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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.

• Let $A$, $B$, and $C$ be the three given straight lines.
• So it is required to find a fourth (straight line) proportional to $A$, $B$, and $C$.

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)

1. Fitzpatrick, Richard: Euclid's "Elements of Geometry"

Adapted from CC BY-SA 3.0 Sources:

1. Prime.mover and others: "Pr∞fWiki", https://proofwiki.org/wiki/Main_Page, 2016