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The Resource Redefining Geometrical Exactness : Descartes’ Transformation of the Early Modern Concept of Construction, by Henk J.M. Bos, (electronic resource)
Redefining Geometrical Exactness : Descartes’ Transformation of the Early Modern Concept of Construction, by Henk J.M. Bos, (electronic resource)
Resource Information
The item Redefining Geometrical Exactness : Descartes’ Transformation of the Early Modern Concept of Construction, by Henk J.M. Bos, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.This item is available to borrow from all library branches.
Resource Information
The item Redefining Geometrical Exactness : Descartes’ Transformation of the Early Modern Concept of Construction, by Henk J.M. Bos, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.
This item is available to borrow from all library branches.
 Summary
 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
 Language

 eng
 eng
 Edition
 1st ed. 2001.
 Extent
 1 online resource (XIX, 472 p.)
 Note
 Softcover reprint of the hardcover 1st edition 2001
 Contents

 1 General introduction
 2 The legitimation of geometrical procedures before 1590
 3 1588: Pappus’ “Collection”
 4 The early modern tradition of geometrical problem solving; survey and examples
 5 Early modern methods of analysis
 6 Arithmetic, geometry, algebra, and analysis
 8 Using algebra — Viète’s analysis
 9 Clavius
 10 Viète
 11 Kepler
 12 Molther
 13 Fermat
 14 Geometrical problem solving —the state of the art c. 1635
 15 Introduction to Part II
 16 Construction and the interpretation of exactness in Descartes’ studies of c. 1619
 17 Descartes’ general construction of solid problems c. 1625
 18 Problem solving and construction in the “Rules for the direction of the mind” (c. 1628)
 19 Descartes’ first studies of Pappus’ problem (early 1632)
 20 The Geometry, introduction and survey
 21 Algebraic operations in geometry
 22 The use of algebra in solving plane and indeterminate problems
 23 Descartes’ solution of Pappus’ problem
 24 Curves and the demarcation of geometry in the Geometry
 25 Simplicity and the classification of curves
 26 The canon of geometrical construction
 27 The theory of equations in the Geometry
 28 Conclusion of Part II
 29 Epilogue
 List of problems
 Name Index
 Isbn
 9781461300878
 Label
 Redefining Geometrical Exactness : Descartes’ Transformation of the Early Modern Concept of Construction
 Title
 Redefining Geometrical Exactness
 Title remainder
 Descartes’ Transformation of the Early Modern Concept of Construction
 Statement of responsibility
 by Henk J.M. Bos
 Language

 eng
 eng
 Summary
 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
 http://library.link/vocab/creatorName
 Bos, Henk J.M
 Dewey number
 516
 http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
 VcDjnqtkd2s
 Image bit depth
 0
 Language note
 English
 LC call number
 QA440699
 Literary form
 non fiction
 Nature of contents
 dictionaries
 Series statement

 Sources and studies in the history of mathematics and physical sciences
 Sources and Studies in the History of Mathematics and Physical Sciences,
 http://library.link/vocab/subjectName

 Geometry
 Geometry
 Label
 Redefining Geometrical Exactness : Descartes’ Transformation of the Early Modern Concept of Construction, by Henk J.M. Bos, (electronic resource)
 Note
 Softcover reprint of the hardcover 1st edition 2001
 Antecedent source
 mixed
 Bibliography note
 Includes bibliographical references (p. [433]453) and indexes
 Carrier category
 online resource
 Carrier category code

 cr
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Contents
 1 General introduction  2 The legitimation of geometrical procedures before 1590  3 1588: Pappus’ “Collection”  4 The early modern tradition of geometrical problem solving; survey and examples  5 Early modern methods of analysis  6 Arithmetic, geometry, algebra, and analysis  8 Using algebra — Viète’s analysis  9 Clavius  10 Viète  11 Kepler  12 Molther  13 Fermat  14 Geometrical problem solving —the state of the art c. 1635  15 Introduction to Part II  16 Construction and the interpretation of exactness in Descartes’ studies of c. 1619  17 Descartes’ general construction of solid problems c. 1625  18 Problem solving and construction in the “Rules for the direction of the mind” (c. 1628)  19 Descartes’ first studies of Pappus’ problem (early 1632)  20 The Geometry, introduction and survey  21 Algebraic operations in geometry  22 The use of algebra in solving plane and indeterminate problems  23 Descartes’ solution of Pappus’ problem  24 Curves and the demarcation of geometry in the Geometry  25 Simplicity and the classification of curves  26 The canon of geometrical construction  27 The theory of equations in the Geometry  28 Conclusion of Part II  29 Epilogue  List of problems  Name Index
 Dimensions
 unknown
 Edition
 1st ed. 2001.
 Extent
 1 online resource (XIX, 472 p.)
 File format
 multiple file formats
 Form of item
 online
 Isbn
 9781461300878
 Level of compression
 uncompressed
 Media category
 computer
 Media type code

 c
 Other control number
 10.1007/9781461300878
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number

