in their orbits, but these ellipses will be near to parabolas, 466COMET S parabolic trajectory found from three observations given, 472corrected when found, ... 495" place in a parabola found to a given time, 466"velocity compared with the velocity of the planets, .... . 466JoMKTs TAILS directed from the sun, 489" " brightest and large>t immediately after their passage through the neighbourhood of the sun, 487" " their wonderful rarity, 490* " their origin and nature, ...... . . . 46S" in what space of time they ascend from their heads, . . 4907V576 INDEX TO THE PRINCIPIAr?OMET of the years 1664 and 1665 the observations of its motion compared with the theory, . 496u 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- -l seems to have appeared in the year 1607, and likely to return again after a period of75 years, 501,502" of the year 1683 its motion compared with the theory, 499" of the year 1723 its motion compared with the theory, . . * . 501CONIC 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, 131when the centres or asymptotes are given, ....... 147CURVATURE of figures how estimated, 271, 423CURVES distinguished into geometrically rational and geometrically irrational, . . . 157CYCLOID, or EPICYCLOID, its rectification, 184" " its evoluta, 185CYLINDER, the attraction of a cylinder composed of attracting particles, whose forces are reciprocally as the square of the distances, 239DESCENT of heavy bodies in vacuo, how much it is, 405" and ascent of bodies in resisting mediums, 252,265,281,283,345DESCENT or ASCENT rectilinear, the spaces described, the times of decription, and the velocitiesacquired in such ascent or descent, compared, on the supposition of anykind of centripetal force, 160EARTH, its dimension by Norwood, by Picart, and by Cassini, 405" its figure discovered, with the proportion of its diameters, and the meattire of the degreesupon the meridian, ............ 405, 40?)" 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, 404ELLIPSES, by what law of centripetal force tending to the centre of the figure it is described by arevolving body, 114" by what law of centripetal force tending to the focus of the figure it is described by arevolving body 116FLUID, the definition thereof, 108FLUIDS, the laws of their density and compression shewn, ....... 293" their motion in running out at a hole in a vessel determined, . . . . . 331FORCES, their composition and resolution, 84" attractive forces of spherical bodies, composed of particles attracting according to anylaw, determined, 218" attractive forces of bodies not spherical, composed of particles attracting according toany law, determined, 233" the invention of the centripetal forces, when a body is revolved in a non-resisting spaceabout an immoveable centre in any orbit, 103, 116" the centripetal forces tending to any point by which any figure may be described by arevolving body being given, the centripetal forces tending to any other point by whichthe same figure may be described in the same periodic time are also given, . . . liev 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 areaugmented or diminished in any given ratio, or the angle of their inclination be anyhow changed, the periodic time remaining the same, 116Mcentripetal forces decreasing in the duplicate proportion of the distances, what figuresmay be described by them, 120 1 9fINDEX TO THE PRINCIPIA. 577FomcE, centripetal force defined, 74" the absolute quantity of centripetal force defined, 75M the accelerative quantity of the same defined, 76w the mutive quantity of the same defined, 76" the proportion thereof to any known force how collected, 109" a centripetal force that if reciprocally as the cube of the ordinate tending to a vastlyremote centre of lorce will e 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 offorce will cau^e a body to move in an hyperbola, 243centrifugal force of bodies on the earth s equator, how great, 405GOD, his nature, 506ClaAviTY 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 pi anets, 393" from the surfaces of the planets upwards decreases in the duplicate ratio of the distances from the centre, 400" fruin the same downwards decreases nearly in the simple ratio of the same, . . 400" tends towards all b dies, ami 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 areretained in their orbits, 393HEAT, an iron rod increases in length by heat, ......... 112" 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, ... , , 486HEAVENS are void of any sensible re.-iotauce, 401, 445, 492; and, therefore, of almost any corporeal fluid whatever, 355 356" suffer light to pass through them without any refraction, .... 485HYDROSTATICS, the principles thereof delivered, . .... 293SYPERBOLA, by what law of centrifugal force tending from the centre of the figure it is describedby a revolving body, 116" by what law of centrifugal force tending from the focus of the figure it is describedby a revolving body, 117" by what law of o* itripetal force tending to the focus of the figure it is describedby a revi living body, 118HYPOTHESES of what kind oever rejected from this philosophy, 508JUPITER, its periodic time, 388" its distance from the sun, 388" its apparent diameter, 386" its true diameter, . 399" its attractive t rce, how great, 398" the weights of bi 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 comftared with observations, ........ . 409" its rotation about its axis, in what time performed, ..... . 