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Proposition: 7.38: Divisor is Reciprocal of Divisor of Integer

(Proposition 38 from Book 7 of Euclid's “Elements”)

If a number has any part whatever then it will be measured by a number called the same as the part.

• For let the number $A$ have any part whatever, $B$.
• And let the [number] $C$ be called the same as the part $B$ (i.e., $B$ is the $C$th part of $A$).
• I say that $C$ measures $A$.

Modern Formulation

If $\frac AC=B$ for some natural number $B,$ then $A$ is a multiple of $C.$

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