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Euclid: Elementa
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PROPOSITION 12. 
 
第十二題 
To three given straight lines to find a fourth proportional. 
 
三直線。求別作一線。相與為斷比例。 
Let A, B, C be the three given straight lines; thus it is required to find a fourth proportional to A, B, C. 
 
 
Let two straight lines DE, DF be set out containing any angle EDF;  let DG be made equal to A, GE equal to B, and further DH equal to C;  let GH be joined, and let EF be drawn through E parallel to it. [I. 31] 
     
     
Since, then, GH has been drawn parallel to EF, one of the sides of the triangle DEF,  therefore, as DG is to GE, so is DH to HF. [VI. 2]  But DG is equal to A, GE to B, and DH to C;  therefore, as A is to B, so is C to HF. 
       
       
Therefore to the three given straight lines A, B, C a fourth proportional HF has been found.  Q. E. F. 
   
   
 
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Enhet: Det humanistiske fakultet   Utviklet av: IT-seksjonen ved HF
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