Definition:Axis of Solid Figure

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Definition

Axis of Cone

RightCircularCone.png


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

Cylinder.png


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.