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 256
Line through A perpendicular tothe Ideal Line BC; and the circle which passes through A,and touches the circle OBC at O, separates the circlesthrough A, which cut BC on the one side of 31, from thosewhich cut it on the other. Ideal Parallels. 241 We are thus led to define Parallel Ideal Lines as… … Thus any two circles of the system which touch eachother at O will be Ideal Parallel Lines. Two Ideal Lines,which are each parallel to a third Ideal Line, are parallel toeach other, etc. § 5. Ideal Leiigths. Since Euclids Parallel Postulate is equivalent to theassumption that one, and only one,…
Geometry, Non-Euclidean
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