elem.5.25
如果四个量成比例，则最大量与最小量之和大于其余两量之和。
若四量成比例，则最大与最小之和大于另两量之和。G、H 为辅助标号。
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Let the four magnitudes AB, CD, E, F be proportional so that, as AB is to CD, so is E to F, and let AB be the greatest of them and F the least; I say that AB, F are greater than CD, E. For let AG be made equal to E, and CH equal to F.
设四个量AB、CD、E、F成比例，即AB比CD等于E比F，且AB最大，F最小。
Since, as AB is to CD, so is E to F, and E is equal to AG, and F to CH, therefore, as AB is to CD, so is AG to CH. And since, as the whole AB is to the whole CD, so is the part AG subtracted to the part CH subtracted, the remainder GB will also be to the remainder HD as the whole AB is to the whole CD.
取AG等于E，CH等于F。由比例关系，AB比CD等于AG比CH。
[V. 19] But AB is greater than CD; therefore GB is also greater than HD. And, since AG is equal to E, and CH to F, therefore AG, F are equal to CH, E.
根据V.19，整体AB比整体CD等于减去的部分AG比减去的部分CH，因此余量GB比余量HD也等于AB比CD。
And if, GB, HD being unequal, and GB greater, AG, F be added to GB and CH, E be added to HD, it follows that AB, F are greater than CD, E.
由于AB大于CD，故GB大于HD。又AG等于E，CH等于F，所以AG加F等于CH加E。将GB与HD的不等关系代入，得AB加F大于CD加E。