Page:First six books of the elements of Euclid 1847 Byrne.djvu/48

14 F two straight lines ( and ) meeting a third straight line, at the same point, and at opposite sides of it, make with it adjacent angles ( and ) equal to two right angles; these straight lines lie in one continuous straight line.

For, if possible let, and not , be the continuation of ,

then +  =

but by the hypothesis +  =

∴ =, (ax. 3.); which is absurd (ax. 9.).

∴, is not the continuation of , and the like may be demonstrated of any other straight line except , ∴ is the continuation of.

Q.E.D.