409" the cause of its belts hinted at, 445fjlOHT, its propagation not instantaneous, .......... 246" its velocity different in different mediums, ... 24J5" a certain reflection it sometimes suffers explained*, 245" its refraction explained, 243u refraction is not made in the single point of incidence, 247 ." an incurvation of light about the extremities of bodies observed by experiments, . . 24fc" not caused by the agitation of any ethereal medium, 368ANETIC force, 94,304,397,45437578 INDEX TO THE PRINCIPIA.WARS, its periodic time, 3^" its distance from the sun, < 339" the motion of its aphelion, 4^/5MATTER, its quantity of matter defined, ..." 73" its msinsita define!. . 74" its impressed force defined, 74its extension, hardness, impenetrability, mobility, rta inertia:, gravity, how discovered, 385subtle mattir of Descartes ii quired into, 320MECHANICAL POWERS explained and demonstrated, 94MERCURY, its periodic time, ........... . 388its distance from the sun, ., 389the ruotion of its aphelion, . ... 405METHOD of first and last ratios, 95" of transforming figures into others of the same analytical order, .... 141" of fluxions, ............... 261differential, ........... 447of finding the quadratures of all curves very nearly true, ...... 448" ot converging series applied to the solution of difficult problems, . . . 271 430MOON, the inclination of its orbit to the ecliptic greatest in the syzygies of the node with the ^un,and least in the quadratures, 208" the figure of its body collected by calculation, 45.)" its librations explained, .......... 405its 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 sem>diameters of the earth contained therein, 453" how many mean semi-diameter?, 454" its force to move the sea how great, 449not perceptible in experiments of pendulums, or any statical or hydrostatical observations, 452" its periodic time, 454" the time of its synodical revolution, 422tt 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 moreswiftly in the aphelion the f-ame, its orbit being contracted, .... 413, 444, 445" revolves more slowly, in a dilated orbit, when tl.e apogteon is in the syzygies with the sun ;and more swiftly, in a contracted orbit, when the apogaeon 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, . . 44G" moves slower in its quadratures with the sun, swifter in the syzygies; and by a radiusdrawn to the earth describes an area, in the fir.<t case less in proportion to the time, in thelast 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 caseits orbit i? less curve, and comes nearer to the earth, 415u 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 apogaenn moves more slowly when the earth is in its aphelion, m< re swiftly in the perihelion, 414,445" its apogaeon goes forward most swiftly when in the syzygies with the sun ; and goes backward in the quadratures, 414, 44l:" its eccentricity greatest when the apogaeon is in the syzygies with the sun ; least when thesame is in the quadratures, 414, 44C* 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 ... . . . .... 41-1INDEX TO THE PRINCIPIA. 579MOON, the motions of the nodes and the inequalities of its motions computed from the theory ofgravity, 427,430,434,436" the same from a different principle, 437the variations of the inclination computed from the theory of gravity, . . . 441, 443" the 3ns of the moon s motions for astronomical uses, 445" the unnual equation of the moon s mean motion, 445" the first semi-annual equation of the same, ... 443" the second serai-annual equation of the same, 447" the first equation of the moon s centre, 447" the second equation of the moon s centre, 448MOON 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 seini-annual equation of the same, .......... 437" the seini-anuual equation of the inclination of the orbit to the ecliptic, . . . 444" the method of fixing the theory of the lunar motions from observations, ... 464MOTION, its quantity defined, 73absolute and relative, 78" absolute and relative, the separation of one from the other possible, demonstrated byan example ...* 82" laws thereof; 83". of concurring bodies after their .reflection, by what experiments collected, ... 91" of bodies in eccentric sections, . . 116" in moveub!e 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 verygreat 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 byan uniform force of gravity, 252,265,281,283" of bodies projected in resisting mediums, and acted on by an uniform force of gravity, 255, 268u of bodies revolving in resisting mediums, 287" of funependulous bodies in resisting mediums, . 304" and resistance of fluids, 32341 propagated through fluids, ... . ..... 356" of fluids after the manner of a vortex, or circular, 370MOTIONS, composition and resolution of them, .......... 84OVALS for optic uses, the method of finding them which Cartesius concealed, .... 246" a general solution of Cartesius s problem, 247, 248OBBITS, the invention of those which are described by bodies going off from a given place witha 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 thecube of the distance, 114, 171, 176" of those which are described by bodies agitated by any centripetal forces whatever, 168PARABOLA., by what law of centripetal force tending to the focus of the figure the same may bedescribed, 120PENDULUMS, their properties explained, 186, 190, 304the diverse length? of isochronous pendulums in different latitudes compared amongthemselves, both by observations and by the theory of gravity, . . 