Category:Euclid Book XIII
Jump to navigation
Jump to search
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