Projective Geometry

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, respectively. The next three chapters develop a self-contained account of von Staudt's 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.

In Euclidean geometry, constructions are made with a 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.

This classic book introduces the important concepts of the subject and provides the logical foundations, including the famous theorems of Desargues and Pappus and a self-contained account of von Staudt's approach to the theory of conics. The modern approach used in this account is then utilized to deal with the simplest finite geometry that is rich enough to illustrate all the theorems nontrivially. The book concludes by demonstrating the connections among projective, Euclidean, and analytic geometry.

From the reviews of Projective Geometry:

...The book is written with all the grace and lucidity that characterize the author's other writings. ... 

-T. G. Room, Mathematical Reviews

This is an elementary introduction to projective geometry based on the intuitive notions of perspectivity and projectivity and, formally, on axioms essentially the same as the classical ones of Vebber and Young...This book is an excellent introduction.

- T. G. Ostrom, Zentralblatt