ProofWiki:Books/Euclid/The Elements
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Contents |
Euclid : The Elements
Published c. 300 B.C.E.
[edit] Subject Matter
[edit] 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
- Book II: Geometrical Algebra
- Definitions
- Proposition 1: Real Multiplication Distributes over Real Addition
- Proposition 2: Square is Sum of Two Rectangles
- Proposition 3: Rectangle is Sum of Square and Rectangle
- Proposition 4: Square of Sum
- Proposition 5: Difference of Two Squares
- Proposition 6: Square of Sum less Square
- Proposition 7: Square of Difference
- Proposition 8: Square of Sum with Double
- Propositions 9 and 10: Sum of Squares of Sum and Difference
- Proposition 11: Construction of Square Equal to Rectangle
- Proposition 12: Relative Sizes of Sides of Obtuse Triangle
- Proposition 13: Relative Sizes of Sides of Acute Triangle
- Proposition 14: Construction of Square Equal to Given Polygon
- Book III: Circles
- Definitions
- Proposition 1: Finding Center of Circle
- Proposition 2: Chord Lies Inside its Circle
- Proposition 3: Conditions for Diameter to be Perpendicular Bisector
- Proposition 4: Chords Do Not Bisect Each Other
- Proposition 5: Intersecting Circles Have Different Centers
- Proposition 6: Touching Circles Have Different Centers
- Proposition 7: Relative Lengths of Lines Inside Circle
- Proposition 8: Relative Lengths of Lines Outside Circle
- Proposition 9: Condition for Point to be Center of Circle
- Proposition 10: Two Circles Have At Most Two Points of Intersection
- Proposition 11: Line Joining Centers of Two Circles Touching Internally
- Proposition 12: Line Joining Centers of Two Circles Touching Externally
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- Book V: Theory of Proportions
- Book VI: Theory of Proportions as applied to Plane Geometry
- Book VII: Number Theory
- Book VIII: Theory of Proportions as applied to Number Theory
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- Book X: Irrational Numbers, steps towards Calculus
- Book XI: Spatial Geometry
- Book XII: Cones, Pyramids and Cylinders
- Book XIII: The Five Platonic Solids
[edit] Notable Translations and Editions
- c. 364: Theon of Alexandria
- 1620: Henry Briggs (the first 6 books)
- 1908 (2nd edition 1925): Sir Thomas L. Heath - 3 volumes:
- Vol. 1: Books I and II (ISBN 0-486-60088-2)
- Vol. 2: Books II - IX (ISBN 0-486-60089-0)
- Vol. 3: Books X - XIII (ISBN 0-486-60090-4)
[edit] Online
- Java -version [1].
