elem.5.22
若有任意多个量，以及与其个数相等的另一些量，它们两两成相同比例，则它们也成相同比例（经等距传递）。
若任意多个量成同比例传递（A:B = D:E, B:C = E:F），则首尾也成同比例：A:C = D:F。G、H、K、L、M、N 为对应等倍量。
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Let there be any number of magnitudes A, B, C, and others D, E, F equal to them in multitude, which taken two and two together 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 they will also be in the same ratio ex aequali, <that is, as A is to C, so is D to F>. For of A, D let equimultiples G, H be taken, and of B, E other, chance, equimultiples K, L; and, further, of C, F other, chance, equimultiples M, N.
设量A、B、C与量D、E、F个数相等，且A:B=D:E，B:C=E:F。
Then, since, as A is to B, so is D to E, and of A, D equimultiples G, H have been taken, and of B, E other, chance, equimultiples K, L, therefore, as G is to K, so is H to L. [V. 4] For the same reason also, as K is to M, so is L to N.
取A、D的等倍数G、H，B、E的任意等倍数K、L，C、F的任意等倍数M、N。
Since, then, there are three magnitudes G, K, M, and others H, L, N equal to them in multitude, which taken two and two together are in the same ratio, therefore, ex aequali, if G is in excess of M, H is also in excess of N; if equal, equal; and if less, less. [V. 20] And G, H are equimultiples of A, D, and M, N other, chance, equimultiples of C, F.
由A:B=D:E得G:K=H:L；同理K:M=L:N。
Therefore, as A is to C, so is D to F.
由V.20，若G>M则H>N，若G=M则H=N，若G<M则H<N；故由V.定义5得A:C=D:F。