Projective Transformations

Geometric Transformations, Volume 2: Projective Transformations focuses on collinearity-preserving transformations of the projective plane.
The book first offers information on projective transformations, as well as the concept of a projective plane, definition of a projective mapping, fundamental theorems on projective transformations, cross ratio, and harmonic sets. Examples of projective transformations, projective transformations in coordinates, quadratic curves in the projective plane, and projective transformations of space are also discussed.
The text then examines inversion, including the power of a point with respect to a circle, definition and properties of inversion, and circle transformations and the fundamental theorem. The manuscript elaborates on the principle of duality.
The manuscript is designed for use in geometry seminars in universities and teacher-training colleges. The text can also be used as supplementary reading by high school teachers who want to extend their range of knowledge on projective transformations.

Preface to Volume 2 of the English Edition

Translator's Note

Preface to The Russian Edition

Chapter I. Projective Transformations

1. The Concept of a Projective Plane

2. Definition of a Projective Mapping

3. Two Fundamental Theorems on Projective Transformations

4. Cross Ratio

5. Harmonic Sets

6. Examples of Projective Transformations

7. Projective Transformation in Coordinates

8. Huadratic Curves in the Projective Plane

9. Projective Transformation of Space

Appendix 1 to Chapter I. The Topology of the Projective Plane

Chapter II. Inversion

10. The Power of a Point with Respect to a Circle

11. Definition of Inversion

12. Properties of Inversion

13. Circle Transformations and the Fundamental Theorem

Appendix 2 to Chapter I. Principle of Duality

Subject Index