Efnisyfirlit

• Cover
• Half Title
• Subvention
• Frontispiece
• Title
• Copyright
• Dedication
• Contents
• Contents of the Guide
• Contents of the Principia
• Preface
• A Guide to Newton’s Principia
• Abbreviations
• Chapter One: A Brief History of the Principia
• 1.1 The Origins of the Principia
• 1.2 Steps Leading to the Composition and Publication of the Principia
• 1.3 Revisions and Later Editions
• Chapter Two: Translating the Principia
• 2.1 Translations of the Principia: English Versions by Andrew Motte (1729), Henry Pemberton (1729-?), and Thomas Thorp (1777)
• 2.2 Motte’s English Translation
• 2.3 The Motte-Cajori Version; The Need for a New Translation
• 2.4 A Problem in Translation: Passive or Active Voice in Book 1, Secs. 2 and 3; The Sense of “Acta” in Book 1, Prop. 1
• 2.5 “Continuous” versus “Continual”; The Problem of “Infinite”
• Chapter Three: Some General Aspects of the Principia
• 3.1 The Title of Newton’s Principia; The Influence of Descartes
• 3.2 Newton’s Goals: An Unpublished Preface to the Principia
• 3.3 Varieties of Newton’s Concepts of Force in the Principia
• 3.4 The Reorientation of Newton’s Philosophy of Nature; Alchemy and the Principia
• 3.5 The Reality of Forces of Attraction; The Newtonian Style
• 3.6 Did Newton Make the Famous Moon Test of the Theory of Gravity in the 1660s?
• 3.7 The Continuity in Newton’s Methods of Studying Orbital Motion: The Three Approximations (Polygonal, Parabolic, Circular)
• 3.8 Hooke’s Contribution to Newton’s Thinking about Orbital Motion
• 3.9 Newton’s Curvature Measure of Force: New Findings (by Michael Nauenberg)
• 3.10 Newton’s Use of “Centrifugal Force” in the Principia
• Chapter Four: Some Fundamental Concepts of the Principia
• 4.1 Newton’s Definitions
• 4.2 Quantity of Matter: Mass (Def. 1)
• 4.3 Is Newton’s Definition of Mass Circular?
• 4.4 Newton’s Determination of Masses
• 4.5 Newton’s Concept of Density
• 4.6 Quantity of Motion: Momentum (Def. 2)
• 4.7 “Vis Insita”: Inherent Force and the Force of Inertia (Def. 3)
• 4.8 Newton’s Acquaintance with “Vis Insita” and “Inertia”
• 4.9 Impressed Force; Anticipations of Laws of Motion (Def. 4)
• 4.10 Centripetal Force and Its Three Measures (Defs. 5, 6-8)
• 4.11 Time and Space in the Principia; Newton’s Concept of Absolute and Relative Space and Time and of Absolute Motion; The Rotating-Bucket Experiment
• Chapter Five: Axioms, or the Laws of Motion
• 5.1 Newton’s Laws of Motion or Laws of Nature
• 5.2 The First Law; Why Both a First Law and a Second Law?
• 5.3 The Second Law: Force and Change in Motion
• 5.4 From Impulsive Forces to Continually Acting Forces: Book 1, Prop. 1; Is the Principia Written in the Manner of Greek Geometry?
• 5.5 The Third Law: Action and Reaction
• 5.6 Corollaries and Scholium: The Parallelogram Rule, Simple Machines, Elastic and Inelastic Impact
• 5.7 Does the Concept of Energy and Its Conservation Appear in the Principia?
