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Euclid: Elementa

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Euclid: Elementa
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Therefore etc. 
 
 
PROPOSITION 8. 
 
 
If two magnitudes have not to one another the ratio which a number has to a number, the magnitudes will be incommensurable. 
 
 
For let the two magnitudes A, B not have to one another the ratio which a number has to a number;  I say that the magnitudes A, B are incommensurable. 
   
   
For, if they are commensurable, A will have to B the ratio which a number has to a number. [X. 5]  But it has not;  therefore the magnitudes A, B are incommensurable. 
     
     
Therefore etc. 
 
 
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