Vaughan Herbert E., - A Vector Approach to Euclidean Geometry, Vol. I-II

Vaughan Herbert E., - A Vector Approach to Euclidean Geometry, Vol. I-II - Herbert E. Vaughan

A Vector Approach to Euclidean Geometry: Vector Spaces and Affine Geometry, Volume 1. Teacher's Edition. The course bases plane and solid geometry and trigonometry on the fact that the translations of a Euclidean space constitute a vector space which has an inner product. Volume 1 deals largely with affine geometry, and the notion of dimension is introduced only in the last chapter. The principal geometric topics of this volume are parallelism of lines and planes, and ratios. This makes possible a good deal of the geometry of triangles and quadrilaterals. A Vector Approach to Euclidean Geometry: Inner Product Spaces, Euclidean Geometry and Trigonometry, Volume 2. Teacher's Edition. Congruence is a geometric topic reserved for Volume 2. Volume 2 opens with an analysis of basic properties of perpendicularity and distance which leads to the introduction of an inner product of translations and to the development of Euclidean geometry and trigonometry. The basic facts concerning volume-measures of solids are dealt with in an appendix to Volume 2.