GEOMETRY (Greek geometria=the measurement of land; geo, for geios=be longing to the earth, and urement), properly the measurement of the earth or of land, but now used exclu sively 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 cul tivated geometry is uncertain. The Hindus have a geometry apparently of indigenous growth. Some knowledge of geometry was apparently possessed by the builders of the Egyptian pyra mids. Diodorus and others attribute the invention or discovery of geometry to Egypt, which is doubtful. The Greeks surpassed all ancient nations in their at tainments in the science. Euclid founded a school of mathematics at Alexandria some time in the reign of Ptolemy Lagus, B. e. 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 com mence with definitions of the terms em• ployed. Then follow in Euclid's "Ele ments" postulates or concessions de manded as to what is possible to be done; then axioms, simple mathematical state ments worthy of being believed. A popu
lar 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 prop erties of geometrical magnitudes. It is divided into determinate and indeter minate geometry, according as the num ber 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.
Elementary Geometry. — 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.