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Motion and Genetic Definitions in the Sixteenth-Century Euclidean Tradition

  • Book
  • © 2021

Overview

Authors:
  1. Angela Axworthy

    1. Max Planck Institute for the History of Science, Berlin, Germany

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  • Contains the conceptions and treatment of genetic definitions in the 16th century Euclidean tradition
  • Tackles the status and uses of motion in pre- and early modern geometry
  • Provides insight into the mathematical practices of leading 16th century commentators of Euclid’s Elements

Part of the book series: Frontiers in the History of Science (FRHIS)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xv
    Download chapter PDF

  2. Introduction

    • Angela Axworthy
    Pages 1-37

  3. Oronce Fine

    • Angela Axworthy
    Pages 39-74

  4. Jacques Peletier

    • Angela Axworthy
    Pages 75-97

  5. François de Foix-Candale

    • Angela Axworthy
    Pages 99-142

  6. Henry Billingsley

    • Angela Axworthy
    Pages 143-166

  7. John Dee

    • Angela Axworthy
    Pages 167-181

  8. Federico Commandino

    • Angela Axworthy
    Pages 183-193

  9. Christoph Clavius

    • Angela Axworthy
    Pages 195-227

  10. Synthesis: Continuities and Transformations in the Status of Geometrical Motion and Genetic Definitions from Fine to Clavius

    • Angela Axworthy
    Pages 229-249

  11. Later Developments in the Seventeenth Century: A Cartesian Epilogue

    • Angela Axworthy
    Pages 251-269

  12. Back Matter

    Pages 271-300
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Keywords

About this book

A significant number of works have set forth, over the past decades, the emphasis laid by seventeenth-century mathematicians and philosophers on motion and kinematic notions in geometry. These works demonstrated the crucial role attributed in this context to genetic definitions, which state the mode of generation of geometrical objects instead of their essential properties. While the growing importance of genetic definitions in sixteenth-century commentaries on Euclid’s Elements has been underlined, the place, uses and status of motion in this geometrical tradition has however never been thoroughly and comprehensively studied. This book therefore undertakes to fill a gap in the history of early modern geometry and philosophy of mathematics by investigating the different treatments of motion and genetic definitions by seven major sixteenth-century commentators on Euclid’s Elements, from Oronce Fine (1494–1555) to Christoph Clavius (1538–1612), including Jacques Peletier (1517–1582), John Dee (1527–1608/1609) and Henry Billingsley (d. 1606), among others. By investigating the ontological and epistemological conceptions underlying the introduction and uses of kinematic notions in their interpretation of Euclidean geometry, this study displays the richness of the conceptual framework, philosophical and mathematical, inherent to the sixteenth-century Euclidean tradition and shows how it contributed to a more generalised acceptance and promotion of kinematic approaches to geometry in the early modern period.

Reviews

“Axworthy's book fills a gap in the history of the understanding of Euclid's Elements by showing how various commentators have understood the use of kinematic concepts in Euclidean geometry. She concludes her work by showing how the ideas of these commentators contributed to the further acceptance of kinematic approaches to geometry in the work of Descartes and others in the following century.” (Victor J. Katz, Mathematical Reviews, November, 2023)

Authors and Affiliations

  • Max Planck Institute for the History of Science, Berlin, Germany

    Angela Axworthy

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