TY - CHAP

T1 - Introduction

T2 - Euclidean Background

AU - Corry, Leo

N1 - Publisher Copyright:
© 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.

PY - 2022

Y1 - 2022

N2 - 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.

AB - 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.

KW - British mathematics

KW - Early algebraic symbolism

KW - Euclidean tradition

KW - Euclid’s Book II

KW - Euclid’s Elements

KW - François Viète

KW - Renaissance mathematics

UR - http://www.scopus.com/inward/record.url?scp=85138170725&partnerID=8YFLogxK

U2 - 10.1007/978-3-031-11538-7_1

DO - 10.1007/978-3-031-11538-7_1

M3 - פרק

AN - SCOPUS:85138170725

T3 - SpringerBriefs in History of Science and Technology

SP - 1

EP - 11

BT - SpringerBriefs in History of Science and Technology

PB - Springer Nature

ER -