The Complete Aristotle (eng.)

which violates the proportion. But the justice in transactions
between man and man is a sort of equality indeed, and the injustice
a sort of inequality; not according to that kind of proportion,
however, but according to arithmetical proportion. For it makes no
difference whether a good man has defrauded a bad man or a bad man
a good one, nor whether it is a good or a bad man that has
committed adultery; the law looks only to the distinctive character
of the injury, and treats the parties as equal, if one is in the
wrong and the other is being wronged, and if one inflicted injury
and the other has received it. Therefore, this kind of injustice
being an inequality, the judge tries to equalize it; for in the
case also in which one has received and the other has inflicted a
wound, or one has slain and the other been slain, the suffering and
the action have been unequally distributed; but the judge tries to
equalize by means of the penalty, taking away from the gain of the
assailant. For the term ‘gain’ is applied generally to such cases,
even if it be not a term appropriate to certain cases, e.g. to the
person who inflicts a woundand ‘loss’ to the sufferer; at all
events when the suffering has been estimated, the one is called
loss and the other gain. Therefore the equal is intermediate
between the greater and the less, but the gain and the loss are
respectively greater and less in contrary ways; more of the good
and less of the evil are gain, and the contrary is loss;
intermediate between them is, as we saw, equal, which we say is
just; therefore corrective justice will be the intermediate between
loss and gain. 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. It therefore exceeds the intermediate by one, and the
intermediate exceeds by one that from which something was taken. By
this, then, we shall recognize both what we must subtract from that
which has more, and what we must add to that which has less; we
must add to the latter that by which the intermediate exceeds it,
and subtract from the greatest that by which it exceeds the
intermediate. Let the lines AA’, BB’, CC’ be equal to one another;
from the line AA’ let the segment AE have been subtracted, and to
the line CC’ let the segment CD have been added, so that the whole
line DCC’ exceeds the line EA’ by the segment CD and the segment
CF; therefore it exceeds the line BB’ by the segment CD. (See
diagram.)
    These names, both loss and gain, have come from voluntary
exchange; for to have more than one’s own is called gaining, and to
have less than one’s original share is called losing, e.g. in
buying and selling and in all other matters in which the law has
left people free to make their own terms; but when they get neither
more nor less but just what belongs to themselves, they say that
they have their own and that they neither lose nor gain.
    Therefore the just is intermediate between a sort of gain and a
sort of loss, viz. those which are involuntary; it consists in
having an equal amount before and after the transaction.
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5
    Some think that reciprocity is without qualification just, as
the Pythagoreans said; for they defined justice without
qualification as reciprocity. Now