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A Property of the Harmonic Triangle of the Complete Quadrangle formed by the four points of contact of the four tangents to the Cubic Curve from a point on it

Published online by Cambridge University Press:  20 January 2009

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The following two propositions are necessary for what is to follow, and are very easy to prove.

I. If A, B, C be three points such that B and C are conjugate with respect to the Polar Conic of A, then are C and A conjugate points with respect to the Polar Conic of B, and similarly with regard to the third vertex.

A triangle possessing the property defined above, viz. that each pair of vertices are conjugate points with respect to the Polar Conic of the third vertex, is called an Apolar Triangle.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1910