Source : Webster's Revised Unabridged Dictionary (1913)

   7. (Arith.) Three figures taken together in numeration; thus,
      140 is one degree, 222,140 two degrees.

   8. (Algebra) State as indicated by sum of exponents; more
      particularly, the degree of a term is indicated by the sum
      of the exponents of its literal factors; thus, a^{2}b^{3}c
      is a term of the sixth degree. The degree of a power, or
      radical, is denoted by its index, that of an equation by
      the greatest sum of the exponents of the unknown
      quantities in any term; thus, ax^{4} + bx^{2} = c, and
      mx^{2}y^{2} + nyx = p, are both equations of the fourth
      degree.

   9. (Trig.) A 360th part of the circumference of a circle,
      which part is taken as the principal unit of measure for
      arcs and angles. The degree is divided into 60 minutes and
      the minute into 60 seconds.

   10. A division, space, or interval, marked on a mathematical
       or other instrument, as on a thermometer.

   11. (Mus.) A line or space of the staff.

   Note: The short lines and their spaces are added degrees.

   {Accumulation of degrees}. (Eng. Univ.) See under
      {Accumulation}.

   {By degrees}, step by step; by little and little; by moderate
      advances. ``I'll leave it by degrees.'' --Shak.

   {Degree of a} {curve or surface} (Geom.), the number which
      expresses the degree of the equation of the curve or
      surface in rectilinear co["o]rdinates. A straight line
      will, in general, meet the curve or surface in a number of
      points equal to the degree of the curve or surface and no
      more.

   {Degree of latitude} (Geog.), on the earth, the distance on a
      meridian between two parallels of latitude whose latitudes
      differ from each other by one degree. This distance is not
      the same on different parts of a meridian, on account of
      the flattened figure of the earth, being 68.702 statute
      miles at the equator, and 69.396 at the poles.

   {Degree of longitude}, the distance on a parallel of latitude
      between two meridians that make an angle of one degree
      with each other at the poles -- a distance which varies as
      the cosine of the latitude, being at the equator 69.16
      statute miles.

   {To a degree}, to an extreme; exceedingly; as, mendacious to
      a degree.

            It has been said that Scotsmen . . . are . . . grave
            to a degree on occasions when races more favored by
            nature are gladsome to excess.        --Prof.
                                                  Wilson.