- 01Portrait of Sir Isaac Newton
Principia Mathematica
Mathematical foundations of classical mechanics.
52Chapters
276Lessons
623Topics
Certificate of completion included
This course was produced by Cavua from a public-domain text.
Skills this course leaves you with.
- Explain Newton's three laws of motion and how they underpin classical mechanics
- Apply the principia's mathematical definitions and axioms to physical problems
- Analyze motion of bodies using core lemmas and corollaries from the text
- Describe Newton's historical contributions to mechanics, optics, and gravitation
- Interpret the structure and arguments of the Principia within the context of natural philosophy
Curriculum
The full table of contents.
Every chapter, every lesson, every topic — laid out before you enroll. Click any chapter to expand it.
- Chapters
- 52
- Lessons
- 276
- Topics
- 623
- 01Title page and publication details
- 01Copyright notice and imprint
- 01Dedication to the Teachers of the Normal School of the State of New-York
- 01Value of the Principia in America
- 02Geometry and educational development
- 03Welcome to teachers and students
- 01Book I: Definitions and Laws of Motion
- 02Sections I-XIV: Motion of Bodies under Centripetal Forces
- 03Book II: Motion of Bodies Resisted by Velocity
- 01Sections II-IX: Motion in resisting mediums and fluids
- 01Birth at Woolsthorpe and family background
- 02Widowed mother and early schooling
- 01School discipline and scientific play
- 02Early drawings, verses, and Miss Storey
- 03Return to school and Cambridge studies
- 01Barrow’s lectures and Newton’s early mathematical discoveries
- 02Method of Fluxions and the Binomial Theorem
- 03Experiments on light and the prism
- 01Reflection and the possibility of perfect optical instruments
- 02Woolsthorpe retreat and the apple-tree meditation
- 03Gravity, lunar motion, and the inverse-square law
- 01Newton's early gravity calculation and pause
- 02Reflecting telescope and optical labours
- 03Advice to Francis Aston on travel
- 01Publication of the Method of Fluxions
- 01Publication of the theory of light and opposition
- 02Reflecting microscopes and fluxions
- 03Inflection and diffraction of light
- 01Colours of natural bodies
- 02Colours of thin plates and fits of easy reflection and transmission
- 01Newton's theory of light and polarization
- 02Ether and electric spirit
- 03Refractive power and the diamond
- 04Chemical papers and elective attraction
- 01Experiments on the retina
- 02Spectrum of the sun
- 01Universal gravitation and elliptical orbits
- 02Composition and publication of the Principia
- 01Publication of the Principia and its three books
- 02Universal gravitation and Kepler's laws
- 03Newton's theological argument from the Principia
- 04Reception of the Principia in Europe and England
- 05Newton's defense of Cambridge independence
- 01Newton's theological researches and view of Scripture
- 02Observations upon the Prophecies of Holy Writ
- 01Newton's theological writings and religious character
- 02The Diamond accident and lost optical papers
- 01Loss of the colours-and-light manuscript
- 02Newton's health and continued scientific work
- 03Appointment as Warden of the Mint
- 01Mastership of the Mint and coinage reform
- 02Bernoulli's problems and Newton's rapid solutions
- 03Newton's concentration and habits of thought
- 01Opticks and the mathematical treatises
- 02Knighthood and Algebraical Lectures
- 01Second edition of the Principia
- 02Newton and Leibnitz on fluxions
- 01Longitude reward petition and parliamentary report
- 02Princess of Wales, chronology, and the short chronicle
- 03London household and domestic character
- 01Declining health and charitable habits
- 02Conjectures on comets and planetary revolutions
- 03Publication of the chronological manuscript in Paris
- 01Chronological writings and the 1728 Chronology of the Ancient Kingdoms Amended
- 02Third edition of the Principia and Pemberton's recollections
- 01Newton's appearance and manner
- 02Modesty, generosity, and humility
- 03Final illness and return to Kensington
- 01Newton's final illness and death
- 02Burial and memorials in Westminster Abbey and Trinity College
- 03Estate distribution and surviving manuscripts
- 01Woolsthorpe manor-house and Newton relics
- 01Principia
- 01Mechanics as the foundation of geometry
- 02Mathematical principles of philosophy
- 03Publication history and edition notes
- 01Quantity of matter
- 02Quantity of motion
- 03Vis insita, or innate force of matter
- 01Impressed force and centripetal force
- 02Absolute, accelerative, and motive quantities of centripetal force
- 01Motive, accelerative, and absolute forces
- 02Absolute and relative time
- 03Absolute and relative space
- 04Absolute and relative motion
- 05Immovable space and true motion
- 06Circular motion and centrifugal effect
- 07Relative quantities and sensible measures
- 08Detecting true motion from causes and effects
- 01Law I: inertia and persistence of motion
- 02Law II: proportional change of motion
- 03Law III: equal and opposite reaction
- 01Composition of forces in a parallelogram
- 02Resolution of a direct force into oblique forces
- 01Mechanical powers from oblique forces
- 02Conservation of quantity of motion
- 01Reflexion of spherical bodies and velocity after impact
- 02Common centre of gravity and uniform motion
- 01Corollary V
- 01Corollary VI
- 01Mechanical advantage in simple machines
- 01OF THE MOTION OF BODIES. SECTION I.
