Adjacent Words

Spherical excess definitions

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Webster's 1913 Dictionary

Spherical Spher"ic*al, Spheric Spher"ic, a. [L. sphaericus, Gr. ???: cf. F. sph['e]rique.] 1. Having the form of a sphere; like a sphere; globular; orbicular; as, a spherical body. 2. Of or pertaining to a sphere. 3. Of or pertaining to the heavenly orbs, or to the sphere or spheres in which, according to ancient astronomy and astrology, they were set. Knaves, thieves, and treachers by spherical predominance. --Shak. Though the stars were suns, and overburned Their spheric limitations. --Mrs. Browning. Spherical angle, Spherical co["o]rdinate, Spherical excess, etc. See under Angle, Coordinate, etc. Spherical geometry, that branch of geometry which treats of spherical magnitudes; the doctrine of the sphere, especially of the circles described on its surface. Spherical harmonic analysis. See under Harmonic, a. Spherical lune,portion of the surface of a sphere included between two great semicircles having a common diameter. Spherical opening, the magnitude of a solid angle. It is measured by the portion within the solid angle of the surface of any sphere whose center is the angular point. Spherical polygon,portion of the surface of a sphere bounded by the arcs of three or more great circles. Spherical projection, the projection of the circles of the sphere upon a plane. See Projection. Spherical sector. See under Sector. Spherical segment, the segment of a sphere. See under Segment. Spherical triangle,re on the surface of a sphere, bounded by the arcs of three great circles which intersect each other. Spherical trigonometry. See Trigonometry. -- Spher"ic*al*ly, adv. -- Spher"ic*al*ness, n.

Webster's 1913 Dictionary

Excess Ex*cess", n. [OE. exces, excess, ecstasy, L. excessus a going out, loss of self-possession, fr. excedere, excessum, to go out, go beyond: cf. F. exc[`e]s. See Exceed.] 1. The state of surpassing or going beyond limits; the being of a measure beyond sufficiency, necessity, or duty; that which exceeds what is usual or prover; immoderateness; superfluity; superabundance; extravagance; as, an excess of provisions or of light. To gild refined gold, to paint the lily, To throw a perfume on the violet, . . . Is wasteful and ridiculous excess. --Shak. That kills me with excess of grief, this with excess of joy. --Walsh. 2. An undue indulgence of the appetite; transgression of proper moderation in natural gratifications; intemperance; dissipation. Be not drunk with wine, wherein is excess. --Eph. v. 18. Thy desire . . . leads to no excess That reaches blame. --Milton. 3. The degree or amount by which one thing or number exceeds another; remainder; as, the difference between two numbers is the excess of one over the other. Spherical excess (Geom.), the amount by which the sum of the three angles of a spherical triangle exceeds two right angles. The spherical excess is proportional to the area of the triangle.