doctrine of the sphere

Sphere \Sphere\, n. [OE. spere, OF. espere, F. sph[`e]re, L.
   sphaera,. Gr. ??? a sphere, a ball.]
   1. (Geom.) A body or space contained under a single surface,
      which in every part is equally distant from a point within
      called its center.
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   2. Hence, any globe or globular body, especially a celestial
      one, as the sun, a planet, or the earth.
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            Of celestial bodies, first the sun,
            A mighty sphere, he framed.           --Milton.
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   3. (Astron.)
      (a) The apparent surface of the heavens, which is assumed
          to be spherical and everywhere equally distant, in
          which the heavenly bodies appear to have their places,
          and on which the various astronomical circles, as of
          right ascension and declination, the equator,
          ecliptic, etc., are conceived to be drawn; an ideal
          geometrical sphere, with the astronomical and
          geographical circles in their proper positions on it.
      (b) In ancient astronomy, one of the concentric and
          eccentric revolving spherical transparent shells in
          which the stars, sun, planets, and moon were supposed
          to be set, and by which they were carried, in such a
          manner as to produce their apparent motions.
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   4. (Logic) The extension of a general conception, or the
      totality of the individuals or species to which it may be
      applied.
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   5. Circuit or range of action, knowledge, or influence;
      compass; province; employment; place of existence.
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            To be called into a huge sphere, and not to be seen
            to move in 't.                        --Shak.
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            Taking her out of the ordinary relations with
            humanity, and inclosing her in a sphere by herself.
                                                  --Hawthorne.
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            Each in his hidden sphere of joy or woe
            Our hermit spirits dwell.             --Keble.
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   6. Rank; order of society; social positions.
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   7. An orbit, as of a star; a socket. [R.] --Shak.
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   {Armillary sphere}, {Crystalline sphere}, {Oblique sphere},.
      See under {Armillary}, {Crystalline},.

   {Doctrine of the sphere}, applications of the principles of
      spherical trigonometry to the properties and relations of
      the circles of the sphere, and the problems connected with
      them, in astronomy and geography, as to the latitudes and
      longitudes, distance and bearing, of places on the earth,
      and the right ascension and declination, altitude and
      azimuth, rising and setting, etc., of the heavenly bodies;
      spherical geometry.

   {Music of the spheres}. See under {Music}.
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   Syn: Globe; orb; circle. See {Globe}.
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