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 259
ength of anIdeal Segment we may take the radius of inversion—k—tobe unity. Consider the segment AB and the rectihnear segmentaP to which it corresponds. Then we have (Fig. 86)^P _ Op _ op. OB _ _^2AB ~ OA ^ OA. OB ~ ÒA~.0B I See Note on p. 236. 16* 244 Appendix V. Impossibility of proving Euclids… … Fig. So. Let OD be any circle of the system and let C be itscentre (Fig. 87). Then inversion changes an Ideal Line into an IdealLine. Let the Ideal Segment AB invert into the Ideal SegmentAB. These two Ideal Lines intersect at the point D, wherethe circle of inversion^meets AB.Then the Ideal Length…
Geometry, Non-Euclidean
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