第7卷命题 13 · 比例数的更比性质

Let the four numbers A, B, C, D be proportional, so that, as A is to B, so is C to D; I say that they will also be proportional alternately, so that, as A is to C, so will B be to D.

设四个数A、B、C、D成比例，即A比B等于C比D。

For since, as A is to B, so is C to D, therefore, whatever part or parts A is of B, the same part or the same parts is C of D also.

根据定义20，A是B的若干部分或几部分，C也是D的相同部分或几部分。

[VII. Def. 20] Therefore, alternately, whatever part or parts A is of C, the same part or the same parts is B of D also.

由第七卷命题10，交替地，A是C的若干部分或几部分，B也是D的相同部分或几部分。

因此，A比C等于B比D，即它们成更比比例。