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Spher·ic·al Spher·ic a.

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 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.

-- Spher*ic*al*ly, adv. -- Spher*ic*al*ness, n.

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Ex·cess n.

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.

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