Projective Geometry

About this book

In Euclidean geometry constructions are made with ruler and compass. Projective geometry is simpler: its constructions require only a ruler. In projective geometry one never measures anything instead one relates one set of points to another by a projectivity. The first two chapters of this book introduce the important concepts of the subject and provide the logical foundations. The third and fourth chapters introduce the famous theorems of Desargues and Pappus. Chapters 5 and 6 make use of projectivities on a line and plane repectively. The next three chapters develop a self-contained account of von Staudts approach to the theory of conics. The modern approach used in that development is exploited in Chapter 10 which deals with the simplest finite geometry that is rich enough to illustrate all the theorems nontrivially. The concluding chapters show the connections among projective Euclidean and analytic geometry.