The First Book of Geometry

Abstract

OF late years a very remarkable change has been made in the theory of elementary geometry, the general effect of which has been to make it more abstract, and to reduce a great deal of it to the application of logic without any appeal to intuition. It has been realised that geometry must be based on the assumption of certain undefinable entities, of elementary relations between them, and a complete system of independent axioms. For the purposes of ordinary Euclidean geometry, it is probably the simplest way to assume the straight line as the one undefinable entity, and intersection as the elementary relation from which the notions of point and plane may be derived. What system of axioms we adopt will partly depend upon the nature of the geometry we study; for instance, the axioms which are necessary and sufficient for the purposes of projective geometry require supplementing when we discuss the theory of measurement. The First Book of Geometry. By Grace Chisholm Young W. H. Young Pp. xvi + 222. (London: J. M. Dent and Co., 1905.) Price 1s. 6d. net.