In this post, we will see the book *Configuration Theorems* by B. I. Argunov, L. A. Skornyakov. The book is a part of *Topics in Mathematics* series. We will see some more books in this series in the future.

About the book

This booklet presents several important configuration theorems, along with their applications to the study of the properties of figures and to the solutions of several practical problems. In doing this, the authors introduce the reader to some fundamental concepts of projective geometry-central projection and ideal elements of space. Only the most elementary knowledge of plane and solid geometry is presupposed.

Chapters 2 and 3 are devoted to the two most important configuration theorems, the Pappus-Pascal theorem and that of Desargues. The chapters which follow present applications of these theorems. Chapter 6 touches upon the algebraic interpretation of configuration theorems and the general method of arriving at such theorems.

Students who wish to learn more about this subject should consult the bibliography given at the end of the booklet.

The book was translated from Russian by Edgar E. Enochs and Robert B. Brown and was published in 1963.

Credits to the original uploader.

You can get the book here.

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**Contents**

**Introduction 1**

1. What is a configuration theorem? 1

2. Example of a configuration theorem 2

**Chapter 1 Central Projection and Ideal Elements 4**

3. Central projection in a plane; ideal elements

4. Elimination of exceptional cases

5. Basic theorems about projective lines

6. Central projection in space

**Chapter 2 Theorem of Pappus and Pascal**

7. The Pappus-Pascal Theorem 9

8. Introduction to the proof of Pappus-Pascal Theorem 11

9. Completion of the proof of Pappus-Pascal Theorem 13

10. Brianchon’s Theorem 14

**Chapter 3 Desargue’s Theorem 16**

11. Desargue’s Theorem 16

12. Alternative proofs of Desargues’s theorem 19

13. The converse of Desargue’s Theorem 23

**Chapter 4 Some Properties of Polygons 24**

14. Some properties of quadrilaterals 24

15. Some properties of pentagons 25

16. More properties of quadrilaterals 26

**Chapter 5. Problems 29**

17. Inaccessible points or lines 29

18. Constructions involving inaccessible points or lines30

19. Problems for solutions by the reader 34

**Chapter 6. The Algebraic Meaning of Configuration Theorems 37**

20. Algebraic Identities as Configuration Theorems 37

21. Schematic notation of Configuration Theorems 38

**Bibliography 41**

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