British versions of Book II of Euclid's Elements: Geometry, arithmetic, algebra (1550-1750)

Research output: Book/ReportBook


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 Francois Viete 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 Billingsleys first English translation of the Elements (1570), Clavis Mathematicae by William Oughtred and Artis Analyticae Praxis by Thomas Harriot (both published in 1631), Isaac Barrows 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.
Original languageEnglish
Place of PublicationCham, Switzerland
Number of pages74
ISBN (Electronic)3031115384, 9783031115387
ISBN (Print)3031115376, 9783031115370
StatePublished - 2022

Publication series

NameSpringerBriefs in History of Science and Technology
ISSN (Print)2211-4564
ISSN (Electronic)2211-4572


  • 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

ULI Keywords

  • uli
  • Euclid -- Elements
  • Euclid's Elements -- History -- 16th century
  • Euclid's Elements -- History -- 17th century
  • Mathematical literature -- Great Britain -- History -- 16th century
  • Mathematical literature -- Great Britain -- History -- 17th century


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