Degree of a surface

Degree De*gree", n. [F. degr['e], OF. degret, fr. LL. degradare. See {Degrade}.] 1. A step, stair, or staircase. [Obs.] [1913 Webster]

By ladders, or else by degree. --Rom. of R. [1913 Webster]

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. [1913 Webster]

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. [1913 Webster]

4. Measure of advancement; quality; extent; as, tastes differ in kind as well as in degree. [1913 Webster]

The degree of excellence which proclaims genius, is different in different times and different places. --Sir. J. Reynolds. [1913 Webster]

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. [1913 Webster +PJC]

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}. [1913 Webster]

The youth attained his bachelor's degree, and left the university. --Macaulay. [1913 Webster]

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. [1913 Webster]

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. [1913 Webster]

7. (Arith.) Three figures taken together in numeration; thus, 140 is one degree, 222,140 two degrees. [1913 Webster]

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. [1913 Webster]

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. [1913 Webster]

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. [1913 Webster]

Note: The short lines and their spaces are added degrees. [1913 Webster]

{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 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. [1913 Webster]

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. [1913 Webster]