Conflicts Between Generalization, Rigor, and Intuition: Number Concepts Underlying the Development of Analysis in 17th-19th Century France and Germany

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Springer Science & Business Media, 10 de juny 2006 - 678 pàgines
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This volume is, as may be readily apparent, the fruit of many years’ labor in archives and libraries, unearthing rare books, researching Nachlässe, and above all, systematic comparative analysis of fecund sources. The work not only demanded much time in preparation, but was also interrupted by other duties, such as time spent as a guest professor at universities abroad, which of course provided welcome opportunities to present and discuss the work, and in particular, the organizing of the 1994 International Graßmann Conference and the subsequent editing of its proceedings. If it is not possible to be precise about the amount of time spent on this work, it is possible to be precise about the date of its inception. In 1984, during research in the archive of the École polytechnique, my attention was drawn to the way in which the massive rupture that took place in 1811—precipitating the change back to the synthetic method and replacing the limit method by the method of the quantités infiniment petites—significantly altered the teaching of analysis at this first modern institution of higher education, an institution originally founded as a citadel of the analytic method.
 

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Continguts

Developments
8
Paths Toward Algebraization Development to the Eighteenth
14
Cardanos refutation of the rule of signs
44
relative position of opposite segments
77
the four quadrants
82
the hyperbola in the quadrants
83
Early Modern Times
157
lesion of continuity
180
Reproduction of Carnots figure in his 1785 memoir
341
Reproduction of Carnots operating with the limitsymbol
345
Content structure of Lacroixs lecture course on analysis 1804
388
Example of de Pronys tableaux in his Mécanique Philosophique
392
Cauchys Compromise Concept
427
Believing Myself Infallible
441
Contents of Cauchys lecture course on analysis 181617
459
Reproduction of Dirksens operating with double limits
473

jump discontinuities and continuity
181
continuous and discontinuous lines
243
area of curves
246
intermediate values on lines
249
Culmination of Algebraization and Retour du Refoulé
257
the graphs of the circle parabola and hyperbola 2745
277
the four quadrants
290
The Renaissance of the Synthetic
295
From the Perspective of Mathematical
309
Limit to the Infinitely Small
334
Development of Pure Mathematics in PrussiaGermany
481
Diesterweg interpreting directions in figures
518
number lines as coordinate axes in 1829
527
Conflicts Between Confinement to Geometry
567
Summary and Outlook
601
Appendix 619
618
References
631
Index of Names
671
Copyright

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