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.
Tailored for historians specializing in mathematics and geometry, this monograph also beckons philosophers of mathematics and science, offering profound insights into the philosophical, epistemological, and methodological dimensions of Chasles' groundbreaking contributions. Providing a comprehensive understanding of Chasles' distinctive perspective on 19
th-century geometry, this work stands as a valuable resource for scholars and enthusiasts alike.
Rezensionen / Stimmen
"An extended bibliography, with a separate list of Chasles's work quoted throughout the book, and an index of names complete the volume. . Concluding, rich in information and stimulating ideas, the book may be of use to a large audience of scholars who wish to learn more about Michel Chasles, a central figure in mid-nineteenth century geometry and mechanics." (Andrea Del Centina, zbMATH 1557.01001, 2025)
Sprache
Verlagsort
Verlagsgruppe
Springer International Publishing
Illustrationen
41
63 s/w Abbildungen, 41 farbige Abbildungen
XIII, 572 p. 104 illus., 41 illus. in color.
Maße
Höhe: 235 mm
Breite: 155 mm
Dicke: 32 mm
Gewicht
ISBN-13
978-3-031-54268-8 (9783031542688)
DOI
10.1007/978-3-031-54266-4
Schweitzer Klassifikation
Paolo Bussotti is Associate Professor in History of Science and Techniques at the University of Udine (Italy). His research areas are history of science and mathematics, in particular history of geometry and number theory between the 17th and the 19th centuries, and history of physics and astronomy in the 17th century. He is the author of more than 150 scientific publications, among which a monograph on the history of the method of infinite descent (number theory), From Fermat to Gauss. Indefinite descent and methods of reduction in Number Theory (2006), one on Leibniz's planetary theory, The complex itinerary of Leibniz's planetary theory (Birkhäuser, 2015) and one, written jointly with Prof. Brunello Lotti, titled Cosmology in the Early Modern Age. A Web of Ideas (Springer, 2022). He is the co-author (jointly with prof. R. Pisano) of many papers on the Geneva Edition of Newton's Principia published in important journals dedicated to the history of science. Furthermore, he is reviewer for leading scientific journals and well-known reviewing services such as Zentralblatt für Mathematik.
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.
