Proposition: 6.25: Construction of Figure Similar to One and Equal to Another

(Proposition 25 from Book 6 of Euclid's “Elements”)

To construct a single (rectilinear figure) similar to a given rectilinear figure, and equal to a different given rectilinear figure.


Modern Formulation

It is possible to construct a rectilinear figure ($KGH$) similar to a given rectilinear figure ($ABC$) and having the same area as another given rectilinear figure ($D$).

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