Square
Square names 3 different subjects across the 6 encyclopedias on this shelf. Each is set out below.
Square in geometry, a quadrilateral figure
Collier's New Encyclopedia (1921)
in geometry, a quadrilateral figure, both equilateral and equiangular, or, in other words, a figure with four equal sides and equal angles. In measuring superficial areas it is only necessary to multiply one side by itself to have the area of the square, because each of the sides may be considered as the basis or as the perpendicular height. Thus a square the sides of which measure 4 feet is equal to 16 square feet, that is, 16 squares each 1 foot high and 1 foot long. To square a figure (for example, a polygon) is to reduce the surface to a square of equivalent area by mathematical means. It has often been attempted to square the circle, but this has been proven impossible. In arithmetic and algebra the square of a number is the number or quantity produced by multiplying a number or quantity by itself. Thus 64 is the square of 8, for 8 × 8 = 64.
Square in military tactics
Collier's New Encyclopedia (1921)
in military tactics, a body of infantry formed into a rectangular figure with several ranks or rows of men facing on each side, with officers, horses, colors, etc., in the center. The front rank kneels, the second and third stoop, and the remaining ranks (generally two) stand. This formation is usually employed to resist a cavalry charge. Hollow squares are frequently formed with the faces fronting inward when orders and instructions, etc., are to be read, and the like.
Square A mechanic's square consists of two pieces of wood
The Encyclopedia of Founding (1892)
A mechanic's square consists of two pieces of wood or metal at exact right angles to each other, and used either for testing or describing work. In geometry, a square is described as a four-sided rectilinear figure, of which all the angles are right angles and all the sides equal.
What Has Changed in the Last Century
The geometry is exactly as Collier's had it in 1921, and the impossibility of squaring the circle it mentions had been settled in 1882, when Ferdinand von Lindemann proved pi transcendental — that remains the last word, though amateur circle-squarers still write in. The mechanic's square of the 1892 account is still two arms at a right angle, now usually pressed steel or aluminium and joined by digital angle finders and laser levels rather than replaced by them. What has gone is the military square: the kneeling, stooping and standing ranks Collier's described for resisting cavalry were already a museum piece when it wrote in 1921, made suicidal by the machine gun and quick-firing artillery of the war just ended. Massed infantry squares had their last serious outings in colonial campaigns of the late nineteenth century.
Written for this edition, 2026.