elem.5.18
如果量成分离比例，则它们也成合成比例。
若 AE:EB = CF:FD，则 AB:EB = CD:FD（由分离比例得合成比例）。G 是辅助点用来截取等比。
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Let AE, EB, CF, FD be magnitudes proportional separando, so that, as AE is to EB, so is CF to FD; I say that they will also be proportional componendo, that is, as AB is to BE, so is CD to FD. For, if CD be not to DF as AB to BE, then, as AB is to BE, so will CD be either to some magnitude less than DF or to a greater. First, let it be in that ratio to a less magnitude DG.
设AE、EB、CF、FD成分离比例，即AE比EB等于CF比FD。
Then, since, as AB is to BE, so is CD to DG, they are magnitudes proportional componendo; so that they will also be proportional separando. [V. 17] Therefore, as AE is to EB, so is CG to GD. But also, by hypothesis, as AE is to EB, so is CF to FD.
假设AB比BE不等于CD比FD，则设AB比BE等于CD比某个小于FD的量DG。
Therefore also, as CG is to GD, so is CF to FD. [V. 11] But the first CG is greater than the third CF; therefore the second GD is also greater than the fourth FD. [V. 14] But it is also less: which is impossible.
由合成比例性质，AE比EB等于CG比GD；但已知AE比EB等于CF比FD，故CG比GD等于CF比FD。
Therefore, as AB is to BE, so is not CD to a less magnitude than FD. Similarly we can prove that neither is it in that ratio to a greater; it is therefore in that ratio to FD itself.
由于CG大于CF，则GD应大于FD，但GD小于FD，矛盾。同理可证不能大于FD，故AB比BE等于CD比FD。