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 86
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… … Fig. 37- Case (ii). In this case let Z> be any arbitrary point uponAM. Then with the same argument as above,■^ EBB = <^ GBH, But ^ ABD < < ^^C. Therefore <^ ^^Z> < ^ iV^^iV. Therefore <^ GBH<.^NBN. Therefore BN must cut AM. But ^iV is any line through B, between BA and…
Geometry, Non-Euclidean
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