College Geometry: An Introduction to the Modern Geometry of the Triangle and the Circle (Dover Books on Mathematics)

Translated into many languages, this book was in continuous use as the standard university-level text for a quarter-century, until it was revised and enlarged by the author in 1952. World-renowned writer and researcher Nathan Altshiller-Court (1881–1968) was a professor of mathematics at the University of Oklahoma for more than thirty years. His revised introduction to modern geometry offers today's students the benefits of his many years of teaching experience.The first part of the text stresses construction problems, proceeding to surveys of similitude and homothecy, properties of the triangle and the quadrilateral, and harmonic division. Subsequent chapters explore the geometry of the circle—including inverse points, orthogonals, coaxals, and the problem of Apollonius and triangle geometry, focusing on Lemoine and Brocard geometry, isogonal lines, Tucker circles, and the orthopole. Numerous exercises of varying degrees of difficulty appear throughout the text. CONTENTS PREFACE ACKNOWLEDGMENTS To THE INSTRUCTOR To THE STUDENT 1 GEOMETRIC CONSTRUCTIONS A. Preliminaries Exercises B. General Method of Solution of Construction Problems Exercises C. Geometric Loci Exercises D. Indirect Elements Exercises 22, 23, 24, 25, 27, Supplementary Exercises Review Exercises Constructions Propositions Loci 2 SIMILITUDE AND HOMOTHECY A. Similitude Exercises B. Homothecy Exercises 43, 45, 49, Supplementary Exercises 3 PROPERTIES OF THE TRIANGLE A. Preliminaries Exercises B. The Circumcircle Exercises 59, C. Medians Exercises 67, 69, D. Tritangent Circles a. Bisectors Exercises b. Tritangent Centers Exercises c. Tritangent Radii Exercises d. Points of Contact Exercises E. Altitudes a. The Orthocenter.. Exercises b. The Orthic Triangle Exercises 99, c. The Euler Line Exercises F. The Nine-Point Circle Exercises G. The Orthocentric Quadrilateral Exercises 111, Review Exercises The Circumcircle Medians Tritangent Circles Altitudes The Nine-Point Circle Miscellaneous Exercises 4 THE QUADRILATERAL A. The General Quadrilateral Exercises B. The Cyclic Quadrilateral Exercises C. Other Quadrilaterals Exercises 5 THE SIMSON LINE Exercises 145, 6 TRANSVERSALS A. Introductory Exercises B. Stewart's Theorem Exercises C. Menelaus' Theorem Exercises D. Ceva's Theorem Exercises161, 161, Supplementary Exercises 7 H Aizmoz is DI