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Descartess Mathematical Thought 2004 ed. [Kietas viršelis]

  • Formatas: Hardback, 496 pages, aukštis x plotis: 234x156 mm, weight: 1980 g, XIV, 496 p., 1 Hardback
  • Serija: Boston Studies in the Philosophy and History of Science 237
  • Išleidimo metai: 30-Nov-2003
  • Leidėjas: Springer-Verlag New York Inc.
  • ISBN-10: 1402017464
  • ISBN-13: 9781402017469
Kitos knygos pagal šią temą:
Descartess Mathematical Thought 2004 ed.Didesnis paveikslėlis
  • Formatas: Hardback, 496 pages, aukštis x plotis: 234x156 mm, weight: 1980 g, XIV, 496 p., 1 Hardback
  • Serija: Boston Studies in the Philosophy and History of Science 237
  • Išleidimo metai: 30-Nov-2003
  • Leidėjas: Springer-Verlag New York Inc.
  • ISBN-10: 1402017464
  • ISBN-13: 9781402017469
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9781402017469.html
Raktažodžiai:
Covering both the history of mathematics and of philosophy, Descartes's Mathematical Thought reconstructs the intellectual career of Descartes most comprehensively and originally in a global perspective including the history of early modern China and Japan. Especially, it shows what the concept of "mathesis universalis" meant before and during the period of Descartes and how it influenced the young Descartes. In fact, it was the most fundamental mathematical discipline during the seventeenth century, and for Descartes a key notion which may have led to his novel mathematics of algebraic analysis.

Recenzijos

From the reviews:









"The book is a study about the formation of Descartess mathematical thought and its philosophical significance. The book is well documented as one can see also looking at the footnotes and the bibliography. There are also some interesting digressions as that concerning Jesuit mathematical education." (Raffaella Franci, Zentralblatt MATH, Vol. 1045 (20), 2004)



"This magnificent volume originates in a 1989 Ph.D. thesis from Princeton University. The author aims at a reconstruction of R. Descartes early mathematical career, studying the formation of his mathematical thought and relating it to his methodological and philosophical ideas. The volume, containing a wealth of material, is made accessible by indexes of names, subjects and treatises." (Volker Peckhaus, Mathematical Reviews, 2005 d)

Preface vii
List of Abbreviations and A Note on the Quotation and Translation
xiv
Introduction 1(10)
Rene Descartes
Part I: THE FORMATION OF DESCARTES'S MATHEMATICAL THOUGHT
11(276)
Descartes and Jesuit Mathematical Education
13(32)
Descartes and the Jesuit College of La Fleche
13(3)
The Curriculum at La Fleche
16(3)
Mathematical Studies in the Ratio Studiorum
19(11)
Motives for the Teaching of Mathematics in the Jesuit Colleges
30(15)
The Mathematical Thought of Christoph Clavius
45(50)
Descartes and Clavius
45(5)
The Philosophy of Mathematics of Clavius
50(13)
Pappus in the Works of Clavius
63(9)
Diophantus in the Works of Clavius
72(12)
Descartes's Mathematical Background before the Encounter with Beeckman
84(11)
The First Attempt at Reforming Mathematics
95(64)
``An Entirely New Science'': The Idea for the Unification of Arithmetic and Geometry
95(14)
The Mathematics in the Cogitationes privatae
109(23)
The Plan of a Book Titled Thesaurus mathematicus
109(3)
The Mesolabe Compass
112(9)
The Other Mathematical Instruments
121(6)
The Interest in Figurate Numbers, the Extension of the Pythagorean Theorem and Other Results
127(5)
The De Solidorum Elementis
132(17)
A History of the Manuscript
132(1)
Solid Geometry
133(5)
Figurate Numbers
138(7)
The Date of the Original Manuscript
145(4)
Descartes's Mathematical and Philosophical Dream of 1619
149(10)
The Mathematical Background of the Regulae Ad Directionem Ingenii
159(46)
The Old Algebra: The First Fruit of ``An Entirely New Science''
159(17)
The Mathematics in the Regulae ad Directionem Ingenii
176(13)
Pure Mathematics as the Paradigm for Certainty
176(6)
Algebra as the Method of Analysis
182(7)
Mathesis Universalis
189(16)
The Geometrie of 1637
205(82)
The Pappus Problem
205(20)
The Composition of the Geometrie
225(10)
Descartes's Place in the Formative Period of the Modern Analytic Tradition
235(39)
Plagiarism Debates with Jean Beaugrand in 1637-1638
235(10)
Descartes's Acquaintance with Viete before the Composition of the Geometrie
245(3)
The Beginning of the Tradition of Algebraic Analysis in Arabic Mathematics and the Ramean Restart
248(12)
The Supposed Intermediary Adriaan van Roomen
260(10)
From Viete to Descartes
270(4)
Beyond Cartesian Mathematics
274(7)
Interim Consideration
Descartes and the Beginnings of Mathematicism in Modern Thought
281(6)
Part II: THE CONCEPT OF `MATHESIS UNIVERSALIS' IN HISTORICAL PERSPECTIVE
287(152)
`Universal Mathematics' In Aristotle
289(44)
Aristotle's Metaphysics and Posterior Analytics
289(7)
Greek Commentators: Alexander of Aphrodisias and Asclepius of Tralles
296(5)
Medieval Commentators: Ibn Rushd (Averroes), Albertus Magnus, Thomas Aquinas, and the Scotist Antonius Andreae
301(17)
Albertus Magnus and Thomas Aquinas
301(8)
Ibn Rushd (Averroes) 's Commentary on the Metaphysics
309(3)
Albert and Thomas against the Oxford `Platonists'
312(3)
The Scotist Antonius Andreae
315(3)
Renaissance Commentators: Agostino Nifo and Pedro da Fonseca
318(8)
Agostino Nifo
318(3)
The Jesuit Commentator Pedro da Fonseca
321(5)
The Status of Mathematics in the Aristotelian Scheme of Learning
326(7)
`Mathesis Universalis' in the Sixteenth Century
333(26)
Proclus Diadochus and Francesco Barozzi
333(9)
Adriaan van Roomen
342(17)
`Mathesis Universalis' in the Seventeenth Century
359(80)
Reviewing Descartes's Concept of `Mathesis Universalis' from His Philosophy of Mathematics
359(39)
The Philosophy of Mathematics in the Regulae ad Directionem Ingenii
359(3)
The Later Philosophy of Mathematics: Mathematical Truths as Creatures of God
362(11)
Descartes against the Skeptical Arguments on Mathematics: How Was the Philosophy of ``Cogito, Ergo Sum'' Discovered?
373(13)
Difficulties of the Later Philosophy of Mathematics: The `Cartesian Spiral'
386(5)
The Disuse of the Concept of `Mathesis Universalis' in the Later Writings
391(3)
`Mathesis Universalis' as the Discipline of Symbolic Algebra among Other Mathematicians
394(4)
The Leibnizian Synthesis
398(21)
`Mathesis Universalis' Extended
398(7)
Leibniz's `Logicist-Formalist' Philosophy of Mathematics
405(14)
Conclusion
Descartes and the Modern Scheme of Learning
419(20)
Bibliography
439(29)
Indices
468(19)
Name Index
468(10)
Subject Index
478(9)
Treatise Index
487