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 272
rcle ofinversion [cf. Fig. 95]. Then we have: BV _ CVAU~CA> AV CV ^^^ BU ~ CB Thus AV BV CV2 CV2 AU BU CA.CB CM2 Therefore AV I MV MV I BV /MV\ 2 AU MU MU\ BU Ideal Reflection. 257 Hence the Ideal Length of AM is equal to the IdealLength of MB. Thus we have the following result: Inversion with… … Fig. 95 In other words, inversion with regard to such a circlecauses any Ideal Point A to take the position of its image inthe corresponding Ideal Line. We proceed to examine what effect such inversion hasupon an Ideal Line. Since a circle^ orthogonal to the fundamental circle, 17 2 e 8 Appendix V.…
Geometry, Non-Euclidean
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![An illustration from Nicolai Copernici Torinensis De reuolutionibus orbium coelestium, libri VI : Habes in hoc opere iam recens nato, & aedito, studiose lector, motus stellarum, tam fixarum, quàm erraticarum, cum ex ueteribus, tum etiam ex recentibus obseruationibus restitutos: & nouis insuper ac admirabilibus hypothesibus ornatos. Habes etiam tabulas expeditissimas, ex quibus eosdem ad quoduis tempus quàm facillime caculare poteris. Igitur eme, lege, fruere. [Line in Greek] (1543)](https://img.insideoutlibrary.com/img/200/ia-nicolaicopernici00cope-348-238.webp)
