To find the (straight line) in mean proportion3 to two given straight lines. * Let $AB$ and $BC$ be the two given straight lines. * So it is required to find the (straight line) in mean proportion3 to $AB$ and $BC$.
It is possible to construct a segment with a length being the geometric mean3 of the lengths of two given other segments.
Proofs: 1
Corollaries: 1
Proofs: 2 3 4 5
Propositions: 6 7
Solutions: 8
In other words, to find the geometric mean of two given straight lines (translator's note). ↩