Proposition: 6.12: Construction of Fourth Proportional Straight Line
(Proposition 12 from Book 6 of Euclid's “Elements”)
To find a fourth (straight line) proportional to three given straight lines.
Modern Formulation
Given two segments $\overline{A}$, $\overline{B}$ with the ratio of lengths $$\frac{\overline{A}}{\overline{B}},$$ and a third segment $\overline{C}$ it is possible to construct a segment $\overline{D}$ with the proportion.
$$\frac{\overline{A}}{\overline{B}}=\frac{\overline{C}}{\overline{D}}.$$
Table of Contents
Proofs: 1
Mentioned in:
Proofs: 1 2 3 4 5 6 7 8 9
Propositions: 10 11
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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