Key Features:* Some representative topicswhich illustrate the extensionof three dimensionalgeometry.* No treatise on N dimensions.* Projective aspect is discussedwith ideas relating toalgebraic varieties and accountof quadrics with referenceto linear spaces.* Metrical aspects give, in additionto Cartesian formulae,some accounts and applicationsof the Pliicher-Grassmann coordinates of alinear space and applicationsto line-geometry.* Polytopes are discussed indetail leading to regularpolytopes.* References are of originalworks.About the Book:The present book deals with the metrical and to a slighter extent with theprojective aspect. A third aspect, which has attracted much attention recently,from its application to relativity, is the differential aspect.

This is altogetherexcluded from the present book.In this book, a complete systematic treatise has not been attempted but rather aselected certain representative topics have been discussed which not onlyillustrate the extension of theorems of three-dimensional geometry, but alsoreveal results which are unexpected and where analogy would be a faithlessguide.The first four chapters explain the fundamental ideas of incidence,parallelism, perpendicularity, and angles between linear spaces. Chapters 5and 6 are analytical, the former projective, the latter largely metrical. In theformer are given some of the simplest ideas relating to algebraic varieties and amore detailed account of quadrics, especially with reference to their linearspaces. The remaining chapters deal with polytopes and contain, especially inChapter 9, some of the elementary ideas in analysis situs. Chapter 8 treatshyperspatial figures and the final chapter establishes the regular polytopes.