Proof: (Euclid)

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.
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