Etymology
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square (adj.)

early 14c., "containing four equal sides and right angles," from square (n.), or from Old French esquarre, past participle of esquarrer. Meaning "honest, fair," is first attested 1560s; that of "straight, direct" is from 1804. Of meals, from 1868.

Sense of "old-fashioned" is 1944, U.S. jazz slang, said to be from shape of a conductor's hand gestures in a regular four-beat rhythm. Square-toes meant nearly the same thing late 18c.: "precise, formal, old-fashioned person," from the style of men's shoes worn early 18c. and then fallen from fashion. Squaresville is attested from 1956. Square dance attested by 1831; originally one in which the couples faced inward from four sides; later of country dances generally.

[T]he old square dance is an abortive attempt at conversation while engaged in walking certain mathematical figures over a limited area. [The Mask, March 1868]
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deal (n.1)

"a part or portion," Middle English del, from from Old English dæl "a part of a whole, a share;" with qualification (great, etc.), "an extent, degree, quantity, amount," from Proto-Germanic *dailaz (source also of Old Norse deild, Old Frisian del "part; juridical district," Dutch deel, Old High German and German teil, Gothic dails "part, share, portion"), from PIE *dail- "to divide" (source also of Old Church Slavonic delu, Lithuanian dalis "part"), ‌‌perhaps a Northern Indo-European extended form of the root *da- "to divide," or perhaps a substratum word.

Formerly used in many senses now taken by part. Meaning "a share (of something), one's allotted portion" is from c. 1200. Business sense of "transaction, bargain" is 1837, originally slang, from the older sense of "arrangement among a number of persons for mutual advantage." In American history, New Deal is from Franklin D. Roosevelt's speech of July 2, 1932 (the phrase itself is by 1834). Big deal is from 1928 as "important transaction;" ironic use first recorded 1951 in "Catcher in the Rye." Deal-breaker is attested by 1975.

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deal (n.2)

"plank or board," especially of fir or pine, late 14c., dele, from Low German (compare Middle Low German dele), from Proto-Germanic *theljon." From late 13c. in surnames. An Old English derivative was þelu"hewn wood, board, flooring."

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deal (v.)

Middle English delen, from Old English dælan "to divide, distribute, separate;" hence "to share with others, bestow, dispense," and also "take part in, have to do with," from Proto-Germanic *dailjanan (source also of Old Saxon deljan, Old Frisian dela "to divide, distribute," Middle Dutch, Dutch deelen, German teilen, Gothic dailjan),from PIE *dail- "to divide," ‌‌perhaps a Northern Indo-European extended form of root *da- "to divide," or a word from a substrate language.

Meaning "to deliver (to another) as his share" is from c. 1300. Meaning "to distribute cards before a game" is from 1520s (the associated noun meaning "distribution of cards before a game" is from c. 1600). Hence colloquial deal (someone) in "include in an undertaking" (1942).

To deal with "handle, act toward (in some way)" is attested from mid-15c., from the notion of "engage in mutual intercourse, have to do with;" in late 14c. the phrase also mean "have sexual intercourse with." Related: Dealt; dealing.

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square (v.)

late 14c. of stones, from Old French esquarrer, escarrer "to cut square," from Vulgar Latin *exquadrare "to square," from Latin ex "out" (see ex-) + quadrare "make square; set in order, complete," from quadrus "a square" (from PIE root *kwetwer- "four"). Meaning "regulate according to standard" is from 1530s; sense of "to accord with" is from 1590s. With reference to accounts from 1815. In 15c.-17c. the verb also could mean "to deviate, vary, digress, fall out of order." Related: Squared; squaring.

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square (n.)

mid-13c., "tool for measuring right angles, carpenter's square," from Old French esquire "a square, squareness," from Vulgar Latin *exquadra, back-formation from *exquadrare "to square," from Latin ex "out" (see ex-) + quadrare "make square, set in order, complete," from quadrus "a square" (from PIE root *kwetwer- "four").

Meaning "square shape or area" is recorded by late 14c. (Old English used feower-scyte). Geometric sense "four-sided rectilinear figure" is from 1550s; mathematical sense of "a number multiplied by itself" is first recorded 1550s. Sense of "open space in a town or park" is from 1680s; that of "area bounded by four streets in a city" is from c. 1700. As short for square meal, from 1882. Square one "the very beginning" (often what one must go back to) is from 1960, probably a figure from board games.

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square (adv.)

1570s, "fairly, honestly," from square (adj.). From 1630s as "directly, in line." Sense of "completely" is American-English, colloquial, by 1862.

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big deal (n.)

1860s, "a good deal, a large amount;" by 1878 in financial speculation, originally in California publications; see deal (n.1). As an ironic expression, popular in American English from c. 1965, perhaps a translated Yiddishism (such as a groyser kunst).

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four-square (adj.)

also foursquare, c. 1300, "having four equal sides," from four + square (adj.). As an adverb, in figurative use, "forthrightly, honestly" from 1845.

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Sloane Square 

neighborhood near Chelsea in London, named for Sir Hans Sloane (1660-1753), who purchased the manor of Chelsea in 1712 and whose celebrated collections contributed to the British Museum. Previous to development the place was known as Great Bloody Field ["Oxford Dictionary of London Place Names"]. The tree genus Sloanea was named for him. Sloane Ranger is attested from 1975, with a play on Lone Ranger.

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