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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.