Textbook in PDF format

This is a comprehensive two-volumes text on plane and space geometry, transformations and conics, using a synthetic approach. The first volume focuses on Euclidean Geometry of the plane, and the second volume on Circle measurement, Transformations, Space geometry, Conics.
The book is based on lecture notes from more than 30 courses which have been taught over the last 25 years. Using a synthetic approach, it discusses topics in Euclidean geometry ranging from the elementary (axioms and their first consequences), to the complex (the famous theorems of Pappus, Ptolemy, Euler, Steiner, Fermat, Morley, etc.). Through its coverage of a wealth of general and specialized subjects, it provides a comprehensive account of the theory, with chapters devoted to basic properties of simple planar and spatial shapes, transformations of the plane and space, and conic sections. As a result of repeated exposure of the material to students, it answers many frequently asked questions. Particular attention has been given to the didactic method; the text is accompanied by a plethora of figures (more than 2000) and exercises (more than 1400), most of them with solutions or expanded hints. Each chapter also includes numerous references to alternative approaches and specialized literature.
The book is mainly addressed to students in mathematics, physics, engineering, school teachers in these areas, as well as, amateurs and lovers of geometry. Offering a sound and self-sufficient basis for the study of any possible problem in Euclidean geometry, the book can be used to support lectures to the most advanced level, or for self-study.
Preface
Symbol index
Euclidean Geometry of the plane
The basic notions
Undefined terms, axioms
Line and line segment
Length, distance
Angles
Angle kinds
Triangles
Congruence, the equality of shapes
Isosceles and right triangle
Triangle congruence criteria
Triangle’s sides and angles relations
The triangle inequality
The orthogonal to a line
The parallel from a point
The sum of triangle’s angles
The axiom of parallels
Symmetries
Ratios, harmonic quadruples
Comments and exercises for the
References
Circle and polygons
The circle, the diameter, the chord
Circle and line
Two circles
Constructions using ruler and compass
Parallelograms
Quadrilaterals
The middles of sides
The triangle’s medians
The rectangle and the square
Other kinds of quadrilaterals
Polygons, regular polygons
Arcs, central angles
Inscribed angles
Inscriptible or cyclic quadrilaterals
Circumscribed quadrilaterals
Geometric loci
Comments and exercises for the
References
Areas, Thales, Pythagoras, Pappus
Area of polygons
The area of the rectangle
Area of parallelogram and triangle
Pythagoras and Pappus
Similar right triangles
The trigonometric functions
The theorem of Thales
Pencils of lines
Similar triangles
Similar polygons
Triangle’s sine and cosine rules
Stewart, medians, bisectors, altitudes
Antiparallels, symmedians
Comments and exercises for the
References
The power of the circle
Power with respect to a circle
Golden section and regular pentagon
Radical axis, radical center
Apollonian circles
Circle pencils
Orthogonal circles and pencils
Similarity centers of two circles
Inversion
Polar and pole
Comments and exercises for the
References
From the classical theorems
Escribed circles and excenters
Heron’s formula
Euler’s circle
Feuerbach’s Theorem
Euler’s theorem
Tangent circles of Apollonius
Theorems of Ptolemy and Brahmagupta
Simson’s and Steiner’s lines
Miquel point, pedal triangle
Arbelos
Sangaku
Fermat’s and Fagnano’s theorems
Morley’s theorem
Signed ratio and distance
Cross ratio, harmonic pencils
Theorems of Menelaus and Ceva
The complete quadrilateral
Desargues’ theorem
Pappus’ theorem
Pascal’s and Brianchon’s theorems
Castillon’s problem, homographic relations
Malfatti’s problem
Calabi’s triangle
Comments and exercises for the
References
Index