 (CKB)2550000001040159
 (SSID)ssj0000808256
 (PQKBManifestationID)11490717
 (PQKBTitleCode)TC0000808256
 (PQKBWorkID)10778462
 (PQKB)11688851
 (DEHe213)9781461300878
 (MiAaPQ)EBC3069479
 (EXLCZ)992550000001040159
 Label
 Redefining Geometrical Exactness : Descartes’ Transformation of the Early Modern Concept of Construction, by Henk J.M. Bos, (electronic resource)
 Note
 Softcover reprint of the hardcover 1st edition 2001
 Antecedent source
 mixed
 Bibliography note
 Includes bibliographical references (p. [433]453) and indexes
 Carrier category
 online resource
 Carrier category code

 cr
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Contents
 1 General introduction  2 The legitimation of geometrical procedures before 1590  3 1588: Pappus’ “Collection”  4 The early modern tradition of geometrical problem solving; survey and examples  5 Early modern methods of analysis  6 Arithmetic, geometry, algebra, and analysis  8 Using algebra — Viète’s analysis  9 Clavius  10 Viète  11 Kepler  12 Molther  13 Fermat  14 Geometrical problem solving —the state of the art c. 1635  15 Introduction to Part II  16 Construction and the interpretation of exactness in Descartes’ studies of c. 1619  17 Descartes’ general construction of solid problems c. 1625  18 Problem solving and construction in the “Rules for the direction of the mind” (c. 1628)  19 Descartes’ first studies of Pappus’ problem (early 1632)  20 The Geometry, introduction and survey  21 Algebraic operations in geometry  22 The use of algebra in solving plane and indeterminate problems  23 Descartes’ solution of Pappus’ problem  24 Curves and the demarcation of geometry in the Geometry  25 Simplicity and the classification of curves  26 The canon of geometrical construction  27 The theory of equations in the Geometry  28 Conclusion of Part II  29 Epilogue  List of problems  Name Index
 Dimensions
 unknown
 Edition
 1st ed. 2001.
 Extent
 1 online resource (XIX, 472 p.)
 File format
 multiple file formats
 Form of item
 online
 Isbn
 9781461300878
 Level of compression
 uncompressed
 Media category
 computer
 Media type code

 c
 Other control number
 10.1007/9781461300878
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number

 (CKB)2550000001040159
 (SSID)ssj0000808256
 (PQKBManifestationID)11490717
 (PQKBTitleCode)TC0000808256
 (PQKBWorkID)10778462
 (PQKB)11688851
 (DEHe213)9781461300878
 (MiAaPQ)EBC3069479
 (EXLCZ)992550000001040159
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Architecture LibraryBorrow itGould Hall 830 Van Vleet Oval Rm. 105, Norman, OK, 73019, US35.205706 97.445050



Chinese Literature Translation ArchiveBorrow it401 W. Brooks St., RM 414, Norman, OK, 73019, US35.207487 97.447906

Engineering LibraryBorrow itFelgar Hall 865 Asp Avenue, Rm. 222, Norman, OK, 73019, US35.205706 97.445050

Fine Arts LibraryBorrow itCatlett Music Center 500 West Boyd Street, Rm. 20, Norman, OK, 73019, US35.210371 97.448244

Harry W. Bass Business History CollectionBorrow it401 W. Brooks St., Rm. 521NW, Norman, OK, 73019, US35.207487 97.447906

History of Science CollectionsBorrow it401 W. Brooks St., Rm. 521NW, Norman, OK, 73019, US35.207487 97.447906

John and Mary Nichols Rare Books and Special CollectionsBorrow it401 W. Brooks St., Rm. 509NW, Norman, OK, 73019, US35.207487 97.447906


Price College Digital LibraryBorrow itAdams Hall 102 307 West Brooks St., Norman, OK, 73019, US35.210371 97.448244

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