Source : Webster's Revised Unabridged Dictionary (1913)

Magic \Mag"ic\, Magical \Mag"ic*al\, a. [L. magicus, Gr. ?, fr.
   ?: cf. F. magique. See {Magi}.]
   1. Pertaining to the hidden wisdom supposed to be possessed
      by the Magi; relating to the occult powers of nature, and
      the producing of effects by their agency.

   2. Performed by, or proceeding from, occult and superhuman
      agencies; done by, or seemingly done by, enchantment or
      sorcery. Hence: Seemingly requiring more than human power;
      imposing or startling in performance; producing effects
      which seem supernatural or very extraordinary; having
      extraordinary properties; as, a magic lantern; a magic
      square or circle.

            The painter's magic skill.            --Cowper.

   Note: Although with certain words magic is used more than
         magical, -- as, magic circle, magic square, magic wand,
         -- we may in general say magic or magical; as, a magic
         or magical effect; a magic or magical influence, etc.
         But when the adjective is predicative, magical, and not
         magic, is used; as, the effect was magical.

   {Magic circle}, a series of concentric circles containing the
      numbers 12 to 75 in eight radii, and having somewhat
      similar properties to the magic square.

   {Magic humming bird} (Zo["o]l.), a Mexican humming bird
      ({Iache magica}), having white downy thing tufts.

   {Magic lantern}. See {Lantern}.

   {Magic square}, numbers so disposed in parallel and equal
      rows in the form of a square, that each row, taken
      vertically, horizontally, or diagonally, shall give the
      same sum, the same product, or an harmonical series,
      according as the numbers taken are in arithmetical,
      geometrical, or harmonical progression.

   {Magic wand}, a wand used by a magician in performing feats
      of magic.

Square \Square\, 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},
   {Squer} a square.]
   1. (Geom.)
      (a) The corner, or angle, of a figure. [Obs.]
      (b) A parallelogram having four equal sides and four right
          angles.

   2. Hence, anything which is square, or nearly so; as:
      (a) A square piece or fragment.

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

   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.

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

   {On}, 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 square}, 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.

Source : WordNet®

magic square
     n : a square matrix of n rows and columns; the first n-squared
         integers are arranged in the cells of the matrix is such
         a way that the sum of any row or column or diagonal is
         the same