Etymology
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*medhyo- 
Proto-Indo-European root meaning "middle." Perhaps related to PIE root *me- (2) "to measure."

It forms all or part of: amid; intermediate; mean (adj.2) "occupying a middle or intermediate place;" medal; medial; median; mediate; medieval; mediocre; Mediterranean; medium; meridian; mesic; mesial; meso-; meson; Mesopotamia; Mesozoic; mezzanine; mezzo; mezzotint; mid (prep., adj.); middle; Midgard; midriff; midst; midwife; milieu; minge; mizzen; moiety; mullion.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit madhyah, Avestan madiya- "middle," Greek mesos, Latin medius "in the middle, between; from the middle," Gothic midjis, Old English midd "middle," Old Church Slavonic medzu "between," Armenian mej "middle."
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*mei- (1)
Proto-Indo-European root meaning "to change, go, move," "with derivatives referring to the exchange of goods and services within a society as regulated by custom or law" [Watkins].

It forms all or part of: amiss; amoeba; azimuth; common; commune; communicate; communication; communism; commute; congee; demean; emigrate; emigration; excommunicate; excommunication; immune; immutable; incommunicado; mad; mean (adj.1) "low-quality;" mew (n.2) "cage;" mews; migrate; migration; mis- (1) "bad, wrong;" mistake; Mithras; molt; Mstislav; municipal; munificent; mutable; mutant; mutate; mutation; mutatis mutandis; mutual; permeable; permeate; permutation; permute; remunerate; remuneration; transmutation; transmute; zenith.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit methati "changes, alternates, joins, meets;" Avestan mitho "perverted, false;" Hittite mutai- "be changed into;" Latin mutare "to change," meare "to go, pass," migrare "to move from one place to another," mutuus "done in exchange;" Old Church Slavonic mite "alternately;" Czech mijim "to go by, pass by," Polish mijać "avoid;" Gothic maidjan "to change."
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*geus- 
Proto-Indo-European root meaning "to taste; to choose." It forms words for "taste" in Greek and Latin, but its descendants in Germanic and Celtic mostly mean "try" or "choose." The semantic development could have been in either direction.

It forms all or part of: Angus; choice; choose; degustation; disgust; Fergus; gustation; gustatory; gusto; ragout; Valkyrie.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit jus- "enjoy, be pleased;" Avestan zaosa- "pleasure," Old Persian dauš- "enjoy;" Greek geuesthai "to taste;" Latin gustare "to taste, take a little of;" Old English cosan, cesan, Gothic kausjan "to test, to taste of," Old High German koston "try," German kosten "taste of."
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