Page:First six books of the elements of Euclid 1847 Byrne.djvu/63

Rh 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.