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The Double Six of Lines and a Theorem in Euclidean Plane Geometry

Published online by Cambridge University Press:  18 May 2009

John Dougall
John Dougall
Affiliation:
Glasgow
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The object of the present paper is to establish the equivalence of the well-known theorem of the double-six of lines in projective space of three dimensions and a certain theorem in Euclidean plane geometry. The latter theorem is of considerable interest in itself for two reasons. In the first place, it is a natural extension of Euler's classical theorem connecting the radii of the circumscribed and the inscribed (or the escribed) circles of a triangle with the distance between their centres. Secondly, it gives in a geometrical form the invariant relation between the circle circumscribed to a triangle and a conic inscribed in the triangle. For a statement of the theorem, see § 13 (4).

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 1 , Issue 1 , January 1952 , pp. 1 - 7
Copyright
Copyright © Glasgow Mathematical Journal Trust 1952

References

* Salmon, , Analytic Geometry of Three Dimensions, Vol. II (5th edition) §§ 534, 536aGoogle Scholar. Baker, H. F., Principles of Geometry, Vol. III, p. 159Google Scholar; Vol. IV, pp. 58–64.

* Salmon, Conic Sections, Chapter on Invariants and Covariants of Systems of Conies.