The assumption that the sum of the three angles of a triangle is less than 180° leads to a curious geometry, quite different from ours [i.e. Euclidean geometry] but thoroughly consistent, which I have developed to my entire satisfaction, so that I can solve every problem in it excepting the determination of a constant, which cannot be fixed a priori. .... the three angles of a triangle become as small as one wishes, if only the sides are taken large enough, yet the area of the triangle can never exceed, or even attain a certain limit, regardless of how great the sides are.