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Publisher:

Kluwer Academic Publishers

Publication Date:

2003

Number of Pages:

496

Format:

Hardcover

Series:

Boston Studies in the Philosophy of Science 237

Price:

158.00

ISBN:

1-4020-1746-4

Category:

Monograph

[Reviewed by , on ]

Annette Imhausen

03/14/2006

René Descartes is considered to be a central figure not only in one but several disciplines, including philosophy, physics and mathematics. In regard to the latter, he is also known as the “father of modern mathematics”, and the Cartesian coordinates are named after him. Yet his writings in mathematics are not especially numerous — in the strictest sense, there is only one, and it is not an opus of many pages.

*La Géométrie* was first published in 1637 (this 1637 edition is the focus of chapter 5) as one of three appendices to his major work *Discours de la méthode pour bien conduire sa raison et chercher la vérité dans les sciences.* In this first edition, *La Géométrie* only had 118 pages (pp. 295–413). Sasaki sketches its immediate reception, especially the debate with Jean Beaugrand, who had accused Descartes of plagiarizing several other mathematicians, e.g. Viète and Harriot (p. 235 ff.), an accusation which may have led to a delay in the work’s success. *La Géométrie* proved influential enough, however, to merit a translation into Latin (by Frans van Schooten) and the addition of various commentaries (1^{st} edition 1649, 2^{nd} edition in two parts in 1659 and 1661). The first volume of the second Latin edition comprised more than 500 pages and was the one that Newton read as an undergraduate at Cambridge in 1664 (p. 275).

Sasaki begins his study of Descartes earlier, however, with his education at the Jesuit college La Flèche (chapter 1), where he studied from 1607 to 1615 (p.13), followed by an account of the mathematics of Christoph Clavius (chapter 2), which influenced the mathematical education in Jesuit colleges (p. 45), and finally of Descartes’s meeting with John Pell (p. 46–47). Chapters 3 and 4 describe Descartes’ predecessors’ attempt to restructure the system of mathematics — a goal Descartes would ultimately achieve with *La Géométrie*.

The second part of Sasaki’s book focuses on the concept of “mathesis universalis” – looking at the concept in Aristotle (chapter 6), and then in the 16^{th} (chapter 7) and 17^{th} (chapter 8) centuries — in an effort to place Descartes’ contribution within its cultural context.

Numerous books and articles about the mathematical and scientific contributions of Descartes have been published in history and philosophy of mathematics, most notably the recent publication by Henk Bos, *Redefining Geometrical Exactness : Descartes' Transformation of the Early Modern Concept of Construction* (Springer, 2001). What is it, then, that distinguishes the book under review from other publications?

*Descartes’s Mathematical Thought* is the revised and enlarged version of the author’s dissertation, which earned him a Ph.D. from Princeton University in 1989. He began the work for this dissertation in 1978 (p. vii). Thus this book is the outcome of about thirty years worth of research. The diligence that went into its creation is obvious at first glance: numerous footnotes provide references to a wide variety of primary sources as well as secondary literature, and the bibliography comprises more than 164 primary sources.

My impression is that the focus of Sasaki’s work is not so much an overview or a critical analysis of Descartes’s mathematics, as an effort to place him within his historical and cultural context. This has been attempted by collecting what Sasaki considers possible relevant primary sources and it succeeds in establishing a very detailed account of Descartes and his contemporary culture. It is this level of detail that makes the book valuable. While the dense detail makes the book a demanding read, the time and energy spent with it are likely to be rewarding.

Annette Imhausen is an historian of Egyptian mathematics. She is currently a research fellow at the University of Cambridge.

Preface. List of Abbreviations and a Note on the Quotation and Translation. Introduction. René Descartes and Modern European Mathematics.
The Old Algebra: The First Fruit of "An Entirely New Science". Directionem Ingenii. 1.2. The Mathematics in the Regulae ad Directionem Ingenii. 3. Mathesis Universalis .
1. The Pappus Problem. 2. The Composition of the Géométrie. 3. Descartes's Place in the Formative Period of the Modern Analytic Tradition. 4. Beyond Cartesian Mathematics. Interim Consideration. Descartes and the Beginnings of Mathematicism in Modern Thought.
Bibliography. |

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