Etymology
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olive (n.)

c. 1200, "olive tree," from Old French olive "olive, olive tree" (13c.) or directly from Latin oliva "olive, olive tree," from Greek elaia "olive tree, olive," probably from the same Aegean language (perhaps Cretan) as Armenian ewi "oil."

Applied to the fruit or berry of the tree in English from late 14c. As the color of the unripe olive from 17c. Olive branch as a token of peace is from early 13c., an allusion to the olive leaf brought by the dove sent out by Noah from the ark. Olive oil "oil expressed from the pulp of the common olive" is by 1540s (Oliue oyle). In early writings oil of olive(s) was more common. 

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Olivia 
fem. proper name, from Italian Olivia, from Latin oliva "olive" (see olive).
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oleaginous (adj.)

"oily, unctuous, having the qualities of oil," early 15c., oleaginose (modern from by 1630s), from Old French oléagineux (14c.) and directly from Medieval Latin oleaginus, literally "of the olive," from olea "olive," alteration of oliva (see olive) by influence of oleum "oil." Related: Oleaginousness.

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oil (n.)

late 12c., "olive oil," from Anglo-French and Old North French olie, from Old French oile, uile "oil" (12c., Modern French huile), from Latin oleum "oil, olive oil" (source of Spanish, Italian olio), from Greek elaion "olive tree," from elaia (see olive).

Nearly all the European languages' words for "oil" (Croatian ulje, Polish olej, Hungarian olaj, Albanian uli, Lithuanian alejus, etc.) are from the Greek word; the Germanic (except Gothic) and Celtic one coming from Greek via Latin: Old English æle, Dutch olie, German Öl, Welsh olew, Gaelic uill, etc. 

In English it meant "olive oil" exclusively till c. 1300, when the word began to be extended to any fatty, greasy liquid substance (usually flammable and insoluble in water). Often especially "oil as burned in a lamp to afford light" (as in midnight oil, symbolizing late work). Use for "petroleum" is recorded from 1520s but not common until 19c.

The artist's oils (1660s), short for oil-color (1530s), are paints made by grinding pigment in oil. Oil-painting is attested from 1782.  The ocean-going oil-tanker is from 1900; oil-spill is from 1970. As a condiment, oil and vinegar is attested from 1620s. The figurative expression pour oil upon the waters "appease strife or disturbance" is by 1840, from an ancient trick of sailors.

Another historical illustration which involves monolayers, was when sailors poured oil on the sea in order to calm 'troubled waters' and so protect their ship. This worked by wave damping or, more precisely, by preventing small ripples from forming in the first place so that the wind could have no effect on them. [J. Lyklema, "Fundamentals of Interface and Colloid Science," Academic Press, 2000]

The phenomenon depends on what are called Marangoni effects; Benjamin Franklin experimented with it in 1765.

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Oliver 

masc. personal name, in medieval lore the name of one of Charlemagne's peers, friend of Roland, from French Olivier, from Middle Low German Alfihar, literally "elf-host, elf-army," from alf "elf" (see elf) + hari "host, army" (see harry (v.)). It is cognate with the Anglo-Saxon name Ælfhere. The form in Old French was influenced by olivier "olive tree."

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latke (n.)
"pancake made with grated potatoes," 1925, American English, from Yiddish, from Russian latka "pastry," said to mean literally "a patch," but by Watkins traced to Greek elaia "olive."
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bruschetta (n.)

garlic bread, 1967, from Italian bruschetta, Tuscan name for bread roasted on both sides, dribbled with olive oil and sometimes seasoned with garlic, from bruscare "to roast over coals."

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Lucca 
city and region in Italy, formerly an independent state. Anglicized in Middle and early Modern English as Luke. Noted in England for olive oil and lambskins used in hat-making. Related: Lucchese (adj.), the Italian form, alongside English Luccan (mid-15c.).
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pesto (n.)

green, aromatic, olive oil-based pasta sauce, a Genoese specialty, 1937, from Italian pesto, contracted form of pestato, past participle of pestare "to pound, to crush," in reference to the crushed herbs and garlic in it, from Latin root of pestle.

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ratatouille (n.)

Provençal dish of mixed vegetables simmered in olive oil, 1877, from French ratatouille (19c.). The first element is of uncertain etymology, the second is evidently touiller "to stir up," which Ayto writes was "applied, often disparagingly, to any stew," and which Gamillscheg writes is ultimately from Latin tudes "hammer."

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