Geometry
Geometry
Originally abstracted from the measurement of, and the study of relations of position among, material objects, geometry received in Euclid’s Elements (c. 300 B.C.) a treatment which (despite, of course, certain defects by modern standards) became the historical model for the abstract deductive development of a mathematical discipline. The general nature of the subject of geometry may be illustrated by reference to the synthetic geometry of Euclid, and the analytic geometry which resulted from the introduction of coordinates into Euclidean geometry by Descartes (1637) (q.v.). In the mathematical usage of today the name geometry is given to any abstract mathematical discipline of a certain general type, as thus illustrated, without any requirement of applicability to spatial relations among physical objects or the like.
See Mathematics, and Non-Euclidean geometry. For a very brief outline of the foundations of plane Euclidean geometry, both from the synthetic and the analytic viewpoint, see the appendix to Eisenhart’s book cited below. A more complete account is given bv Forder. — A.C.
L. P. Eisenhart,
Coordinate Geometry, 1939.
H. G. Forder,
The Foundations of Euclidean Geometry, Cambridge, England, 1927.
T. L. Heath,
The Thirteen Books of Euclid’s Elements, translated from the text of Heiberg, with introduction and commentary, 3 vols., Cambridge, England, 1908.