Page:First six books of the elements of Euclid 1847 Byrne.djvu/40

6 N any triangle if two angles ( and  ) are equal, the sides ( and ) opposite to them are also equal.

For if the sides be not equal, let one of them be greater than the other, and from it cut off  =  (pr. 3.), draw.

Then in and,  = , (conft.)  =  (hyp.) and  common, ∴ the triangles are equal (pr. 4.) a part equal to the whole, which is absurd; ∴ neither of the sides  or  is greater than the other, ∴ hence they are equal

Q.E.D.