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SQUARE, in geometry; a quadrilateral .figure, both equilateral and equiangular, or, in other words, a figure with four equal sides and equal angles, which geometry proves must be right angles. It holds the first place among the,parallelograms. The height and width of a square are equal: all squares are geometrically similar, and the diagonal line, or the line through two opposite vertices, divides the square into two equal and similar triangles. On account of its perfect regularity, the square is of great importance both in pure and applied mathematics. In the measurement of surfaces, it is the form to which all others are reduced. From the rules for calculating the superficial contents of parallelograms in general (to multiply the base by the perpendicular height), and from the nature of the square, it appears that it is only necessary to multiply one side b} itself to have the area of the square, because each of the sides may be considered as the basis, or as the perpen dicular height. Thus a square, the sides of which measure four feet, is equal to sixteen square feet; i. e. sixteen squares each a foot high and a foot long. The area of countries is generally given in square miles. Sometimes a great mistake is made by using square miles for miles square: 300 square miles is an area of 800 squares, each of which measures one mile in length and breadth, whilst 300 miles square is a square each side of which measures 300 mileshence the whole square contains 90,000 square miles. To square a figure (e. g. a polygon) is to reduce the surface to a square by mather.iatical means. It has often been attempted to square the circle, but as yet without success. (See Circle.) To obtain1 the square of a number, the number is multiplied by itself (see Power); and to extract the square root of a number is to find that magnitude which, multiplied by itself gives the magnitude from which we have to extract the root. (See Root) Square, in tactics, is the figure formed by infantry to resist most effectually an attack of cavalry in the open field. It can be formed in different ways ; and it was once customary to spend much time in drilling troops to execute all the varieties of squares and other figures having the same object; but experience has shown that the so called solid square is the best, on account of its movability and simplicity, as well as its power of resistance, though it is, perhaps more exposed to the effects of artillery. In some armies (e. g. the Prussian), all other squares are abandoned. A column, being of a square shape, can be thrown into a solid square immediately by making the men face to each of the four sides. (See the article Column.) If a solid square is broken, the parts again form squares by facing to the four sides. Magic Squares are square tables with divisions, like a chess board, filled with numbers in the natural series, or any other arithmetical progression, in such a way that the numbers in the horizontal and vertical lines, and sometimes, also, those in the diagonal lines, yield equal sums if added together; for instance,1 1 15 14 ~T12 6 7 9 J8 10 11 513 3 ! 2 16l Euler, Kircher, Franklin and others have made investigations respecting this subject.See, among other works, Mollweide's Commented;, de Quadratis Magicis (Leipsic, 1816). In India, in which country these tables were probably invented, they are used as talismans. Squarerigged vessels are contradistinguished to all whose sails are extended by stays, lateen, or lugsail yards, or by gaffs and booms, the usual situation of which is nearly in a plane with the keel. SquareSail is any sail extended to a yard suspended by the middle, and hanging parallel to the horizon, as distinguished from sails extended obliquely. SquATTERS. (See Public Lands.) SQUILL. (See .Appendix, end of this vol.) SQJJINTIJNG. (See Optics, head Vision.) SQUIRREL. (See Appendix to this vol.) STAAL, madame de, an ingenious French writer, first known as mademoiselle de Launai, was the daughter of a painter of Paris j where she was born, towards the close of the seventeenth century. Her father, being obliged to quit the kingdom, left her in great indigence; but some female recommendation procured her a good education at a priory in Rouen. Her patroness dying, she was compelled to hire herself as bedchamber woman to the duchess of Maine. Unfit, however, for the duties of such an office, she was about to quit it, when a singular event rescued her from obscurity. A beautiful ^irl of Paris, named Tetard, was induced Dy her mother to counterfeit being possessed ; and all Paris, including the court, flocking to witness this wonder, mademoiselle de Launai wrote a very witty letter on the occasion to M. de Fontenelle, which was universally admired. The duchess of Maine, having discovered the writer in the person of her waitingwoman, employed her, from that time, in all her entertainments given atSceaux, and treated her as a confidante. Thus encouraged, she wrote verses for some of the pieces acted atSceaux, drew up the plans of others, and was consulted in all. She was involved in the disgrace incurred by the duchess, her patroness, during the regency, and was kept two years a prisoner in the Bastile. On her release, the duchess found her a husband in M. de Staal, lieutenant in the Swiss guard, having previously refused the learned, but then too aged, Dacier. She died in 1750; and some Memoirs of her Life, written by herself, were soon after published in 3 vols,, 12ino. They contain nothing of much importance, but are composed in a pure and elegant style, and are very enVOL. xi. 47 tertaining. A fourth voLime has since appeared, consisting of two comedies acted at Sceaux, entitled L'Engouement, and La Mode. This lady, who, even by her own description, did not abound in personal attractions, was, nevertheless, engaged in various gallantries or amoura more or less sentimental. Being asked how she would treat such matters in her Life, "I will paint myself en buste" was the reply. Her Memoirs have been poorly translated into English.