• 5.8 Methods of Proof versus Method of Discovery; The “New Analysis” and Newton’s Allegations about How the Principia Was Produced; The Use of Fluxions in the Principia
• Chapter Six: The Structure of Book 1
• 6.1 The General Structure of the Principia
• 6.2 Sec. 1: First and Ultimate Ratios
• 6.3 Secs. 2-3: The Law of Areas, Circular Motion, Newton’s Dynamical Measure of Force; The Centripetal Force in Motion on an Ellipse, on a Hyperbola, and on a Parabola
• 6.4 The Inverse Problem: The Orbit Produced by an Inverse-Square Centripetal Force
• 6.5 Secs. 4-5: The Geometry of Conics
• 6.6 Problems of Elliptical Motion (Sec. 6); Kepler’s Problem
• 6.7 The Rectilinear Ascent and Descent of Bodies (Sec. 7)
• 6.8 Motion under the Action of Any Centripetal Forces (Sec. 8); Prop. 41
• 6.9 Specifying the Initial Velocity in Prop. 41; The Galileo-Plato Problem
• 6.10 Moving Orbits (Sec. 9) and Motions on Smooth Planes and Surfaces (Sec. 10)
• 6.11 The Mutual Attractions of Bodies (Sec. 11) and the Newtonian Style
• 6.12 Sec. 11: The Theory of Perturbations (Prop. 66 and Its Twenty-Two Corollaries)
• 6.13 Sec. 12 (Some Aspects of the Dynamics of Spherical Bodies); Sec. 13 (The Attraction of Nonspherical Bodies); Sec. 14 (The Motion of “Minimally Small” Bodies)
• Chapter Seven: The Structure of Book 2
• 7.1 Some Aspects of Book 2
• 7.2 Secs. 1, 2, and 3 of Book 2: Motion under Various Conditions of Resistance
• 7.3 Problems with Prop. 10
• 7.4 Problems with the Diagram for the Scholium to Prop. 10
• 7.5 Secs. 4 and 5: Definition of a Fluid; Newton on Boyle’s Law; The Definition of “Simple Pendulum”
• 7.6 Secs. 6 and 7: The Motion of Pendulums and the Resistance of Fluids to the Motions of Pendulums and Projectiles; A General Scholium (Experiments on Resistance to Motion)
• 7.7 The Solid of Least Resistance; The Design of Ships; The Efflux of Water
• 7.8 Sec. 8: Wave Motion and the Motion of Sound
• 7.9 The Physics of Vortices (Sec. 9, Props. 51—53); Vortices Shown to Be Inconsistent with Keplerian Planetary Motion
• 7.10 Another Way of Considering Book 2: Some Achievements of Book 2 (by George E. Smith)
• Chapter Eight: The Structure of Book 3
• 8.1 The Structure of Book 3
• 8.2 From Hypotheses to Rules and Phenomena
• 8.3 Newton’s “Rules for Natural Philosophy”
• 8.4 Newton’s “Phenomena”
• 8.5 Newton’s Hyp. 3
• 8.6 Props. 1-5: The Principles of Motion of Planets and of Their Satellites; The First Moon Test
• 8.7 Jupiter’s Perturbation of Saturn as Evidence for Universal Gravity
• 8.8 Planetary Perturbations: The Interaction of Jupiter and Saturn (by George E. Smith)
• 8.9 Props. 6 and 7: Mass and Weight
• 8.10 Prop. 8 and Its Corollaries (The Masses and Densities of the Sun, Jupiter, Saturn, and the Earth)
• 8.11 Props. 9-20: The Force of Gravity within Planets, the Duration of the Solar System, the Effects of the Inverse-Square Force of Gravity (Further Aspects of Gravity and the System of the World): Newton’s Hyp. 1
• 8.12 Prop. 24: Theory of the Tides; The First Enunciation of the Principle of Interference
• 8.13 Props. 36-38: The Tidal Force of the Sun and the Moon; The Mass and Density (and Dimensions) of the Moon
• 8.14 Props. 22, 25-35: The Motion of the Moon
• 8.15 Newton and the Problem of the Moon’s Motion (by George E. Smith)
• 8.16 The Motion of the Lunar Apsis (by George E. Smith)
• 8.17 Prop. 39: The Shape of the Earth and the Precession of the Equinoxes
• 8.18 Comets (The Concluding Portion of Book 3)
• Chapter Nine: The Concluding General Scholium
• 9.1 The General Scholium: “Hypotheses non fingo”
• 9.2 “Satis est”: Is It Enough?
• 9.3 Newton’s “Electric and Elastic” Spirit
• 9.4 A Gloss on Newton’s “Electric and Elastic” Spirit: An Electrical Conclusion to the Principia
• Chapter Ten: How to Read the Principia
• 10.1 Some Useful Commentaries and Reference Works; Newton’s Directions for Reading the Principia
• 10.2 Some Features of Our Translation; A Note on the Diagrams
• 10.3 Some Technical Terms and Special Translations (including Newton’s Use of “Rectangle” and “Solid”)
• 10.4 Some Trigonometric Terms (“Sine,” “Cosine,” “Tangent,” “Versed Sine” and “Sagitta,” “Subtense,” “Subtangent”); “Ratio” versus “Proportion”; “Q.E.D.,” “Q.E.F.,” “Q.E.I.,” and “Q.E.O.”
