What is "spherical excess"

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. [1913 Webster] -- Spher"ic*al*ly, adv. -- Spher"ic*al*ness, n.

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 proper; 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.

n. (context geometry English) 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.