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TABLE OF CONTENTS. 
CHAPTER I. 
PAGE 
PROJECTIVE TRANSFORMATIONS IN ONE-DIMENSIONAL SPACE.............. 1 
General Properties of One-dimensional Projective Transformations ....... 2 
Types and Normal Forms of Projective Transformations. .................. 9 
One-parameter Groups of Projective Transformations............ ‘ 20 
Two- and Three-parameter Groups of Projective Transformation ......... 25 
Realebrojyective:kransformationSsrnnmrecciei\seicieiecissere seicteene cies ase ae 2 
SURGUIAY. Che JETT Se) Ns bos mosses bau odOOROOd BEAaes done Stes pod on te ee a one Cee 37 
Geometric Theory of Projective Transformations.................... Somes 45 
Geometric Theory of Transformations of Pencils of Lines and Planes...... 56 
Mxercises;oni Chapter ea sepeta sau Voavsroiey sve oie aleiorerstetaysis ale loiaisie, soveisictsis ele seve coinraves 59 
CHAPTER II. 
COLLINEATIONS IN THE PLANE; TYPES AND NORMAL FOoORMS............. 65 
General Analytic Theory of Plane Collineations............................ 65 
Geometric Construction of Plane Collineations................ eC Reco aoe 12 
‘By pestore Plane Collineation sic ni--vs clare. sto aise sate trons eras eiaya hee ase erin ceore os 8? 
Normal) Formsiof Equations of the Bive Types... 2 ...-.<.2-020-:-2.ns0e ss 98 
Canonical Forms of Equations of Collineations............................ 119 
RealCollineations inlay blane vers soseac ce. ae es saemeeie ee acini ete 124 
BxercisesyoniGhapterslli yar cienscwicractae cis a minseicrecinle scree Hesteene see 127 
CHAPTER III. 
GONTINUOUS) GROUPS) OF COLEINEATIONS =). ees seccicisce less seca seme cnacss 130 
Theory of Continuous Groups of Collineations.........................000. 131 
ResultantioL uwowollineations! Gasseaceiercicc-aercn cee tac ccr «neces 137 
AnalyticeGonditions;tor a subgroupion Gaseeecrere sees rsd. ce es cece ee 147 
Groups of Type I Determined by Linear and Quadratic Relations Before seta avers 163 
ACen Subp roupsoiaGa) GeometricuMethod ere ernmecencn: nee eee eee 163 
B. Groups Defined by Linear and Quadratic Relations.................... 168 
C. Reducible Groups and Canonical Forms of Groups. ................... 182 
Groups of Other Types Defined by Linear Relations........................ 188 
Normaletiorms)ofiGroups of Type lense ceten eee eeteee cece ene ee 197 
Fundamental Groups, One-parameter Groups and their Path-curves........ 205 
ACeeHundamentaliGroups of Types) lVeand Vises. sees soeseeeneeees- ose... 206 
B. Fundamental Group of Type I and its Subgroups...........-.......... 208 
C. Fundamental Group of Type II and its Subgroups..................... 215 
D. Fundamental Group of Type III and its Subgroups............... see pels 
—b (iii) 
