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Proposition 32

Any number is either 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 A prime number.
| If now A is prime, then that which was proposed is done.
But if it is composite, then some prime number measures it. | VII.31
Therefore any number either is prime or is measured by some prime number.
Therefore, any number is either prime or is measured by some prime number.
Q.E.D.

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(Forthcoming)

Book VII Introduction - Proposition VII.31 - Proposition VII.33.

© 1996
D.E.Joyce
Clark University