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Euclid: Elementa

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Euclid: Elementa
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PROPOSITION 21. 
 
第二十一題 
Figures which are similar to the same rectilineal figure are also similar to one another. 
 
兩直線形。各與他直線形相似。則自相似。 
For let each of the rectilineal figures A, B be similar to C;  I say that A is also similar to B. 
   
   
For, since A is similar to C,  it is equiangular with it and has the sides about the equal angles proportional. [VI. Def. 1]  Again, since B is similar to C,  it is equiangular with it and has the sides about the equal angles proportional.  Therefore each of the figures A, B is equiangular with C and with C has the sides about the equal angles proportional;  therefore A is similar to B.  Q. E. D. 
             
             
 
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