in their orbits, but these ellipses will be near to parabolas, 466
COMET S parabolic trajectory found from three observations given, 472
corrected when found, ... 495
" place in a parabola found to a given time, 466
"
velocity compared with the velocity of the planets, .... . 466
JoMKTs TAILS directed from the sun, 489
" " brightest and large>t immediately after their passage through the neighbour
hood of the sun, 487
" " their wonderful rarity, 490
* " their origin and nature, ...... . . . 46S
" in what space of time they ascend from their heads, . . 490
7V
576 INDEX TO THE PRINCIPIA
r?OMET of the years 1664 and 1665 the observations of its motion compared with the theory, . 496
u of the years 1680 and 1681 observations of its motion, ...... 474
" its motion computed in a parabolic orbit, 478
" in an elliptic orbit, ....... 479
" its trajectory, and its tail in the several parts of its orbit, delineated, .... 484
" of the year 1682 its motion compared with the theory, 500- -
l seems to have appeared in the year 1607, and likely to return again after a period of
75 years, 501,502
" of the year 1683 its motion compared with the theory, 499
" of the year 1723 its motion compared with the theory, . . * . 501
CONIC SECTIONS, by what law of centripetal force tending to any given point they may be de
scribed by revolving bodies, . 125
" the geometrical description of them when the foci are given, .... 125
" when the foci are not given, 131
when the centres or asymptotes are given, ....... 147
CURVATURE of figures how estimated, 271, 423
CURVES distinguished into geometrically rational and geometrically irrational, . . . 157
CYCLOID, or EPICYCLOID, its rectification, 184
" " its evoluta, 185
CYLINDER, the attraction of a cylinder composed of attracting particles, whose forces are recip
rocally as the square of the distances, 239
DESCENT of heavy bodies in vacuo, how much it is, 405
" and ascent of bodies in resisting mediums, 252,265,281,283,345
DESCENT or ASCENT rectilinear, the spaces described, the times of decription, and the velocities
acquired in such ascent or descent, compared, on the supposition of any
kind of centripetal force, 160
EARTH, its dimension by Norwood, by Picart, and by Cassini, 405
" its figure discovered, with the proportion of its diameters, and the meattire of the degrees
upon the meridian, ............ 405, 40?)
" the excess of its height at the equator above its height at the poles, . . . 407, 412
" its greatest and least semi-diameter, .......... 407
" its mean semi-diameter, 407
" the globe of the earth more dense than if it was entirely water, 400
" the nutation of its axis, 413
" the annual motion thereof in the orbis magnus demonstrated, 498
" the eccentricity thereof how much, 452
" the motion of its aphelion how much, 404
ELLIPSES, by what law of centripetal force tending to the centre of the figure it is described by a
revolving body, 114
" by what law of centripetal force tending to the focus of the figure it is described by a
revolving body 116
FLUID, the definition thereof, 108
FLUIDS, the laws of their density and compression shewn, ....... 293
" their motion in running out at a hole in a vessel determined, . . . . . 331
FORCES, their composition and resolution, 84
" attractive forces of spherical bodies, composed of particles attracting according to any
law, determined, 218
" attractive forces of bodies not spherical, composed of particles attracting according to
any law, determined, 233
" the invention of the centripetal forces, when a body is revolved in a non-resisting space
about an immoveable centre in any orbit, 103, 116
" the centripetal forces tending to any point by which any figure may be described by a
revolving body being given, the centripetal forces tending to any other point by which
the same figure may be described in the same periodic time are also given, . . . lie
v the centripetal forces by which any figure is described by a revolving body being given,
there are given the forces by which a new figure may be described, if the ordinates are
augmented or diminished in any given ratio, or the angle of their inclination be any
how changed, the periodic time remaining the same, 116
M
centripetal forces decreasing in the duplicate proportion of the distances, what figures
may be described by them, 120 1 9f
