That which is just in the way of redress, then, is the mean between loss and gain. When disputes arise, therefore, men appeal to the judge: 106 and an appeal to the judge is an appeal to that which is just; for the judge is intended to be as it were a living embodiment of that which is just; and men require of a judge that he shall be moderate [or observe the mean], and sometimes even call judges “mediators” ( μεσιδίους ), signifying that if they get the mean they will get that which is just.

That which is just, then, must be a sort of mean, if the judge be a “mediator.”

But the judge restores equality; it is as if he found a line divided into two unequal parts, and were to cut off from the greater that by which it exceeds the half, and to add this to the less.

But when the whole is equally divided, the parties are said to have their own, each now receiving an equal or fair amount.