What is "fair and 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.)

   1. The corner, or angle, of a figure. [Obs.]

   2. A parallelogram having four equal sides and four right angles.

2. Hence, anything which is square, or nearly so; as:

   1. A square piece or fragment.

      He bolted his food down his capacious throat in squares of three inches.
      --Sir W. Scott.

   2. A pane of glass.

   3. (Print.) A certain number of lines, forming a portion of a column, nearly square; -- used chiefly in reckoning the prices of advertisements in newspapers.

   4. (Carp.) One hundred superficial feet.

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.

   The statue of Alexander VII. stands in the large square of the town.
   --Addison.

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.

5. Hence, a pattern or rule. [Obs.]

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.

7. Exact proportion; justness of workmanship and conduct; regularity; rule. [Obs.]

   They of Galatia [were] much more out of square.
   --Hooker.

   I have not kept my square.
   --Shak.

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.

9. Fig.: The relation of harmony, or exact agreement; equality; level.

   We live not on the square with such as these.
   --Dryden.

10. (Astrol.) The position of planets distant ninety degrees from each other; a quadrate. [Obs.]

11. The act of squaring, or quarreling; a quarrel. [R.]

12. The front of a woman's dress over the bosom, usually worked or embroidered. [Obs.] --Shak. 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,

    1. in an open, fair manner; honestly, or upon honor; justly. [Obs or Colloq.]

    2. 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.

       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.

fair and square \fair and square\ adv. justly; honestly; equitably; impartially. Opposite of unfairly. [Colloq.]

adv. 1 (context idiomatic English) Totally fairly and undoubtedly. 2 (context idiomatic English) Within the applicable rules.