Contents

General

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Book I. Planimetry

Translator's Foreword

Introduction

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Ch. 1. THE STRAIGHT LINE

  1. Angles (2)
  2. Perpendicular lines (2)
  3. Mathematical propositions
  4. Polygons and triangles (4)
  5. Isosceles triangles and symmetry (2)
  6. Congruence tests for triangles (1)
  7. Inequalities in triangles (5)
  8. Right triangles (1)
  9. Segment and angle bisectors (2)
  10. Basic construction problems (1)
  11. Parallel lines (2)
  12. The angle sum of a polygon (1)
  13. Parallelograms and trapezoids (2)
  14. Methods of construction and symmetries (1)

Ch. 2. THE CIRCLE

  1. Circles and chords
  2. Relative positions of a line and a circle
  3. Relative positions of two circles (1)
  4. Inscribed and some other angles (1)
  5. Construction problems
  6. Inscribed and circumscribed polygons (1)
  7. Four concurrency points in a triangle

Ch. 3. SIMILARITY

  1. Mensuration
  2. Similarity of triangles
  3. Similarity of polygons
  4. Proportionality theorems (1)
  5. Homothety (1)
  6. Geometric mean (2)
  7. Trigonometric functions (2)
  8. Applications of algebra to geometry
  9. Coordinates (5)

Ch. 4. REGULAR POLYGONS AND CIRCUMFERENCE

  1. Regular polygons (2)
  2. Limits
  3. Circumference and arc length (1)

Ch. 5. AREAS

  1. Areas of polygons
  2. Several formulas for areas of triangles (1)
  3. Areas of similar figures
  4. Areas of disks and sectors
  5. The Pythagorean theorem revisited

Bibliography / Index

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Book II. Stereometry

Ch. 1. LINES AND PLANES

  1. Drawing a plane
  2. Parallel lines and planes
  3. Perpendiculars and slants
  4. Dihedral and some other angles
  5. Polyhedral angles

Ch. 2. POLYHEDRA

  1. Parallelepipeds and pyramids
  2. Volumes of prisms and pyramids
  3. Similarity of polyhedra
  4. Symmetries of space figures
  5. Regular polyhedra

Ch. 3. ROUND SOLIDS

  1. Cylinders and cones
  2. The ball

Ch. 4. VECTORS AND FOUNDATIONS

  1. Algebraic operations with vectors
  2. Applications of vectors to geometry
  3. Foundations of geometry
  4. Introduction to non-Euclidean geometry
  5. Isometries

Translator's Afterword

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Bibliography / Index

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