Etymology
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company (n.)

mid-12c., "large group of people," from Old French compagnie "society, friendship, intimacy; body of soldiers" (12c.), from Late Latin companio, literally "bread fellow, messmate," from Latin com "with, together" (see com-) + panis "bread," from PIE root *pa- "to feed." Abbreviation co. dates from 1670s. 

Meaning "companionship, consort of persons one with another, intimate association" is from late 13c. Meaning "person or persons associated with another in any way" is from c. 1300. In Middle English the word also could mean "sexual union, intercourse" (c. 1300).

From late 14c. as "a number of persons united to perform or carry out anything jointly," which developed a commercial sense of "business association" by 1550s, the word having been used in reference to trade guilds from late 14c. Meaning "subdivision of an infantry regiment" (in 19c. usually 60 to 100 men, commanded by a captain) is from c. 1400. 

Meaning "person or persons with whom one voluntarily associates" is from c. 1600; phrase keep company "consort" is from 1560s (bear company in the same sense is from c. 1300). Expression two's company "two persons are just right" (for conversation, etc.), is attested from 1849; the following line varies: but three is none (or not), 1849; three's trumpery (1864); three's a crowd (1856). 

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co. 

by 1670s as an abbreviation of company in the business sense, indicating the partners in the firm whose names do not appear in its name. Hence and co. to indicate "the rest" of any group (1757).

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*pa- 
*pā-, Proto-Indo-European root meaning "to protect, feed."

It forms all or part of: antipasto; appanage; bannock; bezoar; companion; company; feed; fodder; food; forage; foray; foster; fur; furrier; impanate; pabulum; panatela; panic (n.2) "type of grass;" pannier; panocha; pantry; pastern; pastor; pasture; pester; repast; satrap.

It is the hypothetical source of/evidence for its existence is provided by: Greek pateisthai "to feed;" Latin pabulum "food, fodder," panis "bread," pasci "to feed," pascare "to graze, pasture, feed," pastor "shepherd," literally "feeder;" Avestan pitu- "food;" Old Church Slavonic pasti "feed cattle, pasture;" Russian pishcha "food;" Old English foda, Gothic fodeins "food, nourishment."
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troupe (n.)
1825, "company, band," especially of performers, actors, dancers, etc., from French troupe "company" (see troop (n.)).
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Lacoste 
Paris-based high-end apparel company, founded 1933, named for company co-founder René Lacoste (1904-1996).
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Dictaphone (n.)

dictation recording and reproduction machine, trademarked by the Columbia Graphophone Company in 1907; from dictation + -phone. A separate company from 1923.

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Avis 

U.S. car rental company, according to company history founded 1946 at Willow Run Airport in Detroit by U.S. businessman Warren Avis and named for him.

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LLC 
abbreviation of Limited Liability Company (see limited).
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companionship (n.)

"fellowship, association, company," 1540s, from companion + -ship.

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klaxon (n.)
"loud warning horn," 1908, originally on automobiles, said to have been named for the company that sold them (The Klaxon Company; distributor for Lovell-McConnell Manufacturing Co., Newark, New Jersey), but probably the company was named for the horn, from a made-up word likely based on Greek klazein "to roar," which is cognate with Latin clangere "to resound" (compare clang).
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