Non-Euclidean geometry; a critical and historical study of its development (1912)
Bonola, Roberto, 1874-1911, Carslaw, H. S. (Horatio Scott), 1870-1954 · LaSalle, Ill. : Open Court Publishing Co. · leaf 85
hird side RB, and thereforeAM is parallel to BN. II. The Reciprocity of the Parallelism can also be estab-lished. In other words, if AM is parallel to BN, then BN isalso parallel to AM. Gauss proves this result as follows: From any point B upon BN draw BA perpendicular toAM. Through B draw any line… … Fig. 36. Case (i). Let BC cut AM in D. Take AE = AD, andjoin BE. Make ^BDF^^BED. Since AM is parallel to BN^ DF must cut BM^ forexample, in G. From EM cut off EH equal to DG. Then, in the triangles BEH s^nà BDG, it follows that Gausss Theory of Parallels (contd.). 71 JM. Therefore «^ EBD = ^HBG.But…
Geometry, Non-Euclidean
Internet Archive · California Digital Library · Public Domain Mark 1.0. Free to use for anything.
