Book 9
36
Therefore the product of B, L is equal to the product of D, E. [VII. 19]
36
But the product of D, E is equal to the product of Q, P; therefore the product of Q, P is also equal to the product of B, L.
36
Therefore, as Q is to B, so is L to P. [VII. 19]
36
And Q is the same with B; therefore L is also the same with P; which is impossible, for by hypothesis P is not the same with any of the numbers set out.
36
Therefore no number will measure FG except A, B, C, D, E, HK, L, M and the unit.
36
And FG was proved equal to A, B, C, D, E, HK, L, M and the unit; and a perfect number is that which is equal to its own parts; [VII. Def. 22] therefore FG is perfect. Q. E. D.
