Descartes' parabola and the traditional parabola

This study concentrates on Descartes geometry,especially for the Descartes parabola and traditionalparabola. Who is Descartes? René Descartes(1596-1650) was a 17th century French philosopher,mathematician and a man of science whose work, Lagéométrie, includes his application of algebra togeometry from which we now have Cartesian geometry.First, this study concentrates on the Descartes'studies of Pappus' problem. Also I explicitly explainhow Descartes' found the traditional parabola andDescartes' parabola, and how he used the four fivelines Pappus' problems. Also this study concentrateson the Descartes' ''construction'' (that meansgeometrical solution) of equations by usingDescartes' parabola and the traditional parabola. Iclearly explain Descartes' construction of third andfourth degree equations by circle and traditionalparabola, and the construction for fifth and sixthdegree equations by using circle and Descartes'parabola. Finally, I also explain the construction ofhigher degree equations. Furthermore I give threenumerical examples by solving them with themathematica program, which was designed by Stephenwolfram.