◀ ▲ ▶Branches / Geometry / Euclidean-geometry / Elements-euclid / Book--6-similar-figures / Proposition: 6.18: Construction of Similar Polygon

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. * Let $AB$ be the given straight line, and $CE$ the given rectilinear figure. * So it is required to describe a rectilinear figure similar, and similarly laid down, to the rectilinear figure $CE$ on the straight line $AB$.

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.

Table of Contents

Proofs: 1

Mentioned in:

Proofs: 1 2 3 4 5 6

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References

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", https://proofwiki.org/wiki/Main_Page, 2016