By C. R. Wylie Jr., Mathematics

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**Extra resources for Introduction to Projective Geometry**

**Sample text**

Chapters 6 to 9 constitute the third major subdivision of the book, which is devoted to an axiomatic development of plane projective geometry. In Chap. 6 the axioms of incidence and connection and the projectivity axiom are introduced, and various systems, both finite and infinite, are discussed as concrete representations. The theorems of Desargues and Pappus are deduced, the basic properties of projectivities are developed, and the logical interrelations of these results are explored. In Chap.

The first, consisting only of Chap. 1, is a historical introduction dealing with the elementary aspects of perspective, both in three dimensions, as the artists of the Middle Ages developed it, and in two dimensions, after the process of rabattement has brought the picture plane into coincidence with the object plane. The second major portion of the book consists of Chaps. 2 to 5 and is devoted to a development of analytic projective geometry as an extension of the geometry of the euclidean plane.

While the nonhomogeneous coordinates of a point in E2 are unrestricted (except, of course, that they must be real), it is clear from Definition 1 that the third homogeneous coordinate, x3, of a point in E2 can never be zero. Clearly, if the homogeneous coordinates (xl, x2, x3) of a point are given, its rectangular coordinates (x, y) are uniquely determined. On the other hand, if the rectangular coordinates of a point are given, the homogeneous coordinates of the point are not uniquely determined.