Definition:Quadratrix of Hippias/Definition 2

Definition
The quadratrix of Hippias is the plane curve be generated as follows.

Let $\Box ABCD$ be a square of side length $a$.

Let a quarter circle be inscribed in $\Box ABCD$ with the center at $A$, the arc going from $B$ to $D$.

Let $E$ be a point travelling around the arc $BD$ at a constant angular velocity.

Let $F$ be a point travelling along the side of $\Box ABCD$ at a constant velocity such that $E$ and $F$ take the same time to travel from the top $CD$ to the bottom $AB$ of $\Box ABCD$.

Let $S$ be the point at which the line $AE$ intersects the line through $F$ parallel to $AB$.


 * QuadratrixOfHippias2.png

The path traced out by $S$ is the quadratrix of Hippias.

Also see

 * Equivalence of Definitions of Quadratrix of Hippias