may be called discrete proportion is plain and obvious, but it is true also in continual proportion, for this uses the one 1131bterm as two, and mentions it twice; thus A:B:C may be expressed A:B::B:C. In the first, B is named twice; and so, if, as in the second, B is actually written twice, the proportionals will be four): and the Just likewise implies four terms at the least, and the ratio between the two pair of terms is the same, because the persons and the things are divided similarly. It will stand then thus, A:B::C:D, and then permutando A:C::B:D, and then (supposing C and D to represent the things) A+C:B+D::A:B. The distribution in fact consisting in putting together these terms thus: and if they are put together so as to preserve this same ratio, the distribution puts them together justly.1 So then the joining together of the first and third and second and fourth proportionals is the Just in the distribution, and this Just is the mean relatively to that which violates the proportionate, for the proportionate is a mean and the Just is proportionate. Now mathematicians call this kind of proportion geometrical: for in geometrical proportion the whole is to the whole as each part to each part. Furthermore this proportion is not continual, because the person and thing do not make up one term.
The Just then is this proportionate, and the Unjust that which violates the proportionate; and so there comes to be the greater and the less: which in fact is the case in actual transactions, because he who acts unjustly has the greater share and he who is treated unjustly has the less of what is good: but in the case of what is bad this is reversed: for the less evil compared with the greater comes to be reckoned for good, because the less evil is more choiceworthy than the greater, and what is choiceworthy is good, and the more so the greater good.
This then is the one species of the Just.
