ALL CHAPTERS COVERED
, CONTENTS
PREFACE xi
SYMBOLS EMPLOYED IN THIS BOOK xiii
CHAPTER 1 - Triangles and Polygons
Theorems and corollaries I
Solved problems 4
Miscellaneous exercises 25
CHAPTER 2 - Areas, Squares, and Rectangles
Theorems and corollaries 33
Solved problems 35
Miscellaneous exercises 56
CHAPTER 3 - Circles and Tangency
Theorems and corollaries 64
Solved problems 67
Miscellaneous exercises 95
CHAPTER 4 -Ratio and Proportion
Theorems and corollaries 105
Solved problems io8
Miscellaneous exercises 133
CHAPTER 5 Loci and Transversals
Definitions and theorems 144
Solved problems 145
Miscellaneous exercises 169
CHAPTER 6 -Geometry of Lines and Rays
HARMONIC RANGES AND PENCILS
Definitions and propositions 178
Solved problems 182
ISOGONAL AND SYMMEDIAN LINES-BROCARD POINTS
Definitions and propositions 186
Solved problems 189
Miscellaneous exercises 191
ix
,X CONTENTS
CHAPTER 7 -Geometry of the Circle
SIMSON LINE
Definitions and propositions
Solved problems
RADICAL AXIS-COAXAL CIRCLES
Definitions and propositions
Solved problems
POLES AND POLARS
Definitions and propositions
Solved problems
SIMILITUDE AND INVERSION
Definitions and propositions
Solved problems
Miscellaneous exercises
CHAPTER 8 -Space Geometry
Theorems and corollaries
Solved problems
Miscellaneous exercises
INDEX
, PREFACE
This book is intended as a second course in Euclidean geometry.
Its purpose is to give the reader facility in applying the theorems of
Euclid to the solution of geometrical problems. Each chapter begins
with a brief account of Euclid's theorems and corollaries for simpli-
city of reference, then states and proves a number of important
propositions. Chapters close with a section of miscellaneous problems
of increasing complexity, selected from an immense mass of material
for their usefulness and interest. Hints of solutions for a large number
of problems are also included.
Since this is not intended for the beginner in geometry, such
familiar concepts as point, line, ray, segment, angle, and polygon
are used freely without explicit definition. For the purpose of clarity
rather than rigor the general term line is used to designate sometimes
a ray, sometimes a segment, sometimes the length of a segment;
the meaning intended will be clear from the context.
Definitions of less familiar geometrical concepts, such as those of
modern and space geometry, are added for clarity, and since the
use of symbols might prove an additional difficulty to some readers,
geometrical notation is introduced gradually in each chapter.
January, 1968 M. N. AREF
WILLIAM WERNICK
xi
, CONTENTS
PREFACE xi
SYMBOLS EMPLOYED IN THIS BOOK xiii
CHAPTER 1 - Triangles and Polygons
Theorems and corollaries I
Solved problems 4
Miscellaneous exercises 25
CHAPTER 2 - Areas, Squares, and Rectangles
Theorems and corollaries 33
Solved problems 35
Miscellaneous exercises 56
CHAPTER 3 - Circles and Tangency
Theorems and corollaries 64
Solved problems 67
Miscellaneous exercises 95
CHAPTER 4 -Ratio and Proportion
Theorems and corollaries 105
Solved problems io8
Miscellaneous exercises 133
CHAPTER 5 Loci and Transversals
Definitions and theorems 144
Solved problems 145
Miscellaneous exercises 169
CHAPTER 6 -Geometry of Lines and Rays
HARMONIC RANGES AND PENCILS
Definitions and propositions 178
Solved problems 182
ISOGONAL AND SYMMEDIAN LINES-BROCARD POINTS
Definitions and propositions 186
Solved problems 189
Miscellaneous exercises 191
ix
,X CONTENTS
CHAPTER 7 -Geometry of the Circle
SIMSON LINE
Definitions and propositions
Solved problems
RADICAL AXIS-COAXAL CIRCLES
Definitions and propositions
Solved problems
POLES AND POLARS
Definitions and propositions
Solved problems
SIMILITUDE AND INVERSION
Definitions and propositions
Solved problems
Miscellaneous exercises
CHAPTER 8 -Space Geometry
Theorems and corollaries
Solved problems
Miscellaneous exercises
INDEX
, PREFACE
This book is intended as a second course in Euclidean geometry.
Its purpose is to give the reader facility in applying the theorems of
Euclid to the solution of geometrical problems. Each chapter begins
with a brief account of Euclid's theorems and corollaries for simpli-
city of reference, then states and proves a number of important
propositions. Chapters close with a section of miscellaneous problems
of increasing complexity, selected from an immense mass of material
for their usefulness and interest. Hints of solutions for a large number
of problems are also included.
Since this is not intended for the beginner in geometry, such
familiar concepts as point, line, ray, segment, angle, and polygon
are used freely without explicit definition. For the purpose of clarity
rather than rigor the general term line is used to designate sometimes
a ray, sometimes a segment, sometimes the length of a segment;
the meaning intended will be clear from the context.
Definitions of less familiar geometrical concepts, such as those of
modern and space geometry, are added for clarity, and since the
use of symbols might prove an additional difficulty to some readers,
geometrical notation is introduced gradually in each chapter.
January, 1968 M. N. AREF
WILLIAM WERNICK
xi