- 01LEMMA VIII.
- 01Spaces described by finite forces and corollaries on proportionality
- 02Scholium on direct and inverse proportionality
- 03Evanescent subtense of the angle of contact
- 01Angles of contact and infinite curvature
- 02Limits of nascent and evanescent quantities
- 03Objection about ultimate proportion and velocity
- 01Ultimate velocities and limits of evanescent quantities
- 02Proposition I: equal areas in equal times
- 03Corollaries on centripetal force and versed sines
- 04Proposition II: force directed to the point
- 01Area law and centripetal force composition
- 01Velocity and radius ratios of centripetal force
- 01Centripetal force in celestial bodies and gravity
- 02Polygonal proof of the preceding proposition
- 03Finding the centre of force from velocities
- 01Force from versed sine and time
- 02Corollaries on centripetal force
- 01Law of centripetal force for a circular orbit about a given point
- 01Force in a circle about a remote centre
- 02Law of centripetal force in a semicircle
- 01Spiral motion and inverse-cube centripetal force
- 02Elliptical orbit and force proportional to distance
- 03Periodic times and conic-section degenerations
- 01Inverse-square centripetal force toward the focus
- 01Hyperbola: force to the focus
- 01Force toward the focus in a parabola
- 01Corollaries on inverse-square centripetal force
- 02Principal latera recta and swept areas
- 01Periodic times in ellipses and greater axes
- 01Velocity relations in conic sections
- 02Determining the orbit from a given launch
- 03Corollaries on finding the other focus and orbit
- 01Motion after an impulse in a conic orbit
- 02Orbit under a continual foreign force
- 03Centripetal force for a conic section from the focus
- 04Finding elliptic and hyperbolic orbits from the focus
- 01Elliptic and hyperbolic trajectories through given points and tangents
- 02Parabolic trajectory through given points and tangents
- 01Constructing a trajectory through two given points
- 02Constructing a trajectory tangent to two given lines
- 03Constructing a trajectory tangent to a line at a given point
- 01Construction of a conic through a point and tangent to a line
- 02Lemma XVI: drawing three right lines from three given points
- 01Problem XIII: constructing a trajectory from a focus, points, and tangents
- 01Lemma XVII: product ratio of lines to a trapezium's sides
- 01Converse proof for the trapezium locus
- 02Corollary on tangent conic sections
- 03Scholium on the meaning of conic sections
- 01Construction of a point from four given lines
- 02Tangents and the locus of points P
- 03Determining the conic locus from the diameter
- 01Ratio of intercepted sides in a parallelogram
- 01Conic section from intersecting moving lines
- 02Inverse locus of the moving point M
- 01Constructing a conic through five given points
- 02Alternative construction using revolving angles
- 03Tangents and conic elements from the trajectory
- 04Simplified construction in the scholium
- 01Trajectory through four points with a given tangent
- 01Three-point trajectory with two tangents
- 01Transformation by parallel ordinates and abscissas
- 01Transforming curves and tangents by the lemma
- 02Trajectory through two points and three tangents
- 01Trajectory through a given point and four tangents
- 01Parallel tangents and the mean proportional semi-diameter
- 01Tangents and segment ratios in a parallelogram
- 02Constructing a trajectory tangent to five given lines
- 01Finding the axes and foci from a described trajectory
- 02Constructing a trajectory of given kind through four points
- 03Related lemmas on trajectories through points and touching lines
- 01Placing a triangle by three given lines
- 02Drawing a trajectory with given intercepted parts
- 03Constructing a trapezium by four given lines
- 01Alternative construction of the corollary
- 02Proposition XXIX: trajectory cut by four lines
- 03Scholium: second construction method
- 01Finding the place in a parabolic trajectory
- 01Corollaries on arc time and velocity
- 02Impossibility of universal area equations for ovals
- 01Why spirals and ovals resist finite equations
