Analytical Geometry | A. V. Pogorelov

Analytical geometry has no strictly defined contents. It is the   method but not the subject under investigation, that constitutes the   leading feature of this branch of geometry.   The essence of this method consists in that geometric objects are   associated in some standard way with equations (or systems of   equations) so that geometric relations of figures are expressed   through properties of their equations.   For instance, in case of Cartesian coordinates any straight line in   the plane is uniquely associated with a linear equation ax+by+ c =   0.   The intersection of three straight, lines at one point is     expressed by the condition of compatibility of a system of three     equations which specify these lines.

Due to a multi purpose approach to solving various problems, the     method of analytic geometry has become the leading method in     geometric investigations and is widely applied in other fields of     exact natural sciences, such as mechanics and physics.     Analytical geometry joined geometry with algebra and analysis -     the fact which has told fruitfully on further development of     these three subject of mathematics.     The principal ideas of analytical geometry are traced back to the     French mathematician, Rene Descartes (1595-1650), who in 1637     described the fundamentals of its method in his famous work     "Geometric".

The present book, which is a course of lectures, treats the
fundamentals of the method of analytic geometry as applied to the
simplest geometric objects. It is designed for the university
students majoring in physics and mathematics,

This book was translated from the Russian by Leonid Levant and
was first published by Mir Publishers in 1980.