國立虎尾科技大學 |

Chasles and the projective geometry = the birth of a global foundational programme for mathematics, mechanics and philosophy /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Chasles and the projective geometry/ by Paolo Bussotti.
其他題名:	the birth of a global foundational programme for mathematics, mechanics and philosophy /
作者:	Bussotti, Paolo.
出版者:	Cham :Springer Nature Switzerland : : 2024.,
面頁冊數:	xiii, 572 p. :ill. (some col.), digital ; : 24 cm.;
Contained By:	Springer Nature eBook
標題:	Differential Geometry. -
電子資源:	https://doi.org/10.1007/978-3-031-54266-4
ISBN:	9783031542664

Chasles and the projective geometry = the birth of a global foundational programme for mathematics, mechanics and philosophy /
Bussotti, Paolo.

Chasles and the projective geometrythe birth of a global foundational programme for mathematics, mechanics and philosophy /[electronic resource] :by Paolo Bussotti. - Cham :Springer Nature Switzerland :2024. - xiii, 572 p. :ill. (some col.), digital ;24 cm.

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.

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 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.

ISBN: 9783031542664

Standard No.: 10.1007/978-3-031-54266-4doiSubjects--Personal Names:

1455647
Chasles, M.
1793-1880.Subjects--Topical Terms:

671118
Differential Geometry.

LC Class. No.: QA471

Dewey Class. No.: 516.5

Chasles and the projective geometry = the birth of a global foundational programme for mathematics, mechanics and philosophy /
LDR:03137nam a2200325 a 4500 001 1134260
003 DE-He213
005 20240718102239.0
006 m d
007 cr nn 008maaau
008 241213s2024 sz s 0 eng d
020 $a 9783031542664 $q (electronic bk.)
020 $a 9783031542657 $q (paper)
024 7 $a 10.1007/978-3-031-54266-4 $2 doi
035 $a 978-3-031-54266-4
040 $a GP $c GP
041 0 $a eng
050 4 $a QA471
072 7 $a PBX $2 bicssc
072 7 $a MAT015000 $2 bisacsh
072 7 $a PBX $2 thema
082 0 4 $a 516.5 $2 23
090 $a QA471 $b .B981 2024
100 1 $a Bussotti, Paolo. $3 1069847
245 1 0 $a Chasles and the projective geometry $h [electronic resource] : $b the birth of a global foundational programme for mathematics, mechanics and philosophy / $c by Paolo Bussotti.
260 $a Cham : $b Springer Nature Switzerland : $b Imprint: Birkhäuser, $c 2024.
300 $a xiii, 572 p. : $b ill. (some col.), digital ; $c 24 cm.
505 0 $a 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.
520 $a 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 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.
600 1 0 $a Chasles, M. $q (Michel), $d 1793-1880. $3 1455647
650 2 4 $a Differential Geometry. $3 671118
650 2 4 $a Geometry. $3 579899
650 1 4 $a History of Mathematical Sciences. $3 785417
650 0 $a Geometry, Projective. $3 672454
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
856 4 0 $u https://doi.org/10.1007/978-3-031-54266-4
950 $a Mathematics and Statistics (SpringerNature-11649)