The Foundations of Geometry by David Hilbert
The Foundations of Geometry - Table of Contents
0. Introduction
1. THE FIVE GROUPS OF AXIOMS.
2. THE COMPATIBILITY AND MUTUAL INDEPENDENCE OF THE AXIOMS.
3. THE THEORY OF PROPORTION.
4. THE THEORY OF PLANE AREAS.
5. DESARGUES’S THEOREM.
6. PASCAL’S THEOREM.
7. GEOMETRICAL CONSTRUCTIONS BASED UPON THE AXIOMS I–V.
What You Will Learn in The Foundations of Geometry
This is a well known landmark mathematical work that redefined the study of "geometry through axiomatic principles". First published in 1899, the book systematically examines the basic elements of geometry—"points, lines, and planes" and establishes a consistent framework of axioms. Hilbert’s work addresses both "Euclidean and non-Euclidean geometries", offering rigorous insights into the independence, consistency, and completeness of geometric systems.
The book is structured to provide a "step-by-step logical development" of geometry from first principles. Hilbert carefully analyzes "the five groups of axioms": incidence, order, congruence, continuity, and parallels, ensuring each concept is clearly defined and logically connected. Detailed proofs, examples, and reasoning make complex ideas accessible to students, educators, and researchers, while highlighting the modern approach to axiomatic thinking in mathematics.
Now "Foundations of Geometry" is now in the "public domain", freely accessible for educational and research purposes. Its systematic approach to geometry has influenced generations of mathematicians and remains a "classic reference" in the study of geometric theory, logic, and the foundations of mathematics. The text continues to serve as an essential resource for understanding the structure and rigor of modern geometric systems.
Book Details & Specifications
Title:
The Foundations of Geometry by David Hilbert
Publisher:
The Open Court Pub. Co., Chicago
Year:
1910
Pages:
170
Type:
PDF
Language:
English
ISBN-10 #:
0486828093
ISBN-13 #:
978-0486828091
License:
Public Domain Work
Amazon:
Amazon
About the Author: David Hilbert
The author
David Hilbert
was a leading mathematician and Professor of Mathematics at University of Gottingen whose work transformed many areas of mathematics. He is well known for his efforts to make mathematics more rigorous and logical, especially through his work on the foundations of geometry. His ideas helped many other mathematicians and still influence math today.
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