- 02Finding a body’s place in an elliptic orbit
- 03Approximate and hyperbolic methods for orbital position
- 01Rectilinear ascent and descent of bodies
- 02Spaces described in direct fall under inverse-square centripetal force
- 01Hyperbola and parabola descent cases
- 02Velocity ratio for falling bodies
- 01Falling body and circular motion in a parabola
- 01Times of descent from a given place
- 01Bodies falling under force proportional to distance from the centre
- 02Velocity and time under any centripetal force
- 01Equal velocities at equal altitudes under centripetal force
- 02Finding trajectories and times from a centripetal force
- 03Apsides, trajectory angles, and conic-section orbits
- 01Motion from a given place and velocity
- 02Bodies in moveable orbits and the apsides
- 01Difference of forces in a revolving orbit
- 02Elliptical orbit corollaries
- 01Examples for uniform and power-law centripetal forces
- 02Motion of the apsides in nearly circular orbits
- 03General rule for mixed forces and corollaries
- 01Motion in eccentrical planes and given superficies
- 02Cycloids on the outside and inside of a globe
- 03Cycloidal pendulum and equal oscillations
- 04Isochronous oscillations in cycloids
- 05Forces for equal-time oscillations in arbitrary curves
- 06Area proportional to time for projected motion
- 07Finding a trajectory on a curve superficies
- 01Mutual attraction and the common center of gravity
- 02Similar figures described by two mutually attracting bodies
- 01Mutual attraction and similar curves
- 02Case 1: centre of gravity at rest
- 01Mutual ellipses and inverse-square conic sections
- 01Mutual attraction and the common center of gravity
- 01Mutual attraction with forces proportional to distance
- 01Multiple bodies in elliptical motion about a common center of gravity
- 02Bodies with inverse-square forces moving in nearly elliptical orbits
- 03Perturbations from a nearby great body
- 01Mutual attraction and orbital perturbation
- 02Different orbital planes and latitude perturbation
- 01Variation of orbital period under changing central force
- 02Forward motion of the line of apsides
- 01Apsidal motion under diminished centripetal force
- 02Eccentricity changes from increasing or decreasing force
- 01Errors in apsidal distance and eccentricity
- 02Errors as to latitude and orbital inclination
- 01Retrograde motion of the nodes in quadratures
- 02Scaling of errors with distance and period
- 03Fluid annulus and tidal flux
- 04Oscillation of a hard globe and node precession
- 05Equatorial redundancy and consequentia of nodes
- 06Rotation of a homogeneous globe under multiple impulses
- 07Effect of centripetal force and a mountain on the poles
- 08Exterior body S orbiting the common centre of gravity
- 01Orbits of exterior bodies around the common center of gravity
- 01Absolute attractive force proportional to mass
- 02Corollaries on inverse-square and general laws
- 03Analogy between centripetal forces and central bodies
- 01Attraction inside a spherical surface
- 01Inverse-square attraction of spherical surfaces
- 01Attraction proportional to sphere diameter
- 02Equal periodic times for proportional distances
- 03Attraction inside a sphere proportional to distance
- 01Attraction of a corpuscle outside a sphere
- 02Homogeneous sphere attraction corollaries
- 03Mutual attraction of similar spheres
- 01Corollaries on spherical attraction
- 02Spheres with varying density and attraction
- 01Mutual attraction of similar spheres
- 02Attraction proportional to distance between centres
- 03Attraction of a corpuscle within a sphere
- 01Scholium on principal cases of attraction
- 01Force of a vanishing spherical superficies
- 02Attraction of a spherical solid
- 03Force of a sphere and area ANB
- 04Measuring the area ANB
- 01Construction of the ordinate DN
- 02Example 1: inverse-distance force and area construction
- 03Example 2: inverse-cube force
- 01Attraction of a corpuscle within a sphere
- 01Force ratios for spherical particles
- 02Force on a corpuscle in a sphere's centre
- 01Force of a segment on a corpuscle in its axis
