Source : Webster's Revised Unabridged Dictionary (1913)

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.

Trigonometry \Trig`o*nom"e*try\, n.; pl. {-tries}. [Gr. ? a
   triangle + -metry: cf. F. trigonom['e]trie. See {Trigon}.]
   1. That branch of mathematics which treats of the relations
      of the sides and angles of triangles, which the methods of
      deducing from certain given parts other required parts,
      and also of the general relations which exist between the
      trigonometrical functions of arcs or angles.

   2. A treatise in this science.

   {Analytical trigonometry}, that branch of trigonometry which
      treats of the relations and properties of the
      trigonometrical functions.

   {Plane trigonometry}, and {Spherical trigonometry}, those
      branches of trigonometry in which its principles are
      applied to plane triangles and spherical triangles
      respectively.

Source : WordNet®

spherical trigonometry
     n : the trigonometry of spherical triangles