A Background to Geometry by T. G. Room - 9780521090636

A Background to GeometryNatural, Synthetic and Algebraic\nAuthor(s): T. G. Room\nFormat: Paperback\nPublisher: Cambridge University Press, United Kingdom\nImprint: Cambridge University Press\nISBN-13: 9780521090636, 978-0521090636\nSynopsis\nThe central theme of the book is the development of the idea of congruence, that relation between geometric figures which is basic to ordinary Euclidean geometry. The text is divided into four books corresponding to stages in the development of a geometrical system from simple axioms: 1. 'Geometry without numbers': the relations of order and sense. 2. 'Geometry and counting': properties of the systems obtained by repetitions of the operation of displacement. 3. 'Geometry and algebra': the consequences of adjoining new points to the system developed in Book 2. In particular the properties of an algebraic field are deduced from the geometric axioms. 4. 'Congruence': properties derived from the operation of reflexion. An early introduction of parall.