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Euclid: Elementa

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Euclid: Elementa
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PROPOSITION 24. 
 
 
The rectangle contained by medial straight lines commensurable in length is medial. 
 
 
For let the rectangle AC be contained by the medial straight lines AB, BC which are commensurable in length;  I say that AC is medial. 
   
   
For on AB let the square AD be described;  therefore AD is medial.  And, since AB is commensurable in length with BC, while AB is equal to BD, therefore DB is also commensurable in length with BC;  so that DA is also commensurable with AC. [VI. 1, X. 11]  But DA is medial;  therefore AC is also medial. [X. 23, Por.]  Q. E. D. 
             
             
 
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