Abstract
The adoption of algebraic methods of analysis induced a gradual fusion of arithmetic, algebra, and geometry, which in turn gave rise to a number of technical, terminological, and conceptual questions. The fusion also spurred issues of legitimation, in particular the question whether it was allowed to use numbers in geometry. The present chapter deals with the technical, terminological, and conceptual questions; the issues of legitimation are the subject 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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© 2001 Springer Science+Business Media New York
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Bos, H.J.M. (2001). Arithmetic, geometry, algebra, and analysis. In: Redefining Geometrical Exactness. Sources and Studies in the History of Mathematics and Physical Sciences. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-0087-8_6
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DOI: https://doi.org/10.1007/978-1-4613-0087-8_6
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6521-4
Online ISBN: 978-1-4613-0087-8
eBook Packages: Springer Book Archive