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 21
raw also from A the line AF, whose productionwill cut CD in G (Theorem 16.) Thus we get a triangle AGC, into which goes the production of theline EF; since now this line can not cut AC a second time, and alsocan not cut AG, since the angle BAG = BEC, (Theorem 7), thereforemust it meet CD somewhere… … 18. Two lines are always mutually parallel. Let AC be a perpendicular on CD, to which AB is parallelif we draw from C the lineCE making any acute angleECD with CD, and let fallfrom A the perpendicular AFupon CE, we obtain a right-angled triangle ACF, in whichAC, being the hypothenuse,is greater…
Geometry, Non-Euclidean
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