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. $$\frac{|\overline{A}|}{|\overline{B}|}=\frac{|\overline{C}|}{|\overline{D}|}.$$

Proofs: 1

Proofs: 1 2 3 4 5 6 7 8 9
Propositions: 10 11

Thank you to the contributors under CC BY-SA 4.0!



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",, 2016