| 書目名稱 | Chasles and the Projective Geometry | | 副標(biāo)題 | The Birth of a Globa | | 編輯 | Paolo Bussotti | | 視頻video | http://file.papertrans.cn/243/242074/242074.mp4 | | 概述 | Offers a novel perspective on the foundations of geometry in the 19th Century.Explores new relations among mathematics, physics and philosophy.Studies the historical interactions between pure and anal | | 圖書封面 |  | | 描述 | This monograph meticulously examines the contributions of French mathematician Michel Chasles to?19.th.-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, | | 出版日期 | Book 2024 | | 關(guān)鍵詞 | Michel Chasles; Projective Geometry; Metric/Graphic Properties; Pure/Analytic Geometry; Movement of a Ri | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-031-54266-4 | | isbn_softcover | 978-3-031-54268-8 | | isbn_ebook | 978-3-031-54266-4 | | copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl |
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