Etymology
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mean (adj.2)

"occupying a middle or intermediate place;" mid-14c., of persons, "of middle rank" (but this is possibly from, or mixed with, mean (adj.1)); from Anglo-French meines (plural), Old French meien, variant of moiien "mid-, medium, common, middle-class" (12c., Modern French moyen), from Late Latin medianus "of the middle," from Latin medius "in the middle" (from PIE root *medhyo- "middle").

From late 14c. as "in a middle state, between two extremes." Meaning "intermediate in time, coming between two events or points in time" is from mid-15c. (the sense in meanwhile, meantime). The mathematical sense "intermediate in a number of greater or lesser values, quantities, or amounts" is from late 14c.

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meso- 
before vowels mes-, word-forming element meaning "middle, intermediate, halfway," from Greek mesos "middle, in the middle; middling, moderate; between" (from PIE root *medhyo- "middle").
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mediate (adj.)

early 15c., "intermediate," from Medieval Latin mediatus, past-participle adjective from Latin mediare "to be in the middle," from medius "middle" (from PIE root *medhyo- "middle"). Related: Mediately.

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mesne (adj.)

mid-15c., "middle, intervening, intermediate;" altered spelling (by French influence) of Anglo-French meen "mean" (Old French meien "middle;" see mean (adj.); also see demesne).

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root (v.2)
"cheer, support," 1889, American English, originally in a baseball context, probably from root (v.1) via intermediate sense of "study, work hard" (1856). Related: Rooted; rooting.
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media (n.)

"newspapers, radio, TV, etc." 1927, perhaps abstracted from mass-media (1923, a technical term in advertising); plural of medium (n.) as "intermediate agency," a sense attested in English from c. 1600. Also see -a (2).

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mullion (n.)

in architecture, "a vertical column between the lights of a window or screen," 1560s, metathesis of Middle English moyniel (early 14c.), from Anglo-French moinel, noun use of moienel (adj.) "middle," from Old French meien "intermediate, mean" (see mean (adj.)). Related: Mullioned.

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extrapolation (n.)

"an approximate calculation made by inferring unknown values from trends in the known data," 1867, noun of action from extrapolate by analogy of interpolation. The original sense was "an inserting of intermediate terms in a mathematical series." The transferred sense of "drawing of a conclusion about the future based on present tendencies" is from 1889.

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jag (n.1)
"period of unrestrained activity," 1887, American English, perhaps via intermediate sense of "as much drink as a man can hold" (1670s), from earlier meaning "load of hay or wood" (1590s), of unknown origin. Used in U.S. colloquial speech from 1834 to mean "a quantity, a lot."
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directly (adv.)

late 14c., "completely;" early 15c., "in a straight line," also, figuratively (of speaking or writing) "clearly, unmistakably, expressly," from direct (adj.) + -ly (2). Meaning "at once, straightway, immediately in time" (c. 1600) is from earlier sense of "without intermediate steps" (1520s).

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