• 10.5 Newton’s Way of Expressing Ratios and Proportions
• 10.6 The Classic Ratios (as in Euclid’s Elements, Book 5)
• 10.7 Newton’s Proofs; Limits and Quadratures; More on Fluxions in the Principia
• 10.8 Example No. 1: Book 1, Prop. 6 (Newton’s Dynamical Measure of Force), with Notes on Prop. 1 (A Centrally Directed Force Acting on a Body with Uniform Linear Motion Will Produce Motion according to the Law of Areas)
• 10.9 Example No. 2: Book 1, Prop. 11 (The Direct Problem: Given an Ellipse, to Find the Force Directed toward a Focus)
• 10.10 Example No. 3: A Theorem on Ellipses from the Theory of Conics, Needed for Book 1, Props. 10 and 11
• 10.11 Example No. 4: Book 1, Prop. 32 (How Far a Body Will Fall under the Action of an Inverse-Square Force)
• 10.12 Example No. 5: Book 1, Prop. 41 (To Find the Orbit in Which a Body Moves When Acted On by a Given Centripetal Force and Then to Find the Orbital Position at Any Specified Time)
• 10.13 Example No. 6: Book 1, Lem. 29 (An Example of the Calculus or of Fluxions in Geometric Form)
• 10.14 Example No. 7: Book 3, Prop. 19 (The Shape of the Earth)
• 10.15 Example No. 8: A Theorem on the Variation of Weight with Latitude (from Book 3, Prop. 20)
• 10.16 Example No. 9: Book 1, Prop. 66, Corol. 14, Needed for Book 3, Prop. 37, Corol. 3
• 10.17 Newton’s Numbers: The “Fudge Factor”
• 10.18 Newton’s Measures
• 10.19 A Puzzle in Book 1, Prop. 66, Corol. 14 (by George E. Smith)
• Chapter Eleven: Conclusion
• Notes to the Guide
• The Principia
• Halley’s Ode to Newton
• Newton’s Preface to the First Edition
• Newton’s Preface to the Second Edition
• Cotes’s Preface to the Second Edition
• Newton’s Preface to the Third Edition
• Definitions
• Axioms, or The Laws of Motion
• Book 1: The Motion of Bodies
• Section 1
• Lemma 1
• Lemma 2
• Lemma 3
• Corollary 1
• Corollary 2
• Corollary 3
• Corollary 4
• Lemma 4
• Corollary
• Lemma 5
• Lemma 6
• Lemma 7
• Corollary 1
• Corollary 2
• Corollary 3
• Lemma 8
• Corollary
• Lemma 9
• Lemma 10
• Corollary 1
• Corollary 2
• Corollary 3
• Corollary 4
• Corollary 5
• Scholium
• Lemma 11
• Case 1
• Case 2
• Case 3
• Corollary 1
• Corollary 2
• Corollary 3
• Corollary 4
• Corollary 5
• Scholium
• Section 2
• Proposition 1, Theorem 1
• Corollary 1
• Corollary 2
• Corollary 3
• Corollary 4
• Corollary 5
• Corollary 6
• Proposition 2, Theorem 2
• Case 1
• Case 2
• Corollary 1
• Corollary 2
• Scholium
• Proposition 3 Theorem 3
• Corollary 1
• Corollary 2
• Corollary 3
• Corollary 4
• Scholium
• Proposition 4, Theorem 4
• Corollary 1
• Corollary 2
• Corollary 3
• Corollary 4
• Corollary 5
• Corollary 6
• Corollary 7
• Corollary 8
• Corollary 9
• Scholium
• Proposition 5, Problem 1
• Proposition 6, Theorem 5
• Corollary 1
• Corollary 2
• Corollary 3
• Corollary 4
• Corollary 5
• Proposition 7, Problem 2
• Corollary 1
• Corollary 2
• Corollary 3
• Proposition 8, Problem 3
• Scholium
• Proposition 9, Problem 4
• Lemma 12
• Proposition 10, Problem 5
• Corollary 1
• Corollary 2
• Scholium
• Section 3
• Proposition 11, Problem 6
• Proposition 12, Problem 7
• Lemma 13
• Lemma 14
• Corollary 1
• Corollary 2
