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 $C$.
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