Geometric Square

Collier's New Encyclopedia (1921)

an instrument for measuring distances and heights, and useful for its portability as well as for the facility, by the common rule of three, of solving most of the problems arising from its use. It is made of brass or wood, 12 or 18 inches square, and the quadrant is graduate in each direction. The two sides opposite to the axial point of the alidade are graduated to 100 equal parts, with major divisions of 10 of said parts. The 100 point finishes at the angle obliquely opposite the center from which the arc is struck. One side represents the horizon, and the alidade with two side sides is equal in length to the diagonal of the square. The alidade has divisions equal to those on the sides of the square. GEOMETRY (Greek geometria=the measurement of land; geo, for geios-belonging to the earth, and metria measurement), properly the measurement of the earth or of land, but now used exclusively of the abstract science to which practical land measurement gave or may have given birth. It is the science of space, whether linear, superficial, or solid. History. Who first invented or cultivated geometry is uncertain. The Lias, Marlstone, Upper Lias, Kössen Hindus have a geometry apparently of indigenous growth. Some knowledge part; Keuper, Muschelkalk, Bunter- of geometry was apparently possessed by the builders of the Egyptian pyramids. Diodorus and others attribute the invention or discovery of geometry to Egypt, which is doubtful. The Greeks surpassed all ancient nations in their attainments in the science. Euclid founded a school of mathematics at Alexandria some time in the reign of Ptolemy Lagus, B. C. 323 to 284. His "Elements" are still in use in many schools and colleges. See MATHEMATICS. Nature of the Science. - Geometry, like mathematics, is built up on rigorous demonstration. To prevent the possibility of error in reasoning it is needful to commence with definitions of the terms employed. Then follow in Euclid's "Elements" postulates or concessions demanded as to what is possible to be done; then axioms, simple mathematical statements worthy of being believed. A popular belief is that the whole science of geometry rests on the axioms; it is really, however, based on the definitions; thus the whole third book of Euclid follows naturally from the definition of a circle. Analytical Geometry. - The analytical investigation of the relations and properties of geometrical magnitudes. It is divided into determinate and indeterminate geometry, according as the number of possible solutions in any given case is limited or unlimited. Descriptive Geometry. -Geometry of which the feature is to represent solid bodies with accurate form, perspective, etc., on paper, or other plane surface. Geometry Elementary Geometry. treating of points, lines, surfaces, or the ordinary solids, as distinguished from conic sections, etc., called the higher geometry. Higher geometry, see under paragraph above. Plane Geometry. - Geometry relating to surfaces, or to lines drawn or points placed on them. Solid Geometry.-Geometry relating to solids.