Euclid:Proposition/XIV/7
Jump to navigation
Jump to search
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 $7$)
Sources
- 1926: Sir Thomas L. Heath: Euclid: The Thirteen Books of The Elements: Volume 3 (2nd ed.) ... (previous) ... (next): The Contents of the So-Called Book $\text{XIV}$. By Hypsicles