Definition:Axis of Solid Figure

Definition

Axis of Cone

Let $K$ be a cone whose base has a center of symmetry $C$.

Let $\LL$ be the straight line from the apex of $K$ to $C$.

Then $\LL$ is known as the axis of $K$.

Axis of Right Circular 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 Right Circular 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 $15$)

Axis of Helix

The axis of a helix $\HH$ is the fixed line to which the tangent to $\HH$ makes a makes a constant angle.

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.