Etymology
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grade (v.)
1650s, "to arrange in grades," from grade (n.). Meaning "to reduce (a road, etc.) to a level or degree of inclination" is from 1835. Meaning "assign a letter mark to" is from 1931. Related: Graded; grading.
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grade (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.

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high-grade (adj.)
1870, in mining, of ores, from high (adj.) + grade (n.).
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low-grade (adj.)
1867, originally in mining, with reference to ores, from low (adj.) + grade (n.).
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grader (n.)
1868, of machines; 1870, of persons, agent noun from grade (v.).
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upgrade (n.)
also up-grade, 1847, "upward slope," from up (adj.) + grade (n.). The meaning "upgraded version" is recorded from 1980.
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upgrade (v.)
"increase to a higher grade or rank," 1904 (transitive); 1950 (intransitive), from up (adv.) + grade (v.). Related: Upgraded; upgrading.
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downgrade (v.)

also down-grade, "to lower in rank, status, etc.," 1930, from down (adv.) + grade (v.). Related: Downgraded; downgrading. As a noun, "a downward slope," from 1858.

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gradient (n.)
"steep slope of a road or railroad," 1835, principally in American English, probably from grade (n.) by analogy of quotient, etc. [OED]. It was used 17c. as an adjective, of animals, "characterized by walking;" in that case it is probably from Latin gradientem, present participle of gradi "to walk."
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*ghredh- 

Proto-Indo-European root meaning "to walk, go." 

It forms all or part of: aggress; aggression; aggressive; centigrade; congress; degrade; degree; degression; digress; digression; egress; gradation; grade; gradual; graduate; grallatorial; gravigrade; ingredient; ingress; plantigrade; progress; progression; regress; regression; retrograde; retrogress; tardigrade; transgress; transgression.

It is the hypothetical source of/evidence for its existence is provided by: Latin gradus "a step, a pace, gait," figuratively "a step toward something, a degree of something rising by stages;" gradi "to walk, step, go;" Lithuanian gridiju, gridyti "to go, wander;" Old Church Slavonic gredo "to come;" Old Irish in-greinn "he pursues."  

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