Euclid's Elements
Book VII
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.

java applet or image 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.

Guide

(Forthcoming)


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

© 1996
D.E.Joyce
Clark University