The Mathematical Principles of Natural Philosophy (1846)/Index

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INDEX TO THE PRINCIPIA.



Aequinoxes, their praecession the cause of that motion shewn, 413
the quantity of that motion computed from the causes, 458
Air, its density at any height, collected by Prop. XXII, Book II, and its density at the height of one semi-diameter of the earth, shewn, 489
its elastic force, what cause it may be attributed to, 302
its gravity compared with that of water, 489
its resistance, collected by experiments of pendulums, 315
the same more accurately by experiments of falling bodies, and a theory, 355
Angles of contact not all of the same kind, but some infinitely less than others, 101
Apsides, their motion shewn, 172, 173
Areas which revolving bodies, by radii drawn to the centre of force describe, compared with the times of description, 103, 105, 106,
195, 200
As, the mathematical signification of this word defined, 100
Attraction of all bodies demonstrated, 397
the certainty of this demonstration shewn, 384
the cause or manner thereof no where defined by the author, 507
the common centre of gravity of the earth, sun, and all the planets, is at rest, confirmed by Cor. 2, Prop. XIV, Book III, 401
the common centre of gravity of the earth and moon goes round the orbis magnus, 402
its distance from the earth and from the moon, 452
Centre, the common centre of gravity of many bodies does not alter its state of motion or rest by the actions of the bodies among themselves, 87
of the forces by which revolving bodies are retained in their orbits, how indicated by the description of areas, 107
how found by the given velocities of the revolving bodies, 110
Circle, by what law of centripetal force tending to any given point its circumference may be described, 108, 111, 114
Comets, a sort of planets, not meteors, 465, 486
higher than the moon, and in the planetary regions, 460
their distance how collected very nearly by observations, 461
more of them observed in the hemisphere towards the sun than in the opposite hemisphere; and how this comes to pass, 464
shine by the sun s light reflected from them, 464
surrounded with vast atmospheres, 463, 465
those which come nearest to the sun probably the least, 495
why they are not comprehended within a zodiac, like the planets, but move differently into all parts of the heavens, 502
may sometimes fall into the sun, and afford a new supply of fire, 502
the use of them hinted, 492
move in conic sections, having their foci in the sun s centre, and by radii drawn to the sun describe areas proportional to the times. Move in ellipses if they come round again 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
Comets' Tails directed from the sun, 489
“ “ brightest and largest immediately after their passage through the neighbourhood of the sun, 487
“ “ their wonderful rarity, 490
“ “ their origin and nature, 463
“ “ in what space of time they ascend from their heads, 490
Comet of the years 1664 and 1665 — the observations of its motion compared with the theory, 496
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
seems to have appeared in the year 1607, and likely to return again after a period of 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 described 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 reciprocally 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 decryption, 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 measure of the degrees upon the meridian, 405, 409
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, 113
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
centripetal forces decreasing in the duplicate proportion of the distances, what figures may be described by them, 120, 196
Force, centripetal force defined, 74
the absolute quantity of centripetal force defined, 75
the accelerative quantity of the same defined, 76
the motive quantity of the same defined, 76
the proportion thereof to any known force how collected, 109
a centripetal force that is reciprocally as the cube of the ordinate tending to a vastly remote centre of force will cause 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 cause a body to move in an hyperbola, 243
centrifugal force of bodies on the earth s equator, how great, 405
God, his nature, 506
Gravity 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 planets, 393
from the surfaces of the planets upwards decreases in the duplicate ratio of the distances from the centre, 400
from the same downwards decreases nearly in the simple ratio of the same, 400
tends towards all bodies, and 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, 412
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 resistance, 401, 445, 492; and, therefore, of almost any corporeal fluid whatever, 355, 356
suffer light to pass through them without any refraction, 485
Hydrostatics, the principles thereof delivered, 293
Hyperbola, 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 centripetal force tending to the focus of the figure it is described by a revolving body, 118
Hypotheses of what kind soever 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 force, how great, 398
the weights of b 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 compared with observations, 409
its rotation about its axis, in what time performed, 409
the cause of its belts hinted at, 445
Light, its propagation not instantaneous, 246
its velocity different in different mediums, 245
