[1] : The Collaborative International Dictionary of English v.0.48

square \square\ skw^ar, n. of. esquarre, esquierre, f.
   'equerre a carpenter's square cf. it. squadra, fr.
   assumed ll. exquadrare to make square; l. ex + quadrus a
   square, fr. quattuor four. see four, and cf. quadrant,
   squad, squire a square.
   1. geom.
      a the corner, or angle, of a figure. obs.
      b a parallelogram having four equal sides and four right
          angles.
          1913 webster

   2. hence, anything which is square, or nearly so; as:
      a a square piece or fragment.
          1913 webster

                he bolted his food down his capacious throat in
                squares of three inches.          --sir w.
                                                  scott.
          1913 webster
      b a pane of glass.
      c print. a certain number of lines, forming a portion
          of a column, nearly square; -- used chiefly in
          reckoning the prices of advertisements in newspapers.
      d carp. one hundred superficial feet.
          1913 webster

   3. an area of four sides, generally with houses on each side;
      sometimes, a solid block of houses; also, an open place or
      area for public use, as at the meeting or intersection of
      two or more streets.
      1913 webster

            the statue of alexander vii. stands in the large
            square of the town.                   --addison.
      1913 webster

   4. mech.  joinery an instrument having at least one right
      angle and two or more straight edges, used to lay out or
      test square work. it is of several forms, as the t square,
      the carpenter's square, the try-square., etc.
      1913 webster

   5. hence, a pattern or rule. obs.
      1913 webster

   6. arith.  alg. the product of a number or quantity
      multiplied by itself; thus, 64 is the square of 8, for 8
      times 8 = 64; the square of a + b is a^2 + 2ab +
      b^2.
      1913 webster

   7. exact proportion; justness of workmanship and conduct;
      regularity; rule. obs.
      1913 webster

            they of galatia were much more out of square.
                                                  --hooker.
      1913 webster

            i have not kept my square.            --shak.
      1913 webster

   8. mil. a body of troops formed in a square, esp. one
      formed to resist a charge of cavalry; a squadron. "the
      brave squares of war." --shak.
      1913 webster

   9. fig.: the relation of harmony, or exact agreement;
      equality; level.
      1913 webster

            we live not on the square with such as these.
                                                  --dryden.
      1913 webster

   10. astrol. the position of planets distant ninety degrees
       from each other; a quadrate. obs.
       1913 webster

   11. the act of squaring, or quarreling; a quarrel. r.
       1913 webster

   12. the front of a woman's dress over the bosom, usually
       worked or embroidered. obs. --shak.
       1913 webster

   fair and square in a fair, straightforward, and honest
      manner; justly; as, he beat me fair and square.

   geometrical square. see quadrat, n., 2.

   hollow square mil., a formation of troops in the shape of
      a square, each side consisting of four or five ranks, and
      the colors, officers, horses, etc., occupying the middle.
      

   least square, magic square, etc. see under least,
      magic, etc.

   on the square, or upon the square,
       a in an open, fair manner; honestly, or upon honor;
           justly. obs or colloq.
       b at right angles.

   on the square with, or upon the square with, upon
      equality with; even with. --nares.

   to be all squares, to be all settled. colloq. --dickens.

   to be at square, to be in a state of quarreling. obs.
      --nares.

   to break no squares, to give no offense; to make no
      difference. obs.

   to break squares, to depart from an accustomed order.
      obs.

   to see how the squares go, to see how the game proceeds; --
      a phrase taken from the game of chess, the chessboard
      being formed with squares. obs. --l'estrange.
      1913 webster
see also:
four quadrant squad squire 2 fair and square 
geometrical square quadrat hollow square least square magic square 
least magic on the square upon the square on the square with 
upon the square with to be all squares to be at square to break no squares to break squares 
to see how the squares go 

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