The Collaborative International Dictionary of English v.0.48:

Degree \De*gree"\, n. [F. degr['e], OF. degret, fr. LL.
   degradare. See Degrade.]
   1. A step, stair, or staircase. [Obs.]
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            By ladders, or else by degree.        --Rom. of R.
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   2. One of a series of progressive steps upward or downward,
      in quality, rank, acquirement, and the like; a stage in
      progression; grade; gradation; as, degrees of vice and
      virtue; to advance by slow degrees; degree of comparison.
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   3. The point or step of progression to which a person has
      arrived; rank or station in life; position. "A dame of
      high degree." --Dryden. "A knight is your degree." --Shak.
      "Lord or lady of high degree." --Lowell.
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   4. Measure of advancement; quality; extent; as, tastes differ
      in kind as well as in degree.
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            The degree of excellence which proclaims genius, is
            different in different times and different places.
                                                  --Sir. J.
                                                  Reynolds.
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   5. Grade or rank to which scholars are admitted by a college
      or university, in recognition of their attainments; also,
      (informal) the diploma provided by an educational
      institution attesting to the achievement of that rank; as,
      the degree of bachelor of arts, master, doctor, etc.; to
      hang one's degrees on the office wall.
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   Note: In the United States diplomas are usually given as the
         evidence of a degree conferred. In the humanities the
         first degree is that of bachelor of arts (B. A. or A.
         B.); the second that of master of arts (M. A. or A.
         M.). The degree of bachelor (of arts, science,
         divinity, law, etc.) is conferred upon those who
         complete a prescribed course of undergraduate study.
         The first degree in medicine is that of doctor of
         medicine (M. D.). The degrees of master and doctor are
         also conferred, in course, upon those who have
         completed certain prescribed postgraduate studies, as
         doctor of philosophy (Ph. D.); the degree of doctor
         is also conferred as a complimentary recognition of
         eminent services in science or letters, or for public
         services or distinction (as doctor of laws (LL. D.)
         or doctor of divinity (D. D.), when they are called
         honorary degrees.
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               The youth attained his bachelor's degree, and
               left the university.               --Macaulay.
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   6. (Genealogy) A certain distance or remove in the line of
      descent, determining the proximity of blood; one remove in
      the chain of relationship; as, a relation in the third or
      fourth degree.
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            In the 11th century an opinion began to gain ground
            in Italy, that third cousins might marry, being in
            the seventh degree according to the civil law.
                                                  --Hallam.
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   7. (Arith.) Three figures taken together in numeration; thus,
      140 is one degree, 222,140 two degrees.
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   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^2b^3c
      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^2y^2 + nyx = p, are both equations of the fourth
      degree.
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   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.
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   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.
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   Note: The short lines and their spaces are added degrees.
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   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 Degree of a surface (Geom.), the
      number which expresses the degree of the equation of the
      curve or surface in rectilinear coordinates. 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.
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            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.
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WordNet (r) 3.0 (2006):

Doctor of Medicine
    n 1: a doctor's degree in medicine [syn: Doctor of Medicine,
         MD]