Page:Newton's Principia (1846).djvu/586

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 * style="width:90%" colspan=2|, their periodic times,||388
 * style="text-align:center"|“||their distances from the sun,||389
 * style="text-align:center"|“||the aphelia and nodes of their orbits do almost rest,||405
 * style="text-align:center"|“||their orbits determined,||406
 * style="text-align:center"|“||the way of finding their places in their orbits,||347 to 350
 * style="text-align:center"|“||their density suited to the heat they receive from the sun,||400
 * style="text-align:center"|“||their diurnal revolutions equable.||406
 * style="text-align:center"|“||their axes less than the diameters that stand upon them at right angles,||406
 * colspan=2|,, surround the sun,||387
 * style="text-align:center" nowrap="nowrap"|“ “||move in ellipses whose focus is in the sun s centre,||403
 * style="text-align:center" nowrap="nowrap"|“ “||by radii drawn to the sun describe areas proportional to the times,||nowrap="nowrap"|388, 403
 * style="text-align:center" nowrap="nowrap"|“ “||revolve in periodic times that are in the sesquiplicate proportion of the distances from the sun,||387
 * style="text-align:center" nowrap="nowrap"|“ “||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,||nowrap="nowrap"|389, 393
 * colspan=2|,, move in ellipses having their focus in the centre of the primary,||413
 * style="text-align:center" nowrap="nowrap"|“ “||by radii drawn to their primary describe areas proportional to the times,||nowrap="nowrap"|386, 387, 390
 * style="text-align:center" nowrap="nowrap"|“ “||revolve in periodic times that are in the sesquiplicate proportion of their distances from the primary,||nowrap="nowrap"|386, 387
 * colspan=2|, solved by the trochoid and by approximations,||nowrap="nowrap"|157 to 160
 * style="text-align:center" nowrap="nowrap"|“ “||of the ancients, of four lines, related by Pappus, and attempted by Cartesius, by an algebraic calculus solved by a geometrical composition,||135
 * colspan=2| move in parabolas when the resistance of the medium is taken away,||nowrap="nowrap"|91, 115, 243, 273
 * style="text-align:center"|“||their motions in resisting mediums,||255, 268
 * colspan=2| of the air, by which sounds are propagated, their intervals or breadths determined,||nowrap="nowrap"|368, 370
 * style="text-align:center"|“||these intervals in sounds made by open pipes probably equal to twice the length of the pipes,||370
 * colspan=2| general of oval figures not to be obtained by finite terms,||153
 * colspan=2| of bodies how discovered, and when to be supposed universal,||384
 * colspan=2|, the quantity thereof in mediums not continued,||329
 * style="text-align:center"|“||in continued mediums,||409
 * style="text-align:center"|“||in mediums of any kind whatever,||331
 * style="text-align:center"|“||of mediums is as their density, cæteris paribus,||nowrap="nowrap"|320, 321, 324, 329, 344, 355
 * style="text-align:center"|“||is in the duplicate proportion of the velocity of the bodies resisted, cæteris paribus,||nowrap="nowrap"|258, 314, 374, 329, 344,351
 * style="text-align:center"|“||is in the duplicate proportion of the diameters of spherical bodies resisted, cæteris paribus,||nowrap="nowrap"|317, 318, 329, 344
 * style="text-align:center"|“||of fluids threefold, arises either from the inactivity of the fluid matter, or the tenacity of its parts, or friction,||286
 * style="text-align:center"|“||the resistance found in fluids, almost all of the first kind,||nowrap="nowrap"|321, 354
 * style="text-align:center"|“||cannot be diminished by the subtilty of the parts of the fluid, if the density remain,||355
 * style="text-align:center"|“||of a globe, what proportion it bears to that of a cylinder, in mediums not continued,||327
 * style="text-align:center"|“||in compressed mediums,||343
 * style="text-align:center"|“||of a globe in mediums not continued,||329
 * style="text-align:center"|“||in compressed mediums,||344
 * style="text-align:center"|“||how found by experiments,||nowrap="nowrap"|345 to 355
 * style="text-align:center"|“||to a frustum of a cone, how made the least possible,||328
 * style="text-align:center"|“||what kind of solid it is that meets with the least,||329
 * colspan=2|, the theory thereof confirmed by experiments of pendulums,||nowrap="nowrap"|313 to 321
 * style="text-align:center"|“||by experiments of falling bodies,||nowrap="nowrap"|345 to 356
 * colspan=2|, true and relative,||78
 * colspan=2| of philosophy,||384
 * colspan=2|, the greatest heliocentric elongation of Jupiter's satellites,||387
 * style="text-align:center"|“||the greatest heliocentric elongation of the Huygenian satellite from Saturn's centre,||398
 * style="text-align:center"|“||the periodic times of Jupiter s satellites, and their distances from his centre,||nowrap="nowrap"|386, 387
