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for whom it is just and two shares which are just. 3. [6] And there will be the same equality between the shares as between the persons, since the ratio between the shares will be equal to the ratio between the persons; for if the persons are not equal, they will not have equal shares; it is when equals possess or are allotted unequal shares, or persons not equal equal shares, that quarrels and complaints arise.3. [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. 3. [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.3. [9]

(That a discrete proportion1 has four terms is plain, but so also has a continuous proportion, since it treats one term as two, and repeats it:

1 A ‘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.

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