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The thirteenth and last book of the Elements of Euclid deals with the construction of the five "Platonic solids": the tetrahedron, octahedron, cube, icosahedron and dodecahedron. It applies Eudoxus' method of exhaustion to prove that the areas of circles are to one another as the squares of their diameters and that the volumes of spheres are to one another as the cubes of their diameters. It includes the construction of the five regular Platonic solids (pyramid, cube, octahedron, dodecahedron, icosahedron) inside a sphere.

See the related link to read all thirteen books of the Elements.

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Q: What is the 13th book in euclid's elements?
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