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 27
22 THEORY OF PARALLELS. 25. Two straight lines which are parallel to a third are also parallel toeach other. … Fig. 12. We will first assume that the three lines AB, CD, EF (Fig. 12) lie inone plane. If two of them in order, AB and CD, are parallel to theoutmost one, BF, so are AB and CD parallel to each other. In orderto prove this, let fall from any point A of the outer line AB upon theother outer line…
Geometry, Non-Euclidean
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