• Corollary 3
• Proposition 13, Problem 8
• Corollary 1
• Corollary 2
• Proposition 14, Theorem 6
• Corollary
• Proposition 15, Theorem 7
• Corollary
• Proposition 16, Theorem 8
• Corollary 1
• Corollary 2
• Corollary 3
• Corollary 4
• Corollary 5
• Corollary 6
• Corollary 7
• Corollary 8
• Corollary 9
• Proposition 17, Problem 9
• Corollary 1
• Corollary 2
• Corollary 3
• Corollary 4
• Scholium
• Section 4
• Lemma 15
• Proposition 18, Problem 10
• Proposition 19, Problem 11
• Proposition 20, Problem 12
• Case 1
• Case 2
• Case 3
• Case 4
• Lemma 16
• Case 1
• Case 2
• Case 3
• Proposition 21, Problem 13
• Scholium
• Section 5
• Lemma 17
• Case 1
• Case 2
• Case 3
• Lemma 18
• Corollary
• Scholium
• Lemma 19
• Corollary 1
• Corollary 2
• Lemma 20
• Case 1
• Case 2
• Corollary 1
• Corollary 2
• Corollary 3
• Lemma 21
• Proposition 22, Problem 14
• Corollary 1
• Corollary 2
• Scholium
• Proposition 23, Problem 15
• Case 1
• Case 2
• Proposition 24, Problem 16
• Lemma 22
• Proposition 25, Problem 17
• Proposition 26, Problem 18
• Lemma 23
• Corollary
• Lemma 24
• Corollary 1
• Corollary 2
• Lemma 25
• Corollary 1
• Corollary 2
• Corollary 3
• Proposition 27, Problem 19
• Scholium
• Lemma 26
• Corollary
• Proposition 28, Problem 20
• Lemma 27
• Corollary
• Proposition 29, Problem 21
• Scholium
• Section 6
• Proposition 30, Problem 22
• Corollary 1
• Corollary 2
• Corollary 3
• Lemma 28
• Corollary
• Proposition 31, Problem 23
• Scholium
• Section 7
• Proposition 32, Problem 24
• Case 1
• Case 2
• Case 3
• Proposition 33, Theorem 9
• Corollary 1
• Corollary 2
• Proposition 34, Theorem 10
• Proposition 35, Theorem 11
• Case 1
• Case 2
• Proposition 36, Problem 25
• Proposition 37, Problem 26
• Proposition 38, Theorem 12
• Corollary 1
• Corollary 2
• Proposition 39, Problem 27
• Corollary 1
• Corollary 2
• Corollary 3
• Section 8
• Proposition 40, Theorem 13
• Corollary 1
• Corollary 2
• Proposition 41, Problem 28
• Corollary 1
• Corollary 2
• Corollary 3
• Proposition 42, Problem 29
• Section 9
• Proposition 43, Problem 30
• Proposition 44, Theorem 14
• Corollary 1
• Corollary 2
• Corollary 3
• Corollary 4
• Corollary 5
• Corollary 6
• Proposition 45, Problem 31
• Example 1
• Example 2
• Example 3
• Corollary 1
• Corollary 2
• Section 10
• Proposition 46, Problem 32
• Proposition 47, Theorem 15
• Scholium
• Proposition 48, Theorem 16
• Proposition 49, Theorem 17
• Corollary 1
• Corollary 2
• Proposition 50, Problem 33
• Corollary
• Proposition 51, Theorem 18
• Corollary
• Proposition 52, Problem 34
• Corollary 1
• Corollary 2
• Proposition 53, Problem 35
• Corollary 1
• Corollary 2
• Proposition 54, Problem 36
• Proposition 55, Theorem 19
• Corollary
• Proposition 56, Problem 37
• Section 11
• Proposition 57, Theorem 20
• Proposition 58, Theorem 21
• Case 1
• Case 2
• Corollary 1
• Corollary 2
• Corollary 3
• Proposition 59, Theorem 22
• Proposition 60, Theorem 23
• Proposition 61, Theorem 24
• Proposition 62, Problem 38
• Proposition 63, Problem 39
• Proposition 64, Problem 40
• Proposition 65, Theorem 25
• Case 1
• Case 2
• Corollary 1
• Corollary 2
• Corollary 3
