Titlebook: Redefining Geometrical Exactness; Descartes’ Transform Henk J. M. Bos Book 2001 Springer-Verlag New York, Inc. 2001 Canon.Discard.Mathemati

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2196-8810 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 c

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The legitimation of geometrical procedures before 1590e classical ideas on the legitimacy of constructions here; rather I can restrict myself to dealing with those few classical sources that actually influenced the early modern debates. Besides, and fortunately, I can refer to an excellent recent study on the classical tradition of geometrical problem solving, Wilbur Knorr’s ...

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Arithmetic, geometry, algebra, and analysissubject of Chapter 7. We find the first successful merging of the fields of algebra, arithmetic, and geometry in the work of Viète; Chapter 8 explains how Viète overcame the obstacles and the legitimation issues involved.

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Geometrical problem solving — the state of the art c. 1635therefore appropriate to conclude Part I by a sketch of the state of the art of geometrical problem solving around 1635, that is, just before Descartes published his innovations (and also before Fermat’s new techniques began to circulate among cognoscenti).

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Introduction to Part IIe early modern period Descartes was the key figure with respect to these issues. His . of 1637 was to be the dominating influence in mathematics for more than 50 years. It was, as I will show, largely motivated by the need, as perceived by its author, for a more precise and reasoned definition of exactness in geometry.

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Construction and the interpretation of exactness in Descartes’ studies of c. 1619se the text has ad value because Descartes formulated his program entirely in terms of a classification of mathematical problems with respect to their solution by calculation or construction. Thus the letter to Beeckman provides a natural starting point of my inquiry into the development of Descartes’ ideas about construction.

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https://doi.org/10.1007/978-1-4613-0087-8Canon; Discard; Mathematica; analytic geometry; arithmetic; construction; development; equation; field; form;