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 74
of this kind a triangle will have beenconstructed whose defect is greater than 2 a. But for n sufficiently great, this defect, 2 a, must begreater than 2 right angles [Postulate of Archimedes], whichis absurd. It follows that (X = o, and ■^A-^^B-^^C=2right angles. This demonstration is founded upon… … Fig. 31- Draw the straight line AB symmetrical to AB with re-gard to AH. Through the point H there passes, in virtue ofLegendres hypothesis, a line r which cuts the two arms ofthe angle BAB. If this line is different from HK^ then alsothe line /, symmetrical to it with respect to AH, enjoys thesame…
Geometry, Non-Euclidean
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