Advanced Euclidean GeometryFor many years, this elementary treatise on advanced Euclidean geometry has been the standard textbook in this area of classical mathematics; no other book has covered the subject quite as well. It explores the geometry of the triangle and the circle, concentrating on extensions of Euclidean theory, and examining in detail many relatively recent theorems. Several hundred theorems and corollaries are formulated and proved completely; numerous others remain unproved, to be used by students as exercises. The author makes liberal use of circular inversion, the theory of pole and polar, and many other modern and powerful geometrical tools throughout the book. In particular, the method of "directed angles" offers not only a powerful method of proof but also furnishes the shortest and most elegant form of statement for several common theorems. This accessible text requires no more extensive preparation than high school geometry and trigonometry. |
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Common terms and phrases
A₁ altitudes antihomologous bisectors bisects Brocard angle Brocard circle Brocard points Brocard triangle C₁ center of inversion center of similitude chapter chord circle of inversion circle whose center circles of antisimilitude circles of Apollonius circumcenter circumcircle circumscribed coaxal system common tangents concurrent congruent connectors Corollary corresponding diagonals diameter directly similar distances drawn equal angles equation fixed circle fixed point four points geometry given circles given points given triangle H₁ Hence homologous points infinity inscribed inverse with regard inversely similar isogonal conjugates line joining locus median point mid-points Miquel point mutually inverse Neuberg circle nine point circle opposite sides orthocenter orthocentric system orthopole P₁ pairs parallel passes pedal circle pedal triangle perpendicular perspective plane point of intersection polar proof proved quadrangle quadrilateral radical axis radii radius ratio respectively similar figures Simson line straight line symmedian point tangent tangent circles three circles triangle A1A2A3 vertex vertices