# Definition:Axis of Solid Figure

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## Definition

### Axis of Cone

Let $K$ be a right circular cone.

Let point $A$ be the apex of $K$.

Let point $O$ be the center of the base of $K$.

Then the line $AO$ is the **axis** of $K$.

In the words of Euclid:

*The***axis of the cone**is the straight line which remains fixed and about which the triangle is turned.

(*The Elements*: Book $\text{XI}$: Definition $19$)

### Axis of Cylinder

In the words of Euclid:

*The***axis of the cylinder**is the straight line which remains fixed and about which the parallelogram is turned.

(*The Elements*: Book $\text{XI}$: Definition $22$)

In the above diagram, the **axis** of the cylinder $ACBEFD$ is the straight line $GH$.

### Axis of Sphere

By definition, a sphere is made by turning a semicircle around a straight line.

That straight line is called the **axis of the sphere**.

In the words of Euclid:

*The***axis of the sphere**is the straight line which remains fixed about which the semicircle is turned.

(*The Elements*: Book $\text{XI}$: Definition $15$)

## Linguistic Note

The plural of **axis** is **axes**, which is pronounced **ax-eez** not **ax-iz**.

Compare basis.

## Sources

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