内容 第6卷 · 163
命题 Propositio VI.21
elem.6.21
与同一直线形相似的直线形彼此相似。
若两个直线形 A、B 都与同一直线形 C 相似，则 A 与 B 互相相似。
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分步证明Step-by-step proof
1 / 4For let each of the rectilineal figures A, B be similar to C; I say that A is also similar to B.
设直线形A和B均与C相似。
For, since A is similar to C, it is equiangular with it and has the sides about the equal angles proportional.
由于A与C相似，故A与C等角且对应边成比例。
[VI. Def. 1] Again, since B is similar to C, it is equiangular with it and has the sides about the equal angles proportional.
同理，B与C相似，故B与C等角且对应边成比例。
因此A与B等角，且通过C传递对应边比例，故A与B相似。
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