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Euclid: Elementa

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Euclid: Elementa
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PROPOSITION 32. 
 
 
Any number either is prime or is measured by some prime number. 
 
 
Let A be a number;  I say that A either is prime or is measured by some prime number. 
   
   
If now A is prime, that which was enjoined will have been done.  But if it is composite, some prime number will measure it. [VII. 31] 
   
   
Therefore any number either is prime or is measured by some prime number.  Q. E. D. 
   
   
 
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