Theorem: Prop. 9.14: Fundamental Theorem of Arithmetic
(Proposition 14 from Book 9 of Euclid's “Elements”)
If a least number is measured by (some) prime numbers then it will not be measured by any other prime number except (one of) the original measuring (numbers).
 For let $A$ be the least number measured by the prime numbers $B$, $C$, $D$.
 I say that $A$ will not be measured by any other prime number except (one of) $B$, $C$, $D$.
Modern Formulation
see fundamental theorem of arithmetic.
Table of Contents
Proofs: 1
Mentioned in:
Proofs: 1 2
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References
Bibliography
 Kramer Jürg, von Pippich, AnnaMaria: "Von den natürlichen Zahlen zu den Quaternionen", SpringerSpektrum, 2013
Adapted from (subject to copyright, with kind permission)
 Fitzpatrick, Richard: Euclid's "Elements of Geometry"