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Proposition: 7.37: Integer Divided by Divisor is Integer

(Proposition 37 from Book 7 of Euclid's “Elements”)

If a number is measured by some number then the (number) measured will have a part called the same as the measuring (number).

• For let the number $A$ be measured by some number $B$.
• I say that $A$ has a part called the same as $B$.

Modern Formulation

If $A=BC$ and $A,B,C$ are natural numbers, then $B$ is a divisor of $A.$

Table of Contents

Proofs: 1

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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