Green’s Dictionary of Slang

square n.

1. [mid-19C+] (US) a proper or square meal [abbr.].

2. [mid-19C–1960s] (Aus., also square gin) gin, a bottle of gin [the shape of the bottle].

3. in fig. senses, implying gullibility, innocence, a failure to fit in with group norms [American Dialect Society (Nov. 1958) suggests the steady 1-2-3-4 rhythm played without variation].

(a) [mid-19C] (UK Und.) a respectable pose; an excuse, thus a shield from arrest.

(b) [20C+] (orig. US) in general use, a respectable working man or woman .

(c) [1940s+] (US) a respectable woman.

(d) [1930s+] (orig. US black) one who is lacking in sophistication or ‘cool’ as judged by the norms of a given peer group.

(e) [1940s–60s] (US drugs) one who eschews drugs.

(f) [1940s+] (US black) a man who pursues women and is thus tricked out of his money.

(g) [1950s+] (gay) a heterosexual, or a gay man who is not used to the gay scene.

4. [1920s+] (US, usu. prison) a factory-made cigarette, whether prison-issue or commercially produced [square adj. (1)].

5. [1970s] (US black) a sexual deviant.

In phrases

half-square (n.) (also half-squarie)

[1910s–60s] (Aus.) a sexually experienced woman, positioned in the contemporary moral spectrum between an all-out prostitute and a respectable woman; an ‘amateur’ prostitute.

SE in slang uses

In compounds

square-bashing (n.) [SE square, the parade ground + bash v. (1)]

[1950s+] military drill.

square one (n.) [the image of children’s board-games, e.g. snakes and ladders]

[1960s+] (orig. US) the starting point, the beginning.

In phrases

catch a square (v.) [the corners in a boxing ring]

[2000s] (US prison) to prepare for a fight.

in the square

[1960s] (US) in the respectable world.

square in a social circle (n.) [var. on SE square peg in a round hole]

[1930s–40s] (US black) a misfit.

take it to the square (v.) [a square boxing ring]

[2000s] (US prison) to call out to have a fight.