Rational Geometry: A Textbook for the Science of Space, Based on Hilbert's Foundations (1904)

Rational Geometry is a textbook written by David Hilbert in 1904, which serves as a comprehensive guide to the science of space. The book is based on Hilbert's own foundations, and it provides an in-depth analysis of the principles of rational geometry. The text is divided into four main sections, each of which covers a specific aspect of the subject.The first section of the book deals with the basic concepts of geometry, including points, lines, and planes. Hilbert provides a rigorous treatment of these concepts, using axioms and logical reasoning to build a solid foundation for the rest of the book.The second section of Rational Geometry focuses on the theory of parallels, which is one of the most important and controversial topics in geometry. Hilbert presents a detailed analysis of the different approaches to this problem, including Euclid's postulate and Lobachevsky's non-Euclidean geometry.The third section of the book covers the theory of area and volume, including the concept of congruence and the measurement of geometric figures. Hilbert provides a clear and concise explanation of these topics, using examples and illustrations to help readers understand the concepts.The final section of the book deals with the geometry of space, including the properties of three-dimensional figures and the principles of perspective. Hilbert provides a comprehensive treatment of these topics, using mathematical formulas and diagrams to illustrate his points.Overall, Rational Geometry is a groundbreaking textbook that provides a rigorous and comprehensive treatment of the science of space. It is an essential resource for students and scholars of mathematics and geometry, and it remains a classic of the field more than a century after its initial publication.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.