Since, then, as A is to C, so is D to E,
while, as D is to E, so is H to K,
therefore also, as A is to C, so is H to K. [V. 11]
Again, since, as C is to B, so is F to G,
while, as F is to G, so is K to L,
therefore also, as C is to B, so is K to L. [V. 11]
But also, as A is to C, so is H to K;
therefore, ex aequali, as A is to B, so is H to L. [V. 22]
Therefore A has to B the ratio which a number has to a number;
therefore A is commensurable with B. [X. 6]
Complete text
Book I