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Euclid: Elementa

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Euclid: Elementa
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PROPOSITION 7. 
 
 
Incommensurable magnitudes have not to one another the ratio which a number has to a number. 
 
 
Let A, B be incommensurable magnitudes;  I say that A has not to B the ratio which a number has to a number. 
   
   
For, if A has to B the ratio which a number has to a number, A will be commensurable with B. [X. 6]  But it is not;  therefore A has not to B the ratio which a number has to a number. 
     
     
 
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