  The method of application of areas as presented in Euclid's Elements, is
employed to generate the three conics as the loci of points with Cartesian
coordinates satisfying quadratic equations with coefficients defined by the
initial settings of the geometric constructions produced by the applications
method. This conceptual reconstruction supports the view that the conics were
most probably discovered as plane curves by fusing the method of the
application of areas with the concept of locus, long before Apollonius studied
them as conic sections.
