Library

Elements

Euclid

John Casey (1885)

Euclid's Elements, composed in Alexandria around 300 BC, is the most influential mathematical work ever written and the West's enduring model of rigorous deductive proof. Book I proceeds from twenty-three definitions, a handful of postulates, and the common notions through the properties of triangles, parallels, and parallelograms to its climax in the Pythagorean theorem (Proposition 47). For two millennia the Elements was, after the Bible, among the most-printed books in the Western world and the foundation of every geometry curriculum. This edition preserves the classic lettered figures on which each demonstration depends.

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Contents

1. Book I
   1. Definitions
   2. Postulates
   3. Axioms
   4. Proposition 1
   5. Proposition 2
   6. Proposition 3
   7. Proposition 4
   8. Proposition 5
   9. Proposition 6
   10. Proposition 7
   11. Proposition 8
   12. Proposition 9
   13. Proposition 10
   14. Proposition 11
   15. Proposition 12
   16. Proposition 13
   17. Proposition 14
   18. Proposition 15
   19. Proposition 16
   20. Proposition 17
   21. Proposition 18
   22. Proposition 19
   23. Proposition 20
   24. Proposition 21
   25. Proposition 22
   26. Proposition 23
   27. Proposition 24
   28. Proposition 25
   29. Proposition 26
   30. Proposition 27
   31. Proposition 28
   32. Proposition 29
   33. Proposition 30
   34. Proposition 31
   35. Proposition 32
   36. Proposition 33
   37. Proposition 34
   38. Proposition 35
   39. Proposition 36
   40. Proposition 37
   41. Proposition 38
   42. Proposition 39
   43. Proposition 40
   44. Proposition 41
   45. Proposition 42
   46. Proposition 43
   47. Proposition 44
   48. Proposition 45
   49. Proposition 46
   50. Proposition 47
   51. Proposition 48
2. Book II
   1. Definitions
   2. Proposition 1
   3. Proposition 2
   4. Proposition 3
   5. Proposition 4
   6. Proposition 5
   7. Proposition 6
   8. Proposition 7
   9. Proposition 8
   10. Proposition 9
   11. Proposition 10
   12. Proposition 11
   13. Proposition 12
   14. Proposition 13
   15. Proposition 14
3. Book III
   1. Definitions
   2. Proposition 1
   3. Proposition 2
   4. Proposition 3
   5. Proposition 4
   6. Proposition 5
   7. Proposition 6
   8. Proposition 7
   9. Proposition 8
   10. Proposition 9
   11. Proposition 10
   12. Proposition 11
   13. Proposition 12
   14. Proposition 13
   15. Proposition 14
   16. Proposition 15
   17. Proposition 16
   18. Proposition 17
   19. Proposition 18
   20. Proposition 19
   21. Proposition 20
   22. Proposition 21
   23. Proposition 22
   24. Proposition 23
   25. Proposition 24
   26. Proposition 25
   27. Proposition 26
   28. Proposition 27
   29. Proposition 28
   30. Proposition 29
   31. Proposition 30
   32. Proposition 31
   33. Proposition 32
   34. Proposition 33
   35. Proposition 34
   36. Proposition 35
   37. Proposition 36
   38. Proposition 37
4. Book IV
   1. Definitions
   2. Proposition 1
   3. Proposition 2
   4. Proposition 3
   5. Proposition 4
   6. Proposition 5
   7. Proposition 6
   8. Proposition 7
   9. Proposition 8
   10. Proposition 9
   11. Proposition 10
   12. Proposition 11
   13. Proposition 12
   14. Proposition 13
   15. Proposition 14
   16. Proposition 15
   17. Proposition 16