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Proposition: Prop. 12.02: Areas of Circles are as Squares on Diameters

Euclid's Formulation

Circles are to one another as the squares on (their) diameters. * Let $ABCD$ and $EFGH$ be circles, and [let] $BD$ and $FH$ [be] their diameters. * I say that as circle $ABCD$ is to circle $EFGH$, so the square on $BD$ (is) to the square on $FH$.

fig02e

Modern Formulation

(not yet contributed)

Table of Contents

Proofs: 1

  1. Lemma: Lem. 12.02: Areas of Circles are as Squares on Diameters

Mentioned in:

Proofs: 1 2 3

Thank you to the contributors under CC BY-SA 4.0!

Github:
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non-Github:
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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