If the two persons were equal, their respective shares would be arithmetically equal: Achilles would have six, Ajax six.

And if we should carry out this arithmetical equality, Thersites would be entitled to as much as Achilles, which would be unjust in the extreme.

To avoid this injustice, the worth of the persons should be estimated, and the spoils divided accordingly.
Suppose that the worth of Achilles is double that of Ajax: the former's share is eight, the latter four.

There is no arithmetical equality, but a proportional equality.

It is this comparison of merits, rationum, that Aristotle calls distributive justice.