ProofWiki:Books/Euclid/The Elements/Book I
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Euclid: The Elements: Book I
Published c. 300 B.C.E.
Contents
- Book I: Straight Line Geometry
- Definitions
- Postulates and Common Notions
- Proposition 1: Construction of Equilateral Triangle
- Proposition 2: Construction of an Equal Straight Line
- Proposition 3: Construction of Equal Straight Lines from Unequal
- Proposition 4: Triangle Side-Angle-Side Equality
- Proposition 5: Isosceles Triangles have Two Equal Angles
- Proposition 6: Triangle with Two Equal Angles is Isosceles
- Proposition 7: Two Lines Meet at Unique Point
- Proposition 8: Triangle Side-Side-Side Equality
- Proposition 9: Bisection of an Angle
- Proposition 10: Bisection of a Straight Line
- Proposition 11: Construction of a Perpendicular
- Proposition 12: Perpendicular through a Given Point
- Proposition 13: Two Angles on a Straight Line make Two Right Angles
- Proposition 14: Two Angles making Two Right Angles make a Straight Line
- Proposition 15: Two Straight Lines make Equal Opposite Angles (Vertical Angle Theorem)
- Proposition 16: External Angle of Triangle Greater than Internal Opposite
- Proposition 17: Two Angles of Triangle Less than Two Right Angles
- Proposition 18: Greater Side of Triangle Subtends Greater Angle
- Proposition 19: Greater Angle of Triangle Subtended by Greater Side
- Proposition 20: Sum of Two Sides of Triangle Greater than Third Side
- Proposition 21: Lines Through Endpoints of One Side of Triangle to Point Inside Triangle is Less than Sum of Other Sides
- Proposition 22: Construction of Triangle from Given Lengths
- Proposition 23: Construction of an Equal Angle
- Proposition 24: Hinge Theorem
- Proposition 25: Converse Hinge Theorem
- Proposition 26: Triangle Angle-Side-Angle and Side-Angle-Angle Equality
- Proposition 27: Equal Alternate Interior Angles Implies Parallel
- Proposition 28: Equal Corresponding Angles or Supplementary Interior Angles Implies Parallel
- Proposition 29: Parallel Implies Equal Alternate Interior Angles, Corresponding Angles, and Supplementary Interior Angles
- Proposition 30: Parallelism is Transitive
- Proposition 31: Construction of a Parallel
- Proposition 32: Sum of Angles of Triangle Equals Two Right Angles
- Proposition 33: Lines Joining Equal and Parallel Straight Lines
- Proposition 34: Opposite Sides and Angles of Parallelogram are Equal
- Proposition 35: Parallelograms with Same Base and Same Height have Equal Area
- Proposition 36: Parallelograms with Equal Base and Same Height have Equal Area
- Proposition 37: Triangles with Same Base and Same Height have Equal Area
- Proposition 38: Triangles with Equal Base and Same Height have Equal Area
- Proposition 39: Equal Sized Triangles on Same Base are Same Height
- Proposition 40: Equal Sized Triangles on Equal Base are Same Height
- Proposition 41: Parallelogram on Same Base as Triangle has Twice its Area
- Proposition 42: Construction of Parallelogram Equal to Triangle in Given Angle
- Proposition 43: Complements of Parallelograms are Equal
- Proposition 44: Construction of Parallelogram on Given Line Equal to Triangle in Given Angle
- Proposition 45: Construction of Parallelogram in Given Angle Equal to Given Polygon
- Proposition 46: Construction of Square on Given Straight Line
- Proposition 47: Pythagoras's Theorem
- Proposition 48: Square equals Sum of Squares implies Right Triangle
