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.


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.

Proofs: 1

Proofs: 1 2 3 4 5 6 7 8 9

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