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Proposition·Untested·2605.00009

Proposition XIII.14

To construct an octahedron and comprehend it in a sphere, as in the preceding case; and to prove that the square on the diameter of the sphere is double of the square on the side of the octahedron.

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Proof

Take two perpendicular diameters in a circle; through the centre erect a perpendicular axis equal in length to the diameter. The four endpoints in the circle and two endpoints on the axis form the six vertices of the octahedron. Diameter-squared / side-squared .

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Full neighborhood

Depends on (2)

Required by (dependents) (2)

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