Page:First six books of the elements of Euclid 1847 Byrne.djvu/74

40 QUAL triangles and  on the same base  and on the same side of it, are between the same parallels.



If, which joins the vertices of the triangles, be not || , draw ||  meeting.

Draw. Because  ||  (const.) =  (pr. 37.):

but =  (hyp.);

∴ =, a part equal to the whole, which is absurd.

∴ $$\nparallel$$ ; and in the same manner it can be demonstrated, that no other line except  is || ; ∴  ||.

Q. E. D.