INDEX TO THE PRINCIPIA. 577
FomcE, centripetal force defined, 74
" the absolute quantity of centripetal force defined, 75
M the accelerative quantity of the same defined, 76
w the mutive quantity of the same defined, 76
" the proportion thereof to any known force how collected, 109
" a centripetal force that if reciprocally as the cube of the ordinate tending to a vastly
remote centre of lorce will e a body to move in any given conic section, . . 114
" a centripetal force that is as the cube of the ordinate tending to a vastly remote centre of
force will cau^e a body to move in an hyperbola, 243
centrifugal force of bodies on the earth s equator, how great, 405
GOD, his nature, 506
ClaAviTY mutual between the earth and its parts, . 94"
* of a different nature from magnetical force, ........ 397
" the cause of it not assigned, 507
" tends towards all the pi anets, 393
" from the surfaces of the planets upwards decreases in the duplicate ratio of the dis
tances from the centre, 400
" fruin the same downwards decreases nearly in the simple ratio of the same, . . 400
" tends towards all b dies, ami is proportional to the quantity of matter in each, . 397
" is the force by which the moon is retained in its orbit, 391
" the same proved by an accurate calculus, 453
" is the force by which the primary planets and the satellites of Jupiter and Saturn are
retained in their orbits, 393
HEAT, an iron rod increases in length by heat, ......... 112
" of the sun, how great at different distances from the sun, 486
" how great in Mercury, 400
" how great in the comet of 1680, when in its perihelion, ... , , 486
HEAVENS are void of any sensible re.-iotauce, 401, 445, 492; and, therefore, of almost any cor
poreal fluid whatever, 355 356
" suffer light to pass through them without any refraction, .... 485
HYDROSTATICS, the principles thereof delivered, . .... 293
SYPERBOLA, by what law of centrifugal force tending from the centre of the figure it is described
by a revolving body, 116
" by what law of centrifugal force tending from the focus of the figure it is described
by a revolving body, 117
" by what law of o* itripetal force tending to the focus of the figure it is described
by a revi living body, 118
HYPOTHESES of what kind oever rejected from this philosophy, 508
JUPITER, its periodic time, 388
" its distance from the sun, 388
" its apparent diameter, 386
" its true diameter, . 399
" its attractive t rce, how great, 398
" the weights of bi dies on its surface, . . 399
" its density, ... .399
" its quantity of matter, . 399
" its perturbation by Saturn, how much, 403
" the proportion of its diameters exhibited by computation, . . 409
" and comftared with observations, ........ . 409
" its rotation about its axis, in what time performed, ..... . 409
" the cause of its belts hinted at, 445
fjlOHT, its propagation not instantaneous, .......... 246
" its velocity different in different mediums, ... 24J5
" a certain reflection it sometimes suffers explained*, 245
" its refraction explained, 243
u refraction is not made in the single point of incidence, 247 .
" an incurvation of light about the extremities of bodies observed by experiments, . . 24fc
" not caused by the agitation of any ethereal medium, 368
ANETIC force, 94,304,397,454
37
578 INDEX TO THE PRINCIPIA.
WARS, its periodic time, 3^
" its distance from the sun, < 339
" the motion of its aphelion, 4^/5
MATTER, its quantity of matter defined, ..." 73
" its msinsita define!. . 74
" its impressed force defined, 74
its extension, hardness, impenetrability, mobility, rta inertia:, gravity, how discovered, 385
subtle mattir of Descartes ii quired into, 320
MECHANICAL POWERS explained and demonstrated, 94
MERCURY, its periodic time, ........... . 388
its distance from the sun, ., 389
the ruotion of its aphelion, . ... 405
METHOD of first and last ratios, 95
" of transforming figures into others of the same analytical order, .... 141
" of fluxions, ............... 261
differential, ........... 447
of finding the quadratures of all curves very nearly true, ...... 448
" ot converging series applied to the solution of difficult problems, . . . 271 430
MOON, the inclination of its orbit to the ecliptic greatest in the syzygies of the node with the ^un,
and least in the quadratures, 208
" the figure of its body collected by calculation, 45.)
