Definition: 7.04: Aliquant Part, a Number Being Not a Divisor of Another Number

But (the lesser number is) parts (of the greater number) when it does not measure it.

Modern Definition

This is any integer \(d\neq 0,~|d| < |n|\), which is not a divisor of \(n\). For such integers we write \(d\not\mid n\). These are exactly those integers $d$ which leave a remainder $r$ with $0 < r < |d|$ in the division with quotient and remainder $$n=dq+r,\quad 0 < r < |d|.$$

Definitions: 1
Proofs: 2 3 4 5 6 7 8 9 10
Propositions: 11 12 13 14 15 16


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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