a certain reflection it sometimes suffers explained, 245
its refraction explained, 243
refraction is not made in the single point of incidence, 247
an incurvation of light about the extremities of bodies observed by experiments, 246
not caused by the agitation of any ethereal medium, 368
Magnetic force, 94, 304, 397,
454
Mars, its periodic time, 388
its distance from the sun, 389
the motion of its aphelion, 405
Matter, its quantity of matter defined, 73
its vis insita defined, 74
its impressed force defined, 74
its extension, hardness, impenetrability, mobility, vis inertiae, gravity, how discovered, 385
subtle matter of Descartes inquired into, 320
Mechanical Powers explained and demonstrated, 94
Mercury, its periodic time, 388
its distance from the sun, 389
the motion 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
of converging series applied to the solution of difficult problems, 271, 436
Moon, the inclination of its orbit to the ecliptic greatest in the syzygies of the node with the sun, and least in the quadratures, 208
the figure of its body collected by calculation, 454
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 semi-diameters of the earth contained therein, 453
how many mean semi-diameters, 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
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 same, its orbit being contracted, 413, 444, 445
revolves more slowly, in a dilated orbit, when the apogaeon 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, 446
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 first 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 is less curve, and comes nearer to the earth, 415
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 apogaeon moves more slowly when the earth is in its aphelion, more swiftly in the perihelion, 414, 445
its apogaeon goes forward most swiftly when in the syzygies with the sun; and goes backward in the quadratures, 414, 446
its eccentricity greatest when the apogaeon is in the syzygies with the sun; least when the same is in the quadratures, 414, 446
its nodes move more slowly when the earth is in its aphelion, and more swiftly in the perihelion, 414, 445
its nodes are at rest in their syzygies with the sun, and go back most swiftly in the quadratures 414
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 equations of the moon s motions for astronomical uses, 445
the annual equation of the moon s mean motion, 445
the first semi-annual equation of the same, 443
the second semi-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 semi-annual equation of the same, 437
the semi-annual 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 moveable 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
of bodies revolving in resisting mediums, 287
of funependulous bodies in resisting mediums, 304
and resistance of fluids, 323
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
Orbits, 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 reciprocally 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 lengths 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
Planets not carried about by corporeal vortices, 378
Planets, their periodic times, 388
their distances from the sun, 389
the aphelia and nodes of their orbits do almost rest, 405
their orbits determined, 406
the way of finding their places in their orbits, 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 distances 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 Keplerian, 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 resisting 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, 384
Resistance, the quantity thereof in mediums not continued, 329
in continued mediums, 409
in mediums of any kind whatever, 331
of mediums is as their density, caeleris paribus, 320, 321, 324,
329, 344, 355
is in the duplicate proportion of the velocity of the bodies resisted, caeleris paribus, 258, 314, 374,
329, 344,351
is in the duplicate proportion of the diameters of spherical bodies resisted, caeleris paribus, 317, 318, 329,
344
of fluids threefold, arises either from the inactivity of the fluid matter, or the tenacity of its parts, or friction, 286
the resistance found in fluids, almost all of the first kind, 321, 354
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 of 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 falling bodies, 345 to 356
Rest, true and relative, 78
Rules of philosophy, 384
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
Sesquiplicate proportion defined, 101
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 atmosphere, 447
Sounds, 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 computed, 368, 369
somewhat swifter by the theory in summer than in winter, 370
cease immediately, when the motion of the sonorous body ceases, 365
how augmented in speaking trumpets, 370
Space, 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 phenomena of Nature, 508
Stars, the fixed stars 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, moves round the common centre of gravity of all the planeta, 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 of 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
Time, absolute and relative, 78, 79
the 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, where 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
Vortices, their nature and constitution examined, 504
Waves, 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
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