n. That branch of mathematics which deduces the properties of figures in space from their defining conditions, by means of assumed properties of space. Abbreviated geometryn. A text-book of geometry.n. Modern projective geometry, commonly written in German Geometrie der Lage, to distinguish it from .n. Higher synthetic geometry in general.n. The art of geometrical drawing.n. Geometry of three dimensions.n. The oldest classification of geometry is , that in which it is divided according to the method of logical procedure, namely into synthetic and analytic, the method of geometrical analysis having been invented or taught by Plato. In modern times this classification intertwines with another, namely , that which is based on the mental instrument or equipment used, giving: pure or synthetic geometry; rational; descriptive; projective; algebraic, algorithmic, analytical, Cartesian, or coördinate; differential, infinitesimal, natural, or intrinsic; enumerative or denumerative. Some of these are subdivided on the same principle, as: (α) geometry of the ruler or straight-edge; (β) of the ruler and sect-carrier; (γ) of the ruler and unitsect-carrier; (δ) of the compasses; of the ruler and compasses; (ζ) of linkages. Further divisions are: By dimensionality: geometry on the straight or on the line; two-dimensional geometry; (α) plane geometry; (β) spherics; (γ) pseudo-spherics; tri-dimensional geometry: (α) geometry of planes; (β) solid geometry; (γ) spherics; four-dimensional geometry: (α) geometry of straight?; (β) of hyperspace; n-dimeimonal geometry. By elements: point geometry; straight or line; plane; point, straight, and plane; straightest or geodesic; geometry of the sphere; of other elements, By subject-matter: pure descriptive, pure projective, or pure positional geometry, or geometry of position; topologic geometry; metric geometry; geometry of curves; of surfaces; of solids; of hyper-solids; of numbers; of motion or kinematic. By assumptions made, omitted, or denied: Euclidean geometry; non-Euclidean; metageometry, or pan-geometry; finite geometry; semi-Euclidean; non-Legendrian; Archimedean; non-Archimedean; non-Arguesian; non-Pascalian. By the kind of space or universe of the geometry: Euclidean or parabolic geometry; Bolyaian, Lobachevskian, Bolyai-Lobachevskian, absolute, or hyperbolic; Riemannian, spherical, or double elliptic; Killing's, single elliptic, or simple elliptic; Clifford's or Clifford-Kleinian. By the complexity or difficulty of the part treated: elementary geometry; higher, By the period of its development: ancient or the antique geometry; modern; recent, of the triangle, or the Lemoine-Brocard.