- 02Scholium on non-spherical attractive bodies
- 01Attraction increasing at contact
- 02Triplicate decrease and contact attraction
- 03Similar bodies and proportional corpuscles
- 01Attraction toward whole bodies from proportional particles
- 02Force proportional to distance and centre of gravity
- 01Attraction of a body composed of particles
- 02Attraction toward the common centre of gravity
- 03Force of a corpuscle on a circle
- 04Annular summation and corollaries
- 01Attraction of a corpuscle toward a solid
- 02Cylinder attraction by inverse-square forces
- 03Spheroid attraction along the axis
- 01Attraction of an interior spheroid
- 02Finding the decrease of centripetal forces
- 03Plane solid with inverse-power attraction
- 01Scholium on motion toward a plane and curve laws
- 02Refraction through parallel planes and sine ratios
- 03Reflection between parallel planes
- 04Optical analogy and converging superficies
- 05Construction of a refracting surface between two media
- 06Extension to multiple superficies and spherical telescope lenses
- 01Motion lost under resistance proportional to velocity
- 02Geometrical progression of velocities and spaces
- 03Ascending and descending motion in a resisting medium
- 04Projectile motion with linear resistance
- 01Parabolic construction for resistance and velocity
- 02Experimental method for finding the resistance ratio
- 01Resistance proportional to the square of velocity
- 02Geometrical progression of velocities and equal spaces
- 01Corollaries on motion in a resisting medium
- 02Proposition VI: equal spaces and proportional loss of velocity
- 01Bodies equally swift resisted by diameter
- 01Definition of genitum and moments
- 02Moments of generated quantities
- 03Rectangle AB under flux
- 01Moments of rectangles, powers, and generated quantities
- 01Absolute forces in uniform resistance
- 01Circular and hyperbolic sectors as time measures
- 02Spaces described in falling and ascending
- 03Velocity comparisons in resisting and non-resisting media
- 01Density of the medium for a prescribed curve
- 01Density of the medium for a semicircular path
- 01Parabolic projectile motion in a resisting medium
- 01Hyperbola AGK with reciprocal power law density
- 01Hyperbolic projectile paths in resisting media
- 02Practical rules for determining the hyperbola from phenomena
- 03Application to parabolic trajectories
- 01Projectile path in a non-resisting space
- 02Motions resisted partly in the ratio and partly in the duplicate ratio of velocity
- 01Velocity and hyperbolic area relation
- 02Spaces in arithmetic progression and velocities in geometric progression
- 01Ascending motion with linear and quadratic resistance
- 02Ascending motion with hyperbolic sector
- 03Descending motion with rectangular hyperbola
- 01Space described in ascent or descent
- 01Resistance of spherical bodies in fluids
- 01Lemma III: spiral geometry and ultimate ratios
- 02Density inversely as distance; spiral motion in a resisting medium
- 03Generalization to any power of distance
- 04Finding centripetal and resisting forces from a given spiral
- 01Definition of a fluid and equal pressure in a rigid vessel
- 02Weight sustained by a spherical fluid on a concentric bottom
- 03Apparent and absolute gravity of bodies in fluids
- 04Compression of immersed bodies in fluids
- 05Density proportional to compression under centripetal force
- 01Density proportional to compression under inverse-square gravity
- 01General laws of fluid condensation
- 01Elastic fluid and inverse-distance forces
- 01Scholium on compressing forces and particle distances
- 02Motion and resistance of funependulous bodies
- 01Quantity of matter from pendulum oscillations
- 02Corollaries on weight, time, and pendulum length
- 01Cycloidal oscillations in a resisting medium
- 01Equal-time oscillations under proportional resistance
- 02Oscillations in a resisting medium with duplicate-velocity resistance
- 01Resistance proportional to time in a cycloid
- 02Resistance in a duplicate ratio of velocity
- 03Area method for finding resistance and velocity
- 01Effect of resistance on pendulum arc difference
