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Euler's parallel oblique-angled diameters

Published online by Cambridge University Press:  23 January 2015

Thomas J. Osler
Thomas J. Osler*
Affiliation:
Mathematics Department, Rowan University, Glassboro NJ 08028, USA, e-mail:osler@rowan.edu
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Extract

In the paper [1], Euler was examining properties of the conic sections that could be shared by more general curves. Most of the paper is concerned with ‘oblique-angle diameters’, a concept that seems to have been familiar to his readers in the eighteenth century, but has been ignored today. In this paper we will explain this concept and, led by Euler, develop some of its consequences.

Type
Articles
Information
The Mathematical Gazette , Volume 95 , Issue 532 , March 2011 , pp. 40 - 48
Copyright
Copyright © The Mathematical Association 2011

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References

1. Euler, L., Sur quelques proprietés des Sections coniques, qui conviennent à un infinité d'autres lignes courbes (On some properties shared between conic sections and infinitely many other curves), originally published in Memoires de l'academie des sciences de Berlin 1 (1746) pp. 71–98. Available in Opera Omnia: Series 1, 27, Birkhauser (1989) pp. 51-73. Also available on the web site The Euler Archive, http://www.math.dartmouth.edu/~euler/.(An annotated translation in English along extensive explanatory notes and a synopsis by Edward Greve and Thomas J. Osler is also available on the web at the Euler Archive.)Google Scholar
2. Osler, Thomas J. and Greve, Edward. Oblique-angled diameters and the conic sections, The Mathematical Spectrum, 40 (2007/2008), pp. 26–30.Google Scholar