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 277
the inverse of the point M.Also the circle A U becomes the circle au^ touching theradius mu at ?/, and cutting via at an angle TT(/). Theseradii, mu, nib, are also Ideal Lines of the system. The Ideal Length of the Segment AM is taken as p. Then (AB \MB\ ^=^^^^ [ax lire) . /ab I vib \ But ac = k —… … Fig. 99. Finally, in this geometry there will be three kinds ofcircles. There will be the circle^ with its centre at a finitedistance; the Limiting Curve or Horocycle, with its centre atinfinity, (at a point where two parallels meet) ; and the Equi-distant Curve, with its centre at the imaginary…
Geometry, Non-Euclidean
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