Source edition
Euclid. Euclidis Opera omnia, Vols. 1-5. Heiberg, Johan Ludvig, editor. Leipzig: Teubner, 1883-88.
Source data
Perseus Digital Library · CC BY-SA 4.0
Cloned and adapted by Humanitext, with ongoing edits.
Summary
This work is a mathematical treatise that systematically and logically organizes the fundamental principles of geometry, both in planes and in three-dimensional space, as well as the theory of numbers. Throughout the text, the discussion proceeds in a rigorous demonstrative format, starting from a minimal set of definitions, postulates, and common notions. The early books deal with the properties of plane figures, the Pythagorean theorem, and the construction of inscribed and circumscribed polygons, followed by an exploration of similarity based on a general theory of proportion. In the middle section, the focus shifts to number theory—covering divisibility, prime numbers, geometric progressions, and perfect numbers—and leads into an intricate classification of incommensurable irrational magnitudes. The later books transition to solid geometry, establishing the properties of planes, three-dimensional solids, and the volume ratios of cones and spheres using the method of exhaustion. Finally, the work culminates in the geometric construction of the five regular Platonic solids inscribed in a sphere using the properties of the golden ratio, proving that no other regular polyhedra can exist.
Contents
316 chunks
Cited by book.type.number
- §1.def.1-1.def.23
- §1.post.1-1.post.5
- §1.comm_not.1-1.comm_not.9
- §1.prop.1-1.prop.3
- §1.prop.4
- §1.prop.5-1.prop.6
- §1.prop.7-1.prop.8
- §1.prop.9-1.prop.11
- §1.prop.12-1.prop.13
- §1.prop.14-1.prop.15
- §1.prop.16-1.prop.18
- §1.prop.19-1.prop.21
- §1.prop.22-1.prop.23
- §1.prop.24-1.prop.25
- §1.prop.26
- §1.prop.27-1.prop.28
- §1.prop.29-1.prop.31
- §1.prop.32-1.prop.33
- §1.prop.34-1.prop.35
- §1.prop.36-1.prop.38
- §1.prop.39-1.prop.41
- §1.prop.42-1.prop.44
- §1.prop.45-1.prop.46
- §1.prop.47-1.prop.48
- §2.def.1-2.def.2
- §2.prop.1-2.prop.3
- §2.prop.4
- §2.prop.5
- §2.prop.6
- §2.prop.8
- §2.prop.9
- §2.prop.10
- §2.prop.11-2.prop.12
- §2.prop.13-2.prop.14
- §3.def.1-3.def.11
- §3.prop.1-3.prop.2
- §3.prop.3-3.prop.5
- §3.prop.6-3.prop.7
- §3.prop.8#1
- §3.prop.8#2
- §3.prop.9-3.prop.10
- §3.prop.11-3.prop.13
- §3.prop.14
- §3.prop.15
- §3.prop.16
- §3.prop.17-3.prop.19
- §3.prop.20-3.prop.22
- §3.prop.23-3.prop.25
- §3.prop.26-3.prop.27
- §3.prop.28-3.prop.30
