Proposition: 6.26: Parallelogram Similar and in Same Angle has Same Diameter
(Proposition 26 from Book 6 of Euclid's “Elements”)
If from a parallelogram a(nother) parallelogram is subtracted (which is) similar, and similarly laid out, to the whole, having a common angle with it, then (the subtracted parallelogram) is about the same diagonal as the whole.
- For, from parallelogram $ABCD$, let (parallelogram) $AF$ have been subtracted (which is) similar, and similarly laid out, to $ABCD$, having the common angle $DAB$ with it.
- I say that $ABCD$ is about the same diagonal as $AF$.
Modern Formulation
If from a parallelogram ($ABCD$) a similar parellelogram ($AF$) is subtracted and both parallelograms share a common angle ($\angle{GAE}$), then their diagonals going through this angle lie on the same straight line.
Table of Contents
Proofs: 1
Mentioned in:
Proofs: 1 2 3 4 5 6 7 8 9
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
