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BOOK I. PROP. XXVII. THEOR.
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.
