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Analysis and Synthesis in Robert Simson’s The Elements of Euclid

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Research in History and Philosophy of Mathematics

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Abstract

In the eighteenth and nineteenth centuries, three understandings of the terms “analysis” and “synthesis” were particularly influential with the creators and readers of elementary geometry textbooks in Western Europe and North America: as perceived contrasts in styles of mathematical practice in Great Britain and France; as contemporary appeals to ancient methods of proof; and as approaches to mathematics education. One widely used textbook arose from the attempt by University of Glasgow mathematics professor Robert Simson to restore Euclid’s text, which appeared in 1756 as The Elements of Euclid, in simultaneous English and Latin versions. This essay explores what we can learn about the book’s preparation, content, and reception by examining the volume through the lenses of analysis and synthesis.

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Acknowledgements

The author appreciates the helpful feedback from two anonymous referees and the audiences who gathered online for the 2021 Joint Mathematics Meetings and People, Places, Practices: Joint BSHM–CSHPM/SCHPM Conference. She is also deeply grateful to the editors for their patience.

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  1. MAA Convergence, Rockville, MD, USA

    Amy Ackerberg-Hastings

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  1. Amy Ackerberg-Hastings
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Correspondence to Amy Ackerberg-Hastings .

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  1. Department of Mathematical Information, and Computer Sciences,, Point Loma Nazarene University, San Diego, CA, USA

    Maria Zack

  2. Ecole Normale Supérieure, Paris, France

    David Waszek

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Ackerberg-Hastings, A. (2023). Analysis and Synthesis in Robert Simson’s The Elements of Euclid. In: Zack, M., Waszek, D. (eds) Research in History and Philosophy of Mathematics. Annals of the Canadian Society for History and Philosophy of Mathematics/ Société canadienne d’histoire et de philosophie des mathématiques. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-21494-3_8

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