" its librations explained, .......... 405
its mean apparent diameter, . ... 453
" its true diameter, 453
" weight of bodies on its surface, 453
" its density, 453
" its quantity of matter, 453
" its mean distance from the earth, how many greatest sem>diameters of the earth con
tained therein, 453
" how many mean semi-diameter?, 454
" its force to move the sea how great, 449
not perceptible in experiments of pendulums, or any statical or hydrostatical observations, 452
" its periodic time, 454
" the time of its synodical revolution, 422
tt its motions, and the inequalities of the same derived from their causes, . . 413, 144
" revolves more slowly, in a dilated orbit, when the earth is in its perihelion ; and more
swiftly in the aphelion the f-ame, its orbit being contracted, .... 413, 444, 445
" revolves more slowly, in a dilated orbit, when tl.e apogteon is in the syzygies with the sun ;
and more swiftly, in a contracted orbit, when the apogaeon is in the quadratures, . 445
" revolves more slowly, in a dilated orbit, when the node is in the syzygies with the sun ;
and more swiftly, in a contracted orbit, when the node is in the quadratures, . . 44G
" moves slower in its quadratures with the sun, swifter in the syzygies; and by a radius
drawn to the earth describes an area, in the fir.<t case less in proportion to the time, in the
last case greater, ... 413
" the inequality of those areas computed, .... 420
" its orbit is more curve, and goes farther from the earth in the first case; in the last case
its orbit i? less curve, and comes nearer to the earth, 415
u the figure of this orbit, and the proportion of its diameters collected by computation, . 423
" a method of finding the moon s distance from the earth by its horary motion, . . 423
" its apogaenn moves more slowly when the earth is in its aphelion, m< re swiftly in the peri
helion, 414,445
" its apogaeon goes forward most swiftly when in the syzygies with the sun ; and goes back
ward in the quadratures, 414, 44l:
" its eccentricity greatest when the apogaeon is in the syzygies with the sun ; least when the
same is in the quadratures, 414, 44C
* its nodes move more slowly when the earth is in its aphelion, and more swiftly in the peri
helion, 414,445
*
its nodes are at rest in their syzygies with the sun, and go back most swiftly in the quad
ratures ... . . . .... 41-1
INDEX TO THE PRINCIPIA. 579
MOON, the motions of the nodes and the inequalities of its motions computed from the theory of
gravity, 427,430,434,436
" the same from a different principle, 437
the variations of the inclination computed from the theory of gravity, . . . 441, 443
" the 3ns of the moon s motions for astronomical uses, 445
" the unnual equation of the moon s mean motion, 445
" the first semi-annual equation of the same, ... 443
" the second serai-annual equation of the same, 447
" the first equation of the moon s centre, 447
" the second equation of the moon s centre, 448
MOON S first variation, 425
" the annual equation of the mean motion of its apogee, 445
" the semi-annual equation of the same, 447
" the semi-annual equation of its eccentricity, 447
" the annual equation of the mean motion of its nodes, 445
" the seini-annual equation of the same, .......... 437
" the seini-anuual equation of the inclination of the orbit to the ecliptic, . . . 444
" the method of fixing the theory of the lunar motions from observations, ... 464
MOTION, its quantity defined, 73
absolute and relative, 78
" absolute and relative, the separation of one from the other possible, demonstrated by
an example ...* 82
" laws thereof; 83
". of concurring bodies after their .reflection, by what experiments collected, ... 91
" of bodies in eccentric sections, . . 116
" in moveub!e orbits, 172
" in given superficies, and of the reciprocal motion of pendulums, .... 183
" of bodies tending to each other with centripetal forces, 194
" of very small bodies agitated by centripetal forces tending to each part of some very
great body, 233
" of bodies resisted in the ratio of the velocities, 251
" in the duplicate ratio of the velocity, 258
" partly in the simple and partly in the duplicate ratio of the same, . 280
" of bodies proceeding by their vis insita alone in resisting mediums, 251, 258, 259, 280, 281, 330
" of bodies ascending or descending in right lines in resisting mediums, and acted on by
an uniform force of gravity, 252,265,281,283
" of bodies projected in resisting mediums, and acted on by an uniform force of gravity, 255, 268
u of bodies revolving in resisting mediums, 287
" of funependulous bodies in resisting mediums, . 304