- 01Resistance inferred from pendulum oscillations
- 02Experiments with wooden and leaden globes
- 03Resistance of globes and diameters
- 04Resistance of fluids and pendulum oscillations
- 05Resistance in water, air, and quicksilver
- 06Surface resistance and the æthereal medium
- 01Weighing the empty and filled box
- 02Oscillation counts and resistance ratio
- 03Calculation of internal and external resistance
- 04Correction for the weak hook
- 01Similar systems of bodies and proportional motion
- 01Resistance of greater parts in systems
- 02Resistance in elastic fluids and swift motion
- 03Globe versus cylinder resistance
- 01Resistance of a globe in a rare medium
- 02Corollaries on velocity, diameter, and density
- 03Hyperbolic description of motion and resistance
- 04Scholium on continued mediums and fluid resistance
- 01Velocity of effluent water from a cylindrical vessel
- 02Converging stream and corrected hole diameter
- 01Hole off-center in the vessel bottom
- 02Side and upward efflux of water
- 01Velocity independent of hole shape
- 02Efflux into stagnant water
- 03Corollaries on effluent force and weight ratios
- 01Weight sustained by the bottom and hole
- 02Little circle PQ and the falling-water cataract
- 03Upper bound from the spheroid comparison
- 01Resistance of a cylinder in a continued fluid
- 01Equal hindrance of cylinder, sphere, and spheroid
- 02Equal action by flowing water
- 03Equal resistances in opposite motion
- 04Scholium on smooth convex bodies and friction
- 01Resistance of a globe in a compressed fluid
- 02Corollaries on globe resistance and terminal velocity
- 03Globe moving in a cylindric canal
- 01Resistance of a globe in a compressed medium
- 01Table of descent, velocity, and space in a fluid
- 02Experimental method for measuring fluid resistance
- 01Experiments with falling globes in water
- 01Wax globes falling through water
- 01Oscillation effects in falling globes
- 02St. Paul's Church air-globe experiment
- 01Experiments with falling bladders and leaden globe
- 02Comparison of experiments with theory
- 03Resistance in infinitely fluid media and projectiles
- 01Pressure deflecting through a fluid
- 02Motion diverging into unmoved spaces
- 01Propagation of motion through a hole
- 02Pulses from a tremulous body in an elastic medium
- 03Circular motion in a non-elastic medium
- 01Oscillatory motion of water in a canal
- 02Pendulum analogy for equal times
- 01Reciprocation of water in a canal
- 02Velocity of waves and wave breadth
- 01Wave speed corollaries and circular motion caveat
- 02Oscillating pendulum law for fluid pulses
- 03Pulse count equals vibration count
- 01Velocity of pulses in an elastic fluid
- 01Velocity of pulses in a compressed medium
- 01Velocity of the pulses from falling bodies
- 02Finding the distances of the pulses
- 03Scholium on light, sounds, and the speed of sound
- 01Circular motion of fluids under a revolving cylinder
- 02Circular motion of fluids under a revolving sphere
- 01Derivation of the vortex law from annular motion
- 02Corollaries on fluid vortices and interacting globes
- 03Propagation of motion through the fluid
- 04Scholium on fluid density and vessel shape
- 05Celestial phenomena and planetary periodic times
- 01Bodies in a vortex and density law
- 02Why planetary vortices fail
- 01Mathematical principles of philosophy
- 02Purpose and method of Book III
- 01Rule I: no more causes than necessary
- 02Rule II: same causes for same effects
- 03Rule III: universal qualities inferred from experiments
- 04Rule IV: propositions from induction
- 01Circumjovial planets and Keplerian proportions
- 01Saturn’s satellites and periodic times
- 01Primary planets encompassing the sun
- 01Planetary distances from the sun
- 02Kepler's area law for the primary planets
- 03Moon's area law around the earth
- 01Forces governing the circumjovial planets
- 02Forces governing the primary planets
- 03Moon's centripetal force toward the earth
- 01PROPOSITION IV. THEOREM IV.
- 01Scholium on lunar gravity
- 02Planetary gravitation toward Jupiter, Saturn, and the sun
- 01PROPOSITION VI. THEOREM VI.
