This volume serves as an extension of high school-level studies of geometry and algebra, and proceeds to more advanced topics with an axiomatic approach. Includes an introductory chapter on projective geometry, then explores the relations between the basic theorems; higher-dimensional space; conics; coordinate systems and linear transformations; quadric surfaces; and the Jordan canonical form. 1962 edition.
Author(s): A. Seidenberg
Publisher: Dover Publications
Year: 2006
Language: English
Pages: 239
PREFACE......Page 4
CONTENTS......Page 6
1 PROJECTIVE GEOMETRY AS AN EXTENSION OFHIGH SCHOOL GEOMETRY......Page 10
2 THE AXIOMATIC FOUNDATION......Page 51
3 ESTABLISHING COORDINATES IN A PLANE......Page 77
4 RELATIONS BETWEEN THE BASIC THEOREMS......Page 98
5 AXIOMATIC INTRODUCTION OFHIGHER-DIMENSIONAL SPACE......Page 105
6 CONICS......Page 115
7 HIGHER-DIMENSIONAL SPACES RESUMED......Page 131
8 COORDINATE SYSTEMS AND LINEARTRANSFORMATIONS......Page 150
9 COORDINATE SYSTEMS ABSTRACTLYCONSIDERED......Page 174
10 CONIC SECTIONS ANALYTICALLY TREATED......Page 186
11 COORDINATES ON A CONIC......Page 206
12 PAIRS OF CONICS......Page 212
13 QUADRIC SURFACES......Page 217
14 THE JORDAN CANONICAL FORM......Page 227
NDEX......Page 238
