To draw a straight-line parallel to a given straight-line, through a given point.  Let $A$ be the given point, and $BC$ the given straight-line. So it is required to draw a straight-line parallel to the straight-line $BC$, through the point $A$.  Let the point $D$ have been taken a random  on $BC$, and let $AD$ have been joined. And let (angle) $DAE$, equal to angle $ADC$,  have been constructed  on the straight-line $DA$ at the point $A$ on it [Prop.~1.23]. And let the straight-line $AF$ have been produced in a straight-line with $EA$.   And since the straight-line $AD$, (in) falling across the two straight-lines $BC$ and $EF$,  has made the alternate angles $EAD$ and $ADC$ equal to one another, $EAF$ is thus parallel to $BC$ [Prop.~1.27].  Thus, the straight-line $EAF$ has been drawn parallel to the given straight-line $BC$, through the  given point $A$. (Which is) the very thing it was required to do.