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◀ ▲ ▶Branches / Geometry / Elements-euclid / Book-13-platonic-solids / Subsection: Propositions from Book 13

Subsection: Propositions from Book 13

This subsection contains the propositions from Book 13 of Euclid's “Elements”.

Table of Contents

  1. Proposition: Prop. 13.01: Area of Square on Greater Segment of Straight Line cut in Extreme and Mean Ratio
  2. Proposition: Prop. 13.02: Converse of Area of Square on Greater Segment of Straight Line cut in Extreme and Mean Ratio
  3. Proposition: Prop. 13.03: Area of Square on Lesser Segment of Straight Line cut in Extreme and Mean Ratio
  4. Proposition: Prop. 13.04: Area of Squares on Whole and Lesser Segment of Straight Line cut in Extreme and Mean Ratio
  5. Proposition: Prop. 13.05: Straight Line cut in Extreme and Mean Ratio plus its Greater Segment
  6. Proposition: Prop. 13.06: Segments of Rational Straight Line cut in Extreme and Mean Ratio are Apotome
  7. Proposition: Prop. 13.07: Equilateral Pentagon is Equiangular if Three Angles are Equal
  8. Proposition: Prop. 13.08: Straight Lines Subtending Two Consecutive Angles in Regular Pentagon cut in Extreme and Mean Ratio
  9. Proposition: Prop. 13.09: Sides Appended of Hexagon and Decagon inscribed in same Circle are cut in Extreme and Mean Ratio
  10. Proposition: Prop. 13.10: Square on Side of Regular Pentagon inscribed in Circle equals Squares on Sides of Hexagon and Decagon inscribed in sa
  11. Proposition: Prop. 13.11: Side of Regular Pentagon inscribed in Circle with Rational Diameter is Minor
  12. Proposition: Prop. 13.12: Square on Side of Equilateral Triangle inscribed in Circle is Triple Square on Radius of Circle
  13. Proposition: Prop. 13.13: Construction of Regular Tetrahedron within Given Sphere
  14. Proposition: Prop. 13.14: Construction of Regular Octahedron within Given Sphere
  15. Proposition: Prop. 13.15: Construction of Cube within Given Sphere
  16. Proposition: Prop. 13.16: Construction of Regular Icosahedron within Given Sphere
  17. Proposition: Prop. 13.17: Construction of Regular Dodecahedron within Given Sphere
  18. Proposition: Prop. 13.18: There are only Five Platonic Solids

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