asheinin/The_Mathematical_Principles_of_Natural_Philosophy_1846

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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 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, 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 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, 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

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 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, 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 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, 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