Proposition: Prop. 10.028: Construction of Components of Second Bimedial
(Proposition 28 from Book 10 of Euclid's “Elements”)
To find (two) medial (straight lines), containing a medial (area) , (which are) commensurable in square only.
* Let the [three] [rational]bookofproofs$2083 (straight lines) $A$, $B$, and $C$, (which are) commensurable in square only, be laid down.
* And let, $D$, in mean proportion3 (straight line) to $A$ and $B$, have been taken [Prop. 6.13].
* And let it be contrived that as $B$ (is) to $C$, (so) $D$ (is) to $E$ [Prop. 6.12].
Modern Formulation
(not yet contributed)
Table of Contents
Proofs: 1
 Lemma: Lem. 10.028.1: Finding Two Squares With Sum Also Square
 Lemma: Lem. 10.028.2: Finding Two Squares With Sum Not Square
Mentioned in:
Proofs: 1 2
Propositions: 3 4
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References
Adapted from (subject to copyright, with kind permission)
 Fitzpatrick, Richard: Euclid's "Elements of Geometry"
Adapted from CC BYSA 3.0 Sources:
 Prime.mover and others: "Pr∞fWiki", https://proofwiki.org/wiki/Main_Page, 2016