elem.5.20
若有三个量及与之个数相等的另三个量，它们两两成相同比例，则通过等比传递，若第一个量大于第三个量，则第四个量也大于第六个量；若相等，则相等；若小于，则小于。
三对量 A、B、C 与 D、E、F 两两成同比；若 A>C，则 D>F；若 A=C，则 D=F；若 A<C，则 D<F。
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Let there be three magnitudes A, B, C, and others D, E, F equal to them in multitude, 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; and let A be greater than C ex aequali; I say that D will also be greater than F; if A is equal to C, equal; and, if less, less. For, since A is greater than C, and B is some other magnitude, and the greater has to the same a greater ratio than the less has, [V. 8] therefore A has to B a greater ratio than C has to B.
设三个量A、B、C，及另三个量D、E、F，个数相等，且A比B等于D比E，B比C等于E比F。
But, as A is to B, so is D to E, and, as C is to B, inversely, so is F to E; therefore D has also to E a greater ratio than F has to E.
若A大于C，则因A与B的比大于C与B的比（V.8），而A比B等于D比E，C比B的反比等于F比E，故D比E大于F比E（V.13）。
[V. 13] But, of magnitudes which have a ratio to the same, that which has a greater ratio is greater; [V. 10] therefore D is greater than F.
对于与同一量有比的量，比值较大的量更大（V.10），因此D大于F。
Similarly we can prove that, if A be equal to C, D will also be equal to F; and if less, less.
同理可证：若A等于C，则D等于F；若A小于C，则D小于F。