The Normals to a Parabola and the Real Roots of a Cubic.

The article examines geometrical problems encountered in locating or determining the normals to a parabola and the real roots of a cubic. In the book "Tractatus duo, prior de cycloide, posterior de cissoide," John Wallis made the first rectification of a algebraic curve. The transformation of any cubic equation through the horizontal translation do not alter the number of real roots of the equation. Key information about the Neil's parabola and envelope of the family of normals is further presented.