- §3.prop.31
- §3.prop.32
- §3.prop.33
- §3.prop.34-3.prop.35
- §3.prop.36
- §3.prop.37
- §4.def.1-4.def.7
- §4.prop.1-4.prop.2
- §4.prop.3-4.prop.4
- §4.prop.5
- §4.prop.6-4.prop.7
- §4.prop.8-4.prop.9
- §4.prop.10
- §4.prop.11
- §4.prop.12
- §4.prop.13-4.prop.14
- §4.prop.15-4.prop.16
- §5.def.1-5.def.18
- §5.prop.1-5.prop.2
- §5.prop.3
- §5.prop.4-5.prop.5
- §5.prop.6-5.prop.7
- §5.prop.8
- §5.prop.9-5.prop.10
- §5.prop.11-5.prop.12
- §5.prop.13-5.prop.14
- §5.prop.15-5.prop.16
- §5.prop.17-5.prop.18
- §5.prop.19-5.prop.20
- §5.prop.21-5.prop.22
- §5.prop.23
- §5.prop.24-5.prop.25
- §6.def.1-6.def.5
- §6.prop.1
- §6.prop.2
- §6.prop.3
- §6.prop.4
- §6.prop.5
- §6.prop.6
- §6.prop.7
- §6.prop.8
- §6.prop.9-6.prop.11
- §6.prop.12-6.prop.14
- §6.prop.15
- §6.prop.16
- §6.prop.17-6.prop.18
- §6.prop.19
- §6.prop.20#1
- §6.prop.20#2
- §6.prop.21
- §6.prop.22
- §6.prop.23
- §6.prop.24
- §6.prop.25
- §6.prop.26-6.prop.27
- §6.prop.28
- §6.prop.29-6.prop.30
- §6.prop.31-6.prop.32
- §6.prop.33
- §7.def.1-7.def.22
- §7.prop.1-7.prop.2
- §7.prop.3
- §7.prop.4-7.prop.5
- §7.prop.6-7.prop.7
- §7.prop.8-7.prop.9
- §7.prop.10-7.prop.12
- §7.prop.13-7.prop.15
- §7.prop.16-7.prop.18
- §7.prop.19-7.prop.20
- §7.prop.21-7.prop.23
- §7.prop.24-7.prop.26
- §7.prop.27-7.prop.28
- §7.prop.29-7.prop.31
- §7.prop.32-7.prop.33
- §7.prop.34
- §7.prop.35-7.prop.36
- §7.prop.37-7.prop.39
- §8.prop.1
- §8.prop.2
- §8.prop.3
- §8.prop.4#1
- §8.prop.4#2
- §8.prop.5-8.prop.6
- §8.prop.7-8.prop.8
- §8.prop.9
- §8.prop.10
- §8.prop.11-8.prop.12
- §8.prop.13-8.prop.14
- §8.prop.15-8.prop.17
- §8.prop.18
- §8.prop.19#1
- §8.prop.19#2
- §8.prop.20
- §8.prop.21-8.prop.22
- §8.prop.23-8.prop.27
- §9.prop.1-9.prop.3
- §9.prop.4-9.prop.7
- §9.prop.8-9.prop.9
- §9.prop.10-9.prop.11
- §9.prop.12
- §9.prop.13
- §9.prop.14-9.prop.15
- §9.prop.16-9.prop.18
- §9.prop.19
- §9.prop.20-9.prop.26
- §9.prop.27-9.prop.32
- §9.prop.33-9.prop.35
- §9.prop.36#1
- §9.prop.36#2
- §10.def1.1-10.def1.4
- §10.prop1.1-10.prop1.2
- §10.prop1.3
- §10.prop1.4
- §10.prop1.5
- §10.prop1.7-10.prop1.8
- §10.prop1.9#1
- §10.prop1.9#2
- §10.prop1.10-10.prop1.11
- §10.prop1.12-10.prop1.13
- §10.prop1.14
- §10.prop1.15-10.prop1.16
- §10.prop1.17
- §10.prop1.18
- §10.prop1.19-10.prop1.21
- §10.prop1.22-10.prop1.23
- §10.prop1.24-10.prop1.25
- §10.prop1.26-10.prop1.27
- §10.prop1.28#1
- §10.prop1.28#2
- §10.prop1.29
- §10.prop1.30-10.prop1.31
- §10.prop1.32
- §10.prop1.33-10.prop1.34
- §10.prop1.35-10.prop1.37
