Proof
Take a square base (IV.6); erect a parallel square at height equal
to the side. The eight vertices form the cube; the sphere through
them has diameter times the side.
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Full neighborhood
Depends on (3)
- IV.6Proposition IV.6In a given circle to inscribe a square.
- XI.11Proposition XI.11From a given elevated point to draw a straight line perpendicular to a given plane.
- XIII.14Proposition XIII.14To construct an octahedron and comprehend it in a sphere, as in the preceding case; and to prove that the square on the…
Required by (dependents) (3)
- XIII.16Proposition XIII.16To construct an icosahedron and comprehend it in a sphere, as in the case of the aforesaid figures; and to prove that…
- XIII.17Proposition XIII.17To construct a dodecahedron and comprehend it in a sphere, like the aforesaid figures; and to prove that the side of…
- XIII.18Proposition XIII.18To set out the sides of the five figures and to compare them with one another; and that no other figure, besides the…
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