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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.
List of contents
Introduction: René Descartes and Modern European Mathematics.- 1: The Formation of Descartes's Mathematical Thought.- 1 Descartes and Jesuit Mathematical Education.- 2 The Mathematical Thought of Christoph Clavius.- 3 The First Attempt at Reforming Mathematics.- 4 The Mathematical Background of the Regulae ad Directionem Ingenii.- 5 The Géométrie of 1637.- Interim Consideration: Descartes and the Beginnings of Mathematicism in Modern Thought.- II: The Concept of 'Mathesis Universalis' In Historical Perspective.- 6 'Universal Mathematics' in Aristotle.- 7 'Mathesis Universalis' in the Sixteenth Century.- 8 'Mathesis Universalis' in the Seventeenth Century.- Conclusion: Descartes and the Modern Scheme of Learning.- Indices.- Name Index.- Treatise Index.
Summary
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.
Additional text
From the reviews:
"The book is a study about the formation of Descartes’s 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)
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From the reviews:
"The book is a study about the formation of Descartes's 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)
