But the equal or fair amount is here the arithmetic mean between the more or too much and the less or too little. And so it is called δίκαιον (just) because there is equal division ( δίχα ); δίκαιον being in fact equivalent to δίχαιον , and δίκαστής (judge) to δίχαστής .

If you cut off a part from one of two equal lines and add it to the other, the second is now greater than the first by two such parts (for if you had only cut off the part from the first without adding it to the second, the second would have been greater by only one such part); the second exceeds the mean by one such part, and the mean also exceeds the first by one.