Contents of 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 to the Principia