• Proposition 66, Theorem 26
• Case 1
• Case 2
• Corollary 1
• Corollary 2
• Corollary 3
• Corollary 4
• Corollary 5
• Corollary 6
• Corollary 7
• Corollary 8
• Corollary 9
• Corollary 10
• Corollary 11
• Corollary 12
• Corollary 13
• Corollary 14
• Corollary 15
• Corollary 16
• Corollary 17
• Corollary 18
• Corollary 19
• Corollary 20
• Corollary 21
• Corollary 22
• Proposition 67, Theorem 27
• Proposition 68, Theorem 28
• Corollary
• Proposition 69, Theorem 29
• Corollary 1
• Corollary 2
• Corollary 3
• Scholium
• Section 12
• Proposition 70, Theorem 30
• Proposition 71, Theorem 31
• Proposition 72, Theorem 32
• Corollary 1
• Corollary 2
• Corollary 3
• Proposition 73, Theorem 33
• Scholium
• Proposition 74, Theorem 34
• Corollary 1
• Corollary 2
• Corollary 3
• Proposition 75, Theorem 35
• Corollary 1
• Corollary 2
• Corollary 3
• Corollary 4
• Proposition 76, Theorem 36
• Corollary 1
• Corollary 2
• Corollary 3
• Corollary 4
• Corollary 5
• Corollary 6
• Corollary 7
• Corollary 8
• Corollary 9
• Proposition 77, Theorem 37
• Case 1
• Case 2
• Case 3
• Case 4
• Case 5
• Case 6
• Proposition 78, Theorem 38
• Corollary
• Scholium
• Lemma 29
• Proposition 79, Theorem 39
• Proposition 80, Theorem 40
• Corollary 1
• Corollary 2
• Corollary 3
• Corollary 4
• Proposition 81, Problem 41
• Example 1
• Example 2
• Example 3
• Proposition 82, Theorem 41
• Proposition 83, Problem 42
• Proposition 84, Problem 43
• Scholium
• Section 13
• Proposition 85, Theorem 42
• Proposition 86, Theorem 43
• Proposition 87, Theorem 44
• Corollary 1
• Corollary 2
• Proposition 88, Theorem 45
• Corollary
• Proposition 89, Theorem 46
• Corollary
• Proposition 90, Problem 44
• Corollary 1
• Corollary 2
• Corollary 3
• Proposition 91, Problem 45
• Corollary 1
• Corollary 2
• Corollary 3
• Proposition 92, Problem 46
• Proposition 93, Theorem 47
• Case 1
• Case 2
• Corollary 1
• Corollary 2
• Corollary 3
• Scholium
• Section 14
• Proposition 94, Theorem 48
• Case 1
• Case 2
• Proposition 95, Theorem 49
• Proposition 96, Theorem 50
• Scholium
• Proposition 97, Problem 47
• Corollary 1
• Corollary 2
• Proposition 98, Problem 48
• Scholium
• Book 2: The Motion of Bodies
• Section 1
• Proposition 1, Theorem 1
• Corollary
• Lemma 1
• Proposition 2, Theorem 2
• Case 1
• Case 2
• Corollary
• Proposition 3, Problem 1
• Corollary 1
• Corollary 2
• Corollary 3
• Corollary 4
• Proposition 4, Problem 2
• Corollary 1
• Corollary 2
• Corollary 3
• Corollary 4
• Corollary 5
• Corollary 6
• Corollary 7
• Section 2
• Proposition 5, Theorem 3
• Corollary 1
• Corollary 2
• Corollary 3
• Corollary 4
• Corollary 5
• Proposition 6, Theorem 4
• Proposition 7, Theorem 5
• Corollary 1
• Corollary 2
• Corollary 3
• Corollary 4
• Corollary 5
• Lemma 2
• Case 1
• Case 2
• Case 3
• Case 4
• Case 5
• Case 6
• Corollary 1
• Corollary 2
• Corollary 3
• Scholium
• Proposition 8, Theorem 6
• Corollary 1
• Corollary 2
• Corollary 3
• Proposition 9, Theorem 7
• Case 1
• Case 2
• Corollary 1
• Corollary 2
• Corollary 3
• Corollary 4
• Corollary 5
• Corollary 6
• Corollary 7
• Proposition 10, Problem 3
• Corollary 1
• Corollary 2
