Proposition: Prop. 12.01: Areas of Similar Polygons Inscribed in Circles are as Squares on Diameters
Similar polygons (inscribed) in circles are to one another as the squares on the diameters (of the circles).
* Let $ABC$ and $FGH$ be circles, and let $ABCDE$ and $FGHKL$ be similar polygons (inscribed) in them (respectively), and let $BM$ and $GN$ be the diameters of the circles (respectively).
* I say that as the square on $BM$ is to the square on $GN$, so polygon $ABCDE$ (is) to polygon $FGHKL$.
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Table of Contents
Proofs: 1 2
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Adapted from (subject to copyright, with kind permission)
- Fitzpatrick, Richard: Euclid's "Elements of Geometry"
Adapted from CC BY-SA 3.0 Sources:
- Prime.mover and others: "Pr∞fWiki", https://proofwiki.org/wiki/Main_Page, 2016