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 30
the mating or separating 27. A three-sided solid angle equals the half sum of the surface anglesless a right-angle. In the spherical triangle ABC (Fig. 15), where each side < jr, desig.nate the angles by A, B, C; prolong the side AB so that a whole circleABABA is produced; this divides the… … In this way the hemisphere is divided into four triangles, ABC, AOB,BCA, ACB, whose size may he designated hy P, X, Y, Z. It is evi.dent that here P + X = B, P + Z = A. The size of the spherical triangle Y equals that of the opposite triangleABC, having a side AB in common with the triangle P, and…
Geometry, Non-Euclidean
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