Written in the wake of the advent of Relativity by an author who made important contributions to projective and differential geometry, and topology, this early Cambridge Tract in Mathematics and Theoretical Physics aimed to assist students of the time from the fields of differential geometry and mathematical physics. Beginning by introducing formal preliminaries, the text continues, bringing the underlying differential invariant theory that to this day remains relevant in a range of geometrical and physical applications, to the fore.

This book contains a set of axioms for differential geometry and develops their consequences up to a point where a more advanced book might reasonably begin. Analytical operations with co-ordinate systems are continually used in differential geometry, a typical process being to 'choose a co-ordinate system such that ...' It is therefore natural to state the axioms in terms of an undefined class of 'allowable' co-ordinate systems, and to deduce the properties of the space from the nature of the transformations of co-ordinates permitted by the axioms. These earlier axioms are found to be adequate for the differential geometry of an open simply connected space, the most elementary theorems of which occupy the greater part of Chapters III-V. The more general axioms, in terms of allowable co-ordinate systems and without restrictions on the connectivity of the space, are given in Chapter IV.

This scarce antiquarian book is a selection from Kessinger Publishing's Legacy Reprint Series. Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment to protecting, preserving, and promoting the world's literature. Kessinger Publishing is the place to find hundreds of thousands of rare and hard-to-find books with something of interest for everyone!

This scarce antiquarian book is included in our special Legacy Reprint Series. In the interest of creating a more extensive selection of rare historical book reprints, we have chosen to reproduce this title even though it may possibly have occasional imperfections such as missing and blurred pages, missing text, poor pictures, markings, dark backgrounds and other reproduction issues beyond our control. Because this work is culturally important, we have made it available as a part of our commitment to protecting, preserving and promoting the world's literature.

This scarce antiquarian book is a selection from Kessinger Publishing's Legacy Reprint Series. Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment to protecting, preserving, and promoting the world's literature. Kessinger Publishing is the place to find hundreds of thousands of rare and hard-to-find books with something of interest for everyone!

This scarce antiquarian book is a selection from Kessinger Publishing's Legacy Reprint Series. Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment to protecting, preserving, and promoting the world's literature. Kessinger Publishing is the place to find hundreds of thousands of rare and hard-to-find books with something of interest for everyone!

This is a pre-1923 historical reproduction that was curated for quality. Quality assurance was conducted on each of these books in an attempt to remove books with imperfections introduced by the digitization process. Though we have made best efforts - the books may have occasional errors that do not impede the reading experience. We believe this work is culturally important and have elected to bring the book back into print as part of our continuing commitment to the preservation of printed works worldwide.

This book is a facsimile reprint and may contain imperfections such as marks, notations, marginalia and flawed pages.

This scarce antiquarian book is included in our special Legacy Reprint Series. In the interest of creating a more extensive selection of rare historical book reprints, we have chosen to reproduce this title even though it may possibly have occasional imperfections such as missing and blurred pages, missing text, poor pictures, markings, dark backgrounds and other reproduction issues beyond our control. Because this work is culturally important, we have made it available as a part of our commitment to protecting, preserving and promoting the world's literature.

The Unabridged, Second Impression, Including Notes And Corrections, And Over 100 Figures: Theorems Of Alignment And The Principle Of Duality - Projection, Section, Perspectivity, Elementary Configurations - Projectivities Of The Primitive Geometric Forms Of One, Two, And Three Dimensions - Harmonic Constructions And The Fundamental - Theorem Of Projective Geometry - Conic Sections - Algebra Of Points And One Dimensional Coordinate Systems - Coordinate Systems In Two And Three Dimensional Forms - Projectivities In One Dimensional Forms - Geometric Constructions, Invariants - Projective Transformations Of Two Dimensional Forms - Families Of Lines - Comprehensive Index

An Unabridged Printing, To Include All Exercises: Foundations - Elementary Theorems On Order - The Affine Group In The Plane - Euclidean Plane Geometry - Ordinal And Metric Properties Of Conics - Inversion Geometry And Related Topics - Comprehensive Index