This section is from "The American Cyclopaedia", by George Ripley And Charles A. Dana. Also available from Amazon: The New American Cyclopędia. 16 volumes complete..

**Sphere** (Gr. σφαίρα), in geometry, a body bounded by a surface, every point of which is equally distant from a point within called the centre. The figure-may be generated by the revolution of a semicircle about its diameter as an axis. It is easily shown that if a sphere be enclosed in a right cylinder, the portions of the surface between any pair of planes parallel to the bases of the cylinder are equal in area to the portions of the cylindrical surface between the same planes. Accordingly, the total surface of the sphere is equal to the curved surface of the cylinder. This surface is manifestly equal to the rectangle of the height of the cylinder by the circumference of its base; that is, to four times the base, for the height of the cylinder is equal to the diameter of the base. Hence the surface of a sphere is equal to four times the area of a circle of the same diameter. Its solid content is manifestly equal to that of a pyramid, whose base is equal to the surface of the sphere, and whoso altitude is the radius; hence equal to one third of the product of its radius into its surface; or, the cube of the diameter being to the solid content nearly as 300 to 157, the content may be calculated from this proportion, or by multiplying the cube by the decimal •52333. - In geography, sphere denotes a representation of the earth on a globular surface. (See Globe.) In astronomy, it is the concave expanse of the heavens, which appears as the interior surface of a sphere, of which the centre is the earth.

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