The Collaborative International Dictionary of English v.0.48:

Octant \Oc"tant\, n. [L. octans, -antis. fr. octo eight. See
   Octave.]
   1. (Geom.) The eighth part of a circle; an arc of 45 degrees.
      [1913 Webster]

   2. (Astron. & Astrol.) The position or aspect of a heavenly
      body, as the moon or a planet, when half way between
      conjunction, or opposition, and quadrature, or distant
      from another body 45 degrees.
      [1913 Webster]

   3. An instrument for measuring angles (generally called a
      quadrant), having an arc which measures up to 9O[deg],
      but being itself the eighth part of a circle. Cf.
      Sextant.
      [1913 Webster]

   4. (Math. & Crystallog.) One of the eight parts into which a
      space is divided by three coordinate planes.
      [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Quadrant \Quad"rant\, n. [L. quadrans, -antis, a fourth part, a
   fourth of a whole, fr. quattuor four: cf. F. quadrant,
   cadran. See Four, and cf. Cadrans.]
   1. The fourth part; the quarter. [Obs.] --Sir T. Browne.
      [1913 Webster]

   2. (Geom.) The quarter of a circle, or of the circumference
      of a circle, an arc of 90[deg], or one subtending a right
      angle at the center.
      [1913 Webster]

   3. (Anal. (Geom.) One of the four parts into which a plane is
      divided by the coordinate axes. The upper right-hand part
      is the first quadrant; the upper left-hand part the
      second; the lower left-hand part the third; and the lower
      right-hand part the fourth quadrant.
      [1913 Webster]

   4. An instrument for measuring altitudes, variously
      constructed and mounted for different specific uses in
      astronomy, surveying, gunnery, etc., consisting commonly
      of a graduated arc of 90[deg], with an index or vernier,
      and either plain or telescopic sights, and usually having
      a plumb line or spirit level for fixing the vertical or
      horizontal direction.
      [1913 Webster]

   Gunner's quadrant, an instrument consisting of a graduated
      limb, with a plumb line or spirit level, and an arm by
      which it is applied to a cannon or mortar in adjusting it
      to the elevation required for attaining the desired range.


   Gunter's quadrant. See Gunter's quadrant, in the
      Vocabulary.

   Hadley's quadrant, a hand instrument used chiefly at sea to
      measure the altitude of the sun or other celestial body in
      ascertaining the vessel's position. It consists of a frame
      in the form of an octant having a graduated scale upon its
      arc, and an index arm, or alidade pivoted at its apex.
      Mirrors, called the index glass and the horizon glass, are
      fixed one upon the index arm and the other upon one side
      of the frame, respectively. When the instrument is held
      upright, the index arm may be swung so that the index
      glass will reflect an image of the sun upon the horizon
      glass, and when the reflected image of the sun coincides,
      to the observer's eye, with the horizon as seen directly
      through an opening at the side of the horizon glass, the
      index shows the sun's altitude upon the scale; -- more
      properly, but less commonly, called an octant.

   Quadrant of altitude, an appendage of the artificial globe,
      consisting of a slip of brass of the length of a quadrant
      of one of the great circles of the globe, and graduated.
      It may be fitted to the meridian, and being movable round
      to all points of the horizon, serves as a scale in
      measuring altitudes, azimuths, etc.
      [1913 Webster]

WordNet (r) 3.0 (2006):

quadrant
    n 1: a quarter of the circumference of a circle [syn:
         quadrant, quarter-circle]
    2: any of the four areas into which a plane is divided by two
       orthogonal coordinate axes
    3: the area enclosed by two perpendicular radii of a circle
    4: a measuring instrument for measuring altitude of heavenly
       bodies

Moby Thesaurus II by Grady Ward, 1.0:

51 Moby Thesaurus words for "quadrant":
   adjunct, astrolabe, azimuth circle, azimuth compass, bevel,
   bevel protractor, bevel square, clinometer, component, contingent,
   crescent, cross section, detachment, detail, division, dole,
   fraction, goniometer, graphometer, half circle, hemicycle,
   installment, item, pantometer, parcel, part, particular,
   percentage, portion, protractor, quarter, quota, radiogoniometer,
   random sample, remainder, sample, sampling, section, sector,
   segment, semicircle, sextant, share, subdivision, subgroup,
   subspecies, theodolite, transit, transit circle,
   transit instrument, transit theodolite



Bouvier's Law Dictionary, Revised 6th Ed (1856):

QUADRANT. In angular measures, a quadrant is equal to ninety degrees. Vide
Measure.