elem.5.12
若有任意多个成比例的量，则一个前项与一个后项之比，等于所有前项之和与所有后项之和之比。
若 A:B = C:D = E:F，则 A:B = (A+C+E):(B+D+F)。下方 G、H、K、L、M、N 为对应的等倍量。
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Let any number of magnitudes A, B, C, D, E, F be proportional, so that, as A is to B, so is C to D and E to F; I say that, as A is to B, so are A, C, E to B, D, F. For of A, C, E let equimultiples G, H, K be taken, and of B, D, F other, chance, equimultiples L, M, N.
设量A、B、C、D、E、F成比例，即A:B = C:D = E:F。
Then since, as A is to B, so is C to D, and E to F, and of A, C, E equimultiples G, H, K have been taken, and of B, D, F other, chance, equimultiples L, M, N, therefore, if G is in excess of L, H is also in excess of M, and K of N, if equal, equal, and if less, less; so that, in addition, if G is in excess of L, then G, H, K are in excess of L, M, N, 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。
Now G and G, H, K are equimultiples of A and A, C, E, since, if any number of magnitudes whatever are respectively equimultiples of any magnitudes equal in multitude, whatever multiple one of the magnitudes is of one, that multiple also will all be of all.
由比例定义，若G大于L，则H大于M且K大于N；若相等则相等；若小于则小于。因此若G大于L，则G、H、K之和大于L、M、N之和，其余同理。
[V. 1] For the same reason L and L, M, N are also equimultiples of B and B, D, F; therefore, as A is to B, so are A, C, E to B, D, F.
由卷V命题1，G、H、K是A、C、E的等倍量，L、M、N是B、D、F的等倍量，故由比例定义得A:B = (A+C+E):(B+D+F)。