This is why, when
people dispute, they take refuge in the judge; and to go to the
judge is to go to justice; for the nature of the judge is to be a sort
of animate justice; and they seek the judge as an intermediate, and in
some states they call judges mediators, on the assumption that if they
get what is intermediate they will get what is just. The just, then,
is an intermediate, since the judge is so. Now the judge restores
equality; it is as though there were a line divided into unequal
parts, and he took away that by which the greater segment exceeds
the half, and added it to the smaller segment. And when the whole
has been equally divided, then they say they have 'their own'-i.e.
when they have got what is equal. The equal is intermediate between
the greater and the lesser line according to arithmetical
proportion. It is for this reason also that it is called just
(sikaion), because it is a division into two equal parts (sicha), just
as if one were to call it sichaion; and the judge (sikastes) is one
who bisects (sichastes). For when something is subtracted from one
of two equals and added to the other, the other is in excess by
these two; since if what was taken from the one had not been added
to the other, the latter would have been in excess by one only.
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