Abstract: This chapter discusses the consequences of the system of axioms I. The line and the series of points are in fact identical concepts looked upon from different viewpoints, for the line can be interpreted as a linear subspace, while the series of points is taken as a set of linear subspaces. In any case, no sharp distinction is made between them. This also holds for the pairs of concepts; plane and plane field of points on the one hand, and space and point-field of space on the other. A geometric configuration or, more exactly, a point-configuration is a subset of Accordingly, a set of lines or planes will be called a configuration of lines or planes, respectively. A set of configurations lying in a line or in a plane is called collinear or coplanar, respectively. A set of lines or planes passing through a point may be called concurrent, while planes having a line in common are called coaxial.
Publication Year: 1968
Publication Date: 1968-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
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