# Category:Euclid Book XIII

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These proofs can all be found in Book $\text {XIII}$ of Euclid's *The Elements*.

The specific form of these has been adapted from Sir Thomas L. Heath's *Euclid: The Thirteen Books of The Elements: Volume 3, 2nd ed.*

## Pages in category "Euclid Book XIII"

The following 23 pages are in this category, out of 23 total.

### A

### C

- Comparison of Sides of Five Platonic Figures
- Comparison of Sides of Five Platonic Figures/Lemma
- Construction of Cube within Given Sphere
- Construction of Regular Dodecahedron within Given Sphere
- Construction of Regular Dodecahedron within Given Sphere/Porism
- Construction of Regular Icosahedron within Given Sphere
- Construction of Regular Icosahedron within Given Sphere/Porism
- Construction of Regular Octahedron within Given Sphere
- Construction of Regular Tetrahedron within Given Sphere
- Construction of Regular Tetrahedron within Given Sphere/Lemma
- Converse of Area of Square on Greater Segment of Straight Line cut in Extreme and Mean Ratio
- Converse of Area of Square on Greater Segment of Straight Line cut in Extreme and Mean Ratio/Lemma

### S

- Segments of Rational Straight Line cut in Extreme and Mean Ratio are Apotome
- Side of Regular Pentagon inscribed in Circle with Rational Diameter is Minor
- Sides Appended of Hexagon and Decagon inscribed in same Circle are cut in Extreme and Mean Ratio
- Square on Side of Equilateral Triangle inscribed in Circle is Triple Square on Radius of Circle
- Square on Side of Regular Pentagon inscribed in Circle equals Squares on Sides of Hexagon and Decagon inscribed in same Circle
- Straight Line cut in Extreme and Mean Ratio plus its Greater Segment
- Straight Lines Subtending Two Consecutive Angles in Regular Pentagon cut in Extreme and Mean Ratio