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Published online by Cambridge University Press: 24 October 2008
The theorem is attributed to Wallace that, in a euclidean plane, the circumcircles of the triangles determined by four lines, of general position, meet at a point. It is further known that, in euclidean space of n dimensions, the circumhyperspheres of the simplices determined by n + 2 flats, of general position, meet at a point, if and only if n be even.
* ‘Scoticus’, Leybourn's Math. Repos., N.S., 1 (1806), 170;Google Scholarsee Mackay, , Proc. Edin. Math. Soc. 9 (1891), 87.Google Scholar
† Grace, , Trans. Camb. Phil. Soc., 16 (1898), 153–190 (163);Google ScholarKühne, , Crelle, 119 (1898), 186–195Google Scholar (corrected by Baker, H. F., Proc. Camb. Phil. Soc., 22 (1924), 28–33);CrossRefGoogle ScholarHaskell, , Arch. d. Math. u. Phys. (3), 5 (1903), 278–281.Google Scholar
‡ For two dimensions, Miquel, , Liouville, 3 (1838), 485–487;Google Scholar for three dimensions, Roberts, S., Proc. Lond. Math. Soc., 12 (1881), 102, 117–120Google Scholar, ibid. 25 (1894), 306–314; for four dimensions, Grace, , loc. cit., (168);Google Scholar for n dimensions, Haskell, , oc. cit.Google Scholar, Meyer, W. F., Arch. d. Math. u. Phys. (3), 5 (1903), 282–287.Google Scholar
§ See e.g. Scott, and Mathewes, , Theory of Determinants, ed. 2, Cambridge (1904), 92–96.Google Scholar