SPHERE

(Yunanca köken — orijinale bakınız.) In Geometry, a solid body described by the revolution of a semicircle about its diameter; or it may be defined to be a body bounded by a surface of which every point is equally distant from a single point within the surface, called the centre of the sphere. If r denote the radius of the sphere, and i, y, r the rectangular co-ordinates, the origin being at the centre, the equation of the surface is z2 + y* -fz--=. r2. The following are some of the principal properties of the sphere: 1. The surface of the sphere is equal to four times the area of one of its great eircies, i. e.!.1 se lion ma '■; by a plane pa ing through its centre. 2. The cuive surface of any zone, or portion contained between two parallel planes, is equal to the curve surface of a cylinder of the same height with the height of the zone, or the distance between the planes, and of the same diameter with the sphere. Hence it follows, that the whole surface of the sphere is equal to the curve surface of the circumscribing cylinder. 3. The solid content of a sphere is equal to that of a pyramid whose altitude is the radius, and whose base is equal to the surface of the sphere; and hence the content of the sphere is one third of the product of its radius into its surface. 4. The sphere is equal to two thirds of its circumscribing cylinder. Let r denote the radius of the sphere, s its superficies, c its solid content, and tt the ratio of the semi circumference to the radius = 3-14159; then, since the area of a circle of which r is the radius is - r2, the properties above stated give the relations which follow; viz. Surface = s = 4 tt r2 = 12-56637 X ri, Content = c = J rs = jirr3 = 418859 X r3. If we suppose the diameter = l, and consequently r=£, these relations become s = n, c = 4w. Sphere. In Astronomy, the concave expanse of the heavens, which, having no definite limit, appears to the eye as the interior surface of a sphere enclosing the earth, which is placed at the centre. The ancients gave the name of sphere to the orbits of the several heavenly bodies; thus, the sphere of Jupiter, the sphere of Saturn, the sphere of the fixed stars. In the Ptolemaic astronomy, the different spheres were supposed to be solid and transparent, moving about their common centre independently of each other, and each carrying its appropriate body along with it. Sphere, in Geography, denotes a representation of the earth on the surface of a globe, which has also represented on it an a emblage of circles showing the positions of the equator, ecliptic, meridians, . The ancients gave different appellations to the sphere, according to the inclination of the earth's axis to the horizon. When the poles are in the horizon, it was called a right sphere; when the poles arc in the zenith and nadir, a parallel sphere; and in every other position, an oblique sphere. [s. 1160]