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 $A.$

Proofs: 1

Proofs: 1

Thank you to the contributors under CC BY-SA 4.0!



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",, 2016