Book 5
7
This is also clear from the principle of assignment by desert. All are agreed that justice in distributions must be based on desert of some sort, although they do not all mean the same sort of desert; democrats make the criterion free birth; those of oligarchical sympathies wealth, or in other cases birth; upholders of aristocracy make it virtue.
8
Justice is therefore a sort of proportion; for proportion is not a property of numerical quantity only, but of quantity in general, proportion being equality of ratios, and involving four terms at least.
9
(That a discrete proportionA discrete proportion means one in which the two ratios are disconnected, being between different terms, whereas in a continuous proportion they have one term in common. has four terms is plain, but so also has a continuous proportion, since it treats one term as two, and repeats it: for example,Here the lecturer displayed a diagram. as the line representing term one is to the line representing term two, so is the line representing term two to the line representing term three; here the line representing term two is mentioned twice, so that if it be counted twice, there will be four proportionals.)
