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Spherical excess
(gcide) | 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.
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2. Of or pertaining to a sphere.
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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.
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Knaves, thieves, and treachers by spherical
predominance. --Shak.
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Though the stars were suns, and overburned
Their spheric limitations. --Mrs.
Browning.
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Spherical angle, Spherical coordinate, {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.
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Spherical excess
(gcide) | 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.
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To gild refined gold, to paint the lily,
To throw a perfume on the violet, . . .
Is wasteful and ridiculous excess. --Shak.
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That kills me with excess of grief, this with excess
of joy. --Walsh.
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2. An undue indulgence of the appetite; transgression of
proper moderation in natural gratifications; intemperance;
dissipation.
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Be not drunk with wine, wherein is excess. --Eph. v.
18.
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Thy desire . . . leads to no excess
That reaches blame. --Milton.
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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.
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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.
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