Comet's place in a parabola
found to a given time II,
333; I, 143

Comet's velocity compared with
the velocity of the Planets
II, 332

Comets Tails

directed from the Sun II, 364

brightest

brightest and largeft immedi-
ately after their paffage thro'
the neighbourhood of the
Sun II, 361

their wonderful rarity II, 367
their origine and nature II,
327, 509

in what space of time they af-
cend from the heads II, 367
Comet of the years 1664 and
1665

the obfervations of its motion
compared with the theory
II, 377
Comet of the years 1680 and
1681

obfervations of its motion II,
344

its motion computed in a pa-
rabolic orbit II, 350; in an
elliptic orbit II, 352
its trajectory, and its tail in
the feveral parts of its orbit,
delineated II, 358

Comet of the year 1682
its motion compared with the
theory II, 382
feems to have appeared in the
year 1607, and likely to re-
turn again after a period of
75 years II, 384
Comet of the year 1683
its motion compared with the
theory II, 381
Comet of the year 1723
its motion compared with the
theory II, 383
Curves diftinguished into geo-

metrically rational and geo-
metrically irrational I, 148
Curvature of figures how efti

mated II, 32; II, 267
Cycloid or epicycloid,

its rectification I, 199, 200
its evoluta I, 204

its dimenfion by Norwood, by
Picart, and by Caffini II,
240
its figure difcovered, with the
proportion of its diameters,
and the measure of the de-
grees upon the meridian II,
239, 245

the excefs of its height at the

equator above its height at
the poles II, 243, 251
its greatest and leaft femidia-
meter II, 243; its mean
femidiameter ibid.

the globe of Earth more dense
than if it was entirely water
II, 230

the nutation of its axis II, 252

the

the annual motion thereof in
the orbis magnus demon-
ftrated II, 380

the eccentricity thereof how
much II, 299

the motion of its aphelion
how much II, 237
Ellipfis,

by what law of centripetal
force tending to the centre
of the figure it is described
by a revolving body I, 75
by what law of centripetal
force tending to the focus
of the figure it is described
by a revolving body I, 79.

the abfolute quantity of cen-

tripetal force defined I, 6
the accelerative quantity of
the fame defined ib.
the motive quantity of the
same defined I, 7

the proportion thereof to any
known force how collected
I, 66

the invention of the centri-
petal forces, when a body
is revolved in a non-refift-
fting space about an im-
moveable centre, in any or-
bit I, Sect. 2. and 3.
the centripetal forces tending
to any point by which any
figure may be defcribed by
a revolving body, being gi-
ven; the centripetal forces
tending to any other point,
by which the fame figure
may be defcribed in the
fame periodic time, are alfo
given I, 72

the centripetal forces by which
any figure is defcribed by
a revolving body, being
given; there are given the
forces by which a new
figure may be defcribed, if
the ordinates are augment-
ed or diminished in any
given ratio, or the angle
of their inclination be any
how changed, the periodic
time remaining the fame I,
77.
centripetal forces decreasing
in the duplicate proportion
of the distances, what figures
may be defcribed by them
I, 85, 222

a centripetal force that is reci-
procally as the cube of the
ordinate

ordinate tending to a vaftly
remote centre of force will
cause a body to move in
any given conic fection I,
74
a centripetal force that is as
the cube of the ordinate
tending to a vaftly remote
centre of force will caufe a
body to move in an hyper-
bola I, 310

G.

God, his Nature II, 389
Gravity,

of a different nature from
magnetical force II, 225
mutual between the Earth
and its parts I, 37
the cause of it not affigned II,
392
tends towards all the Planets
II, 219; from the furfa-
ces of the Planets upwards
decreases in the duplicate
ratio of the distances from
the centre II, 229; from
the fame downwards de-
creafes nearly in the fimple
ratio of the fame II, 229
tends towards all bodies, and

is proportional to the quan-
tity of matter in each II,
225

is the force by which the Moon
is retained in its orbit II,
215
the fame proved by an accu-

rate calculus II, 311, 312.
is the force by which the
primary Planets and the
Satellites of Jupiter and
Şaturn are retained in their
orbits II, 219

H.

Heat, an iron rod increases in
length by heat II, 250

of the Sun, how great at
different diftances from the
Sun II, 360

how great in Mercury II, 229
how great in the Comet of
1680,when in its perihelion
II, 360
Heavens

are void of any fenfible refift-
ance II, 231, 331, 369,
and therefore of almost any
corporeal fluid whatever
161, 162

fuffer light to pass through
them without any refracti
on, II, 362
Hydroftaties, the principles
thereof delivered II, Sect.5.

Hyperbola

by what law of centrifugal
force tending from the cen-
tre of the figure it is de-
fcribed by a revolving body
I, 77
by what law of centrifugal
force tending from the fo-
cus of the figure it is de-
fcribed by a revolving body
I, 82

by what law of centripetal
force tending to the focus
of the figure it is defcrib-
ed by a revolving body I,
81

Hypothefes of what kind foever
rejected from this philofo
phy II, 393