The square on a first bimedial (straight line) applied to a rational (straight line) produces as breadth a second binomial (straight line).1 * Let $AB$ be a first bimedial (straight line) having been divided into its (component) medial (straight lines) at $C$, of which $AC$ (is) the greater. * And let the rational (straight line) $DE$ be laid down. * And let the parallelogram $DF$, equal to the (square) on $AB$, have been applied to $DE$, producing $DG$ as breadth. * I say that $DG$ is a second binomial (straight line).
(not yet contributed)
In other words, the square of a first bimedial is a second binomial. See [Prop. 10.55] (translator's note) ↩