is not the equal according to geometrical but according to
arithmetical proportion.
1 For it makes no difference
2 whether a good man has defrauded a bad man or a bad one a good one,
nor whether it is a good or a bad man that has committed adultery; the law looks only at
the nature of damage, treating the parties as equal, and merely asking whether one has
done and the other suffered injustice, whether one inflicted and the other has sustained
damage.
[
4]
Hence the unjust being here the unequal, the
judge endeavors to equalize it: inasmuch as when one man has received and the other has
inflicted a blow, or one has killed and the other been killed, the line
3 representing the suffering and doing of the deed
is divided into unequal parts, but the judge endeavors to make them equal by the penalty
or loss
4 he imposes, taking away the gain.
[
5]
（For the term ‘gain’ is used in a general way to apply to
such cases, even though it is not strictly appropriate to some of them, for example to a
person who strikes another, nor is ‘loss’ appropriate to the victim in
this case;
[
6]
but at all events the results are called
‘loss’ and ‘gain’ respectively when the amount of
the damage sustained comes to be estimated.） Thus, while the equal is a mean
between more and less, gain and loss are at once both more and less in contrary ways, more
good and less evil being gain and more evil and less good loss; and as the equal, which we
pronounce to be just, is, as we said, a mean between them, it follows that Justice in
Rectification
5 will be the mean
between loss and gain.
[
7]
This is why when disputes occur men have recourse
to a judge. To go to a judge is to go to justice, for the ideal judge is so to speak
justice personified. Also, men require a judge to be a middle term or
medium—indeed in some places judges are called
mediators—, for they think that if they get the mean they will get
what is just. Thus the just is a sort of mean, inasmuch as the judge is a medium between
the litigants.
[8]
Now the judge restores equality: if we represent the matter by a line divided into two
unequal parts, he takes away from the greater segment that portion by which it exceeds
one-half of the whole line, and adds it to the lesser segment. When the whole has been
divided into two halves, people then say that they ‘have their own,’
having got what is equal.
[9]
6This is indeed the origin of the word dikaion
（just）: it means dicha （in
half）, as if one were to pronounce it dichaion;
and a dikast （judge） is a dichast （halver）. The equal is a mean by way
of arithmetical proportion between the greater and the less.
[10]
For when of two equals7 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.
