LEADER 04000nam 22006015 450 001 9910874683403321 005 20251217134703.0 010 $a9783031542664$b(electronic bk.) 010 $z9783031542657 024 7 $a10.1007/978-3-031-54266-4 035 $a(MiAaPQ)EBC31534291 035 $a(Au-PeEL)EBL31534291 035 $a(CKB)33030837200041 035 $a(DE-He213)978-3-031-54266-4 035 $a(EXLCZ)9933030837200041 100 $a20240717d2024 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aChasles and the Projective Geometry $eThe Birth of a Global Foundational Programme for Mathematics, Mechanics and Philosophy /$fby Paolo Bussotti 205 $a1st ed. 2024. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Birkhäuser,$d2024. 215 $a1 online resource (576 pages) 311 08$aPrint version: Bussotti, Paolo Chasles and the Projective Geometry Cham : Springer Basel AG,c2024 9783031542657 327 $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. 330 $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. 606 $aMathematics 606 $aHistory 606 $aGeometry 606 $aGeometry, Differential 606 $aHistory of Mathematical Sciences 606 $aGeometry 606 $aDifferential Geometry 606 $aGeometria projectiva$2thub 608 $aLlibres electrònics$2thub 615 0$aMathematics. 615 0$aHistory. 615 0$aGeometry. 615 0$aGeometry, Differential. 615 14$aHistory of Mathematical Sciences 615 24$aGeometry. 615 24$aDifferential Geometry. 615 7$aGeometria projectiva 676 $a510.9 700 $aBussotti$b Paolo$0294957 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910874683403321 996 $aChasles and the Projective Geometry$94183787 997 $aUNINA