Proposition: 6.18: Construction of Similar Polygon

(Proposition 18 from Book 6 of Euclid's “Elements”)

To describe a rectilinear figure similar, and similarly laid down, to a given rectilinear figure on a given straight line.


Modern Formulation

Given a segment $\overline{AB}$ and an arbitrary rectilinear figure it is possible to construct a similar figure containing the segment $\overline{AB}$ as one of its sides.

Proofs: 1

Proofs: 1 2 3 4 5 6

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