内容 第5卷 · 126
命题 Propositio V.9
elem.5.9
与同一量有相同比的两个量彼此相等；同一量与两个量有相同比，则这两个量也相等。
A、B 是相等的量，C 是任意量。
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分步证明Step-by-step proof
1 / 4For let each of the magnitudes A, B have the same ratio to C; I say that A is equal to B.
设量A和B与同一量C有相同比。
For, otherwise, each of the magnitudes A, B would not have had the same ratio to C; [V. 8] but it has; therefore A is equal to B.
若A不等于B，则A和B与C的比将不同（据V.8），但已知相同，故A等于B。
Again, let C have the same ratio to each of the magnitudes A, B; I say that A is equal to B.
再设C与量A和B有相同比。
For, otherwise, C would not have had the same ratio to each of the magnitudes A, B; [V. 8] but it has; therefore A is equal to B.
若A不等于B，则C与A和B的比将不同（据V.8），但已知相同，故A等于B。
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