A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within called the center.

The diameter is a straight line drawn through the center and having its extremities in the curved surface. The radius - 1/2 diameter - is the straight line from the center to a point on the surface.

A plane is tangent to a sphere when it touches the sphere in only one point. A plane perpendicular to a radius at its outer extremity is tangent to the sphere, Fig. 83.

Plane Tangent to Sphere.

Fig. 83. Plane Tangent to Sphere.

Great and Small Circle.

Fig. 84. Great and Small Circle.

An inscribed polyhedron is a polyhedron whose vertices lie in the surface of the sphere.

A circumscribed polyhedron is a polyhedron whose faces are tangent to a sphere.

A great circle is the intersection of the spherical surface and a plane passing through the center of the sphere, Fig. 84.

Intersections of Plane with Cone and Cylinder Giving Ellipses as Shown in (b) and (d).

Fig. 85. Intersections of Plane with Cone and Cylinder Giving Ellipses as Shown in (b) and (d).

A small circle is the intersection of the spherical surface and a plane which does not pass through the center, Fig. 84.