elem.5.21
设有三量A、B、C，以及另三量D、E、F，数量相等，且两两取对成相同比例，但比例是扰动的，即A比B等于E比F，B比C等于D比E。那么，若A大于C，则D也大于F；若A等于C，则D等于F；若A小于C，则D小于F。
三对量在“扰动”同比下：A:B = E:F、B:C = D:E；若 A>C，则 D>F；A=C 则 D=F；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, and let the proportion of them be perturbed, so that, as A is to B, so is E to F, and, as B is to C, so is D to E, 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, therefore A has to B a greater ratio than C has to B.
因为A大于C，且B是另一量，所以A与B的比大于C与B的比（V.8）。
[V. 8] But, as A is to B, so is E to F, and, as C is to B, inversely, so is E to D.
但A比B等于E比F，而C比B的反比等于E比D（由扰动比例得）。
Therefore also E has to F a greater ratio than E has to D. [V. 13] But that to which the same has a greater ratio is less; [V. 10] therefore F is less than D; therefore D is greater than F.
因此E与F的比大于E与D的比（V.13）。
Similarly we can prove that, if A be equal to C, D will also be equal to F; and if less, less.
对于同一量E，比之较大的量较小（V.10），故F小于D，即D大于F。同理可证相等和小于的情形。