Elizabeth Buchanan Cowley

Plane Geometry Silver, Burdett and Company, 1932

Preface

An extended experience as a college teacher of mathematics gave the author of this text abundant opportunity to know what had been achieved in mathematics by students coming from various types of secondary schools. In order to study a first hand the problems involved in teaching secondary school mathematics, she obtained leave from her college position (which she later resigned) and engaged in teaching mathematics in a public high school in a large city. From her experience in college and secondary school, she concluded there was need for a textbook in plane geometry which would so develop and present the concepts and ideas of this subject that they could be more readily comprehended and mastered by students in secondary school.

Basing her work upon her experience and a careful study of the available literature on the improvement of the teaching of geometry, she set about the development of materials and methods that would meet this need. These materials and methods were subjected to trial in the classroom, and were modified, improved, and tried again in the classroom before they were embodied in this book. By their use, highly satisfactory results have been achieved, as judged by the pleasure of the students in their work, their ratings on examinations, and their ability to maintain themselves in mathematics in colleges that have the highest standards in that subject.

Contents

INTRODUCTION

BOOK I. STRAIGHT-LINE FIGURES
Parallels, Perpendiculars, and Triangles
Parallelograms
Equal Line Segments
Polygons
Inequalities
Locus
Lines Through a Point

BOOK II. THE CIRCLE
Arcs, Chords, and Central Angles
Tangents and Secants
Measurement of Angles Formed by Radii, Chords, Secants, and Tangents
Unequal Arcs and Unequal Chords

BOOK III. SIMILAR POLYGONS
Proportional Line Segments and Similar Triangles
Similar Polygons of n Sides
Trigonometric Ratios
Functional Relations

BOOK IV. AREAS OF POLYGONS

BOOK V. MEASUREMENT OF THE CIRCLE
Regular Polygons as Related to the Circle
Circumference and Area of the Circle

Exercises to Test Ability in Formal Demonstrations
Useful Reference Material
Congruency of Triangles by Theoretical Superposition