" and resistance of fluids, 323
41 propagated through fluids, ... . ..... 356
" of fluids after the manner of a vortex, or circular, 370
MOTIONS, composition and resolution of them, .......... 84
OVALS for optic uses, the method of finding them which Cartesius concealed, .... 246
" a general solution of Cartesius s problem, 247, 248
OBBITS, the invention of those which are described by bodies going off from a given place with
a given velocity according to a given right line, when the centripetal force is recipro
cally as the square of the distance, and the absolute quantity of that force is known, . 123
" of those which are described by bodies when the centripetal force is reciprocally as the
cube of the distance, 114, 171, 176
" of those which are described by bodies agitated by any centripetal forces whatever, 168
PARABOLA., by what law of centripetal force tending to the focus of the figure the same may be
described, 120
PENDULUMS, their properties explained, 186, 190, 304
the diverse length? of isochronous pendulums in different latitudes compared among
themselves, both by observations and by the theory of gravity, . . 409 to 413
PLACE defined, and distinguished into absolute and relative, .78
PLACES of bodies moving in conic sections found to any assigned time, ..... 153
not carried about by corporeal vortices, ......... 378
">$() INDEX TO THE PRINCIPIA.
PLANET*, their et .imes, . . 3gg
" their distances from the tun, .
. 339
* the at .helia and nodes of their orbits do almost rest, ...... 405
" their orbits determined, 406
" the way of finding their places in their orbit?, 347 to 350
" their density suited to the heat they receive from the sun, ...*.. 400
" their diurnal revolutions equable. 406
" their axes less than the diameters that stand upon them at right angles, . . . 406
PLANETS, PRIMARY, surround the sun, 387
" move in ellipses whose focus is in the sun s centre 403
by radii drawn to the sun describe areas proportional to the times, . 388, 403
revolve in periodic times that are in the sesquiplicate proportion of the dis
tances from the sun, 387
are retained in their orbits by a force of gravity which respects the sun,
and is reciprocally as the square of the distance from the sun s centre, 389, 393
PLANETS, SECONDARY, move in ellipses having their focus in the centre of the primary, . 413
by radii drawn to their primary describe areas proportional to the
times 386,387,390
revolve in periodic times that are in the sesquiplicate proportion of their
distances from the primary, 386, 387
PROBLEM KEPLEHIAN, solved by the trochoid and by approximations, .... 157 to 160
of the ancients, of four lines, related by Pappus, and attempted by Cartesius,
by an algebraic calculus solved by a geometrical composition, . 135
PROJECTILES move in parabolas when the resistance of the medium is taken away, 91, 115, 243, 273
their motions in re.-isting mediums, ........ 255, 268
PULSES of the air, by which sounds are propagated, their intervals or breadths determined, 368, 370
" these intervals in sounds made by open pipes probably equal to twice the length of the
pipes, 370
QUADRATURES general of oval figures not to be obtained by finite terms, 153
QUALITIES of bodies how discovered, and when to be supposed universal, .... 38-1
RESISTANCE, the quantity thereof in mediums not continued, 329
" in continued mediums, 40f
in mediums of any kind whatever, . . . . . . . . 3.i.
of mediums is as their density, cceteris paribus, . . 320, 321, 324, 329, 344. 353
is in the duplicate proportion of the velocity of the bodies resisted, ccrteris ibus,
258, 314, 374, 329, 3J4, 35 i
Ct
is in the duplicate proportion of the diameters of spherical bodies resisted, cceteris
paribus 317, 31 8, 329, 34-1
" of fluids threefold, arises either from the inactivity of the fluid matter, or the te
nacity of its parts, or friction, 286
the resistance found in fluids, almost all of the first kind, .... 321, 35*
" cannot be diminished by the subtilty of the parts of the fluid, if the density remain, 355
" of a globe, what proportion it bears to that of a cylinder, in mediums not continued, 327
" in compressed mediums, 343
" of a globe in mediums not continued, 329
" in compressed mediums, 344
" how found by experiments, 345 to 355
" to a frustum oi a cone, how made the least possible, 328
" what kind of solid it is that meets with the least, 329
RESISTANCES, the theory thereof confirmed by experiments of pendulums, . . . 313 to 321
" by experiments of fa-lling bodies, 345 to 356
REST, true and relative, 78
RULES of philosophy, 38-!
