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 270
take the points A\ B, as definingthe segment AB, instead of the points A\ B. It must makethe complete line infinite in length. It must satisfy the distri-butive law distance AB = distance AC -\- distance CB, Ideal Lengths. 255 if C is any other point on the segment AB^ and it mustalso remain… … Fig. 94. This expression obviously involves the AnharmonicRatio of the points UABV. It will be seen that this de-finition satisfies the first three of the conditions named above.It remains for us to examine what must represent dis-placement in this Ideal Geometry. Let us consider what is the effect…
Geometry, Non-Euclidean
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