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The Eccentric Circle of Boscovich

Published online by Cambridge University Press:  15 September 2017

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 later 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 1 , Issue 1 , April 1894 , pp. 1 - 3
Copyright
Copyright © Mathematical Association 1894

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References

page 1 note 1 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 Universœ Matheseos, tom. iii.) are always to the Venice edition, 1757.

page 2 note 1 This expression ut nusquam jam sit (or sint) is of very frequent occurrence in Boscovich.