If three straight lines be proportional, the parallelepipedal solid formed out of the three is equal to the parallelepipedal solid on the mean which is equilateral, but equiangular with the aforesaid solid.
Proof
For a:b=b:c (with b the mean), abc=b3 and the
parallelepipeds on a,b,c versus b,b,b have equal
volumes by XI.34 / XI.33.