For, if not, A, B, C will measure some number which is less than E.
Let them measure F.
Since A, B, C measure F, therefore also A, B measure F;
therefore the least number measured by A, B will also measure F. [VII. 35]
But D is the least number measured by A, B; therefore D measures F.
But C also measures F; therefore D, C measure F,
so that the least number measured by D, C will also measure F.
But E is the least number measured by C, D;
therefore E measures F, the greater the less: which is impossible.
Therefore A, B, C will not measure any number which is less than E.
Therefore E is the least that is measured by A, B, C.
Q. E. D.