Etymology
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grease (n.)

"oily fat of land animals," c. 1300, from Anglo-French grece, Old French gresse, craisse "grease, fat" (Modern French graisse), from Vulgar Latin *crassia "(melted) animal fat, grease," from Latin crassus "thick, solid, fat" (source also of Spanish grasa, Italian grassa), which is of unknown origin. Grease paint, used by actors, attested from 1880. Grease monkey "mechanic" is from 1918.

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grease (v.)
mid-14c., "smear, lubricate, or anoint with grease or fat," from grease (n.). Sense of "ply with bribe or protection money" is 1520s, from notion of grease the wheels "make things run smoothly" (mid-15c.). To grease (someone's) palm is from 1580s. Expression greased lightning, representing something that goes very fast, is American English, by 1832.
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elbow (v.)
"thrust with the elbow," c. 1600, from elbow (n.). Figurative sense is from 1863. Related: Elbowed; elbowing.
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elbow (n.)

"bend of the arm," c. 1200, elbowe, from a contraction of Old English elnboga "elbow," from Proto-Germanic *elino-bugon, literally "bend of the forearm" (source also of Middle Dutch ellenboghe, Dutch elleboog, Old High German elinbogo, German Ellenboge, Old Norse ölnbogi).

First element is from PIE *elina "arm," from root *el- "elbow, forearm." Second element is from Proto-Germanic *bugon-, from PIE root *bheug- "to bend." To be out at elbows (1620s) was literally to have holes in one's coat. Phrase elbow grease "hard rubbing" is attested from 1670s, from jocular sense of "the best substance for polishing furniture." Elbow-room "room to extend one's elbows," hence, "ample room for activity," is attested from 1530s.

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degrease (v.)

also de-grease, "remove the grease from," 1855; see de- + grease. Related: Degreased; degreaser; degreasing.

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*el- 

Proto-Indo-European root meaning "elbow, forearm." It forms all or part of: elbow; ell (n.1) unit of measure; uilleann; ulna.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit anih "part of the leg above the knee;" Greek ōlenē "elbow;" Latin ulna, Armenian uln "shoulder;" Lithuanian alkūnė "elbow;" Old English eln "forearm."

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uilleann 
in uilleann pipe, from Irish uilleann "elbow," from Old Irish uilenn, from PIE *ol-ena-, from root *el- "elbow, forearm."
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ulna (n.)
inner bone of the forearm, 1540s, medical Latin, from Latin ulna "the elbow," also a measure of length, from PIE *el-ina-, extended form of root *el- "elbow, forearm." Related: Ulnar.
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suet (n.)
late 14c., "solid fat formed in the torsos of cattle and sheep," probably from an Anglo-French diminutive of Old French siu "fat, lard, grease, tallow" (Modern French suif), from Latin sebum "tallow, grease" (see sebum). Related: Suety.
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cubit (n.)

ancient unit of measure (usually from 18 to 22 inches) based on the forearm from elbow to fingertip, early 14c., from Latin cubitum, cubitus "the elbow, the forearm," generally regarded as a derivative of PIE *keu(b)- "to bend," but de Vaan finds this dubious based on the sense of the proposed cognates and the sound changes involved. Also compare cubicle.

It seems much safer to assume that cubitus 'elbow' is a specific instance of the ppp. cubitus of the verb cubare 'to lie down'. People lie down on their elbow if they sleep on their side, and the Romans even reclined when dining. It matters little whether the original meaning was 'forearm' or 'the elbow joint'. One may even suggest that the verb cubitare 'to lie down' ... is not (only) a frequentative to cubare, but (also) arose as a denominative 'to rest on the elbow' to cubitus. [de Vaan]

Such a measure, known by a word meaning "forearm" or the like, was known to many peoples (compare Greek pekhys, Hebrew ammah, English ell).

The word also was used in English in the "forearm, part of the arm from the elbow downward" sense (early 15c.); hence cubital "as long as a cubit" (mid-15c.), also "pertaining to the forearm" (1610s).

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