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

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