elem.5.1
如果有任意多个量，它们分别是同样多个量的等倍数，那么一个量是另一个量的多少倍，所有量之和也是所有量之和的同样倍数。
AB 与 CD 是 E 与 F 的等倍量；AB 被 G 分为 AG、GB（各等于 E），CD 被 H 分为 CH、HD（各等于 F）。横向同段竖直排列，便于比较倍数关系。
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Let any number of magnitudes whatever AB, CD be respectively equimultiples of any magnitudes E, F equal in multitude; I say that, whatever multiple AB is of E, that multiple will AB, CD also be of E, F. For, since AB is the same multiple of E that CD is of F, as many magnitudes as there are in AB equal to E, so many also are there in CD equal to F.
设AB、CD分别是E、F的等倍数，即AB是E的倍数与CD是F的倍数相同。
Let AB be divided into the magnitudes AG, GB equal to E, and CD into CH, HD equal to F; then the multitude of the magnitudes AG, GB will be equal to the multitude of the magnitudes CH, HD.
将AB分为与E相等的AG、GB，将CD分为与F相等的CH、HD，则AG、GB的个数等于CH、HD的个数。
Now, since AG is equal to E, and CH to F, therefore AG is equal to E, and AG, CH to E, F.
由于AG等于E，CH等于F，所以AG等于E，且AG与CH之和等于E与F之和；同理，GB等于E，且GB与HD之和等于E与F之和。
For the same reason GB is equal to E, and GB, HD to E, F; therefore, as many magnitudes as there are in AB equal to E, so many also are there in AB, CD equal to E, F; therefore, whatever multiple AB is of E, that multiple will AB, CD also be of E, F.
因此，AB中有多少个等于E的量，AB与CD之和中就有多少个等于E与F之和的量，故AB是E的多少倍，AB与CD之和就是E与F之和的同样倍数。