BOOK I. PROP. XXVIII. THEOR.
29
F a straight line (
) cutting two other straight lines (
and 
), makes the external equal to the internal and opposite angle, at the same side of the cutting line (namely, 
= 
or 
= 
), or if it makes the two internal angles at the same side ( and 
, or and 
) together equal to two right angles, those two straight lines are parallel.
First, if = , then = (pr. 15.),
∴ = ∴ || (pr. 27.).
Secondly, if + = 
,
then + = , (pr. 13.),
∴ + = + (ax. 3.)
∴ =
∴ || (pr. 27.)
Q. E. D.
