asheinin/The_Mathematical_Principles_of_Natural_Philosophy_1846

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“ 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, cæteris paribus, 320, 321, 324, 329, 344, 355
“ is in the duplicate proportion of the velocity of the bodies resisted, cæteris paribus, 258, 314, 374, 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 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

“ 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, cæteris paribus, 320, 321, 324, 329, 344, 355

“ is in the duplicate proportion of the velocity of the bodies resisted, cæteris paribus, 258, 314, 374, 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 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