Etymology
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medio- 

word-forming element meaning "middle," used as a combining form of Latin medius "in the middle, between; from the middle," from PIE root *medhyo- "middle."

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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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milieu (n.)

"surroundings, medium, environment," 1854, from French milieu, "middle, medium, mean," literally "middle place" (12c.), from mi "middle" (from Latin medius, from PIE root *medhyo- "middle") + lieu "place" (see lieu).

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stripe (v.)
"ornament with stripes," early 15c., from stripe (n.1). Compare Middle Flemish stripen, Middle Low German and Middle Dutch stripen. Related: Striped; striping.
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mesentery (n.)

"a fold of the peritoneum," early 15c., mesenterie, from medical Latin mesenterium "middle of the intestine," from medical Greek mesenterion, literally "the middle intestine," from mesos "middle" (from PIE root *medhyo- "middle") + enteron "intestine" (from PIE *enter-, comparative of root *en "in"). Related: Mesenteric.

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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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moiety (n.)

"an equal half, a half part or share," mid-15c., moite, from Old French moite, earlier meitiet (12c., Modern French moitié) "half; middle; portion, piece," from Latin medietatem (nominative medietas) "half," originally "middle point," from medius "middle" (from PIE root *medhyo- "middle").

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median (adj.)

"pertaining to or situated in the middle, occupying a middle or intermediate position," 1590s, from French médian (15c.) and directly from Latin medianus "of the middle," from medius "in the middle" (from PIE root *medhyo- "middle"). Originally anatomical, of veins, arteries, nerves; general use is by 1640s. Median strip "narrow strip (paved or not) between lanes of a divided road" is by 1939, American English.

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mediation (n.)

late 14c., mediacioun, "intervention, agency or action as a mediator or intermediary," from Medieval Latin mediationem (nominative mediatio) "a division in the middle," noun of action from past-participle stem of Latin mediare "to halve; to be in the middle," from medius "middle" (from PIE root *medhyo- "middle"). Related: Mediational.

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medieval (adj.)
Origin and meaning of medieval

"pertaining to or suggestive of the Middle Ages," 1825 (mediaeval), coined in English from Latin medium "the middle" (from PIE root *medhyo- "middle") + aevum "age" (from PIE root *aiw- "vital force, life; long life, eternity").

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