Geometry Ge*om"e*try, n.; pl. Geometries[F. g['e]om['e]trie, L. geometria, fr. Gr. ?, fr. ? to measure land; ge`a, gh^, the earth + ? to measure. So called because one of its earliest and most important applications was to the measurement of the earth's surface. See Geometer.] 1. That branch of mathematics which investigates the relations, properties, and measurement of solids, surfaces, lines, and angles; the science which treats of the properties and relations of magnitudes; the science of the relations of space. 2. A treatise on this science. Analytical, or Co["o]rdinate, geometry, that branch of mathematical analysis which has for its object the analytical investigation of the relations and properties of geometrical magnitudes. Descriptive geometry, that part of geometry which treats of the graphic solution of all problems involving three dimensions. Elementary geometry, that part of geometry which treats of the simple properties of straight lines, circles, plane surface, solids bounded by plane surfaces, the sphere, the cylinder, and the right cone. Higher geometry, that pert of geometry which treats of those properties of straight lines, circles, etc., which are less simple in their relations, and of curves and surfaces of the second and higher degrees.