← Newton's Principia

Index to the Principia

  • ÆQUINOXES, their præcession—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 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 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
  • description, 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, 506
  • 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 bodies 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
  • inertiæ, 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, 444
  • " 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 apogæon is in the
  • syzygies with the sun; and more swiftly, in a contracted orbit, when
  • the apogæon 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 apogæon moves more slowly when the earth is in its aphelion, more
  • swiftly in the perihelion, 414, 445
  • " its apogæon goes forward most swiftly when in the syzygies with the
  • sun; and goes backward in the quadratures, 414, 446
  • " its eccentricity greatest when the apogæon 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, 446
  • " 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, 338
  • " of mediums is as their density, cæteris paribus, 320, 321,
  • 324, 329, 344, 355
  • " is in the duplicate proportion of the velocity of the bodies
  • resisted, cæteris paribus, 258, 314, 324, 329, 344,
  • 351
  • " is in the duplicate proportion of the diameters of spherical bodies
  • resisted, cæteris 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 phænomena 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 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 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