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 119
lations are obtained from (i), theproportionality of the sines of the angles and the opposite sidesin a spherical triangle. From this it follows that SphericalTrigonometry is independent of the Euclidean Postulate{Appendix 8 26]. This fact makes the importance of Bolyais Theoremstill clearer. § 50.… … Fig. 49. Also the perpendicular DE to the line AE. The angleEDB of the quadrilateral ABDE, in which three angles Bolyais Parallel Construction. IO5 are right angles, is a right angle or an acute angle, accordingas ED is equal to or greater than AB. With centre A describe a circle whose radius is…
Geometry, Non-Euclidean
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