- §10.prop1.38-10.prop1.39
- §10.prop1.40-10.prop1.41
- §10.prop1.42-10.prop1.43
- §10.prop1.44
- §10.prop1.45-10.prop1.47
- §10.def2.1-10.def2.6
- §10.prop2.48-10.prop2.49
- §10.prop2.50
- §10.prop2.51-10.prop2.52
- §10.prop2.53#1
- §10.prop2.53#2
- §10.prop2.54
- §10.prop2.55
- §10.prop2.56-10.prop2.57
- §10.prop2.58-10.prop2.59
- §10.prop2.60
- §10.prop2.61-10.prop2.62
- §10.prop2.63-10.prop2.64
- §10.prop2.65-10.prop2.66
- §10.prop2.67-10.prop2.68
- §10.prop2.69-10.prop2.70
- §10.prop2.71
- §10.prop2.72
- §10.prop2.73-10.prop2.74
- §10.prop2.75-10.prop2.76
- §10.prop2.77-10.prop2.78
- §10.prop2.79-10.prop2.80
- §10.prop2.81
- §10.prop2.82-10.prop2.83
- §10.prop2.84
- §10.def3.1-10.def3.6
- §10.prop3.85-10.prop3.86
- §10.prop3.87
- §10.prop3.88-10.prop3.89
- §10.prop3.90
- §10.prop3.91
- §10.prop3.92
- §10.prop3.93
- §10.prop3.94
- §10.prop3.95
- §10.prop3.96
- §10.prop3.97
- §10.prop3.98
- §10.prop3.99
- §10.prop3.100
- §10.prop3.101
- §10.prop3.102
- §10.prop3.103-10.prop3.104
- §10.prop3.105-10.prop3.106
- §10.prop3.107-10.prop3.108
- §10.prop3.109-10.prop3.110
- §10.prop3.111
- §10.prop3.112
- §10.prop3.113
- §10.prop3.114-10.prop3.115
- §11.def.1-11.def.28
- §11.prop.1-11.prop.3
- §11.prop.4
- §11.prop.5-11.prop.6
- §11.prop.7-11.prop.8
- §11.prop.9-11.prop.10
- §11.prop.11-11.prop.13
- §11.prop.14-11.prop.15
- §11.prop.16-11.prop.17
- §11.prop.18-11.prop.19
- §11.prop.20-11.prop.21
- §11.prop.22
- §11.prop.23#1
- §11.prop.23#2
- §11.prop.24-11.prop.25
- §11.prop.26
- §11.prop.27-11.prop.28
- §11.prop.29-11.prop.30
- §11.prop.31#1
- §11.prop.31#2
- §11.prop.32
- §11.prop.33
- §11.prop.34#1
- §11.prop.34#2
- §11.prop.35#1
- §11.prop.35#2
- §11.prop.36-11.prop.37
- §11.prop.38-11.prop.39
- §12.prop.1
- §12.prop.2#1
- §12.prop.2#2
- §12.prop.3#1
- §12.prop.3#2
- §12.prop.4#1
- §12.prop.4#2
- §12.prop.5
- §12.prop.6#1
- §12.prop.6#2
- §12.prop.8
- §12.prop.9
- §12.prop.10#1
- §12.prop.10#2
- §12.prop.11#1
- §12.prop.11#2
- §12.prop.12#1
- §12.prop.12#2
- §12.prop.12#3
- §12.prop.13-12.prop.14
- §12.prop.15
- §12.prop.16
- §12.prop.17#1
- §12.prop.17#2
- §12.prop.17#3
- §12.prop.18
- §13.prop.1
- §13.prop.2
- §13.prop.3-13.prop.4
- §13.prop.5
- §13.prop.6
- §13.prop.7
- §13.prop.8
- §13.prop.9
- §13.prop.10
- §13.prop.11#1
- §13.prop.11#2
- §13.prop.12
- §13.prop.13#1
- §13.prop.13#2
- §13.prop.14
- §13.prop.15
- §13.prop.16#1
- §13.prop.16#2
- §13.prop.17#1
- §13.prop.17#2
- §13.prop.18#1
- §13.prop.18#2
- §13.prop.18#3