Proposition: 6.13: Construction of Mean Proportional
(Proposition 13 from Book 6 of Euclid's “Elements”)^{1}
To find the (straight line) in mean proportion3 to two given straight lines.
Modern Formulation
It is possible to construct a segment with a length being the geometric mean3 of the lengths of two given other segments.
Table of Contents
Proofs: 1
Mentioned in:
Corollaries: 1
Proofs: 2 3 4 5
Propositions: 6 7
Solutions: 8
Thank you to the contributors under CC BYSA 4.0!
 Github:

 nonGithub:
 @Fitzpatrick
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
Footnotes