03659nam a22004455i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001200153072001600165072002300181072001500204100007800219245017500297250001800472264007300490300006700563336002600630337002600656338003600682347002400718505026600742520184001008650001702848650001302865650001402878650002802892650003802920650001402958650002702972710003402999773002603033776003603059776003603095776003603131856004603167978-3-031-54266-4DE-He21320251030112634.0cr nn 008mamaa240717s2024    sz |    s    |||| 0|eng d  a97830315426647 a10.1007/978-3-031-54266-42doi 4aQA21-27 7aPBX2bicssc 7aMAT0150002bisacsh 7aPBX2thema1 aBussotti, Paolo.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut10aChasles and the Projective Geometryh[electronic resource] :bThe Birth of a Global Foundational Programme for Mathematics, Mechanics and Philosophy /cby Paolo Bussotti.  a1st ed. 2024. 1aCham :bSpringer Nature Switzerland :bImprint: Birkhäuser,c2024.  aXIII, 572 p. 104 illus., 41 illus. in color.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda0 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.  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. 0aMathematics. 0aHistory. 0aGeometry. 0aGeometry, Differential.14aHistory of Mathematical Sciences.24aGeometry.24aDifferential Geometry.2 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303154265708iPrinted edition:z978303154267108iPrinted edition:z978303154268840uhttps://doi.org/10.1007/978-3-031-54266-4