Etymology
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foil (v.1)
c. 1300, foilen "to spoil a trace or scent by running over it" (more commonly defoilen), irregularly from Old French foler, fuler "trample on, injure, maim; ill-treat, deceive, get the better of" (13c., Modern French fouler), from Vulgar Latin *fullare "to clean cloth" (by treading on it), from Latin fullo "one who cleans cloth, a fuller," which is of unknown origin. Compare full (v.).

Hence, "to overthrow, defeat" (1540s; as a noun in this sense from late 15c.); "frustrate the efforts of" (1560s). Related: Foiled; foiling. Foiled again! as a cry of defeat and dismay is from at least 1847.
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foil (n.)

"very thin sheet of metal," early 14c., foile, from Old French foil, fueill, fueille "leaf; foliage; sheet of paper; sheet of metal" (12c., Modern French feuille), from Latin folia, plural (mistaken for fem. singular) of folium "leaf" (from PIE root *bhel- (3) "to thrive, bloom").

The sense of "one who enhances another by contrast" (1580s) is from the practice of backing a gem with metal foil to make it shine more brilliantly. The meaning "light sword used in fencing" (1590s) could be from this sense, or from foil (v.). The sense of "metallic food wrap" is from 1897.

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foil (v.2)
"apply foil to," 1610s, from foil (n.1).
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aerofoil (n.)
"lifting surface of an aircraft, etc.," 1907, from aero- + foil (n.).
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tinfoil (n.)
also tin-foil, late 15c., from tin (n.) + foil (n.).
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hydrofoil (n.)
1959, "boat that travels through water on wings," short for hydrofoil boat, hydrofoil being originally the name of the "wings" themselves (1920); formed in English from hydro- + foil (n.).
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quatrefoil (n.)

"flower with four leaves, leaf with four leaflets (as a four-leaf clover)," early 15c., from Old French quatrefoil, from quatre "four" (see four) + foil "leaf" (see foil (n.)). As the word for an architectural opening or pattern of a similar design, by 1805.

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fuller (n.)
"one who fulls cloth," Old English fullere "fuller" (Mark ix.3), from Latin fullo "fuller" (see foil (v.)). The native word is walker. Fuller's earth (silicate of alumina) is recorded by 1520s; so called because it was used in cleansing cloth.
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defile (v.)

c. 1400, "to desecrate, profane;" mid-15c., "to make foul or dirty," also "to rape, deflower," alteration of earlier defoulen, from Old French defouler "trample down, violate," also "ill-treat, dishonor," from de- "down" (see de-) + foler "to tread," from Latin fullo "person who cleans and thickens cloth by stamping on it" (see foil (v.1)).

The alteration (or re-formation) in English is from influence of Middle English filen (v.) "to render foul; make unclean or impure," literal and figurative, from Old English fylen (trans.), related to Old English fulian (intrans.) "to become foul, rot," from the source of foul (adj.). Compare befoul, which also had a parallel form befilen. Related: Defiled; defiling.

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*bhel- (3)
Proto-Indo-European root meaning "to thrive, bloom," possibly a variant of PIE root *bhel- (2) "to blow, swell."

It forms all or part of: blade; bleed; bless; blood; blow (v.2) "to bloom, blossom;" bloom (n.1) "blossom of a plant;" bloom (n.2) "rough mass of wrought iron;" blossom; cauliflower; chervil; cinquefoil; deflower; defoliation; effloresce; exfoliate; feuilleton; flora; floral; floret; florid; florin; florist; flour; flourish; flower; foil (n.) "very thin sheet of metal;" foliage; folio; folium; gillyflower; Phyllis; phyllo-; portfolio; trefoil.

It is the hypothetical source of/evidence for its existence is provided by: Greek phyllon "leaf;" Latin flos "flower," folio, folium "leaf;" Middle Irish blath, Welsh blawd "blossom, flower;" Gaelic bile "leaflet, blossom;" Old English blowan "to flower, bloom."
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