Proof
Inscribe an equilateral triangle (IV.2); erect an apex above the
centroid at height where is the circumradius.
The four equal edges form the tetrahedron; place the sphere through
its four vertices. The diameter-squared side-squared .
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Depends on (3)
- IV.2Proposition IV.2In a given circle to inscribe a triangle equiangular with a given triangle.
- XI.11Proposition XI.11From a given elevated point to draw a straight line perpendicular to a given plane.
- XIII.12Proposition XIII.12If an equilateral triangle be inscribed in a circle, the square on the side of the triangle is triple of the square on…
Required by (dependents) (2)
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