Etymology
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fumigation (n.)

late 14c., "action of making aromatic smoke as part of a ceremony," from Latin fumigationem (nominative fumigatio) "a smoking," noun of action from past-participle stem of fumigare "to smoke," from fumus "smoke, fume" (from PIE root *dheu- (1) "dust, vapor, smoke") + root of agere "to set in motion, to do, perform" (from PIE root *ag- "to drive, draw out or forth, move"). Sense of "exposure (of someone or something) to aromatic fumes" is c. 1400, originally as a medicinal or therapeutic treatment.

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fumigate (v.)
1520s, "scent with perfumes," back-formation from fumigation. The older verb was simply fume (c. 1400). Meaning "apply smoke or fumes to," especially for cleansing purposes, is from 1781. Related: Fumigated; fumigating; fumigatory.
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*dheu- (1)

Proto-Indo-European root meaning "dust, vapor, smoke." 

It forms all or part of: enthymeme; fewmet; fume; fumigation; funk; perfume; sfumato; typhoid; typhoon; typhus.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit dhuma- "smoke, fume;" Greek thymos "spirit, courage, anger," thymiao "fumigate," thymin "incense;" Latin fumus "smoke, steam, fume;" Lithuanian dūmai "smoke" (plural); Old Prussian dumis "smoke;" Old Church Slavonic dymu "smoke;" Middle Irish dumacha "fog;" perhaps Old High German toum "steam, vapor."

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*ag- 

Proto-Indo-European root meaning "to drive, draw out or forth, move."

It forms all or part of: act; action; active; actor; actual; actuary; actuate; agency; agenda; agent; agile; agitation; agony; ambagious; ambassador; ambiguous; anagogical; antagonize; apagoge; assay; Auriga; auto-da-fe; axiom; cache; castigate; coagulate; cogent; cogitation; counteract; demagogue; embassy; epact; essay; exact; exacta; examine; exigency; exiguous; fumigation; glucagon; hypnagogic; interact; intransigent; isagoge; litigate; litigation; mitigate; mystagogue; navigate; objurgate; pedagogue; plutogogue; prodigal; protagonist; purge; react; redact; retroactive; squat; strategy; synagogue; transact; transaction; variegate.

It is the hypothetical source of/evidence for its existence is provided by: Greek agein "to lead, guide, drive, carry off," agon "assembly, contest in the games," agōgos "leader," axios "worth, worthy, weighing as much;" Sanskrit ajati "drives," ajirah "moving, active;" Latin actus "a doing; a driving, impulse, a setting in motion; a part in a play;" agere "to set in motion, drive, drive forward," hence "to do, perform," agilis "nimble, quick;" Old Norse aka "to drive;" Middle Irish ag "battle."

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