Redefining Geometrical Exactness: Descartes’ Transformation of the Early Modern Concept of Construction
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
2001
|
| Schriftenreihe: | Sources and Studies in the History of Mathematics and Physical Sciences
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | In his "Géométrie" of 1637 Descartes achieved a monumental innovation of mathematical techniques by introducing what is now called analytic geometry. Yet the key question of the book was foundational rather than technical: When are geometrical objects known with such clarity and distinctness as befits the exact science of geometry? Classically, the answer was sought in procedures of geometrical construction, in particular by ruler and compass, but the introduction of new algebraic techniques made these procedures insufficient. In this detailed study, spanning essentially the period from the first printed edition of Pappus' "Collection" (1588, in Latin translation) and Descartes' death in 1650, Bos explores the current ideas about construction and geometrical exactness, noting that by the time Descartes entered the field the incursion of algebraic techniques, combined with an increasing uncertainty about the proper means of geometrical problem solving, had produced a certain impasse. He then analyses how Descartes transformed geometry by a redefinition of exactness and by a demarcation of geometry's proper subject and procedures in such a way as to incorporate the use of algebraic methods without destroying the true nature of geometry. Although mathematicians later essentially discarded Descartes' methodological convictions, his influence was profound and pervasive. Bos' insistence on the foundational aspects of the "Géométrie" provides new insights both in the genesis of Descartes' masterpiece and in its significance for the development of the conceptions of mathematical exactness |
| Beschreibung: | 1 Online-Ressource (XIX, 472 p) |
| ISBN: | 9781461300878 9781461265214 |
| ISSN: | 2196-8810 |
| DOI: | 10.1007/978-1-4613-0087-8 |
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Datensatz im Suchindex
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| author | Bos, Henk J. M. 1940-2024 |
| author_GND | (DE-588)171985451 |
| author_facet | Bos, Henk J. M. 1940-2024 |
| author_role | aut |
| author_sort | Bos, Henk J. M. 1940-2024 |
| author_variant | h j m b hjm hjmb |
| building | Verbundindex |
| bvnumber | BV042420538 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516 |
| dewey-search | 516 |
| dewey-sort | 3516 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4613-0087-8 |
| era | Geschichte 1588-1650 gnd |
| era_facet | Geschichte 1588-1650 |
| format | Electronic eBook |
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| isbn | 9781461300878 9781461265214 |
| issn | 2196-8810 |
| language | English |
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| spelling | Bos, Henk J. M. 1940-2024 Verfasser (DE-588)171985451 aut Redefining Geometrical Exactness Descartes’ Transformation of the Early Modern Concept of Construction by Henk J. M. Bos New York, NY Springer New York 2001 1 Online-Ressource (XIX, 472 p) txt rdacontent c rdamedia cr rdacarrier Sources and Studies in the History of Mathematics and Physical Sciences 2196-8810 In his "Géométrie" of 1637 Descartes achieved a monumental innovation of mathematical techniques by introducing what is now called analytic geometry. Yet the key question of the book was foundational rather than technical: When are geometrical objects known with such clarity and distinctness as befits the exact science of geometry? Classically, the answer was sought in procedures of geometrical construction, in particular by ruler and compass, but the introduction of new algebraic techniques made these procedures insufficient. In this detailed study, spanning essentially the period from the first printed edition of Pappus' "Collection" (1588, in Latin translation) and Descartes' death in 1650, Bos explores the current ideas about construction and geometrical exactness, noting that by the time Descartes entered the field the incursion of algebraic techniques, combined with an increasing uncertainty about the proper means of geometrical problem solving, had produced a certain impasse. He then analyses how Descartes transformed geometry by a redefinition of exactness and by a demarcation of geometry's proper subject and procedures in such a way as to incorporate the use of algebraic methods without destroying the true nature of geometry. Although mathematicians later essentially discarded Descartes' methodological convictions, his influence was profound and pervasive. Bos' insistence on the foundational aspects of the "Géométrie" provides new insights both in the genesis of Descartes' masterpiece and in its significance for the development of the conceptions of mathematical exactness Descartes, René 1596-1650 (DE-588)118524844 gnd rswk-swf Geschichte 1588-1650 gnd rswk-swf Mathematics Geometry Mathematik Geometrische Konstruktion (DE-588)4156714-6 gnd rswk-swf Descartes, René 1596-1650 (DE-588)118524844 p Geometrische Konstruktion (DE-588)4156714-6 s 1\p DE-604 Geschichte 1588-1650 z 2\p DE-604 https://doi.org/10.1007/978-1-4613-0087-8 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bos, Henk J. M. 1940-2024 Redefining Geometrical Exactness Descartes’ Transformation of the Early Modern Concept of Construction Descartes, René 1596-1650 (DE-588)118524844 gnd Mathematics Geometry Mathematik Geometrische Konstruktion (DE-588)4156714-6 gnd |
| subject_GND | (DE-588)118524844 (DE-588)4156714-6 |
| title | Redefining Geometrical Exactness Descartes’ Transformation of the Early Modern Concept of Construction |
| title_auth | Redefining Geometrical Exactness Descartes’ Transformation of the Early Modern Concept of Construction |
| title_exact_search | Redefining Geometrical Exactness Descartes’ Transformation of the Early Modern Concept of Construction |
| title_full | Redefining Geometrical Exactness Descartes’ Transformation of the Early Modern Concept of Construction by Henk J. M. Bos |
| title_fullStr | Redefining Geometrical Exactness Descartes’ Transformation of the Early Modern Concept of Construction by Henk J. M. Bos |
| title_full_unstemmed | Redefining Geometrical Exactness Descartes’ Transformation of the Early Modern Concept of Construction by Henk J. M. Bos |
| title_short | Redefining Geometrical Exactness |
| title_sort | redefining geometrical exactness descartes transformation of the early modern concept of construction |
| title_sub | Descartes’ Transformation of the Early Modern Concept of Construction |
| topic | Descartes, René 1596-1650 (DE-588)118524844 gnd Mathematics Geometry Mathematik Geometrische Konstruktion (DE-588)4156714-6 gnd |
| topic_facet | Descartes, René 1596-1650 Mathematics Geometry Mathematik Geometrische Konstruktion |
| url | https://doi.org/10.1007/978-1-4613-0087-8 |
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