Proposition XIII.12 — If an equilateral triangle be inscribed in a circle, the squ…

Proof

For inscribed equilateral triangle, side

= r 3

. Proven via I.47 on the perpendicular bisector configuration.

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Depends on (2)

I.47Proposition I.47In right-angled triangles the square on the side subtending the right angle is equal to the squares on the sides…
IV.2Proposition IV.2In a given circle to inscribe a triangle equiangular with a given triangle.

Required by (dependents) (1)

XIII.13Proposition XIII.13To construct a pyramid (regular tetrahedron), to comprehend it in a given sphere, and to prove that the square on the…

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