Degree

n.
  1. A step, stair, or staircase.
  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.
  3. The point or step of progression to which a person has arrived; rank or station in life; position.
  4. Measure of advancement; quality; extent; as, tastes differ in kind as well as in degree.
  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.
  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.
  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, a2b3c 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, ax4 + bx2 = c, and mx2y2 + 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.
    12. Accumulation of degrees . (Eng. Univ.)
    See under Accumulation.
    By degrees ,
    step by step; by little and little; by moderate advances.
    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 coördinates. 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.