ProofWiki:Books/Euclid/The Elements/Book VI
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Euclid: The Elements: Book VI
Published c. 300 B.C.E.
Contents
- Book VI: Theory of Proportions as applied to Plane Geometry
- Definitions
- Proposition 1: Areas of Triangles and Parallelograms Proportional to Base
- Proposition 2: Parallel Line in Triangle Cuts Sides Proportionally
- Proposition 3: Angle Bisector Theorem
- Proposition 4: Equiangular Triangles are Similar
- Proposition 5: Triangles with Proportional Sides are Similar
- Proposition 6: Triangles with One Equal Angle and Two Sides Proportional are Similar
- Proposition 7: Triangles with One Equal Angle and Two Other Sides Proportional are Similar
- Proposition 8: Perpendicular in Right-Angled Triangle makes two Similar Triangles
- Proposition 9: Construction of a Part of a Line
- Proposition 10: Construction of Similarly Cut Straight Line
- Proposition 11: Construction of Third Proportional Straight Line
- Proposition 12: Construction of Fourth Proportional Straight Line
- Proposition 13: Construction of Mean Proportional
- Proposition 14: Sides of Equiangular Parallelograms are Reciprocally Proportional
- Proposition 15: Sides of Equiangular Triangles are Reciprocally Proportional
- Proposition 16: Rectangles Contained by Proportional Straight Lines
- Proposition 17: Rectangles Contained by Three Proportional Straight Lines
- Proposition 18: Construction of Similar Polygon
- Proposition 19: Ratio of Areas of Similar Triangles
- Proposition 20: Similar Polygons Composed of Similar Triangles
- Proposition 21: Similarity of Polygons is Equivalence
- Proposition 22: Similar Figures on Proportional Straight Lines
- Proposition 23: Ratio of Areas of Equiangular Parallelograms
- Proposition 24: Parallelograms About Diameter are Similar
- Proposition 25: Construction of Figure Similar to One and Equal to Another
- Proposition 26: Parallelogram Similar and in Same Angle has Same Diameter
- Proposition 27: Similar Parallelogram on Half a Straight Line
- Proposition 28: Construction of Parallelogram Equal to Given Figure Less a Parallelogram
- Proposition 29: Construction of Parallelogram Equal to Given Figure Exceeding a Parallelogram
- Proposition 30: Construction of Golden Section
- Proposition 31: Similar Figures on Sides of Right-Angled Triangle
- Proposition 32: Triangles with Two Sides Parallel and Equal
- Proposition 33: Angles in Circles have Same Ratio as Arcs
