MAGIC SQUARE

A term used to denote a series of numbers in arithmetical progre ion, arranged in the equal cells of a square in such a manner that the vertical, horizontal, and diagonal columns give the same sum. For example, let the first sixteen numbers be arranged as in the annexed table, and a magic square will be produced; for the numbers in each vertical column, in each horizontal column, and in the two diagonal columns, being added together, give the same sum, namely, 34. This is, however, only one of a great number of ways in which the same numbers may be arranged so as to fulfil the conditions. Frenicle {Divers Ouvrages, Paris, 1693) has shown that there are 878 such arrangements. Emanuel Moscopolus, a Greek author of the 14th or 15th century, is the first who is known to have treated of magic squares, and to have given rules for their construction. The principal authors who have written on the subject are Stifels, Leibnitz, Bachet, Poignard, Lahire, Ozanam, Franklin, . For the history of the subject, see Montucla, vol. i. p. 346., or Mutton's Dictionary; and for the methods of constructing them, Ozanam' s or Hutton's Mathematical Recreations. [s. 706]