square (n.) Look up square at Dictionary.com
c.1300, "tool for measuring right angles," from O.Fr. esquire "a square, squareness," from V.L. *exquadra, from *exquadrare "to square," from L. ex- "out" + quadrare "make square," from quadrus "a square," from quattuor "four" (see quart). Meaning "rectangular shape or area" is first recorded before 1382; replaced O.E. feower-scyte. Sense of "open space in a town or park" is from 1687. The mathematical sense of "a number multiplied by itself" is first recorded 1557. The verb is first attested 1382; with ref. to accounts, from 1815.
square (adj.) Look up square at Dictionary.com
c.1300, "containing four equal sides and right angles," from square (n.). Meaning "honest, fair," is first attested 1564; that of "straight, direct" is from 1804. 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 in 1771, from a style of shoes then fallen from fashion.) Squaresville is attested from 1956. Square one "the beginning" is first recorded 1960, probably from board games; square dance first attested 1870.