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 20
distinguish the remaining lines into non-intersect-ing and intersecting. For both assumptions it serves as the mark of parallelism that theline becomes intersecting for the smallest deviation toward the sidewhere lies the parallel, so that if AH is parallel to DC, every line AFcuts DC, how small… … ular. We will consider two points taken at random on the line AB andits production beyond the perpendicular. Let the point E lie on that side of the perpendicular on which AB islooked upon as parallel to CD. Let fall from the point E a perpendicular EK on CD and so draw EFthat it falls within the…
Geometry, Non-Euclidean
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