• Example 1
• Example 2
• Example 3
• Example 4
• Scholium
• Rule 1
• Rule 2
• Rule 3
• Rule 4
• Rule 5
• Rule 6
• Rule 7
• Rule 8
• Section 3
• Proposition 11, Theorem 8
• Corollary 1
• Corollary 2
• Proposition 12, Theorem 9
• Corollary 1
• Corollary 2
• Corollary 3
• Proposition 13, Theorem 10
• Case 1
• Case 2
• Case 3
• Corollary
• Scholium
• Proposition 14, Theorem 11
• Case 1
• Case 2
• Case 3
• Corollary
• Scholium
• Section 4
• Lemma 3
• Proposition 15, Theorem 12
• Corollary 1
• Corollary 2
• Corollary 3
• Corollary 4
• Corollary 5
• Corollary 6
• Corollary 7
• Corollary 8
• Corollary 9
• Proposition 16, Theorem 13
• Corollary 1
• Corollary 2
• Corollary 3
• Scholium
• Proposition 17, Problem 4
• Proposition 18, Problem 5
• Section 5
• Definition of a Fluid
• Proposition 19, Theorem 14
• Case 1
• Case 2
• Case 3
• Case 4
• Case 5
• Case 6
• Case 7
• Corollary
• Proposition 20, Theorem 15
• Corollary 1
• Corollary 2
• Corollary 3
• Corollary 4
• Corollary 5
• Corollary 6
• Corollary 7
• Corollary 8
• Corollary 9
• Proposition 21, Theorem 16
• Corollary
• Proposition 22, Theorem 17
• Corollary
• Scholium
• Proposition 23, Theorem 18
• Scholium
• Section 6
• Proposition 24, Theorem 19
• Corollary 1
• Corollary 2
• Corollary 3
• Corollary 4
• Corollary 5
• Corollary 6
• Corollary 7
• Proposition 25, Theorem 20
• Corollary
• Proposition 26, Theorem 21
• Proposition 27, Theorem 22
• Corollary 1
• Corollary 2
• Proposition 28, Theorem 23
• Proposition 29, Problem 6
• Corollary 1
• Corollary 2
• Corollary 3
• Proposition 30, Theorem 24
• Corollary
• Proposition 31, Theorem 25
• Corollary 1
• Corollary 2
• Corollary 3
• Corollary 4
• Corollary 5
• General Scholium
• Section 7
• Proposition 32, Theorem 26
• Corollary 1
• Corollary 2
• Proposition 33, Theorem 27
• Corollary 1
• Corollary 2
• Corollary 3
• Corollary 4
• Corollary 5
• Corollary 6
• Proposition 34, Theorem 28
• Scholium
• Proposition 35, Problem 7
• Case 1
• Case 2
• Case 3
• Corollary 1
• Corollary 2
• Corollary 3
• Corollary 4
• Corollary 5
• Corollary 6
• Corollary 7
• Scholium
• Proposition 36, Problem 8
• Case 1
• Case 2
• Case 3
• Case 4
• Case 5
• Case 6
• Corollary 1
• Corollary 2
• Corollary 3
• Corollary 4
• Corollary 5
• Corollary 6
• Corollary 7
• Corollary 8
• Corollary 9
• Corollary 10
• Lemma 4
• Proposition 37, Theorem 29
• Corollary 1
• Corollary 2
• Corollary 3
• Scholium
• Lemma 5
• Lemma 6
• Lemma 7
• Scholium
• Proposition 38, Theorem 30
• Corollary 1
• Corollary 2
• Corollary 3
• Corollary 4
• Proposition 39, Theorem 31
• Scholium
• Proposition 40, Problem 9
• Scholium
• Experiment 1
• Experiment 2
• Experiment 3
• Experiment 4
• Experiment 5
• Experiment 6
• Experiment 7
• Experiment 8
• Experiment 9
• Experiment 10
• Experiment 11
• Experiment 12
• Experiment 13
• Experiment 14
• Section 8
• Proposition 41, Theorem 32
• Corollary
• Proposition 42, Theorem 33
• Case 1
• Case 2
• Case 3
• Proposition 43, Theorem 34
• Case 1
• Case 2
• Corollary
• Proposition 44, Theorem 35
• Corollary 1
• Corollary 2
• Corollary 3
• Proposition 45, Theorem 36
• Proposition 46, Problem 10
