Hostname: page-component-7c8c6479df-p566r Total loading time: 0 Render date: 2024-03-29T11:03:02.848Z Has data issue: false hasContentIssue false

On some systems of conics connected with the triangle

Published online by Cambridge University Press:  20 January 2009

Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

I have recently shown that any two straight lines that are isotomically conjugate with reference to a triangle are the asymptotes of a conic circumscribed about the triangle; and that, conversely, any circumscribed conic has for its asymptotes two such lines. Now there is a one-fold infinity of conies having a given pair of straight lines for asymptotes; and, as there is a two-fold infinity of pairs of isotomic lines in the plane (with reference to a given triangle), it follows that two conditions must subsist among the coefficients in the equation of a conic, in order that its asymptotes may be isotomic lines.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1901

References

* Annals of Mathematics, Second Series, Vol. 2, No. 3, p. 148 (04 1901).Google Scholar

* Sur les quatre groupes de deux points d'un triangle ABC qui sont en même temps leg foyers d'une conique inscrite et d'une conique eirconscrite à ce triangle. Association française pour l'avancement des sciences naturelles. (Rouen.) 1883.