Book:Euclid/The Elements/Book XIV
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Hypsicles of Alexandria: The Elements: Book XIV
Published $\text {c. 150 B.C.E}$
Contents
- Proposition $1$: Perpendicular from Center of Circle to Side of Inscribed Pentagon
- Proposition $2$: Circle Circumscribing Pentagon of Dodecahedron and Triangle of Icosahedron in Same Sphere
- Proposition $3$: Size of Surface of Regular Dodecahedron
- Proposition $4$: Size of Surface of Regular Icosahedron
- Proposition $5$: Ratio of Sizes of Surfaces of Regular Dodecahedron and Regular Icosahedron in Same Sphere
- Proposition $6$: Ratio of Sizes of Surfaces of Cube and Regular Icosahedron in Same Sphere
- Proposition $7$: Ratio of Lengths of Sides of Cube and Regular Icosahedron in Same Sphere
- Proposition $8$: Ratio of Volumes of Regular Dodecahedron and Regular Icosahedron in Same Sphere