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Published online by Cambridge University Press: 31 October 2008
§1. The following investigation arose out of a reconsideration of a certain invariant of six points in space
I = (1234)(3456)(5612) – (2345)(4561)(6123)
where (1234) denotes the determinant whose rows are the coordinates of the first four points: and similarly for the other factors. The vanishing of this invariant implies that the sixth point lies upon a certain quadric defined by the other five. The following elementary account brings out several interesting and possibly new theorems upon quadric surfaces.
1 Cf. Journal of the London Math. Soc., 29 (1927), 233–240 (238).Google Scholar Also Blaschke (Math. Zeitschrift, 29 (1920), 83–93).Google Scholar
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