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 38
llel lines have therefore the character ofasymptotes. 34. Boundary surface (orisphere) we call that surface which arisesfrom the revolution of the boundary line about one of its axes, which,together with all other axes of the boundary-line, will be also an axisof the boundary-surface. A chord is… … Fig. 27.AA, the axis of revolution, BB and CC two other axes, hence ABand AC chords to which the axes are inclined at equal angles AAB= BBA, AAO =CCA (Theorem 31.) 34 THEORY OF PARALLELS. Two axes BB, CC, drawn through the end-points of the third chordBC, are likewise parallel and lie in one plane,…
Geometry, Non-Euclidean
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