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Therefore the latter will
exceed the mean by once the part, and the mean will exceed the former, from which the part
was taken, by once that part.
[11]
This process then will
enable us to ascertain what we ought to take away from the party that has too much and
what to add to the one that has too little: we must add to the one that has too little the
amount whereby the mean between them exceeds him, and take away from the greatest1 of the three the
amount by which the mean is exceeded by him.
[12]
Let the
lines AA, BB, CC be equal to one another; let the segment AE be taken away from the line
AA, and let the segment CD be added to the line CC, so that the whole line DCC exceeds the
line EA by CD+CF; then DCC will exceed BB by CD.2
[13]
The terms ‘loss’ and ‘gain’ in these cases are
borrowed from the operations of voluntary exchange. There, to have more than one's own is
called gaining, and to have less than one had at the outset is called losing, as for
instance in buying and selling, and all other transactions sanctioned by law;3
[14]
while if the result of the transaction is neither an
increase nor a decrease, but exactly what the parties had of themselves, they say they
‘have their own’ and have neither lost nor gained. Hence Justice in
Involuntary Transactions is a mean between gain and loss in a sense: it is to have after
the transaction an amount
1 i.e., the party that has too much.
2 The mss. here insert the sentence that appears again at 5.9 init.
3 Literally ‘where the law gives immunity,’ that is, does not give redress for inequality resulting from the contract. Should inequality result from a breach of the contract, this would of course be a case for the intervention of Corrective Justice in Voluntary Transactions (chap. 2 fin.).