To describe a square on a given straight-line. Let $AB$ be the given straight-line.So it is required to describe a square on the straight-line $AB$. <prf> Thus, $ADEB$ is right-angled. And it was also shown (to be) equilateral.Thus, ($ADEB$) is a square [Def.~1.22]. And it is described on the straight-line $AB$.