Page:First six books of the elements of Euclid 1847 Byrne.djvu/62

28 F a straight line meeting two other straight lines, ( and ) makes with them the alternate angles ( and ;  and ) equal, these two straight lines are parallel.

If be not parallel to  they shall meet when produced. If it be possible, let those lines be not parallel, but meet when produced; then the external angle is greater than  (pr. 16), but they are also equal (hyp.), which is absurd: in the same manner it may be shown that they cannot meet on the other side; ∴ they are parallel. Q. E. D.