Construction: Parallel, Using Perpendiculars

Euclid's Elements tells us that there is a unique line parallel/perpendicular to another through a point (in the plane). If we start with an original line $\ell$ and a point $P$, draw a line $\ell'$ perpendicular to $\ell$ through $P$, then draw a line $\ell''$ perpendicular to $\ell'$ through $P$. $\ell''$ must then be parallel to $\ell$, as the two are both perpendicular to the same line ($\ell'$).