Proposition: 6.24: Parallelograms About Diameter are Similar

(Proposition 24 from Book 6 of Euclid's “Elements”)

In any parallelogram the parallelograms about the diagonal are similar to the whole, and to one another.


Modern Formulation

If a parallelogram is divided into four parallelograms, then the two parallelograms lying on the diagonal are similar to each other and to the whole parallelogram.

Proofs: 1

Proofs: 1 2

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