The Foundations of Geometry (Classic Reprint) - Hardcover

David Hilbert

Hardcover

ISBN 10: 0260633674 ISBN 13: 9780260633675

Publisher: Forgotten Books, 2018

Synopsis

A rigorous, landmark look at how geometry is built from simple principles.

This English edition presents Hilbert’s influential program to clarify the logical foundations of Euclidean geometry using a carefully chosen set of axioms and their relationships.

The material surveys how geometry can be developed from basic concepts like points, lines, and planes, and it explains the role of key ideas such as congruence, order, and continuity. It also highlights the importance of analyzing axioms to reveal what is truly necessary for proving the most important geometric theorems. The work discusses several foundational results and introduces methods that illuminate both teaching and understanding of geometry.

What you’ll experience in this edition:

• An accessible introduction to Hilbert’s axiom framework and the goal of logical clarity in geometry.
• Insight into how different groups of axioms interact and why independence matters.
• Exploration of Desargues’s theorem and its implications for plane and space geometry.
• Discussion of algebraic ideas that emerge from geometric reasoning and their pedagogical value.

Ideal for students and teachers of geometry and the history of mathematics, as well as readers seeking a clear account of the foundations of geometric thinking.

Edition details

• Publisher: Forgotten Books
• Publication date: 2018
• Language: English
• ISBN 10: 0260633674
• ISBN 13: 9780260633675
• Binding: Hardcover
• Number of pages: 171