Geometric Square
an instrument for measuring distances and heights, and useful for its portability as well as for the facility, by the common rule of three, of solving most of the problems arising from its use. It is made of brass or wood, 12 or 18 inches square, and the quadrant is graduate in each direction. The two sides opposite to the axial point of the alidade are graduated to 100 equal parts, with major divisions of 10 of said parts. The 100 point finishes at the angle obliquely opposite the center from which the arc is struck.
One side represents the horizon, and the alidade with two side sides is equal in length to the diagonal of the square. The alidade has divisions equal to those on the sides of the square.
GEOMETRY (Greek geometria=the measurement of land; geo, for geios-belonging to the earth, and metria measurement), properly the measurement of the earth or of land, but now used exclusively 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. 9. Quaternary: Pleistocene; 8. Tertiary: English Crag, Upper Molasse, Rupelian and Tongrian of Belgium; 7. Cretaceous: Upper Chalk, Lower Chalk, Chalk Marl, Gault, Neocomian, Lower Greensand; 6. Jura-Trias: Wealden, Purbeck, Portland, Kimmeridge, Oxford Oölites, Lower or Bath Oölite, Lower Lias, Marlstone, Upper Lias, Kössen Hindus have a geometry apparently of History. Who first invented or cultivated geometry is uncertain. The indigenous growth. Some knowledge beds, Dachstein beds; Alpine Trias, in part; Keuper, Muschelkalk, Bunter- of geometry was apparently possessed Sandstein; 5. Carboniferous: Magnesian Limestone, Lower Red Sandstone, or Rothliegendes, Upper Coal Measures, Lower Coal Measures, Millstone Grit, Lower Carboniferous, Mountain Limestone; 4. Devonian: Old Red Sandstone- Catskill Red Sandstone, Chemung, Portage, Genesee Slate, Hamilton beds, Marcellus Shale, Upper Helderberg, Schoharie, Grit, Oriskany Sandstone; 3. Upper Silurian: Lower Helderberg, Onondaga Salt Group, Salina beds, Water Lime, Niagara Group, Wenlock Group, Clinton Group, Medina Sandstone (Upper Llandovery); 2. Lower Silurian:
Hudson River beds, Cincinnati Group, Lower Llandovery, Utica Shales, Trenton Limestone, Caradoc and Bala Limestone, Black Shales, Armorican Grit, Gothlandian Calcareous Sandrock, Magnesian Limestone, Lower, Middle and Upper Cambrian; 1. Archæan: Laurentian, Huronian.
Other Rocks. For these, see IGNEOUS Rocks.
Fossils. For these, see FOSSIL: PA- LÆONTOLOGY.
Applied Geology. - Geology applied to industrial or other practical purposes; as, for instance, to mining, drainage, railway tunneling, etc. by the builders of the Egyptian pyramids. Diodorus and others attribute the invention or discovery of geometry to Egypt, which is doubtful. The Greeks surpassed all ancient nations in their attainments in the science. Euclid founded a school of mathematics at Alexandria some time in the reign of Ptolemy Lagus, B. C. 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 commence with definitions of the terms employed. Then follow in Euclid's "Elements" postulates or concessions demanded as to what is possible to be done; then axioms, simple mathematical statements worthy of being believed. A popular 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 properties of geometrical magnitudes. It is divided into determinate and indeterminate geometry, according as the num- GEORGE 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 Solid Geometry.-Geometry relating to placed on them.
Solid Geometry.-Geometry relating to solids. chiefly for its pas-