Calculating with Conics

Abstract

A major part of classical elementary geometry was concerned with the question of which constructions can be carried out with a straightedge and compass. The decisive primitive operations here are connecting two points by a line, drawing a circle with a radius given by two other points, and marking intersections of objects as new points. In our projective framework we do not have circles, but still can consider elementary constructions with the objects we have studied so far (points, lines, and conics). Since we are interested in particular in calculating with geometric objects, we in particular want to know how we can compute the results of geometric primitive operations if the parameters of the involved objects are given.