For, since A, B are prime to one another,
and A by multiplying itself has made C,
therefore C, B are prime to one another. [VII. 25]
Since then C, B are prime to one another, and B by multiplying itself has made E,
therefore C, E are prime to one another. [id.]
Again, since A, B are prime to one another, and B by multiplying itself has made E,
therefore A, E are prime to one another. [id.]
Since then the two numbers A, C are prime to the two numbers B, E, both to each,
therefore also the product of A, C is prime to the product of B, E. [VII. 26]
And the product of A, C is D, and the product of B, E is F.
Therefore D, F are prime to one another.
Q. E. D.