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◀ ▲ ▶Branches / Geometry / Elements-euclid / Book--1-plane-geometry / Subsection: Propositions from Book 1

Subsection: Propositions from Book 1

This subsection is dedicated to the propositions of Book 1 of "Euclid's Elements".

Table of Contents

  1. Proposition: 1.01: Constructing an Equilateral Triangle
  2. Proposition: 1.02: Constructing a Segment Equal to an Arbitrary Segment
  3. Proposition: 1.03: Cutting a Segment at a Given Size
  4. Proposition: 1.04: "Side-Angle-Side" Theorem for the Congruence of Triangle
  5. Proposition: 1.05: Isosceles Triangles I
  6. Proposition: 1.06: Isosceles Triagles II
  7. Proposition: 1.07: Uniqueness of Triangles
  8. Proposition: 1.08: "Side-Side-Side" Theorem for the Congruence of Triangles
  9. Proposition: 1.09: Bisecting an Angle
  10. Proposition: 1.10: Bisecting a Segment
  11. Proposition: 1.11: Constructing a Perpendicular Segment to a Straight Line From a Given Point On the Straight Line
  12. Proposition: 1.12: Constructing a Perpendicular Segment to a Straight Line From a Given Point Not On the Straight Line
  13. Proposition: 1.13: Angles at Intersections of Straight Lines
  14. Proposition: 1.14: Combining Rays to Straight Lines
  15. Proposition: 1.15: Opposite Angles on Intersecting Straight Lines
  16. Proposition: 1.16: The Exterior Angle Is Greater Than Either of the Non-Adjacent Interior Angles
  17. Proposition: 1.17: The Sum of Two Angles of a Triangle
  18. Proposition: 1.18: Angles and Sides in a Triangle I
  19. Proposition: 1.19: Angles and Sides in a Triangle II
  20. Proposition: 1.20: The Sum of the Lengths of Any Pair of Sides of a Triangle (Triangle Inequality)
  21. Proposition: 1.21: Triangles within Triangles
  22. Proposition: 1.22: Construction of Triangles From Arbitrary Segments
  23. Proposition: 1.23: Constructing an Angle Equal to an Arbitrary Rectilinear Angle
  24. Proposition: 1.24: Angles and Sides in a Triangle III
  25. Proposition: 1.25: Angles and Sides in a Triangle IV
  26. Proposition: 1.26: "Angle-Side-Angle" and "Angle-Angle-Side" Theorems for the Congruence of Triangles
  27. Proposition: 1.27: Parallel Lines I
  28. Proposition: 1.28: Parallel Lines II
  29. Proposition: 1.29: Parallel Lines III
  30. Proposition: 1.30: Transitivity of Parallel Lines
  31. Proposition: 1.31: Constructing a Parallel Line from a Line and a Point
  32. Proposition: 1.32: Sum Of Angles in a Triangle and Exterior Angle
  33. Proposition: 1.33: Parallel Equal Segments Determine a Parallelogram
  34. Proposition: 1.34: Opposite Sides and Opposite Angles of Parallelograms
  35. Proposition: 1.35: Parallelograms On the Same Base and On the Same Parallels
  36. Proposition: 1.36: Parallelograms on Equal Bases and on the Same Parallels
  37. Proposition: 1.37: Triangles of Equal Area I
  38. Proposition: 1.38: Triangles of Equal Area II
  39. Proposition: 1.39: Triangles of Equal Area III
  40. Proposition: 1.40: Triangles of Equal Area IV
  41. Proposition: 1.41: Parallelograms and Triagles
  42. Proposition: 1.42: Construction of Parallelograms I
  43. Proposition: 1.43: Complementary Segments of Parallelograms
  44. Proposition: 1.44: Construction of Parallelograms II
  45. Proposition: 1.45: Construction of Parallelograms III
  46. Proposition: 1.46: Construction of a Square on a Given Segment
  47. Proposition: 1.47: Pythagorean Theorem
  48. Proposition: 1.48: The Converse of the Pythagorean Theorem

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