Now that each of the numbers B, C, D is even-times even is manifest; for it is doubled from a dyad.

I say that it is also even-times even only.

For let an unit be set out.

Since then as many numbers as we please beginning from an unit are in continued proportion, and the number A after the unit is prime, therefore D, the greatest of the numbers A, B, C, D, will not be measured by any other number except A, B, C. [[IX. 13](elem.9.13)]

And each of the numbers A, B, C is even; therefore D is even-times even only. [[VII. Def. 8](elem.7.def.8)]

Similarly we can prove that each of the numbers B, C is even-times even only. Q. E. D.