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 273
t 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. Impossibility of proving Euclids Postulate. inverts into a circle also orthogonal… … Fig. 96. points ti and v on the fundamental circle; and the lines ABand ab are equally inclined to the circle of inversion. It is easy to show that the Ideal Lengths of AM andBM are equal to those of aM a.nd ^J/respectively, and itfollows that the Ideal Length of the segment AB is unalteredby this…
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-215-131.webp)