SATELLITES, the greatest heliocentric elongation of Jupiter s satellites, 387
" the greatest heliocentric elongation of the Huygenian satellite from Saturn s centre. 398
the periodic times of Jupiter s satellites, and their distances from his centre, . 386, 387
" the periodic times of Saturn s satellites, and their distances from his centre, 387, 388
" the inequalities of the motions of the satellites of Jupiter and Saturn derived from
the motions of the moon, 413
SM^UIPLICATE proportion defined, 101
INDEX TO THE PRINCIPLE.
SATURN, its periodic time, . 388
" its distance from the sun, 388
" its apparent diameter, ..* 388
" its true diameter, . . . . 399
" its attractive force, how great, 398
" the weight of bodies on its surface, 399
" its density, ... . . 399
" its quantity of matter, 399
" its perturbation by the approach of Jupiter how great, 403
" the apparent diameter of its ring, . . . 388
SHADOW of the earth to be augmented in lunar eclipses, because of the refraction of the at
mosphere, 44?
SUUNDS, their nature explained, 360,363,365,366,367,368,369
( not propagated in directum, . ... 359
" caused by the agitation of the air, 368
" their velocity c< mputed, 368, 369
" somewhat swifter by the theory in summer than m winter, 370
" cease immediately, when the motion of the sonorous body ceases, .... 365
" how augmented in speaking trumpets, 370
SfACE, absolute and relative, 78, 79
" not equally full. 396
SPHEROID, the attraction of the same when the forces of its particles are reciprocally as the
squares of the distances 239
SPIRAL cutting all its radii in a given angle, by what law of centripetal force tending to the
centre thereof it may be described by a revolving body, .... 107, 287, 291
SPIRIT pervading all bodies, and concealed within them, hinted at, as required to solve a great
many phsenomena of Nature, 508
STARS, the fixed ,-tars demonstrated to be at rest, ... 404
" their twinkling what to be ascribed to, . 487
" new stars, whence they may arise, 502
SUBSTANCES of all things unknown, 507
SUN, m >ves round the common centre of gravity of all the planets, 401
" the periodic time of its revolution about its axis 405
" its mean apparent diameter, ....*.. 453
" its true diameter, 398
" its horizontal parallax, 398
" has a menstrual parallax, 403
" its attractive force how great, ............ 398
" the weight <.f bodies on its surface, 399
" its density, . 399
" its quantity of matter, 399
" its force to disturb the motions of the moon, 391, 419
" its force to move the sea, 448
TIDES of the sea derived from their cause, 415, 448, 449
TIMF, absolute and relative, 78, 79
" tli? astronomical equation thereof proved by pendulum clocks, and the eclipses of Jupiter s
satellites, 79
A VACUUM proved, or that all spaces (if said to be full) are not equally full, .... 396
VELOCITIES of bodies moving in conic sections, whore the centripetal force tends to the focus, . 121
VELOCITY, the greatest that a globe falling in a resisting medium can acquire, . . . 344
VENUS, its periodic time, 388
" its distance from the sun, 388
" the motion of its aphelion, 405
VOHTICES, their nature and constitution examined, 504
W.AVES, the velocity with which they are propagated on the superficies of stagnant water, . 361
WEIGHTS of bodies towards the sun, the earth, or any planet, are, at equal distances from the
centre, as the quantities of matter in the bodies, 394
1 they do not depend upon the forms and textures of bodies 395
" of bodies in different regions of the earth found out, and compared together, . . 409
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