degree (dɪˈɡriː)  
—n  
1.  a stage in a scale of relative amount or intensity: a high degree of competence 
2.  an academic award conferred by a university or college on successful completion of a course or as an honorary distinction (honorary degree) 
3.  See burn any of three categories of seriousness of a burn 
4.  (in the US) any of the categories into which a crime is divided according to its seriousness: firstdegree murder 
5.  genealogy a step in a line of descent, used as a measure of the closeness of a blood relationship 
6.  grammar any of the forms of an adjective used to indicate relative amount or intensity: in English they are positive, comparative, and superlative 
7.  music any note of a diatonic scale relative to the other notes in that scale: D is the second degree of the scale of C major 
8.  Celsius scale See also Fahrenheit scale ° a unit of temperature on a specified scale: the normal body temperature of man is 36.8 degrees Celsius 
9.  minute See also second Compare radian ° a measure of angle equal to one threehundredandsixtieth of the angle traced by one complete revolution of a line about one of its ends 
10.  ° 
a. a unit of latitude or longitude, divided into 60 minutes, used to define points on the earth's surface or on the celestial sphere  
b. a point or line defined by units of latitude and/or longitude  
11.  ° a unit on any of several scales of measurement, as for alcohol content or specific gravity 
12.  maths 
a. the highest power or the sum of the powers of any term in a polynomial or by itself: x^{4} + x + 3 and xyz² are of the fourth degree  
b. the greatest power of the highest order derivative in a differential equation  
13.  obsolete a step; rung 
14.  archaic a stage in social status or rank 
15.  by degrees little by little; gradually 
16.  to a degree somewhat; rather 
17.  degrees of frost See frost 
[C13: from Old French degre, from Latin  
de'greeless  
—adj 
degree de·gree (dĭgrē')
n.
Abbr. deg, deg. A unit of measure on a temperature scale.
A division of a circle, equal to ^{1}/_{360} of its circumference.
A position or rank within a graded series.
degree (dĭgrē') Pronunciation Key

In geometry, a unit of measurement of angles, 1/360 of a circle. In physics, a unit of temperature (see Celsius, Fahrenheit, and Kelvin scale). A degree on the Fahrenheit scale is smaller than a degree on the Celsius or Kelvin scale. Degrees on the Celsius and Kelvin scales are the same size.
by degrees
Gradually, by successive steps or stages. For example, By degrees he began to delegate more and more of his duties to his staff. [Mid1500s] Also see by inches.