Contents

Table of Contents

# General

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# Book I. Planimetry

## Translator's Foreword

## Introduction

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## Ch. 1. THE STRAIGHT LINE

- Angles (2)
- Perpendicular lines (2)
- Mathematical propositions
- Polygons and triangles (4)
- Isosceles triangles and symmetry (2)
- Congruence tests for triangles (1)
- Inequalities in triangles (5)
- Right triangles (1)
- Segment and angle bisectors (2)
- Basic construction problems (1)
- Parallel lines (2)
- The angle sum of a polygon (1)
- Parallelograms and trapezoids (2)
- Methods of construction and symmetries (1)

## Ch. 2. THE CIRCLE

- Circles and chords
- Relative positions of a line and a circle
- Relative positions of two circles (1)
- Inscribed and some other angles (1)
- Construction problems
- Inscribed and circumscribed polygons (1)
- Four concurrency points in a triangle

## Ch. 3. SIMILARITY

- Mensuration
- Similarity of triangles
- Similarity of polygons
- Proportionality theorems (1)
- Homothety (1)
- Geometric mean (2)
- Trigonometric functions (2)
- Applications of algebra to geometry
- Coordinates (5)

## Ch. 4. REGULAR POLYGONS AND CIRCUMFERENCE

## Ch. 5. AREAS

- Areas of polygons
- Several formulas for areas of triangles (1)
- Areas of similar figures
- Areas of disks and sectors
- The Pythagorean theorem revisited

## Bibliography / Index

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# Book II. Stereometry

## Ch. 1. LINES AND PLANES

- Drawing a plane
- Parallel lines and planes
- Perpendiculars and slants
- Dihedral and some other angles
- Polyhedral angles

## Ch. 2. POLYHEDRA

- Parallelepipeds and pyramids
- Volumes of prisms and pyramids
- Similarity of polyhedra
- Symmetries of space figures
- Regular polyhedra

## Ch. 3. ROUND SOLIDS

## Ch. 4. VECTORS AND FOUNDATIONS

- Algebraic operations with vectors
- Applications of vectors to geometry
- Foundations of geometry
- Introduction to non-Euclidean geometry
- Isometries

## Translator's Afterword

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