Page:First six books of the elements of Euclid 1847 Byrne.djvu/42

8 F two triangles have two sides of the one respectively equal to two sides of the other ( =  and  = ), and also their bases ( = ), equal; then the angles ( and ) contained by their equal sides are also equal.

If the equal bases and  be conceived to be placed one upon the other, so that the triangles shall lie at the same side of them, and that the equal sides  and,  and  be conterminous, the vertex of the one must fall on the vertex of the other; for to suppose them not coincident would contradict the last proposition.

Therefore the sides and, being coincident with  and ,

∴ =.

Q.E.D.