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An extension of de Longchamps' chain of theorems

Published online by Cambridge University Press:  20 January 2009

H. W. Richmond
H. W. Richmond
Affiliation:
King's College, Cambridge.
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1. Points, n in number, A, B, C, D, E, … ., are taken at random in a plane, and through each is drawn a line in a random direction. The only condition imposed is that no two of these lines may be parallel.

(i). Two points A, B, define a circle S (AB) which passes through A, B and the intersection of the random lines through A and B. Its centre is denoted by (AB). Each pair of the points gives such a circle and centre.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 6 , Issue 2 , October 1939 , pp. 78 - 84
Copyright
Copyright © Edinburgh Mathematical Society 1939

References

page 79 note 1 De Longchamps, , Noaville correspondence mathématique, 3 (1877), 306 and 340. Published in Brussels; the periodical is now continued under the title Mathexis.Google Scholar

page 79 note 2 Pesci, , Periodico di Mathematica, 5 (1891), 120.Google Scholar

page 79 note 3 Morley, , Trans. American Math. Soc., 1 (1900), 97.Google Scholar

page 79 note 4 White, F. P., Proc. Camb. Phil. Soc., 22 (1925), 684.CrossRefGoogle Scholar

page 79 note 5 Lob, H., Proc. Camb. Phil. Soc., 29 (1933), 45.CrossRefGoogle Scholar

page 79 note 6 Grace, J. H., Proc Camb. Phil. Soc., 24 (1928), 10;CrossRefGoogle Scholar also Proc. London Math. Soc. (2), 33 (1908), 193.Google Scholar

page 79 note 7 Richmond, H. W., Proc Camb. Phil. Soc., 29 (1933), 165.CrossRefGoogle Scholar See also the obituarynotice of Frank, Morley and the note which follows it in Journal London Math. Soc., 14 (1939), 73 and 78.Google Scholar

page 79 note 8 Coolidge, J. L., A treatise on the circle and the sphere (Oxford, 1916), 92. The dategiven for de Longchamps' discovery is wrongly stated as 1887.Google Scholar

page 83 note 1 Miquel, , Liouville's Journal, 10 (1845), 349.Google Scholar See also Clifford, , Messenger of Math.,5 (1870), 124; or Collected Papers, 38.Google Scholar