Leonard E., Lewis J., Liu A., Tokarsky G. Classical Geometry: Euclidean, Transformational, Inverse and Projective

Hoboken: John Wiley & Sons, Inc., 2014. — 493 p.Preface
Euclidean Geometry
Congruency
Introduction
Congruent Figures
Parallel Lines
Angles in a Triangle
Thales' Theorem
Quadrilaterals
More About Congruency
Perpendiculars and Angle Bisectors
Construction Problems
The Method of Loci
Solutions to Selected Exercises
Problems
Concurrency
Perpendicular Bisectors
Angle Bisectors
Altitudes
Medians
Construction Problems
Solutions to the Exercises
Problems
Similarity
Similar Triangles
Parallel Lines and Similarity
Other Conditions Implying Similarity
Examples
Construction Problems
The Power of a Point
Solutions to the Exercises
Problems
Theorems of Ceva and Menelaus
Directed Distances, Directed Ratios
The Theorems
Applications of Ceva's Theorem
Applications of Menelaus' Theorem
Proofs of the Theorems
Extended Versions of the Theorems
Ceva's Theorem in the Extended Plane
Menelaus' Theorem in the Extended Plane
Problems
Area
Basic Properties
Areas of Polygons
Finding the Area of Polygons
Areas of Other Shapes
Applications of the Basic Properties
Other Formulae for the Area of a Triangle
Solutions to the Exercises
Problems
Miscellaneous Topics
The Three Problems of Antiquity
Constructing Segments of Specific Lengths
Construction of Regular Polygons
Construction of the Regular Pentagon
Construction of Other Regular Polygons
Miquel's Theorem
Morley's Theorem
The Nine-Point Circle
Special Cases
The Steiner-Lehmus Theorem
The Circle of Apollonius
Solutions to the Exercises
Problems
Transformational Geometry
The Euclidean Transformations or lsometries
Rotations, Reflections, and Translations
Mappings and Transformations
Isometries
Using Rotations, Reflections, and Translations
Problems
The Algebra of lsometries
Basic Algebraic Properties
Groups of Isometries
Direct and Opposite Isometries
The Product of Reflections
Problems
The Product of Direct lsometries
Angles
Fixed Points
The Product of Two Translations
The Product of a Translation and a Rotation
The Product of Two Rotations
Problems
Symmetry and Groups
More About Groups
Cyclic and Dihedral Groups
Leonardo's Theorem
Problems
Homotheties
The Pantograph
Some Basic Properties
Circles
Construction Problems
Using Homotheties in Proofs
Dilatation
Problems
Tessellations
Tilings
Monohedral Tilings
Tiling with Regular Polygons
Platonic and Archimedean Tilings
Problems
Inversive and Projective Geometries Introduction to Inversive Geometry
Inversion in the Euclidean Plane
The Effect of Inversion on Euclidean Properties
Orthogonal Circles
Compass-Only Constructions
Problems
Reciprocation and the Extended Plane
Harmonic Conjugates
The Projective Plane and Reciprocation
Conjugate Points and Lines
Conics
Problems
Cross Ratios
Cross Ratios
Applications of Cross Ratios
Problems
Introduction to Projective Geometry
Straightedge Constructions
Perspectivities and Projectivities
Line Perspectivities and Line Projectivities
Projective Geometry and Fixed Points
Projecting a Line to Infinity
The Apollonian Definition of a Conic
Problems
Bibliography
Index