Differentials help geometry

This book is devoted to the history of the emergence and development of differential geometry. The authors in a popular form set out the main results of classical differential geometry, widely using vector calculus and the method of mobile rapper --- Methods that played a large role in the future development of classical differential geometry and the expansion of the content of this science. The first ten chapters of the book are devoted to the study of invariants, as well as specific lines and surfaces. Chapter XI considers the so-called internal geometry of the surface, which served as the basis for the creation of Riman geometry and its generalizations, chapter XII tells how differential geometry is used in practical disciplines --- cartography and geodesy.
The book is written in an affordable and at the same time mathematically strict language, the presentation in it is gradually becoming more and more difficult, demanding the conscious application of what was described earlier.

The book is designed primarily for high school students, and it is addressed not so much to the enthusiastic mathematics to readers, but to those who only discover the charm of this science for themselves. It can serve as the basis for the work of a school mathematical circle or optional