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 36
CQ are, however, the angles at A and Q equal,hence in the triangle ABQ must the angle at Q be greater than that atthe point A, consequently is AB>BQ, (Theorem 9); that is c>c. 31. We call houndary line {pricycle) that curve lying in a plane forwhich all perpendiculars erected at the… … rFig. 24. point A in it, making different angles CAB= /7(a), chords AC = 2a; the end C of such a chord will lie on the boundary line, whose points we can thus gradually determine. The perpendicular DE erected upon the chord AC at its mid-point Dwill be parallel to the line AB, which we will call…
Geometry, Non-Euclidean
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