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Proposition: Prop. 8.16: Number does not divide Number iff Square does not divide Square

(Proposition 16 from Book 8 of Euclid's “Elements”)

If a square number does not measure a(nother) square number then the side (of the former) will not measure the side (of the latter) either. And if the side (of a square number) does not measure the side (of another square number) then the (former) square (number) will not measure the (latter) square (number) either.

• Let $A$ and $B$ be square numbers, and let $C$ and $D$ be their sides (respectively).
• And let $A$ not measure $B$.
• I say that $C$ does not measure $D$ either.
• So, again, let $C$ not measure $D$.
• I say that $A$ will not measure $B$ either.

Modern Formulation

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Table of Contents

Proofs: 1

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References

Adapted from (subject to copyright, with kind permission)

1. Fitzpatrick, Richard: Euclid's "Elements of Geometry"

Adapted from CC BY-SA 3.0 Sources:

1. Prime.mover and others: "Pr∞fWiki", https://proofwiki.org/wiki/Main_Page, 2016