- 01Corollaries on gravity, density, and magnetism
- 01Gravity toward whole planets and their parts
- 02Inverse-square attraction between two spheres
- 03Comparing planetary weights, masses, and densities
- 01Gravity decreases with distance from planetary centers
- 02Planetary motions can subsist for an exceedingly long time
- 01Resistance in the celestial regions
- 02Immovable centre of the world
- 03Common centre of gravity of the system
- 04The sun's perpetual motion near the centre of gravity
- 01Common centre of gravity of the solar system
- 02Elliptical planetary orbits and equal areas
- 03Jupiter and Saturn perturbations
- 01Perturbations of planetary orbits
- 02Fixed aphelions and nodes
- 03Distances and motions of inner planets
- 01Finding planetary eccentricities and aphelions
- 02Diurnal motions and lunar libration
- 03Planetary axes and equatorial bulging
- 01Earth’s oblateness from rotation
- 02Jupiter’s measured diameters and theory
- 01Weights of bodies by distance from Earth’s center
- 02Pendulum lengths and meridian degrees by latitude
- 01Pendulum observations near the equator
- 02Latitude comparisons and causes of variation
- 01Backward motion of the equinoctial points
- 02Lunar motions and inequalities
- 01Unequal motions of Jupiter's and Saturn's satellites
- 02Tides raised by the sun and moon
- 03Tidal variation by latitude and channel effects
- 01Forces with which the sun disturbs the moon
- 02Horary increment of the moon's area
- 01Variation of the moon's area in equal times
- 02Distance of the moon from the earth
- 03Diameters of the moon's orbit without eccentricity
- 01Curvature of the moon's orbit in syzygies and quadratures
- 01Moon’s distance in syzygies and quadratures
- 02Variation of the moon
- 03Horary motion of the lunar nodes
- 01Mean motion of the lunar nodes
- 02Corollary 1: motion as area and AZ squared
- 03Corollary 2: mean motion in syzygies
- 01Horary motion of the nodes in an elliptic orbit
- 01Mean horary motion of the nodes from lunar velocity
- 01Correct mean horary motion of the lunar nodes
- 02Yearly mean motion from the sun's apparent course
- 03Abbreviation of time from node motion
- 01True motion of the moon's nodes
- 01Mean motion of the sun from the node
- 01Equation of the moon's nodes
- 01Horary variation of the inclination of the moon's orbit
- 02Elliptical orbit correction and corollaries
- 01Inclination of the Moon's Orbit to the Ecliptic
- 01Variation of the moon's inclination with node position
- 02Annual equation of the moon's mean motion
- 03Annual equations of the moon's apogee and nodes
- 04Semi-annual equation of the moon's mean motion
- 05Semi-annual equation of the apogee and epicycle construction
- 01Moon's second equation and eclipse refraction
- 02Testing lunar theory and Greenwich mean motions
- 03Force of the sun to move the sea
- 01Sun’s force to disturb the sea
- 02Deduction of the moon’s force from tides
- 03Consequences for lunar density and gravity
- 01Moon’s fluid figure and spheroidal bulge
- 02Libration and fixed lunar face
- 03Equatorial particles and rotational force lemma
- 01Force of particles in a lesser circle
- 02Motion of the earth and ring about the axis
- 03Precession of the equinoxes from sun and moon
- 01Parallax as evidence for comet distance
- 02Evidence from curved paths and head brightness
- 03Tail light, perihelion observations, and corollaries
- 01Comets as planets in void celestial spaces
- 02Conic-section orbits and proportional areas
- 01Finding a parabolic curve through given points
- 01Interpolation from observed comet positions
- 01Proportional segment cut off by the chord
- 02Scholium on a more accurate construction
- 03Lemma IX: equal lines and latus rectum
- 01Chord AC from parabolic motion
- 02Free fall toward the sun
- 01Determining a comet's parabolic orbit from three observations
- 01Telescopic observations and fixed-star measurements
- 02Halley’s parabolic orbit for the comet
- 03Observed and computed lunar positions table
- 01Comet observations from Nov. 17 to Nov. 24
- 01Comet observations and orbital agreement
- 02Trajectory diagram and tail measurements
- 01Heat of the comet and formation of the tail
- 02Refutation of optical explanations of comet tails
- 03Laws governing the direction and curvature of tails
- 01Rarity of cometary vapours and tails
- 02Estimating the ascent time of tail vapour
- 03Causes of tail ascent near the sun
