As taught in school books, analytic geometry can be explained more simply: it is concerned with defining geometrical shapes in a numerical way, and extracting numerical information from that representation. The numerical output, however, might also be a vector or a shape.
René Descartes introduced the foundation for the methods of analytic geometry in 1637 in the appendix titled GEOMETRY of the titled Discourse on the Method of Rightly Conducting the Reason in the Search for Truth in the Sciences, commonly referred to as Discourse on Method. This work, written in his native language French, and its philosophical principles, provided the foundation for the calculus, that was later introduced by Isaac Newton and Gottfried Wilhelm Leibniz, independently of each other.
Important themes of analytical geometry are: