The square on a binomial (straight line) applied to a rational (straight line) produces as breadth a first binomial (straight line).^{1} * Let $AB$ be a binomial (straight line), having been divided into its (component) terms at $C$, such that $AC$ is the greater term. * And let the rational (straight line) $DE$ be laid down. * And let the (rectangle) $DEFG$, equal to the (square) on $AB$, have been applied to $DE$, producing $DG$ as breadth. * I say that $DG$ is a first binomial (straight line).
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Proofs: 1
In other words, the square of a binomial is a first binomial. See [Prop. 10.54] (translator's note) ↩