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Theorems concerning Spheres
Author(s) -
Roberts Samuel
Publication year - 1893
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/s1-25.1.306
Subject(s) - citation , mathematics , computer science , combinatorics , mathematical economics , library science
1. I must first of all mention some results relative to plane space, which are suggestively analogous to those referred to in the heading of this paper. The following theorem was the subject of a question by Professor Mannheim (Educational Times, Quest. 10145, Reprint, Vol. LIL, p. 48), and has been discussed at considerable length by the late M. Eugene Catalan (Memorie delta Pontificia Accademia dei Nuevo Lincei, Vol. vi., pp. 223-233, 1890). Let A, B, G be the vertices of a given triangle (Fig. 1). Through A let a circle be drawn meeting the side AB a second time in a