409 to 413PLACE defined, and distinguished into absolute and relative, .78PLACES of bodies moving in conic sections found to any assigned time, ..... 153not carried about by corporeal vortices, ......... 378">$() INDEX TO THE PRINCIPIA.PLANET*, their et .imes, . . 3gg" their distances from the tun, .. 339* the at .helia and nodes of their orbits do almost rest, ...... 405" their orbits determined, 406" the way of finding their places in their orbit?, 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, . . . 406PLANETS, PRIMARY, surround the sun, 387" move in ellipses whose focus is in the sun s centre 403by radii drawn to the sun describe areas proportional to the times, . 388, 403revolve in periodic times that are in the sesquiplicate proportion of the distances from the sun, 387are 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, 393PLANETS, SECONDARY, move in ellipses having their focus in the centre of the primary, . 413by radii drawn to their primary describe areas proportional to thetimes 386,387,390revolve in periodic times that are in the sesquiplicate proportion of theirdistances from the primary, 386, 387PROBLEM KEPLEHIAN, solved by the trochoid and by approximations, .... 157 to 160of the ancients, of four lines, related by Pappus, and attempted by Cartesius,by an algebraic calculus solved by a geometrical composition, . 135PROJECTILES move in parabolas when the resistance of the medium is taken away, 91, 115, 243, 273their motions in re.-isting mediums, ........ 255, 268PULSES 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 thepipes, 370QUADRATURES general of oval figures not to be obtained by finite terms, 153QUALITIES of bodies how discovered, and when to be supposed universal, .... 38-1RESISTANCE, the quantity thereof in mediums not continued, 329" in continued mediums, 40fin mediums of any kind whatever, . . . . . . . . 3.i.of mediums is as their density, cceteris paribus, . . 320, 321, 324, 329, 344. 353is in the duplicate proportion of the velocity of the bodies resisted, ccrteris ibus,258, 314, 374, 329, 3J4, 35 iCtis in the duplicate proportion of the diameters of spherical bodies resisted, cceterisparibus 317, 31 8, 329, 34-1" of fluids threefold, arises either from the inactivity of the fluid matter, or the tenacity of its parts, or friction, 286the resistance found in fluids, almost all of the first kind, .... 321, 35*" 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 oi a cone, how made the least possible, 328" what kind of solid it is that meets with the least, 329RESISTANCES, the theory thereof confirmed by experiments of pendulums, . . . 313 to 321" by experiments of fa-lling bodies, 345 to 356REST, true and relative, 78RULES of philosophy, 38-!SATELLITES, the greatest heliocentric elongation of Jupiter s satellites, 387" the greatest heliocentric elongation of the Huygenian satellite from Saturn s centre. 398the 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 fromthe motions of the moon, 413SM^UIPLICATE proportion defined, 101INDEX TO THE PRINCIPLE.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, . . . 388SHADOW of the earth to be augmented in lunar eclipses, because of the refraction of the atmosphere, 44?SUUNDS, 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 c< mputed, 368, 369" somewhat swifter by the theory in summer than m winter, 370" cease immediately, when the motion of the sonorous body ceases, .... 365" how augmented in speaking trumpets, 370SfACE, absolute and relative, 78, 79" not equally full. 396SPHEROID, the attraction of the same when the forces of its particles are reciprocally as thesquares of the distances 239SPIRAL cutting all its radii in a given angle, by what law of centripetal force tending to thecentre thereof it may be described by a revolving body, .... 107, 287, 291SPIRIT pervading all bodies, and concealed within them, hinted at, as required to solve a greatmany phsenomena of Nature, 508STARS, the fixed ,-tars demonstrated to be at rest, ... 404" their twinkling what to be ascribed to, . 487" new stars, whence they may arise, 502SUBSTANCES of all things unknown, 507SUN, m >ves 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 <.f 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, 448TIDES of the sea derived from their cause, 415, 448, 449TIMF, absolute and relative, 78, 79" tli? astronomical equation thereof proved by pendulum clocks, and the eclipses of Jupiter ssatellites, 79A VACUUM proved, or that all spaces (if said to be full) are not equally full, .... 396VELOCITIES of bodies moving in conic sections, whore the centripetal force tends to the focus, . 121VELOCITY, the greatest that a globe falling in a resisting medium can acquire, . . . 344VENUS, its periodic time, 388" its distance from the sun, 388" the motion of its aphelion, 405VOHTICES, their nature and constitution examined, 504W.AVES, the velocity with which they are propagated on the superficies of stagnant water, . 361WEIGHTS of bodies towards the sun, the earth, or any planet, are, at equal distances from thecentre, as the quantities of matter in the bodies, 3941 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, . . 409NON-CIRCULAT1NQRETURN Astronomy/Mathematics/Statistics Library100 Evans Hall 642-3381FORM NO. 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