Analytical Geometry -

A. V. Pogorelov

Mir Publishers

1980

240 páginas

8h 0m

ISBN-13: 9780828517140

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”.