Proposition: 6.13: Construction of Mean Proportional
(Proposition 13 from Book 6 of Euclid's “Elements”)
To find the (straight line) in mean proportion3 to two given straight lines.
![fig13e](https://github.com/bookofproofs/bookofproofs.github.io/blob/main/_sources/_assets/images/euclid/Book06/fig13e.png?raw=true)
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
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References
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
Footnotes