- 01Portrait of Sir Isaac Newton
Principia Mathematica
by Isaac Newton · 1687 · 52 chapters · 24/7 tutor
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
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01How many chapters are in the Principia Mathematica course?
The Principia Mathematica course has 52 chapters, each with its own lessons and topics.
02How many lessons are in the Principia Mathematica course?
There are 276 lessons across the course, and you can ask your 24/7 tutor about any of them.
03Can I see what the Principia Mathematica course covers before I start?
Yes. The full curriculum is listed on this page, beginning with "SIR ISAAC NEWTON.".
04Do I get a certificate for the Principia Mathematica course?
Yes. Finishing the course earns a personal Cavua certificate of completion.
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