elem.5.2
若第一量是第二量的同一倍量，如同第三量是第四量的同一倍量，且第五量也是第二量的同一倍量，如同第六量是第四量的同一倍量，则第一量与第五量之和也是第二量的同一倍量，如同第三量与第六量之和是第四量的同一倍量。
AB 与 DE 分别是 C 与 F 的同倍量，BG 与 EH 也是 C 与 F 的同倍量；AG = AB + BG 与 DH = DE + EH 各为 C、F 之和的同倍量。两条联合段水平排列，便于核对倍数对应。
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Let a first magnitude, AB, be the same multiple of a second, C, that a third, DE, is of a fourth, F, and let a fifth, BG, also be the same multiple of the second, C, that a sixth, EH, is of the fourth F; I say that the sum of the first and fifth, AG, will be the same multiple of the second, C, that the sum of the third and sixth, DH, is of the fourth, F. For, since AB is the same multiple of C that DE is of F, therefore, as many magnitudes as there are in AB equal to C, so many also are there in DE equal to F.
设第一量AB是第二量C的同一倍量，如同第三量DE是第四量F的同一倍量；又设第五量BG是第二量C的同一倍量，如同第六量EH是第四量F的同一倍量。
For the same reason also, as many as there are in BG equal to C, so many are there also in EH equal to F; therefore, as many as there are in the whole AG equal to C, so many also are there in the whole DH equal to F.
由于AB是C的倍量，如同DE是F的倍量，故AB中有多少个等于C的量，DE中也有同样多个等于F的量。
Therefore, whatever multiple AG is of C, that multiple also is DH of F.
同理，BG中有多少个等于C的量，EH中也有同样多个等于F的量。
Therefore the sum of the first and fifth, AG, is the same multiple of the second, C, that the sum of the third and sixth, DH, is of the fourth, F.
因此，整个AG中有多少个等于C的量，整个DH中也有同样多个等于F的量；故AG是C的倍量，如同DH是F的倍量。