Proposition: Prop. 8.17: Number does not divide Number iff Cube does not divide Cube

(Proposition 17 from Book 8 of Euclid's “Elements”)

If a cube number does not measure a(nother) cube number then the side (of the former) will not measure the side (of the latter) either. And if the side (of a cube number) does not measure the side (of another cube number) then the (former) cube (number) will not measure the (latter) cube (number) either. * For let the cube number $A$ not measure the cube number $B$. * And let $C$ be the side of $A$, and $D$ (the side) of $B$. * I say that $C$ will not measure $D$. * And so let $C$ not measure $D$. * I say that $A$ will not measure $B$ either.


Modern Formulation

(not yet contributed)

Proofs: 1

Thank you to the contributors under CC BY-SA 4.0!



Adapted from (subject to copyright, with kind permission)

  1. Fitzpatrick, Richard: Euclid's "Elements of Geometry"

Adapted from CC BY-SA 3.0 Sources:

  1. Prime.mover and others: "Pr∞fWiki",, 2016