For these terms gain and loss are applied to these cases, though perhaps the term in some particular instance may not be strictly proper, as gain, for instance, to the man who has given a blow, and loss to him who has received it: still, when the suffering has been estimated, the one is called loss and the other gain.
And so the equal is a mean between the more and the less, which represent gain and loss in contrary ways (I mean, that the more of good and the less of evil is gain, the less of good and the more of evil is loss): between which the equal was stated to be a mean, which equal we say is Just: and so the Corrective Just must be the mean between loss and gain. And this is the reason why, upon a dispute arising, men have recourse to the judge: going to the judge is in fact going to the Just, for the judge is meant to be the personification of the Just.106 And men seek a judge as one in the mean, which is expressed in a name given by some to judges (μεσίδιοι, or middle-men) under the notion that if they can hit on the mean they shall hit on the Just. The Just is then surely a mean since the judge is also.
So it is the office of a judge to make things equal, and the line, as it were, having been unequally divided, he takes from the greater part that by which it exceeds the half, and adds this on to the less. And when the whole is divided into two exactly equal portions then men say they have their own, when they have gotten the equal; and the equal is a mean between the greater and the less according to arithmetical equality.
This, by the way, accounts for the etymology of the term by which we in Greek express the ideas of Just and Judge; (δίκαιον quasi δίχαιον, that is in two parts, and δικάστης quasi διχάστης, he who divides into two parts). For when from one of two equal magnitudes somewhat has been