elem.5.11
与同一比相同的比，彼此也相同。
等比传递：若 A:B = C:D 且 C:D = E:F，则 A:B = E:F。下方是辅助等倍量 G、H、K、L、M、N（每个三元组成等倍）。
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For, as A is to B, so let C be to D, and, as C is to D, so let E be to F; I say that, as A is to B, so is E to F. For of A, C, E let equimultiples G, H, K be taken, and of B, D, F other, chance, equimultiples L, M, N.
设A比B等于C比D，且C比D等于E比F。
Then since, as A is to B, so is C to D, and of A, C equimultiples G, H have been taken, and of B, D other, chance, equimultiples L, M, therefore, if G is in excess of L, H is also in excess of M, if equal, equal, and if less, less.
取A、C、E的等倍量G、H、K，以及B、D、F的任意等倍量L、M、N。
Again, since, as C is to D, so is E to F, and of C, E equimultiples H, K have been taken, and of D, F other, chance, equimultiples M, N, therefore, if H is in excess of M, K is also in excess of N, if equal, equal, and if less, less. But we saw that, if H was in excess of M, G was also in excess of L; if equal, equal; and if less, less; so that, in addition, if G is in excess of L, K is also in excess of N, if equal, equal, and if less, less.
由A比B等于C比D，得G与L的大小关系同H与M的大小关系一致；由C比D等于E比F，得H与M的大小关系同K与N的大小关系一致。
And G, K are equimultiples of A, E, while L, N are other, chance, equimultiples of B, F; therefore, as A is to B, so is E to F.
因此G与L的大小关系同K与N的大小关系一致，故A比B等于E比F。