Commentary on Proposition VIII.25

Back to Proposition VIII.25.

[Folio 0387 | p. 381]

If $a : b = c^3 : d^3$, and $a$ is a cube, then $b$ is also a cube. For $c^3, d^3$ have two mean proportionals. [VIII. 19]

Therefore $a, b$ also have two mean proportionals. [VIII. 8]

And $a$ is a cube: therefore $b$ is a cube. [VIII. 23]