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 45
ypothenuse AB. Here the perpendicu-lar DD erected upon AD, and the line AA parallel to it from A, will J* likewise be parallel to the side BC=a,with its prolongation CC. Here we have the angle DAA = II(/9—c), consequently/7(a)+/7(b) =,i—/7(p-c)=J7(o-ft(Theorem 23). The combination of the two… … Fig. 34. =cos/7(c), cos /7(a)we have [tan£/7(c)]2=tan£/7(c—/?) tan£/7(c+/3). Since here 0 is an arbitrary number, as the angle II(ft) at the one THEORY OF PARALLELS. 41 side of c may be chosen at will between the limits 0 and \n, conse-quently ft between the limits 0 and oo , so we may deduce by…
Geometry, Non-Euclidean
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