The Modern Geometry of the Triangle

Abstract

THE principal novelties in this tract are the chapters on the orthopole (with some original propositions by the author) and on orthogonal projection (mostly after Prof. Neuberg). A pretty theorem in the latter is that all equilateral triangles in a given plane project upon another plane into triangles having the same Brocard angle. The other four chapters discuss various kinds of coordinates, the Lemoine and Brocard points, pedal and anti-pedal triangles, the medial triangle, and the Simpson line. No reference is made to the Tucker circles, or to Kiepert's hyperbola; even the Brocard circle is unmentioned, so the tract is deficient, even as a summary of the most important parts of the subject. A rather irritating feature is that the symbol ∞ is used for two entirely different purposes; this might easily have been avoided. Perhaps the figures will be found as useful as anything in the tract, for although they are not particularly good, they are drawn so that the special points are far enough apart, which is not very easy to contrive when a student is drawing figures for himself.