• Corollary 1
• Corollary 2
• Proposition 47, Theorem 37
• Corollary
• Proposition 48, Theorem 38
• Case 1
• Case 2
• Case 3
• Proposition 49, Problem 11
• Corollary 1
• Corollary 2
• Proposition 50, Problem 12
• Scholium
• Section 9
• Hypothesis
• Proposition 51, Theorem 39
• Corollary 1
• Corollary 2
• Corollary 3
• Corollary 4
• Corollary 5
• Corollary 6
• Proposition 52, Theorem 40
• Case 1
• Case 2
• Case 3
• Corollary 1
• Corollary 2
• Corollary 3
• Corollary 4
• Corollary 5
• Corollary 6
• Corollary 7
• Corollary 8
• Corollary 9
• Corollary 10
• Corollary 11
• Scholium
• Proposition 53, Theorem 41
• Corollary 1
• Corollary 2
• Scholium
• Book 3: The System of the World
• Rules for the Study of Natural Philosophy
• Rule 1
• Rule 2
• Rule 3
• Rule 4
• Phenomena
• Phenomenon 1
• Phenomenon 2
• Phenomenon 3
• Phenomenon 4
• Phenomenon 5
• Phenomenon 6
• Propositions
• Proposition 1, Theorem 1
• Proposition 2, Theorem 2
• Proposition 3, Theorem 3
• Corollary
• Proposition 4, Theorem 4
• Scholium
• Proposition 5, Theorem 5
• Corollary 1
• Corollary 2
• Corollary 3
• Scholium
• Proposition 6, Theorem 6
• Corollary 1
• Corollary 2
• Corollary 3
• Corollary 4
• Corollary 5
• Proposition 7, Theorem 7
• Corollary 1
• Corollary 2
• Proposition 8, Theorem 8
• Corollary 1
• Corollary 2
• Corollary 3
• Corollary 4
• Proposition 9, Theorem 9
• Proposition 10, Theorem 10
• Hypothesis 1
• Proposition 11, Theorem 11
• Proposition 12, Theorem 12
• Corollary
• Proposition 13, Theorem 13
• Proposition 14, Theorem 14
• Corollary 1
• Corollary 2
• Scholium
• Proposition 15, Problem 1
• Proposition 16, Problem 2
• Proposition 17, Theorem 15
• Proposition 18, Theorem 16
• Proposition 19, Problem 3
• Proposition 20, Problem 4
• Proposition 21, Theorem 17
• Proposition 22, Theorem 18
• Proposition 23, Problem 5
• Proposition 24, Theorem 19
• Proposition 25, Problem 6
• Proposition 26, Problem 7
• Proposition 27, Problem 8
• Corollary 1
• Corollary 2
• Proposition 28, Problem 9
• Proposition 29, Problem 10
• Proposition 30, Problem 11
• Corollary 1
• Corollary 2
• Proposition 31, Problem 12
• Corollary
• Proposition 32, Problem 13
• Proposition 33, Problem 14
• Corollary
• Scholium
• Proposition 34, Problem 15
• Corollary 1
• Corollary 2
• Corollary 3
• Corollary 4
• Proposition 35, Problem 16
• Scholium
• Proposition 36, Problem 17
• Corollary
• Proposition 37, Problem 18
• Corollary 1
• Corollary 2
• Corollary 3
• Corollary 4
• Corollary 5
• Corollary 6
• Corollary 7
• Corollary 8
• Corollary 9
• Corollary 10
• Proposition 38, Problem 19
• Corollary
• Lemma 1
• Lemma 2
• Lemma 3
• Hypothesis 2
• Proposition 39, Problem 20
• Lemma 4
• Corollary 1
• Corollary 2
• Corollary 3
• Proposition 40, Theorem 20
• Corollary 1
• Corollary 2
• Corollary 3
• Corollary 4
• Lemma 5
• Case 1
• Case 2
• Corollary
• Lemma 6
• Lemma 7
• Lemma 8
• Corollary
• Scholium
• Lemma 9
• Lemma 10
• Corollary
• Lemma 11
• Proposition 41, Problem 21
• Example
• Proposition 42, Problem 22
• Operation 1
• Operation 2
• Operation 3
• General Scholium
• Notes to the Principia
• Notes Added in Second Printing
• Index