1. the pure mathematics of points and lines and curves and surfaces;

The Collaborative International Dictionary of English v.0.48:

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. [1913 Webster] 2. A treatise on this science. [1913 Webster] Analytical geometry, 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. [1913 Webster]The Collaborative International Dictionary of English v.0.48:

Mathematics \Math`e*mat"ics\, n. [F. math['e]matiques, pl., L. mathematica, sing., Gr. ? (sc. ?) science. See Mathematic, and -ics.] That science, or class of sciences, which treats of the exact relations existing between quantities or magnitudes, and of the methods by which, in accordance with these relations, quantities sought are deducible from other quantities known or supposed; the science of spatial and quantitative relations. [1913 Webster] Note: Mathematics embraces three departments, namely: 1. Arithmetic. 2. Geometry, including Trigonometry and Conic Sections. 3. Analysis, in which letters are used, including Algebra, Analytical Geometry, and Calculus. Each of these divisions is divided into pure or abstract, which considers magnitude or quantity abstractly, without relation to matter; and mixed or applied, which treats of magnitude as subsisting in material bodies, and is consequently interwoven with physical considerations. [1913 Webster]WordNet (r) 3.0 (2006):

geometry n 1: the pure mathematics of points and lines and curves and surfaces