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What does "square" mean?

In addition to the idioms beginning with square, also see back to the drawing board (square one); fair and square; on the square; round peg in a square hole; shoot straight (square).

See square in WNW Idioms

on the square

at right angles (to something specified)
Informal honest(ly), fair(ly), genuine(ly), etc.

out of square

not at right angles (with something specified)
Informal not in harmony, order, or agreement

square away

to bring a ship's yards around so as to sail directly before the wind
square off
Informal to get ready; put in order

square off

to assume a posture of attack or self-defense, as in boxing

square oneself

Informal to make amends for damage, a wrong, hurt, etc. done by oneself to another

square the circle

to construct or find a square equal in area to a given circle: an insoluble problem in Euclidean geometry
to do or attempt something that seems impossible

square up

to make a settlement, as by paying, balancing accounts, etc.
to assume a posture of opposition (to an adversary)

See square in American Heritage Dictionary 4 Idioms

on the square

Mathematics

At right angles.
Honestly and openly: has always dealt on the square.

out of square

Mathematics

Not at exact right angles.
Not in agreement.

square peg in a round hole

Informal

A misfit.

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