Projective Differential Geometry of Curves and Ruled Surfaces (1906)

Projective Differential Geometry of Curves and Ruled Surfaces is a comprehensive mathematical treatise written by Ernest Julius Wilczynski and originally published in 1906. The book focuses on projective differential geometry, a branch of mathematics concerned with the properties of curves and surfaces under projective transformations, and is intended for advanced students and researchers in the field.The book is divided into three main parts. The first part provides an introduction to the basic concepts of projective geometry, including projective transformations, projective coordinates, and cross ratios. The second part focuses on the differential geometry of curves, including the theory of curvature and torsion, the Frenet-Serret formulas, and the classification of curves according to their properties. The third part is devoted to the differential geometry of ruled surfaces, including the theory of developable surfaces, the geometry of the tangent plane, and the classification of surfaces according to their properties.Throughout the book, Wilczynski provides a rigorous and detailed treatment of the subject matter, with numerous examples, exercises, and proofs. The book also includes a comprehensive bibliography and index, making it a valuable resource for anyone interested in the study of projective differential geometry.This scarce antiquarian book is a facsimile reprint of the old original and may contain some imperfections such as library marks and notations. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions, that are true to their original work.