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]
And each of the numbers A, B, C is even;
therefore D is even-times even only. [VII. Def. 8]
Similarly we can prove that each of the numbers B, C is even-times even only.
Q. E. D.