Euclid:Proposition/XIV/7

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Proposition

In the words of Hypsicles of Alexandria:

If any straight line whatever be cut in extreme and mean ratio, then, as is $(1)$ the straight line the square on which is equal to the sum of the squares on the whole line and on the greater segment to $(2)$ the straight line the square on which is equal to the sum of the squares on the whole and on the lesser segment, so is $(3)$ the side of the cube to $(4)$ the side of the icosahedron.

(The Elements: Book $\text{XIV}$: Proposition $7$)


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