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)

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
Creator
Author
Author
Subject
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
Member of
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
QA440-699
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)
Instantiates
Publication
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
10.1007/978-1-4613-0087-8
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
  • (DE-He213)978-1-4613-0087-8
  • (MiAaPQ)EBC3069479
  • (EXLCZ)992550000001040159
Label
Redefining Geometrical Exactness : Descartes’ Transformation of the Early Modern Concept of Construction, by Henk J.M. Bos, (electronic resource)
Publication
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
10.1007/978-1-4613-0087-8
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
  • (DE-He213)978-1-4613-0087-8
  • (MiAaPQ)EBC3069479
  • (EXLCZ)992550000001040159

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