Descartes' parabola and the traditional parabola

This study concentrates on Descartes geometry,§especially for the Descartes parabola and traditional§parabola. Who is Descartes? René Descartes§(1596-1650) was a 17th century French philosopher,§mathematician and a man of science whose work, La§géométrie, includes his application of algebra to§geometry from which we now have Cartesian geometry.§First, this study concentrates on the Descartes §studies of Pappus problem. Also I explicitly explain§how Descartes found the traditional parabola and§Descartes parabola, and how he used the four five§lines Pappus problems. Also this study concentrates§on the Descartes construction (that means§geometrical solution) of equations by using§Descartes parabola and the traditional parabola. I§clearly explain Descartes construction of third and§fourth degree equations by circle and traditional§parabola, and the construction for fifth and sixth§degree equations by using circle and Descartes §parabola. Finally, I also explain the construction of§higher degree equations. Furthermore I give three§numerical examples by solving them with the§mathematica program, which was designed by Stephen§wolfram. This study concentrates on Descartes geometry,§especially for the Descartes parabola and traditional§parabola. Who is Descartes? René Descartes§(1596-1650) was a 17th century French philosopher,§mathematician and a man of science whose work, La§géométrie, includes his application of algebra to§geometry from which we now have Cartesian geometry.§First, this study concentrates on the Descartes §studies of Pappus problem. Also I explicitly explain§how Descartes found the traditional parabola and§Descartes parabola, and how he used the four five§lines Pappus problems. Also this study concentrates§on the Descartes construction (that means§geometrical solution) of equations by using§Descartes parabola and the traditional parabola. I§clearly explain Descartes construction of third and§fourth degree equations by circle and traditional§parabola, and the construction for fifth and sixth§degree equations by using circle and Descartes §parabola. Finally, I also explain the construction of§higher degree equations. Furthermore I give three§numerical examples by solving them with the§mathematica program, which was designed by Stephen§wolfram.