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 taken and added to the other, this latter exceeds the former by twice that portion: if it had been merely taken from the former and not added to the latter, then the latter would have exceeded the former only by that one portion; but in the other case, the greater exceeds the mean by one, and the mean exceeds also by one that magnitude from which the portion was taken. By this illustration, then, we obtain a rule to determine what one ought to take from him who has the greater, and what to add to him who has the less. The excess of the mean over the less must be added to the less, and the excess of the greater over the mean be taken from the greater. Thus let there be three straight lines equal to one another. From one of them cut off a portion, and add as much to another of them. The whole line thus made will exceed the remainder of the first-named line, by twice the portion added, and will exceed the untouched line by that portion.[14] And these terms loss and gain are derived from voluntary exchange: that is to say, the having more than what was one’s own is called gaining, and the having less than one’s original stock is called losing; for instance, in buying or selling, or any other transactions which are guaranteed by law: but when the result is neither more nor less, but exactly the same as there was originally,[15] people say they have their own, and neither lose nor gain. So then the Just we have been speaking of is a mean between loss and gain arising in involuntary transactions; that is, it is the having the same after the transaction as one had before it took place. Chapter VIII. There are people who have a notion that Reciprocation is simply just, as the Pythagoreans said: for they defined the Just simply and without qualification as “That which reciprocates with another.” But this simple Reciprocation will not fit on either to the Distributive Just, or the Corrective (and yet this is the interpretation they put on the Rhadamanthian rule of Just, If a man should suffer what he hath done, then there would be straightforward justice;”) for in many cases differences arise: as, for instance, suppose one in authority has struck a man, he is not to be struck in turn; or if a man has struck one in authority, he must not only be struck but punished also.[16] And again, the voluntariness or involuntariness of actions makes a great difference.