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 25
which I in-tend here to expound as far as the development of the equations be-tween the sides and angles of the rectilineal and spherical triangle. 23. For every given angle a there is a line p such that ]J (p) = «.Let AB and AC (Fig. 10) be two straight lines which at the inter. section point A… … Fig. 10. pendicular CD is attained, which no longer intersects AB. This mustof necessity happen, for if in the triangle AAB the sum of all threeangles is equal to jr — a, then in the triangle AB A it equals jt — 2a,in triangle AAB less than jc — 2a (Theorem 20), and so forth, until it finally…
Geometry, Non-Euclidean
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