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 274
nt. 259 Lines 7mt/i regard to the circle which ^ciacides with thisIdeal Line. It is unnecessary to define Ideal Displacements., as anydisplacement can be obtained by a series of reflections andany Ideal Displacement by a series of Ideal Reflections. We notice that the definition of the Ideal Length… … Fig. 97- Then we must have /0V\ PV\ l°g \ou\pu) i. e. 1 PU log py = I. Therefore PU PF ~ ^ and the point P divides the diameter in the ratio e: 1. The Unit Segment is thus fixed for any position in the 17= 200 Appendix V. Impossibility of proving Euclids Postulate. domain of the Ideal Points, since…
Geometry, Non-Euclidean
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