A Desarguesian dual for Nagel's middlespoint
type: Item
instance of: scholarly article
title: A Desarguesian dual for Nagel's middlespoint
zbMATH Open document ID: 0701.51008
author: Roland H. Eddy
published in: Elemente der Mathematik
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/141457
review text: Nagel's middlespoint of a triangle was defined by Nagel in 1836 as follows. For a given triangle ABC, let \(S_ A\), \(S_ B\), \(S_ C\) be the midpoints of BC, CA, AB, and \(I_ a\), \(I_ b\), \(I_ c\) the centres of the excircles; then the lines \(S_ AI_ a\), \(S_ BI_ b\), \(S_ CI_ c\) meet at M, the middlespoint of ABC. In the present paper the author derives a dual of this point, namely a straight line m. This is obtained from Desargues' theorem; since the triangles \(I_ aI_ bI_ c\) and \(S_ AS_ BS_ C\) are perspective from the middlespoint M, they are perspective from a line m, called the middlesline of the triangle ABC. The author shows how the middlesline is related to the Gergonne point G of ABC.
reviewed by: E. J. F. Primrose
Mathematics Subject Classification ID: 51M15
zbMATH DE Number: 4149038
zbMATH Keywords: Nagel's middlespoint
MaRDI profile type: Publication
Recommended article: A generalization of Nagel's middlespoint
Recommended article: Dual theorems on central points and their generalizations
Recommended article: The double midset conjecture for continua in the plane
Recommended article: An affine version of a theorem of Nagata
Recommended article: A generalized dual of Napoleon's theorem and some further extensions
Recommended article: A note on extreme points in dual spaces
Recommended article: Q4282466
Recommended article: The dual of the Bourgain-Delbaen space
description: scientific article; zbMATH DE number 4149038