Geometric Transformations. Volume 1: Motions and Similarity Transformations

This book is devoted to elementary geometry. In addition to specific theorems, elementary geometry contains two large general ideas that formed the basis of the entire further development of geometry. We are talking about the deductive method and the axiomatic substantiation of geometry, firstly, and about geometric transformations and theoretical and group justification of geometry, and secondly. These ideas are very substantial and fruitful, so both of them in their direct development lead to non -Euclidean geometries. The disclosure of one of these ideas-the ideas of geometric transformations and theoretical-group justification of geometry-is the main task of the book.
The publication consists of two volumes. The first volume that makes up this book is dedicated to the movements and transformations of likeness, its content more specifically adjoins the school material. The second volume dedicated to the linear and circular (in other words - projective and conformal) transformations comes out simultaneously with the first in our publishing house. Both volumes contain a large number of problems whose solutions are given at the end.
The book is recommended for high school students and secondary school teachers, students and teachers of the physical and mathematical faculties of pedagogical institutions, and heads of school mathematical circles