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020 _a9783031542664
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024 7 _a10.1007/978-3-031-54266-4
_2doi
050 4 _aQA21-27
072 7 _aPBX
_2bicssc
072 7 _aMAT015000
_2bisacsh
072 7 _aPBX
_2thema
100 1 _aBussotti, Paolo.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_973717
245 1 0 _aChasles and the Projective Geometry
_h[electronic resource] :
_bThe Birth of a Global Foundational Programme for Mathematics, Mechanics and Philosophy /
_cby Paolo Bussotti.
250 _a1st ed. 2024.
264 1 _aCham :
_bSpringer Nature Switzerland :
_bImprint: Birkhäuser,
_c2024.
300 _aXIII, 572 p. 104 illus., 41 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
505 0 _aIntroduction -- 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.
520 _aThis 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 the duality 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 19th-century geometry, this work stands as a valuable resource for scholars and enthusiasts alike.
650 0 _aMathematics.
_965523
650 0 _aHistory.
650 0 _aGeometry.
_968763
650 0 _aGeometry, Differential.
_969684
650 1 4 _aHistory of Mathematical Sciences.
_966197
650 2 4 _aGeometry.
_968763
650 2 4 _aDifferential Geometry.
_969686
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031542657
776 0 8 _iPrinted edition:
_z9783031542671
776 0 8 _iPrinted edition:
_z9783031542688
856 4 0 _uhttps://doi.org/10.1007/978-3-031-54266-4
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
999 _c61681
_d61681