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The Eccentric Circle of Boscovich

Published online by Cambridge University Press:  03 November 2016

E. M. Langley
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Extract

The object of the following paper is to draw attention to a general and powerful but quite elementary method of transformation, by means of which the properties of a conic may be inferred from those of a circle. It has many striking analogies with the method of perspective transformation, and a simple geometrical connection with it. It is, however, of much simpler character for constructive purposes, and though it is intended to show latcr on how well the method is adapted to serve as an introduction to modern methods, it is hoped that readers will begin by dismissing from their minds all notions of cross ratios, homographic ranges, etc., and regard the theorems presented to them from the point of view of a student who has mastered his Elements of Plane Geometry.

Type
Research Article
Information
The Mathematical Gazette , Volume 32 , Issue 300 , July 1948 , pp. 99 - 109
Copyright
Copyright © The Mathematical Association 1948

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References

page 99 note * According to Dr. Taylor, Boscovich was the first to write a really complete elementary treatise on conic sections based on the eccentricity or “ determining ratio ” See Ancient and Modern Geometry of Conics, p. lxxii, where the work of Boscovich is commended as “ a clear and compact treatise, which for simplicity, depth and suggestiveness, will not readily be surpassed ” The references to Boscovich’s own treatise (Elementorum Universae Matheseos, tom, iii) are always to the Venice edition, 1757.

page 102 note * This expression ut nusquam jam sit (or sint) is of very frequent occurrence in Boscovich.

page 106 note * In a paper on The Discovery and the Geometrical Treatment of the Conic Sections, read before the A.I.G.T. in 1884 and published in the Tenth General Report, Dr. Taylor strongly advocated the use of Boscovich’s eccentric circle, and remarked on it as “ one of the simplest introductions to homographic transformation in general ”.

page 107 note * See Dr. Taylor’s Ancient and Modern Geometry of Conics.