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area a medial base binomial straight line bisected circle ABCD circle EFGH commensurable in length commensurable in square cone cube cut in extreme cylinder decagon Deff diameter dodecahedron equiangular equilateral Euclid extreme and mean greater segment height Hence icosahedron inscribed irrational straight line joined Lemma let the square magnitudes mean ratio measure medial area medial straight line medial whole parallelepipedal solids parallelogram pentagon perpendicular plane angles plane of reference polygon prism Proposition proved ratio triplicate rational and incommensurable rational area rational straight line rectangle AC rectangle contained right angles second apotome side similar Similarly solid angle solid CD sphere square number squares on AC straight lines commensurable surable triangle twice the rectangle vertex whence