Through a given point to draw a straight line parallel to a given straight line
Let A be the given point, and BC the given straight line;
thus it is required to draw through the point A a straight line parallel to
the straight line BC.
Let a point D be taken at random on BC, and let AD be joined;
on the straight line DA, and at the point A on it, let the angle DAE be
constructed, equal to the angle ADC;
and let the straight line AF be produced in a straight line with EA
Then, since the straight line AD falling on the two straight lines BC, EF
has make the alternate angles EAD, ADC equal to one another,
therefore EAF is parallel to BC.
Therefore through the given point A the straight line EAF has been drawn
parallel to the given straight line BC.
Q.E.F