British Versions of Book II of Euclid’s Elements: Geometry, Arithmetic, Algebra (1550–1750)

1. Front Matter

   Pages i-vii

   PDF

2. Introduction: Euclidean Background

   • Leo Corry

   Pages 1-11

3. The Main Figures: From Recorde to Wallis and Barrow

   • Leo Corry

   Pages 13-48

4. Some Lesser-Known Figures

   • Leo Corry

   Pages 49-63

5. Summary and Concluding Remarks

   • Leo Corry

   Pages 65-74

This book discusses the changing conceptions about the relationship between geometry and arithmetic within the Euclidean tradition that developed in the British context of the sixteenth and seventeenth century. Its focus is on Book II of the Elements and the ways in which algebraic symbolism and methods, especially as recently introduced by François Viète and his followers, took center stage as mediators between the two realms, and thus offered new avenues to work out that relationship in idiosyncratic ways not found in earlier editions of the Euclidean text.

Texts examined include Robert Recorde's Pathway to Knowledge (1551), Henry Billingsley’s first English translation of the Elements (1570), Clavis Mathematicae by William Oughtred and Artis Analyticae Praxis by Thomas Harriot (both published in 1631), Isaac Barrow’s versions of the Elements (1660), and John Wallis Treatise of Algebra (1685), and the English translations of Claude Dechales’ French Euclidean Elements (1685).

This book offers a completely new perspective of the topic and analyzes mostly unexplored material. It will be of interest to historians of mathematics, mathematicians with an interest in history and historians of renaissance science in general.

• Renaissance mathematics
• British mathematics
• Euclidean tradition
• Euclid's Elements
• Euclid's Book II
• Early algebraic symbolism
• François Viète
• Robert Recorde
• Henry Billingsley
• Thomas Rudd
• William Oughtred
• Thomas Harriot
• John Wallis
• Isaac Barrow

“This short but captivating book represents the latest installment of a series of investigations made by the author into the history of geometric algebra … . The book under review takes a historical perspective in tackling the issue, delving into a comprehensive analysis of the reception of Euclid's Elements in Britain … . the book engages in early modern debates on the quest for a foundational discipline that could underpin the entirety of mathematics.” (Davide Crippa, Mathematical Reviews, November, 2023)

• Cohn Institute for History and Philosophy of Science, Tel Aviv University, Tel Aviv, Israel

  Leo Corry

Leo Corry is a historian of science working at Tel Aviv University. He has published extensively on the history of mathematics, physics and computing, since the turn of the twentieth century, as well as on medieval mathematics. 

He has published two books in the SpringerBriefs Series, as well as one book with Kluwer, one with Birhauser, one with Oxford UP. He also has a very long list of published articles and book chapters.

He was editor of Science in Cintext (published at Cambridge UP).

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