Chasles and the Projective Geometry
The Birth of a Global Foundational Programme for Mathematics, Mechanics and Philosophy
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Product details:
- Publisher Springer Nature Switzerland
- Date of Publication 19 July 2025
- ISBN 9783031542688
- Binding Paperback
- See also 9783031542657
- No. of pages572 pages
- Size 235x155 mm
- Language English
- Illustrations XIII, 572 p. 104 illus., 41 illus. in color. 622
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Long description:
"
This monograph meticulously examines the contributions of French mathematician Michel Chasles to 19th-century geometry. Through an in-depth analysis of Chasles' extensive body of work, the author examines six pivotal arguments which collectively reshape the foundations of geometry. Chasles introduces a novel form of polarity, termed ""parabolic,"" to the graphic context, so expressing the metric properties by means of this specific polarity—a foundational argument. Beyond the celebrated ""Chasles theorem,"" he extends his analysis to the movement of a rigid body, employing concepts derived from projective geometry. This approach is consistently applied across diverse domains. Chasles employs the same methodology to analyze systems of forces. The fourth argument examined by the author concerns the principle of virtual velocities, which can also be addressed through a geometric analysis. In the fifth chapter, Chasles' philosophy of duality is explained. It is grounded on theduality principles of projective geometry. Finally, the author presents Chasles’ synthetic solution for the intricate problem of ellipsoid attraction—the sixth and concluding chapter. Throughout these explorations, Chasles engages in a dynamic scientific dialogue with leading physicists and mathematicians of his era, revealing diverse perspectives and nuances inherent in these discussions.
Table of Contents:
Introduction.- Chasles’ foundational programme for geometry.- Displacement of a rigid body.- Chasles and the systems of forces.- The principle of virtual velocities.- Chasles’ philosophy of duality.- Chasles and the ellipsoid attraction.- Conclusion.
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