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Index
Cover Half Title Subvention Frontispiece Title Copyright Dedication Contents Contents of the Principia Publisher's Note Preface to the 1999 Edition A Brief History of the Principia
The Origins of the Principia Steps Leading to the Composition and Publication of the Principia Revisions and Later Editions
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
Scholium
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 Notes Added in Second Printing
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