# Definition:Cissoid of Diocles

## Definition

Let $C$ be a a circle of radius $a$ with a distinguished point $O$ on its circumference.

Let $L$ be the tangent to $C$ at the other end of the diameter of $C$ through $O$.

Let $R$ be a point on the circumference of $C$.

Let $OR$ be produced to meet $L$ at $S$.

Let $P$ be the point on $OS$ such that $OP$ = $RS$.

The cissoid of Diocles is the locus of points $P$ as $R$ travels around the circumference of $C$.

## Also known as

Some sources refer to the cissoid of Diocles as merely a cissoid, but that term is best used to refer to the more general object of which the cissoid of Diocles was the original instance.

## Also see

• Results about the cissoid of Diocles can be found here.

## Source of Name

This entry was named for Diocles of Carystus.

## Historical Note

Diocles of Carystus designed the curve now known as the cissoid of Diocles in about $180$ BCE, specifically for solving the problem of Doubling the Cube.

It was given its name by Geminus of Rhodes about a century later.

It can also be used to divide an angle into any proportion.