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) $B$, $C$, $D$.
see fundamental theorem of arithmetic.
Table of Contents
Proofs: 1 2
Thank you to the contributors under CC BY-SA 4.0!
- Kramer Jürg, von Pippich, Anna-Maria: "Von den natürlichen Zahlen zu den Quaternionen", Springer-Spektrum, 2013
Adapted from (subject to copyright, with kind permission)
- Fitzpatrick, Richard: Euclid's "Elements of Geometry"