◀ ▲ ▶Branches / Geometry / Elements-euclid / Book-12-proportional-stereometry / Lemma: Lem. 12.02: Areas of Circles are as Squares on Diameters

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

(Lemma to Proposition 2 from Book 12 of Euclid's “Elements”)

So, I say that, area $S$ being greater than circle $EFGH$, as area $S$ is to circle $ABCD$, so circle $EFGH$ (is) to some area less than circle $ABCD$.

Modern Formulation

(not yet contributed)

Table of Contents

Proofs: 1

Mentioned in:

Proofs: 1 2 3 4

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

Github:

non-Github:

@Fitzpatrick

References

Adapted from (subject to copyright, with kind permission)

1. Fitzpatrick, Richard: Euclid's "Elements of Geometry"