In this post, we will see the book from the series Little Mathematics Library titled Geometrical Constructions With Compasses Only by A. Kostovskii.

About the book

This booklet is intended for a wide circle of readers. It should help teachers and pupils of senior classes of secondary schools to acquaint themselves in greater detail with geometrical constructions carried out by compasses alone. It can serve as a teaching aid in school mathematical clubs. The booklet can also be used by students of physical and mathematical departments of universities and teachers’ training colleges to deepen their knowledge of elementary mathematics.

The book was translated from the Russian by Janna Suslovich and was first published by Mir Publishers in 1986. There is a Topics in Mathematics version of this book too.

A big thank you to @4evercla6 for this and two more books from LML series. See the comment in the LML taking stock post. We will see them in the next couple of posts.

Now only The Euler Characteristic by Yu. A. Shaskin remains from the list!

You can get the Little Mathematics Library version of the book here.

Topics in Mathematics version here.

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Contents

Preface 6

Introduction 7

PART 1
CONSTRUCTIONS WITH COMPASSES ALONE
1. On the possibility of solving geometrical construction problems by means of compasses alone: the basic theorem 9
2. Solution of geometrical construction problems by means of compasses alone 19
3. Inversion and its principal properties 33
4. The application of the method of inversion to the geometry of compasses 37

PART 2
GEOMETRIC CONSTRUCTIONS BY MEANS OF COMPASSES ALONE BUT WITH RESTRICTIONS

5. Constructions by means of compasses alone with the opening of the legs restricted from above 46
6. Constructions by means of compasses alone with the angle restricted from below 63
7. Constructions using only compasses with constant opening of the legs 66
8. Constructions with compasses alone on condition that all circles pass through the same point 67

Appendices 76

Appendix 1 Symbols and Notations Used in the Book 76

Appendix 2 Proof for Problem 18 in the General Case 77

References 79