We now come to another title in the Little Mathematics Library series, Geometrical Constructions Using Compasses Only by A. N. Kostovskii.
The author of the present article has on many occasions
given lectures on the theory of geometrical constructions
to participants in mathematical olympiads, which have been
organized every year since 1947, for the pupils of secondary schools in the city of Lvov. These lectures served as a foundation for the writing of the first part of this work.
The second part consists of investigations made by the
author in connection with geometrical constructions carried
out with a limited opening of the ‘legs’.
The present article is written 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 with the help of compasses alone. This work can serve as a teaching aid in the work of school mathematical clubs. It can also be used by students studying elementary mathematics in physics and mathematics departments of teachers’ training colleges and universities.
The book was translated from the Russian by Janna Suslovich and was first published by Mir Publishers in 1986 (77 pp). This book was also part of the Popular Lectures in Mathematics Series (Vol. 4), which was published by Blaisdell in 1961. This edition was translated from the Russian by Halina Moss and was edited by I. N. Sneddon. The link below is for the PLM (1961) edition, we still need to get LML version.
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CONSTRUCTIONS WITH COMPASSES ALONE
1. On the possibility of solving geometrical construction problems by means of compasses alone: the basic theorem 3
2. Solution of geometrical construction problems by means of compasses alone 14
3. Inversion and its principal properties 29
4. The application of the method of inversion to the geometry of compasses 34
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 47
6. Constructions by means of compasses alone with the angle restricted from below 65
7. Constructions using only compasses with constant opening of the legs 69
8. Constructions with compasses alone on condition that all circles pass through the same point 71