The Elements Of Non-Euclidean Geometry by Julian Coolidge
The Elements Of Non-Euclidean Geometry - Table of Contents
1. Foundations of Metrical Geometry in a Limited Region
2. Congruent Transformations
3. The Three Hypotheses
4. Introduction of Trigonometric Formulae
5. Analytic Formulae
6. Consistency and Significance of the Axioms
7. The Geometric and Analytic Extension of Space
8. Groups of Congruent Transformations
9. Points, Lines, and Planes Treated Analytically
10. Higher Line Geometry
11. The Circle and the Sphere
12. Conic Sections
13. Quadric Surfaces
14. Areas and Volumes
15. Introduction to Differential Geometry
16. Differential Line Geometry
17. Multiply Connected Spaces
18. The Projective Basis of Non-Euclidean Geometry
19. The Differential Basis for Euclidean and Non-Euclidean Geometry
What You Will Learn in The Elements Of Non-Euclidean Geometry
"The Elements of Non-Euclidean Geometry" by "Julian Lowell Coolidge" is a classic mathematics book that introduces readers to geometries that move beyond traditional Euclidean rules. The book focuses on "non-Euclidean geometry", explaining how geometric systems change when Euclid’s parallel postulate is modified or replaced. Coolidge presents the subject with clarity and rigor, making it a foundational reference for understanding curved geometric spaces.
The book explores both "hyperbolic geometry" and "elliptic geometry", developing their core principles, metric properties, and trigonometric relationships. It examines geometric transformations, congruence, and analytic methods that describe spaces of constant curvature. Through detailed explanations and mathematical examples, Coolidge shows how these geometries differ fundamentally from Euclidean geometry while remaining logically consistent and mathematically rich.
Written for advanced students and scholars, the book also connects non-Euclidean ideas to "projective geometry" and early "differential geometry", highlighting their historical and theoretical importance. Although originally published in the early 20th century, it remains a valuable reference for mathematicians and historians of science interested in the development of modern geometry and its impact on mathematics and physics.
Book Details & Specifications
Title:
The Elements Of Non-Euclidean Geometry by Julian Coolidge
Publisher:
Palala Press
Year:
2008
Pages:
322
Type:
PDF
Language:
English
ISBN-10 #:
1436561086
ISBN-13 #:
978-1436561082
License:
External Educational Resource
Amazon:
Amazon
About the Author: Julian Lowell Coolidge
The author
Julian Lowell Coolidge
was an American mathematician, historian and a professor and chairman of the Mathematics Department at Harvard University. He was best known for his work in "non-Euclidean geometry" and geometric theory. He taught at "Harvard University", where he focused on geometry, mathematical rigor, and the historical development of mathematical ideas. Coolidge combined clear exposition with deep scholarship, making complex topics accessible without losing precision. His contributions to "geometry", "mathematical history", and academic writing continue to shape how advanced geometry is studied and understood today.
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