ARTICLE GEOMETRY: "The development of the consequences of these metrical definitions is the subject of non-Euclidean geometry." 'subject' amended from 'subjct'. ENCYCLOPAEDIA BRITANNICA A DICTIONARY OF ARTS, SCIENCES, LITERATURE AND GENERAL INFORMATION ELEVENTH EDITION VOLUME XI, SLICE VI GEODESY to GEOMETRY ARTICLES IN THIS SLICE: GEODESY GEOFFROY, ETIENNE FRANCOIS GEOFFREY (Martel) GEOFFROY, JULIEN LOUIS GEOFFREY (Plantagenet) GEOFFROY SAINT-HILAIRE, ETIENNE GEOFFREY (duke of Brittany) GEOFFROY SAINT-HILAIRE, ISIDORE GEOFFREY (archbishop of York) GEOGRAPHY GEOFFREY DE MONTBRAY GEOID GEOFFREY OF MONMOUTH GEOK-TEPE GEOFFREY OF PARIS GEOLOGY GEOFFREY THE BAKER GEOMETRICAL CONTINUITY GEOFFRIN, MARIE THERESE RODET GEOMETRY GEODESY (from the Gr. [Greek: ge], the earth, and [Greek: daiein], to divide), the science of surveying (q.v.) extended to large tracts of country, having in view not only the production of a system of maps of very great accuracy, but the determination of the curvature of the surface of the earth, and eventually of the figure and dimensions of the earth. This last, indeed, may be the sole object in view, as was the case in the operations conducted in Peru and in Lapland by the celebrated French astronomers P. Bouguer, C.M. de la Condamine, P.L.M. de Maupertuis, A.C. Clairault and others; and the measurement of the meridian arc of France by P.F.A. Mechain and J.B.J. Delambre had for its end the determination of the true length of the "metre" which was to be the legal standard of length of France (see EARTH, FIGURE OF THE). The basis of every extensive survey is an accurate triangulation, and the operations of geodesy consist in the measurement, by theodolites, of the angles of the triangles; the measurement of one or more sides of these triangles on the ground; the determination by astronomical observations of the azimuth of the whole network of triangles; the determination of the actual position of the same on the surface of the earth by observations, first for latitude at some of the stations, and secondly for longitude; the determination of altitude for all stations. For the computation, the points of the actual surface of the earth are imagined as projected along their plumb lines on the mathematical figure, which is given by the stationary sea-level, and the extension of the sea through the continents by a system of imaginary canals. For many purposes the mathematical surface is assumed to be a plane; in other cases a sphere of radius 6371 kilometres (20,900,000 ft.). In the case of extensive operations the surface must be considered as a compressed ellipsoid of rotation, whose minor axis coincides with the earth's axis, and whose compression, flattening, or ellipticity is about 1/298.