If there be as many numbers as we please, and others equal to them in multitude, which taken two and two are in the same ratio, they will also be in the same ratio ex aequali.
若有任意多个数，以及同样多个其他数，它们两两成相同比例，则它们也成等距比例。
本页以“等比数列的等距比例定理”整体图解辅助阅读；点、线、角、圆索引已按命题文字和证明步骤校订，可与证明和问答联动。
正文图形由校订坐标生成；点、线、角、圆可与证明和问答联动。
Let there be as many numbers as we please A, B, C, and others equal to them in multitude D, E, F, which taken two and two are in the same ratio, so that, as A is to B, so is D to E, and, as B is to C, so is E to F; I say that, ex aequali, as A is to C, so also is D to F.
设A、B、C与D、E、F分别为两组数，且A:B=D:E，B:C=E:F。
For, since, as A is to B, so is D to E, therefore, alternately, as A is to D, so is B to E.
由A:B=D:E，根据VII.13，交替比例得A:D=B:E。
[VII. 13] Again, since, as B is to C, so is E to F, therefore, alternately, as B is to E, so is C to F.
由B:C=E:F，同样交替得B:E=C:F。
[VII. 13] But, as B is to E, so is A to D; therefore also, as A is to D, so is C to F.
因A:D=B:E且B:E=C:F，故A:D=C:F，即A:C=D:F。