Proposition: 7.11: Proportional Numbers have Proportional Differences
(Proposition 11 from Book 7 of Euclid's “Elements”)
If as the whole (of a number) is to the whole (of another), so a (part) taken away (is) to a (part) taken away, then the remainder will also be to the remainder as the whole (is) to the whole.
- Let the whole $AB$ be to the whole $CD$ as the (part) taken away $AE$ (is) to the (part) taken away $CF$.
- I say that the remainder $EB$ is to the remainder $FD$ as the whole $AB$ (is) to the whole $CD$.
Modern Formulation
In modern notation, this proposition states that if \[\frac{AB}{CD}=\frac{AE+EB}{CF+FD}=\frac{AE}{CF},\] then \[\frac{EB}{FD}=\frac{AB}{CD}.\]
Table of Contents
Proofs: 1
Mentioned in:
Proofs: 1
Thank you to the contributors under CC BY-SA 4.0! 
- Github:
-
- non-Github:
- @Fitzpatrick
References
Adapted from (subject to copyright, with kind permission)
- Fitzpatrick, Richard: Euclid's "Elements of Geometry"
Adapted from CC BY-SA 3.0 Sources:
- Prime.mover and others: "Pr∞fWiki", https://proofwiki.org/wiki/Main_Page, 2016