- 04Growth, fading, and cosmic supply of comet tails
- 05Comet heads dimming as tails grow brighter
- 06Historical examples of faint heads and splendid tails
- 01Correcting a comet's trajectory from observations
- 02Halley's 1664–1665 comet computation
- 03Halley’s 1683 comet comparison table
- 04Bradley’s 1723 comet comparison table
- 05Evidence that comet motions fit the theory
- 01General Scholium on vortices, comets, and gravity
- 02God as Lord over all
- 03Gravity and the rejection of hypotheses
- 01Early heliocentric philosophy
- 02Geocentric alternatives and solid orbs
- 03Comets and the rejection of solid orbs
- 01Centripetal force as the cause of planetary orbits
- 02Evidence from the Moon and the planets
- 01Planetary and satellite motions as astronomical experiments
- 02Evidence for inverse-square planetary forces
- 03Mars, Jupiter, and Saturn as solar-system cases
- 01Circum-solar force from planetary motions
- 02Moon’s distance and terrestrial gravity
- 03Planetary and lunar force comparisons
- 01Apparent diameters of the planets
- 02Telescope light and apparent size
- 01Planetary density and force analogy
- 02Centripetal force proportional to planetary bodies
- 03Experiments on equal gravitational action in earthly bodies
- 01Mutual attraction as a single action
- 02Why terrestrial attraction is imperceptible
- 03Universal attraction proportional to matter
- 01Circumsolar force and planetary descent
- 02The sun as the system's centre of gravity
- 03Planetary orbits, foci, and aphelions
- 01Moon's inequalities from the sun's action
- 02Jupiter and Saturn satellite motions derived from the moon
- 01Planetary and lunar rotations
- 02Moon's libration in longitude and latitude
- 03Planetary oblateness, nutation, and tides
- 01Combined lunar and solar tide forces
- 02Distances, declination, and seasonal tide variation
- 03Earthwide tidal spheroid and local flood tides
- 04Residual motion and delayed tide peaks
- 01Retarded tides in shallow channels and straits
- 02River currents and the timing of influx and reflux
- 03Tidal height and the breadth of the sea
- 01Computation of the sea's ascent and descent
- 01Tidal height in a canal
- 02Spheroidal figure of the water
- 03Latitude and declination effects on tides
- 01Tidal forces under the equator
- 01Moon and Sun Compared by Tides and Density
- 02Earth, Moon, and Sun Mass Ratios
- 03Fixed Stars and Annual Parallax
- 01Distances and brightness of the fixed stars
- 02Comets and annual parallax
- 01Parallax evidence for close comet passages
- 02Brightness of comet heads and apparent size
- 01Comet nuclei and head brightness
- 02Comet distance inferred from tails
- 01Comet tails as evidence of close solar approach
- 02Historical comet observations and inferred solar proximity
- 03Why comets frequent the sun's region
- 01Why comets are seen more often near the sun
- 02The nature of comet tails and the rejection of refraction
- 03Atmospheric rarity and the material of comet tails
- 01Rarefaction and ascent of comet tails
- 02Observed laws of comet-tail deviation
- 01The relation betwixt the velocity of a comet and its distance from the sun's centre being given, the comet's trajectory is required
- 01Geometric construction by linear description
- 02Trigonometric correction of the construction
- 03Arithmetic correction by converging series
- 01Cutting three given lines in a given ratio
- 01Lemma IV
- 01Determining comet trajectories from assumed velocity ratios
- 01Correcting the assumed velocity ratio and trajectory
- 01Celestial matter, circular motion, and centripetal forces
- 02Planetary motions, lunar motion, and tides
- 03Fixed stars and comet trajectories
- 01Comets as planets in the planetary regions
- 01Conic sections and centripetal force
- 01Earth: dimensions, figure, and motion
- 01Centripetal force definitions and properties
- 02Gravity and its relation to bodies and planets
- 01Propagation and velocity of light
- 01Moon: orbital geometry and physical properties
- 02Moon: inequalities, perturbations, and lunar equations
- 03Moon's variations and lunar theory from observations
- 01Planetary motions and orbital laws
- 02Satellites and Saturn
- 03Solar system bodies and tides
- 01Transcriber’s notes on corrections and figure replacements
Keep exploring
View allMore in Physics.
Learn with AI
Ready to start this course?
Create your account to enroll, talk to your 24/7 tutor, and track your progress — across every device.