Let there be as many numbers as we please, B, C, D, and E, beginning from the unit A and in continued proportion.
I say that B, the least of the numbers B, C, D, and E, measures E according to one of the numbers C or D.
Since the unit A is to B as D is to E, therefore the unit A measures the number B the same number of times as D measures E. Therefore, alternately, the unit A measures D the same number of times as B measures E.
But the unit A measures D according to the units in it, therefore B also measures E according to the units in D, so that B the less measures E the greater according to some number of those which have place among the proportional numbers.
Therefore, if as many numbers as we please beginning from a unit are in continued proportion, then the less measures the greater according to some one of the numbers which appear among the proportional numbers.