Geometrical researches on the theory of parallels (1914)
Lobachevskiĭ, N. I. (Nikolaĭ Ivanovich), 1792-1856, Halsted, George Bruce, 1853-1922, Lobachevskiĭ, N. I. (Nikolaĭ Ivanovich), 1792-1856. Geometrische Untersuchungen zur Theorie der Parallellinien English · Chicago [etc.] Open Court Publishing Company · leaf 32
triangle equals the sum of the two equal anglesin the quadrilateral which are not the right angles. Therefore we can, for every spherical triangle, in which the sum ofthe three angles is S, find a quadrilateral with equivalent surface, inwhich are two right angles and two equal perpendicular sides,… … *» Prolong the sides AD and BC until they cut one another in E, andfurther beyond B, make DB = BF and let fall upon the prolongationof BC the perpendicular FG. Bisect the whole arc BG and join themid-point H by great-circle-arcs with A and F. The triangles EFG and DCB are congruent (Theorem 15), so…
Geometry, Non-Euclidean
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