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Some Theorems on Conics

Published online by Cambridge University Press:  03 November 2016

E. D. Camier
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Extract

Some of the properties proved in this essay can hardly have escaped notice, but judging from the lack of reference, they seem to have been forgotten; others are given for the sake of completeness, and a few are probably new. It is hoped that in any case all are of sufficient novelty to be of interest.

The locus of the point from which the tangents to two conics form a harmonic pencil is in general a conic which passes through the eight points of contact of their four common tangents; it is called the harmonic locus of the conics, and it plays an important role in projective geometry.

Type
Research Article
Information
The Mathematical Gazette , Volume 38 , Issue 323 , February 1954 , pp. 18 - 25
Copyright
Copyright © The Mathematical Association 1954

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References

1. Sommerville, Analytical conics, (3rd ed.) p. 283.Google Scholar
2. Loney, Coordinate Geometry, II, p. 83.Google Scholar
3. Loney, . Cf. Ex. 20, p. 103.Google Scholar
4. Casey, , Analytical geometry (1893), p. 72.Google Scholar
5. Casey, , p. 283, Ex. 44.Google Scholar
6. Casey, p. 339, Ex. 6, or Salmon, , Conics, (6th ed., 1879), p. 267, Ex. 2.Google Scholar