Introduction: Euclidean Background

The present book discusses the historically changing conceptions concerning the relationship between geometry and arithmetic within the Euclidean tradition that developed in the British context of the sixteenth and seventeenth century, with a particular focus on Book II of the Elements. The then recently developed algebraic symbolism and methods, especially as promoted by François Viète and his followers, took center stage as mediators between the two realms, thus offering ways to work out that interaction that are not found in earlier editions of the Euclidean text in other European contexts. The book discusses works written by prominent figures in British mathematics, focusing on the way they handled results related with Book II: Robert Recorde’s Pathway to Knowledge (1551), the first two English translations of the Elements (by Henry Billingsley (1570) and Thomas Rudd (1651)), two remarkable books published in 1631, Clavis Mathematicae by William Oughtred and Artis Analyticae Praxis by Thomas Harriot, and the contributions of John Wallis and Isaac Barrow. Also discussed are Euclidean versions written by somewhat lesser-known and less influential, but no less interesting mathematicians, such as John Leeke and George Serle, Reeve Williams and William Halifax, William Alingham and Henry Hill. The introductory chapter comprises summary accounts of three background issues that play a central role in the story: (a) Book II of Euclid’s Elements; (b) the early printed editions of the Elements; (c) the rise of the new symbolic algebra, leading to the work of Viète.