 Of course, from our point of view, the important thing about this demonstration is not so much the truth of its conclusion as the way it proves this conclusion. For the conclusion is a universal theorem, which has to concern all possible triangles inscribed in any possible semicircle whatsoever, not just the one inscribed in the semicircle in the figure above. Yet, apparently, in the demonstration above we were talking only about that triangle. So, how can we claim that whatever we managed to prove concerning that particular triangle will hold for all possible triangles?