The Axioms of Descriptive Geometry (Classic Reprint) - Hardcover

Name: The Axioms of Descriptive Geometry (Classic Reprint)
Author: Alfred North Whitehead
ISBN: 9780331283594

Alfred North Whitehead

9780331283594: The Axioms of Descriptive Geometry (Classic Reprint)

Hardcover

ISBN 10: 033128359X ISBN 13: 9780331283594

Publisher: Forgotten Books, 2017

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Foundations and transformations of descriptive geometry, from order axioms to metrical distance.

This work surveys how geometry can be built from fundamental ideas about points, order, and relationships, without relying on distance or congruence. It traces a path from Peano’s line axioms to the concept of one-one point correspondences and the role of projective transformations.

The book presents a clear progression: defining a plane and space through order, introducing continuous transformation groups, and then deriving distance and angles from congruence concepts. It combines historical approaches with a modern view of how a single three-term relation can organize geometric truth.

How order and between-ness define lines, planes, and spatial relations
How one-one correspondences and transformation groups describe geometry
How to introduce coordinates and derive distance and angles without initial metric assumptions
How different congruence groups yield elliptic, hyperbolic, and parabolic geometries

Ideal for readers who want a rigorous, foundational look at geometry, from axioms to metrical concepts, and for those studying the logical structure of descriptive geometry.

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About the Author

Alfred North Whitehead (1861 1947) was a prominent logician, mathematician and philosopher in the early twentieth century and helped pioneer the 'process philosophy' approach to metaphysics. He was Professor of Philosophy at Harvard University until his retirement in 1937.

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