Pagina 267 van 734

The Just, then, is a certain proportionable thing. For proportion

does not apply merely to number in the abstract,[10] but to

number generally, since it is equality of ratios, and implies

four terms at least (that this is the case in what may be called

discrete proportion is plain and obvious, but it is true also in

continual proportion, for this uses the one term as two, and

mentions it twice; thus A:B:C may be expressed A:B::B:C. In the

first, B is named twice; and so, if, as in the second, B is

actually written twice, the proportionals will be four): and the

Just likewise implies four terms at the least, and the ratio

between the two pair of terms is the same, because the persons

and the things are divided similarly. It will stand then thus,

A:B::C:D, and then permutando A:C::B:D, and then (supposing C and

D to represent the things) A+C:B+D::A:B.