Extension of the Theory of Inversion to Conics

descriptionPublicationkeyboard_double_arrow_right Article 01 Jul 1919 English Publisher:Informa UK LimitedJournal:The Mathematical Gazette, volume 9, pages 365-368 (issn: 0025-5572, eissn: 2056-6328,

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Authors: Milne, J. J.;

doi: 10.2307/3604481

Extension of the Theory of Inversion to Conics

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Abstract

Let t be the centre of a circle, radius r, p any point in its plane, and draw the diameter through p . Then the inverse of p is a point p′ on tp such that tp . tp′ = r2 . This circle is called the circle of inversion, its centre t the pole of inversion and the square of its radius the constant of inversion, and each of the points p , p′ is the inverse of the other. This relation is a metric one: a descriptive relation can be obtained as follows.

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