Book:Euclid/The Elements/Book I

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