This is also plainly indicated by the common phrase “according to merit.” For in distribution all men allow that what is just must be according to merit or worth of some kind, but they do not all adopt the same standard of worth; in democratic states they take free birth as the standard, 102 in oligarchic states they take wealth, in others noble birth, and in the true aristocratic state virtue or personal merit.

We see, then, that that which is just is in some sort proportionate. For not abstract numbers only, but all things that can be numbered, admit of proportion; proportion meaning equality of ratios, and requiring four terms at least.