# Definition:Semicubical Parabola

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## Definition

The **semicubical parabola** is the plane curve whose locus can be described with the equation:

- $y^2 = a^2 x^3$

## Also known as

The **semicubical parabola** is also known as:

**Neile's parabola**, after William Neile- the
**cuspidal cubic**.

## Also see

- Results about
**the semicubical parabola**can be found**here**.

## Historical Note

The **semicubical parabola** was discovered and rectified by William Neile, who published his findings in $1657$.

In $1659$, John Wallis published the method he had used, giving William Neile full credit.

It was the first curve to be rectified, apart from conic sections and some of the spirals.

## Sources

- 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**semicubical parabola** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**semicubical parabola**

- Weisstein, Eric W. "Semicubical Parabola." From
*MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/SemicubicalParabola.html