# 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. * Let $ABC$ be the given rectilinear figure to which it is required to construct a similar (rectilinear figure), and $D$ the (rectilinear figure) to which (the constructed figure) is required (to be) equal. * So it is required to construct a single (rectilinear figure) similar to $ABC$, and equal to $D$.

### 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

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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