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Conjugate Diameters in Areals

Published online by Cambridge University Press:  03 November 2016

N. M. Gibbins
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Extract

Principles. 1. If K be the centre of a conic and P a point not on it, the diameter conjugate to KP is parallel to the polar of P.

2. Conjugate diameters form a pencil in involution. Hence if S=0 and S' =0 be the equations of two known pairs of conjugate diameters, the general equation is S + λS' =0.

The method then is to find the diameters conjugate to KA, KB, KC, where ABC is the triangle of reference, by means of 1, and then to write down the general equation by means of 2.

Type
Research Article
Information
The Mathematical Gazette , Volume 11 , Issue 162 , January 1923 , pp. 226 - 229
Copyright
Copyright © Mathematical Association 1923

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