g.
'as the line A is to the line B, so is the line B to the line C';
the line B, then, has been mentioned twice, so that if the line B be
assumed twice, the proportional terms will be four); and the just,
too, involves at least four terms, and the ratio between one pair is
the same as that between the other pair; for there is a similar
distinction between the persons and between the things. As the term A,
then, is to B, so will C be to D, and therefore, alternando, as A is
to C, B will be to D. Therefore also the whole is in the same ratio to
the whole; and this coupling the distribution effects, and, if the
terms are so combined, effects justly. The conjunction, then, of the
term A with C and of B with D is what is just in distribution, and
this species of the just is intermediate, and the unjust is what
violates the proportion; for the proportional is intermediate, and the
just is proportional. (Mathematicians call this kind of proportion
geometrical; for it is in geometrical proportion that it follows
that the whole is to the whole as either part is to the
corresponding part.) This proportion is not continuous; for we
cannot get a single term standing for a person and a thing.
This, then, is what the just is-the proportional; the unjust is what
violates the proportion.
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