degreeyoudaoicibaDictYouDict[degree 词源字典]
degree: [13] Etymologically, degree means ‘step down’, a sense revealed more clearly in its relative degrade [14]. It comes via Old French degre from Vulgar Latin *dēgradus, a compound noun formed from the prefix dē- ‘down’ and gradus ‘step’ (source of English gradual and a wide range of other words). The word’s modern meanings, such as ‘academic rank’ and ‘unit of temperature’, come from an underlying abstract notion of a hierarchy of steps or ranks. Degrade represents a parallel but distinct formation, originally coined as ecclesiastical Latin dēgradāre and passed into English via Old French degrader.
=> degrade, gradual, progress[degree etymology, degree origin, 英语词源]
degree (n.)youdaoicibaDictYouDict
early 13c., from Old French degré (12c.) "a step (of a stair), pace, degree (of relationship), academic degree; rank, status, position," said to be from Vulgar Latin *degradus "a step," from Late Latin degredare, from Latin de- "down" (see de-) + gradus "step" (see grade (n.)).

Most modern senses date from Middle English, from notion of a hierarchy of steps. Meaning "a grade of crime" is 1670s; that of "a unit of temperature" is from 1727. The division of the circle into 360 degrees was known in Babylon and Egypt. It is perhaps from the daily motion of the sun through the zodiac in the course of a year.