Theorems
The primes are infinite. This is a theorem because Euclid proves it (Book 9, Proposition 20). A proof usually requires some earlier definitions, postulates or axioms, such as the definition of an integer or a prime. In science, facts proven true are usually called scientific laws, such as Newton’s Laws of Motion.
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Euclid Book 1 Proposition 4
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Euclid Book 1 Proposition 5
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Euclid Book 1 Proposition 6
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Euclid Book 1 Proposition 7
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Euclid Book 1 Proposition 8
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Euclid Book 1 Proposition 13
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Euclid Book 1 Proposition 14
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Euclid Book 1 Proposition 15
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Euclid Book 1 Proposition 16
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Euclid Book 1 Proposition 17
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Euclid Book 1 Proposition 18
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Euclid Book 1 Proposition 19
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Euclid Book 1 Proposition 20
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Euclid Book 1 Proposition 21
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Euclid Book 1 Proposition 24
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Euclid Book 1 Proposition 25
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Euclid Book 1 Proposition 26a
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Euclid Book 1 Proposition 26b
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Euclid Book 1 Proposition 27
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Euclid Book 1 Proposition 28a
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Euclid Book 1 Proposition 28b
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Euclid Book 1 Proposition 29
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Euclid Book 1 Proposition 30
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Euclid Book 1 Proposition 32
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Euclid Book 1 Proposition 33
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Euclid Book 1 Proposition 34
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Euclid Book 1 Proposition 35
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Euclid Book 1 Proposition 36
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Euclid Book 1 Proposition 37
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Euclid Book 1 Proposition 38
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Euclid Book 1 Proposition 39
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Euclid Book 1 Proposition 40
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Euclid Book 1 Proposition 41
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Euclid Book 1 Proposition 43
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Euclid Book 1 Proposition 47
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Euclid Book 1 Proposition 48
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Euclid Book 2 Proposition 1
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Euclid Book 2 Proposition 2
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Euclid Book 2 Proposition 3
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Euclid Book 2 Proposition 4
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Euclid Book 2 Proposition 5
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Euclid Book 2 Proposition 6
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Euclid Book 2 Proposition 7
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Euclid Book 2 Proposition 8
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Euclid Book 2 Proposition 9
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Euclid Book 2 Proposition 10
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Euclid Book 2 Proposition 12
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Euclid Book 2 Proposition 13
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Euclid Book 3 Proposition 2
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Euclid Book 3 Proposition 3a
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Euclid Book 3 Proposition 3b
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Euclid Book 3 Proposition 4
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Euclid Book 3 Proposition 5
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Euclid Book 3 Proposition 6
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Euclid Book 3 Proposition 7a
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Euclid Book 3 Proposition 7b
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Euclid Book 3 Proposition 7c
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Euclid Book 3 Proposition 8a
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Euclid Book 3 Proposition 8b
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Euclid Book 3 Proposition 8c
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Euclid Book 3 Proposition 9
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Euclid Book 3 Proposition 10
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Euclid Book 3 Proposition 11
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Euclid Book 3 Proposition 12
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Euclid Book 3 Proposition 13
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Euclid Book 3 Proposition 14a
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Euclid Book 3 Proposition 14b
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Euclid Book 3 Proposition 15a
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Euclid Book 3 Proposition 15b
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Euclid Book 3 Proposition 16
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Euclid Book 3 Proposition 18
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Euclid Book 3 Proposition 19
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Euclid Book 3 Proposition 20
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Euclid Book 3 Proposition 21
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Euclid Book 3 Proposition 22
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Euclid Book 3 Proposition 31a
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Euclid Book 3 Proposition 31b
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Euclid Book 3 Proposition 31c
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Euclid Book 3 Proposition 32
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Euclid Book 3 Proposition 35
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Euclid Book 3 Proposition 36
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Euclid Book 3 Proposition 37
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Euclid Book 5 Proposition 1
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Euclid Book 5 Proposition 2
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Euclid Book 5 Proposition 3
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Euclid Book 5 Proposition 4
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Euclid Book 5 Proposition 5
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Euclid Book 5 Proposition 6
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Euclid Book 5 Proposition 7
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Euclid Book 5 Proposition 8
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Euclid Book 5 Proposition 9a
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Euclid Book 5 Proposition 9b
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Euclid Book 5 Proposition 10a
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Euclid Book 5 Proposition 10b
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Euclid Book 5 Proposition 11
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Euclid Book 5 Proposition 12
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Euclid Book 5 Proposition 13
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Euclid Book 5 Proposition 14
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Euclid Book 5 Proposition 15
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Euclid Book 5 Proposition 16
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Euclid Book 5 Proposition 17
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Euclid Book 5 Proposition 18
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Euclid Book 5 Proposition 19
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Euclid Book 5 Proposition 20
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Euclid Book 5 Proposition 21
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Euclid Book 5 Proposition 22
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Euclid Book 5 Proposition 23
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Euclid Book 5 Proposition 24
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Euclid Book 5 Proposition 25
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Euclid Book 6 Proposition 1a
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Euclid Book 6 Proposition 1b
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Euclid Book 6 Proposition 2a
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Euclid Book 6 Proposition 2b
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Euclid Book 6 Proposition 3a
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Euclid Book 6 Proposition 3b
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Euclid Book 6 Proposition 4
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Euclid Book 6 Proposition 5
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Euclid Book 6 Proposition 6
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Euclid Book 6 Proposition 7a
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Euclid Book 6 Proposition 7b
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Euclid Book 6 Proposition 8
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Euclid Book 6 Proposition 14a
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Euclid Book 6 Proposition 14b
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Euclid Book 6 Proposition 15a
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Euclid Book 6 Proposition 15b
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Euclid Book 6 Proposition 16a
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Euclid Book 6 Proposition 16b
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Euclid Book 6 Proposition 17a
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Euclid Book 6 Proposition 17b
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Euclid Book 6 Proposition 19
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Euclid Book 6 Proposition 20
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Euclid Book 6 Proposition 21
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Euclid Book 6 Proposition 22a
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Euclid Book 6 Proposition 22b
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Euclid Book 6 Proposition 23
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Euclid Book 6 Proposition 24
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Euclid Book 6 Proposition 26
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Euclid Book 6 Proposition 31
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Euclid Book 6 Proposition 32
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Euclid Book 13 Proposition 1
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Euclid Book 13 Proposition 2
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Euclid Book 13 Proposition 3
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Euclid Book 13 Proposition 4
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Euclid Book 13 Proposition 5
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Euclid Book 13 Proposition 7a
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Euclid Book 13 Proposition 7b
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Euclid Book 13 Proposition 8
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Euclid Book 13 Proposition 9
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Euclid Book 13 Proposition 10
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Euclid Book 13 Proposition 12