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 260
IdealLine. Let the Ideal Segment AB invert into the Ideal SegmentAB. These two Ideal Lines intersect at the point D, wherethe circle of inversion^meets AB.Then the Ideal Length of AD AD 1 AD the Ideal Length of^^ ~ OA. ODj OA. OD__ AD OA~ ad OA But from the triangles CAD, CAD and OAC, OAC,we find… … Fig. 87. § 6. Ideal Displacements. The length of a segment must be unaltered by dis-placement. This leads us to consider the definition of IdealDisplacement. Any displacement may be produced by re-peated applications of reflection; that is, by taking the imageof the figure in a line (or in a plane,…
Geometry, Non-Euclidean
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