Page:Newton's Principia (1846).djvu/582

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 * style="width:90%" colspan=2| of the years 1664 and 1665 — the observations of its motion compared with the theory,||496
 * style="text-align:center"|“||of the years 1680 and 1681 — observations of its motion,||474
 * style="text-align:center"|“||its motion computed in a parabolic orbit,||478
 * style="text-align:center"|“||in an elliptic orbit,||479
 * style="text-align:center"|“||its trajectory, and its tail in the several parts of its orbit, delineated,||484
 * style="text-align:center"|“||of the year 1682 — its motion compared with the theory,||500
 * style="text-align:center"|“||seems to have appeared in the year 1607, and likely to return again after a period of years,||nowrap="nowrap"|501, 502
 * style="text-align:center"|“||of the year 1683 — its motion compared with the theory,||499
 * style="text-align:center"|“||of the year 1723 — its motion compared with the theory,||501
 * colspan=2|, by what law of centripetal force tending to any given point they may be described by revolving bodies,||125
 * style="text-align:center"|“||the geometrical description of them when the foci are given,||125
 * style="text-align:center"|“||when the foci are not given,||131
 * style="text-align:center"|“||when the centres or asymptotes are given,||147
 * colspan=2| of figures how estimated,||nowrap="nowrap"|271, 423
 * colspan=2| distinguished into geometrically rational and geometrically irrational,||157
 * colspan=2|, or, its rectification,||184
 * style="text-align:center" nowrap="nowrap"|“ “||its evoluta,||185
 * colspan=2|, the attraction of a cylinder composed of attracting particles, whose forces are reciprocally as the square of the distances,||239
 * colspan=2| of heavy bodies in vacuo, how much it is,||405
 * style="text-align:center"|“||and ascent of bodies in resisting mediums,||nowrap="nowrap"|252, 265, 281, 283, 345
 * colspan=2| or 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
 * colspan=2|, its dimension by Norwood, by Picart, and by Cassini,||405
 * style="text-align:center"|“||its figure discovered, with the proportion of its diameters, and the measure of the degrees upon the meridian,||nowrap="nowrap"|405, 409
 * style="text-align:center"|“||the excess of its height at the equator above its height at the poles,||nowrap="nowrap"|407, 412
 * style="text-align:center"|“||its greatest and least semi-diameter,||407
 * style="text-align:center"|“||its mean semi-diameter,||407
 * style="text-align:center"|“||the globe of the earth more dense than if it was entirely water,||400
 * style="text-align:center"|“||the nutation of its axis,||413
 * style="text-align:center"|“||the annual motion thereof in the orbis magnus demonstrated,||498
 * style="text-align:center"|“||the eccentricity thereof how much,||452
 * style="text-align:center"|“||the motion of its aphelion how much,||404
 * colspan=2|, by what law of centripetal force tending to the centre of the figure it is described by a revolving body,||114
 * style="text-align:center"|“||by what law of centripetal force tending to the focus of the figure it is described by a revolving body,||116
 * colspan=2|, the definition thereof,||108
 * colspan=2|, the laws of their density and compression shewn,||293
 * style="text-align:center"|“||their motion in running out at a hole in a vessel determined,||331
 * colspan=2|, their composition and resolution,||84
 * style="text-align:center"|“||attractive forces of spherical bodies, composed of particles attracting according to any law, determined,||218
 * style="text-align:center"|“||attractive forces of bodies not spherical, composed of particles attracting according to any law, determined,||233
 * style="text-align:center"|“||the invention of the centripetal forces, when a body is revolved in a non-resisting space about an immoveable centre in any orbit,||nowrap="nowrap"|103, 116
 * style="text-align:center"|“||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
 * style="text-align:center"|“||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
 * style="text-align:center"|“||centripetal forces decreasing in the duplicate proportion of the distances, what figures may be described by them,||nowrap="nowrap"|120, 196
 * }
 * style="text-align:center"|“||its figure discovered, with the proportion of its diameters, and the measure of the degrees upon the meridian,||nowrap="nowrap"|405, 409
 * style="text-align:center"|“||the excess of its height at the equator above its height at the poles,||nowrap="nowrap"|407, 412
 * style="text-align:center"|“||its greatest and least semi-diameter,||407
 * style="text-align:center"|“||its mean semi-diameter,||407
 * style="text-align:center"|“||the globe of the earth more dense than if it was entirely water,||400
 * style="text-align:center"|“||the nutation of its axis,||413
 * style="text-align:center"|“||the annual motion thereof in the orbis magnus demonstrated,||498
 * style="text-align:center"|“||the eccentricity thereof how much,||452
 * style="text-align:center"|“||the motion of its aphelion how much,||404
 * colspan=2|, by what law of centripetal force tending to the centre of the figure it is described by a revolving body,||114
 * style="text-align:center"|“||by what law of centripetal force tending to the focus of the figure it is described by a revolving body,||116
 * colspan=2|, the definition thereof,||108
 * colspan=2|, the laws of their density and compression shewn,||293
 * style="text-align:center"|“||their motion in running out at a hole in a vessel determined,||331
 * colspan=2|, their composition and resolution,||84
 * style="text-align:center"|“||attractive forces of spherical bodies, composed of particles attracting according to any law, determined,||218
 * style="text-align:center"|“||attractive forces of bodies not spherical, composed of particles attracting according to any law, determined,||233
 * style="text-align:center"|“||the invention of the centripetal forces, when a body is revolved in a non-resisting space about an immoveable centre in any orbit,||nowrap="nowrap"|103, 116
 * style="text-align:center"|“||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
 * style="text-align:center"|“||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
 * style="text-align:center"|“||centripetal forces decreasing in the duplicate proportion of the distances, what figures may be described by them,||nowrap="nowrap"|120, 196
 * }
 * colspan=2|, the definition thereof,||108
 * colspan=2|, the laws of their density and compression shewn,||293
 * style="text-align:center"|“||their motion in running out at a hole in a vessel determined,||331
 * colspan=2|, their composition and resolution,||84
 * style="text-align:center"|“||attractive forces of spherical bodies, composed of particles attracting according to any law, determined,||218
 * style="text-align:center"|“||attractive forces of bodies not spherical, composed of particles attracting according to any law, determined,||233
 * style="text-align:center"|“||the invention of the centripetal forces, when a body is revolved in a non-resisting space about an immoveable centre in any orbit,||nowrap="nowrap"|103, 116
 * style="text-align:center"|“||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
 * style="text-align:center"|“||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
 * style="text-align:center"|“||centripetal forces decreasing in the duplicate proportion of the distances, what figures may be described by them,||nowrap="nowrap"|120, 196
 * }
 * style="text-align:center"|“||attractive forces of bodies not spherical, composed of particles attracting according to any law, determined,||233
 * style="text-align:center"|“||the invention of the centripetal forces, when a body is revolved in a non-resisting space about an immoveable centre in any orbit,||nowrap="nowrap"|103, 116
 * style="text-align:center"|“||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
 * style="text-align:center"|“||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
 * style="text-align:center"|“||centripetal forces decreasing in the duplicate proportion of the distances, what figures may be described by them,||nowrap="nowrap"|120, 196
 * }
 * style="text-align:center"|“||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
 * style="text-align:center"|“||centripetal forces decreasing in the duplicate proportion of the distances, what figures may be described by them,||nowrap="nowrap"|120, 196
 * }
 * }