◀ ▲ ▶Branches / Geometry / Elements-euclid / Book--6-similar-figures / Subsection: Propositions from Book 6

Subsection: Propositions from Book 6

This subsection contains the propositions from Book 6 of Euclid's “Elements”.

Table of Contents

1. Proposition: 6.01: Areas of Triangles and Parallelograms Proportional to Base
2. Proposition: 6.02: Parallel Line in Triangle Cuts Sides Proportionally
3. Proposition: 6.03: Angle Bisector Theorem
4. Proposition: 6.04: Equiangular Triangles are Similar
5. Proposition: 6.05: Triangles with Proportional Sides are Similar
6. Proposition: 6.06: Triangles with One Equal Angle and Two Sides Proportional are Similar
7. Proposition: 6.07: Triangles with One Equal Angle and Two Other Sides Proportional are Similar
8. Proposition: 6.08: Perpendicular in Right-Angled Triangle makes two Similar Triangles
9. Proposition: 6.09: Construction of Part of Line
10. Proposition: 6.10: Construction of Similarly Cut Straight Line
11. Proposition: 6.11: Construction of Segment in Squared Ratio
12. Proposition: 6.12: Construction of Fourth Proportional Straight Line
13. Proposition: 6.13: Construction of Mean Proportional
14. Proposition: 6.14: Characterization of Congruent Parallelograms
15. Proposition: 6.15: Characterization of Congruent Triangles
16. Proposition: 6.16: Rectangles Contained by Proportional Straight Lines
17. Proposition: 6.17: Rectangles Contained by Three Proportional Straight Lines
18. Proposition: 6.18: Construction of Similar Polygon
19. Proposition: 6.19: Ratio of Areas of Similar Triangles
20. Proposition: 6.20: Similar Polygons are Composed of Similar Triangles
21. Proposition: 6.21: Similarity of Polygons is Transitive
22. Proposition: 6.22: Similar Figures on Proportional Straight Lines
23. Proposition: 6.23: Ratio of Areas of Equiangular Parallelograms
24. Proposition: 6.24: Parallelograms About Diameter are Similar
25. Proposition: 6.25: Construction of Figure Similar to One and Equal to Another
26. Proposition: 6.26: Parallelogram Similar and in Same Angle has Same Diameter
27. Proposition: 6.27: Similar Parallelogram on Half a Straight Line
28. Proposition: 6.28: Construction of Parallelogram Equal to Given Figure Less a Parallelogram
29. Proposition: 6.29: Construction of Parallelogram Equal to Given Figure Exceeding a Parallelogram
30. Proposition: 6.30: Construction of the Inverse Golden Section
31. Proposition: 6.31: Similar Figures on Sides of Right-Angled Triangle
32. Proposition: 6.32: Triangles with Two Sides Parallel and Equal
33. Proposition: 6.33: Angles in Circles have Same Ratio as Arcs

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