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is not the equal according to geometrical but according to arithmetical proportion.1 For it makes no difference2 whether a good man has defrauded a bad man or a bad one a good one, nor whether it is a good or a bad man that has committed adultery; the law looks only at the nature of damage, treating the parties as equal, and merely asking whether one has done and the other suffered injustice, whether one inflicted and the other has sustained damage. [4] Hence the unjust being here the unequal, the judge endeavors to equalize it: inasmuch as when one man has received and the other has inflicted a blow, or one has killed and the other been killed, the line3 representing the suffering and doing of the deed is divided into unequal parts, but the judge endeavors to make them equal by the penalty or loss4 he imposes, taking away the gain. [5] (For the term ‘gain’ is used in a general way to apply to such cases, even though it is not strictly appropriate to some of them, for example to a person who strikes another, nor is ‘loss’ appropriate to the victim in this case; [6] but at all events the results are called ‘loss’ and ‘gain’ respectively when the amount of the damage sustained comes to be estimated.) Thus, while the equal is a mean between more and less, gain and loss are at once both more and less in contrary ways, more good and less evil being gain and more evil and less good loss; and as the equal, which we pronounce to be just, is, as we said, a mean between them, it follows that Justice in Rectification5 will be the mean between loss and gain. [7]

This is why when disputes occur

1 That is, two pairs of terms (e.g. 1, 3; 7, 9), of which the second term exceeds the first by the same amount as the fourth exceeds the third. We do not call this a proportion at all, but, if also the third term exceeds the second by the same amount (e.g. 1, 3, 5, 7), an arithmetical progression.

2 For Corrective Justice the merits of the parties are immaterial.

3 Again a diagram is employed, cf. 3.9,10, and infra 4.8.

4 ζημία has both senses.

5 A slightly different term is here introduced, but apparently without difference of meaning.

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