Definition:Solid Angle

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In the words of Euclid:

A solid angle is the inclination constituted by more than two lines which meet one another and are not in the same surface, towards all the lines.
Otherwise: A solid angle is that which is contained by more than two plane angles which are not in the same plane and are constructed to one point.

(The Elements: Book $\text{XI}$: Definition $11$)

Containment of Solid Angle

The three plane angles which together form a solid angle are said to contain that solid angle.

Vertex of Solid Angle

The common vertex of the angles containing a solid angle is known as the vertex of that solid angle.