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[10]
For when of two equals1 a
part is taken from the one and added to the other, the latter will exceed the former by
twice that part, since if it had been taken from the one but not added to the other, the
latter would exceed the former by once the part in question only. Therefore the latter will
exceed the mean by once the part, and the mean will exceed the former, from which the part
was taken, by once that part.
1 If a=b, then （b+n）-（a-n）=2n, and （b+n）-a=N, and （b+n）-（b+n）+（a-n）/2=n=（b+n）+（a-n）/2-（a-n）. Aristotle, of course, represented the quantities by lines, not algebraically.
Aristotle in 23 Volumes, Vol. 19, translated by H. Rackham. Cambridge, MA, Harvard University Press; London, William Heinemann Ltd. 1934.
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