Page:First six books of the elements of Euclid 1847 Byrne.djvu/61

Rh but =  (hyp.)

and therefore =  which is absurd; hence neither of the sides and  is greater than the other; and ∴ they are equal;

∴ =, and  = , (pr. 4.).

CASE II.

Again, let =  which lie opposite the equal angles and. If it be possible, let >, then take = , draw. Then in and  we have  = ,

= and  = ,

∴ =  (pr. 4.)

but =  (hyp.) ∴ =  which is absurd (pr. 16.).

Consequently, neither of the sides or  is greater than the other, hence they must be equal. It follows (by pr. 4.) that the triangles are equal in all respects. Q. E. D.