## 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 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.
After the previous proposition, this one really doesn't need to be stated at all.

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 Select from Book VII Book VII intro VII.Def.1-2 VII.Def.3-5 VII.Def.6-10 VII.Def.11-14 VII.Def.15-19 VII.Def.20 VII.Def.21 VII.Def.22 VII.1 VII.2 VII.3 VII.4 VII.5 VII.6 VII.7 VII.8 VII.9 VII.10 VII.11 VII.12 VII.13 VII.14 VII.15 VII.16 VII.17 VII.18 VII.19 VII.20 VII.21 VII.22 VII.23 VII.24 VII.25 VII.26 VII.27 VII.28 VII.29 VII.30 VII.31 VII.32 VII.33 VII.34 VII.35 VII.36 VII.37 VII.38 VII.39 Select book Book I Book II Book III Book IV Book V Book VI Book VII Book VIII Book IX Book X Book XI Book XII Book XIII Select topic Introduction Table of Contents Geometry applet About the text Euclid Web references A quick trip