gradient (n.)

1510s, "degree of measurement," from French grade "grade, degree" (16c.), from Latin gradus "a step, a pace, gait; a step climbed (on a ladder or stair);" figuratively "a step toward something, a degree of something rising by stages," from gradi (past participle gressus) "to walk, step, go," from PIE root *ghredh- "to walk, go." It replaced Middle English gree "a step, degree in a series," from Old French grei "step," from Latin gradus.

Meaning "inclination of a road or railroad" is from 1811. Meaning "class of things having the same quality or value" is from 1807; meaning "division of a school curriculum equivalent to one year" is from 1835; that of "letter-mark indicating assessment of a student's work" is from 1886 (earlier used of numerical grades). Grade A "top quality, fit for human consumption" (originally of milk) is from a U.S. system instituted in 1912. To figuratively make the grade "be successful" is from 1912; early examples do not make clear whether the literal grade in mind was one of elevation, quality, or scholarship.

in mathematics, "the result of the process of division, quantity resulting from the division of one number by another, number of times one quantity is contained in another," mid-15c., quocient, from Latin quotiens "how often? how many times?; as often as," pronominal adverb of time, from quot "how many?" (from PIE root *kwo-, stem of relative and interrogative pronouns). The Latin adverb quotiens was mistaken in Middle English for a present participle of quot in -ens.