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Isogonal Conjugates: A new approach to certain Geometrical Theorems and to a General Theory of Conics

Published online by Cambridge University Press:  03 November 2016

H. E. Piggott  and
A. Steiner
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Extract

ABC is a triangle; BX, CX′ are equal arcs of the circumcircle taken in opposite senses from B and C. AX, AX′ are then said to be isogonally conjugate with respect to AB and AC. (The usual textbook definition is to say that the angles BAX, CAX′ are equal. The definition by equal arcs is used throughout this paper both because it has practical advantages and because it leads easily to theoretical development.)

Type
Research Article
Information
The Mathematical Gazette , Volume 31 , Issue 295 , July 1947 , pp. 130 - 144
Copyright
Copyright © Mathematical Association 1947

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References

page note 134 * Steiner’ ellipse for our purposes is defined by the areal equation yz+zx+xy=0. But we may remind readers that it is the ellipse which passes through the vertices. A, B, C of a triangle such that the tangent to it A is parallel to BC. Obviously its centre is the point G.