Etymology
Advertisement
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]
Related entries & more 
Advertisement
public (adj.)

late 14c., publike, "open to general observation," from Old French public (c. 1300) and directly from Latin publicus "of the people; of the state; done for the state," also "common, general, of or belonging to the people at large; ordinary, vulgar," and as a noun, "a commonwealth; public property." This Latin word was altered (probably by influence of Latin pubes "adult population, adult;" see pubis) from Old Latin poplicus "pertaining to the people," from populus "people" (see people (n.)).

Attested in English from early 15c. as "of or pertaining to the people at large" and from late 15c. as "pertaining to public affairs." The meaning "open to all in the community, to be shared or participated in by people at large" is from 1540s in English. An Old English adjective in this sense was folclic. The sense of "done or made by or on behalf of the community as a whole" is by 1550s; that of "regarding or directed to the interests of the community at large, patriotic" is from c. 1600.

Public relations "the management of the relationship between a company or corporation and the general public" is recorded by 1913 (with an isolated use by Thomas Jefferson in 1807). Public office "position held by a public official" is from 1821; public service is from 1570s; public interest "the common well-being" is from 1670s. Public enemy, one considered a nuisance to the general community, is attested from 1756. Public sector attested from 1949. Public funds (1713) are the funded debts of a government.

Public woman "prostitute" is by 1580s, on the notion of "open for the use of all." For public house, see pub.

Related entries & more 
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.

Related entries & more 
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.

Related entries & more 
square (adv.)

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

Related entries & more 
Advertisement
public (n.)

"the general body of people constituting a nation, state, or community; the nation or state," 1610s, from public (adj.); the meaning "people in general" is from 1660s. In public "in open view, publicly, before the people at large" is attested from c. 1500.

Related entries & more 
public school (n.)

1570s, originally, in Britain, "a grammar school endowed for the benefit of the public," but most have evolved into boarding-schools for the well-to-do. From public (adj.) + school (n.1). The main modern meaning in U.S., "school (usually free) provided at public expense and run by local authorities," is attested from 1640s. 

Related entries & more 
Sloane Square 

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

Related entries & more 
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.

Related entries & more 
public-mindedness (n.)

"disposition to promote the public interest, public spirit," 1690s, from public (adj.) in the sense of "directed to the interests of the community at large."

Related entries & more