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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.

• Let $ABCD$ be a parallelogram, and $AC$ its diagonal.
• And let $EG$ and $HK$ be parallelograms about $AC$.
• I say that the parallelograms $EG$ and $HK$ are each similar to the whole (parallelogram) $ABCD$, 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.

Table of Contents

Proofs: 1

Mentioned in:

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