Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-05T21:41:37.150Z Has data issue: false hasContentIssue false

Note on the Treatment of Conic Sections and Conicoids By Pure Geometry

Published online by Cambridge University Press:  03 November 2016

C. A. Rumsey*
Affiliation:
Dulwich College

Extract

The object of the following note is to derive Pascal’s theorem and the Anharmonic and Harmonic properties of Conic Sections directly from the focus and directrix definition by the early introduction of an extended form of Carnot’s theorem, viz. “the product of the ratios in which the sides of a closed polygon, taken in order, are cut by a conic = +1.” When the above have been demonstrated the simpler properties are known to be easily deducible. Subsequently the treatment of Conicoids by Pure Geometry is introduced by means of the same theorem.

Type
Research Article
Copyright
Copyright © Mathematical Association 1903

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)