least square

Square \Square\ (skw[^a]r), n. [OF. esquarre, esquierre, F.
   ['e]querre 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.
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   2. Hence, anything which is square, or nearly so; as:
      (a) A square piece or fragment.
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                He bolted his food down his capacious throat in
                squares of three inches.          --Sir W.
                                                  Scott.
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      (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.
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   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.
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            The statue of Alexander VII. stands in the large
            square of the town.                   --Addison.
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   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.
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   5. Hence, a pattern or rule. [Obs.]
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   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}.
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   7. Exact proportion; justness of workmanship and conduct;
      regularity; rule. [Obs.]
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            They of Galatia [were] much more out of square.
                                                  --Hooker.
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            I have not kept my square.            --Shak.
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   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.
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   9. Fig.: The relation of harmony, or exact agreement;
      equality; level.
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            We live not on the square with such as these.
                                                  --Dryden.
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   10. (Astrol.) The position of planets distant ninety degrees
       from each other; a quadrate. [Obs.]
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   11. The act of squaring, or quarreling; a quarrel. [R.]
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   12. The front of a woman's dress over the bosom, usually
       worked or embroidered. [Obs.] --Shak.
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   {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.
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