For let C by multiplying D make E.
Now, since A is a square and C is its side,
therefore C by multiplying itself has made A.
For the same reason also D by multiplying itself has made B.
Since then C by multiplying the numbers C, D has made A, E respectively,
therefore, as C is to D, so is A to E. [VII. 17]
For the same reason also, as C is to D, so is E to B. [VII. 18]
Therefore also, as A is to E, so is E to B.
Therefore between A, B there is one mean proportional number.