 * style="text-align:center"|“||the periodic times of Saturn s satellites, and their distances from his centre,||nowrap="nowrap"|387, 388
 * style="text-align:center"|“||the inequalities of the motions of the satellites of Jupiter and Saturn derived from the motions of the moon,||413
 * colspan=2| proportion defined,||101
 * }
 * style="text-align:center"|“||in continued mediums,||409
 * style="text-align:center"|“||in mediums of any kind whatever,||331
 * style="text-align:center"|“||of mediums is as their density, cæteris paribus,||nowrap="nowrap"|320, 321, 324, 329, 344, 355
 * style="text-align:center"|“||is in the duplicate proportion of the velocity of the bodies resisted, cæteris paribus,||nowrap="nowrap"|258, 314, 374, 329, 344,351
 * style="text-align:center"|“||is in the duplicate proportion of the diameters of spherical bodies resisted, cæteris paribus,||nowrap="nowrap"|317, 318, 329, 344
 * style="text-align:center"|“||of fluids threefold, arises either from the inactivity of the fluid matter, or the tenacity of its parts, or friction,||286
 * style="text-align:center"|“||the resistance found in fluids, almost all of the first kind,||nowrap="nowrap"|321, 354
 * style="text-align:center"|“||cannot be diminished by the subtilty of the parts of the fluid, if the density remain,||355
 * style="text-align:center"|“||of a globe, what proportion it bears to that of a cylinder, in mediums not continued,||327
 * style="text-align:center"|“||in compressed mediums,||343
 * style="text-align:center"|“||of a globe in mediums not continued,||329
 * style="text-align:center"|“||in compressed mediums,||344
 * style="text-align:center"|“||how found by experiments,||nowrap="nowrap"|345 to 355
 * style="text-align:center"|“||to a frustum of a cone, how made the least possible,||328
 * style="text-align:center"|“||what kind of solid it is that meets with the least,||329
 * colspan=2|, the theory thereof confirmed by experiments of pendulums,||nowrap="nowrap"|313 to 321
 * style="text-align:center"|“||by experiments of falling bodies,||nowrap="nowrap"|345 to 356
 * colspan=2|, true and relative,||78
 * colspan=2| of philosophy,||384
 * colspan=2|, the greatest heliocentric elongation of Jupiter's satellites,||387
 * style="text-align:center"|“||the greatest heliocentric elongation of the Huygenian satellite from Saturn's centre,||398
 * style="text-align:center"|“||the periodic times of Jupiter s satellites, and their distances from his centre,||nowrap="nowrap"|386, 387
 * style="text-align:center"|“||the periodic times of Saturn s satellites, and their distances from his centre,||nowrap="nowrap"|387, 388
 * style="text-align:center"|“||the inequalities of the motions of the satellites of Jupiter and Saturn derived from the motions of the moon,||413
 * colspan=2| proportion defined,||101
 * }
 * style="text-align:center"|“||to a frustum of a cone, how made the least possible,||328
 * style="text-align:center"|“||what kind of solid it is that meets with the least,||329
 * colspan=2|, the theory thereof confirmed by experiments of pendulums,||nowrap="nowrap"|313 to 321
 * style="text-align:center"|“||by experiments of falling bodies,||nowrap="nowrap"|345 to 356
 * colspan=2|, true and relative,||78
 * colspan=2| of philosophy,||384
 * colspan=2|, the greatest heliocentric elongation of Jupiter's satellites,||387
 * style="text-align:center"|“||the greatest heliocentric elongation of the Huygenian satellite from Saturn's centre,||398
 * style="text-align:center"|“||the periodic times of Jupiter s satellites, and their distances from his centre,||nowrap="nowrap"|386, 387
 * style="text-align:center"|“||the periodic times of Saturn s satellites, and their distances from his centre,||nowrap="nowrap"|387, 388
 * style="text-align:center"|“||the inequalities of the motions of the satellites of Jupiter and Saturn derived from the motions of the moon,||413
 * colspan=2| proportion defined,||101
 * }
 * style="text-align:center"|“||the greatest heliocentric elongation of the Huygenian satellite from Saturn's centre,||398
 * style="text-align:center"|“||the periodic times of Jupiter s satellites, and their distances from his centre,||nowrap="nowrap"|386, 387
 * style="text-align:center"|“||the periodic times of Saturn s satellites, and their distances from his centre,||nowrap="nowrap"|387, 388
 * style="text-align:center"|“||the inequalities of the motions of the satellites of Jupiter and Saturn derived from the motions of the moon,||413
 * colspan=2| proportion defined,||101
 * }
 * style="text-align:center"|“||the inequalities of the motions of the satellites of Jupiter and Saturn derived from the motions of the moon,||413
 * colspan=2| proportion defined,||101
 * }
 * colspan=2| proportion defined,||101
 * }