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Euclid: Elementa
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PROPOSITION 13. 
 
第十三題 
To two given straight lines to find a mean proportional. 
 
兩直線。求別作一線。為連比例之中率。 
Let AB, BC be the two given straight lines;  thus it is required to find a mean proportional to AB, BC. 
   
   
Let them be placed in a straight line, and let the semicircle ADC be described on AC;  let BD be drawn from the point B at right angles to the straight line AC,  and let AD, DC be joined. 
     
     
Since the angle ADC is an angle in a semicircle, it is right. [III. 31]  And, since, in the right-angled triangle ADC, DB has been drawn from the right angle perpendicular to the base,  therefore DB is a mean proportional between the segments of the base, AB, BC. [VI. 8, Por.] 
     
     
Therefore to the two given straight lines AB, BC a mean proportional DB has been found.  Q. E. F. 
   
   
 
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