A Discourse Concerning Algebra English Algebra to 1685

by Stedall, Jacqueline A.

• ISBN13: 9780198524953
• ISBN10: 0198524951
• Format: Hardcover
• Copyright: 2003-03-27
• Publisher: Oxford University Press

Summary

For historians of mathematics and those interested in the history of science, 'A Discourse Concerning Algebra' provides an new and readable account of the rise of algebra in England from the Medieval period to the later years of the 17th century. Including new research, this is the most detailed study to date of early modern English algebra, which builds on work published in 1685 by John Wallis (Savilian Professor of Geometry at Oxford) on the history of algebra. Stedall's book follows the reception and dissemination of important algebraic ideas and methods from continental Europe (especially those of Viete) and the consequent revolution in the state of English mathematics in the 17th century. The text emphasises the contribution of Wallis, but substantialreference is also provided to other important mathematicans such as Harriot, Oughtred, Pell and Brouncker.

Author Biography

Jacqueline A. Stedall is a member of the Centre for the History of the Mathematical Sciences at the Open University.

Table of Contents

A large discourse concerning algebra	p. 1
English mathematics before 1649	p. 5
A treatise of algebra	p. 8
How algebra was entertained and cultivated in Europe	p. 19
'In Arabic it is called al-jabr'	p. 35
'The Italians have given it the name of Regula cosae'	p. 36
'Cardan gives it the name of Ars magna'	p. 45
'What we commonly call algebra is by a Greek name called Analysis'	p. 50
Wallis's account of early algebra	p. 52
Ariadne's thread: William Oughtred's Clavis	p. 55
The first edition: 1631	p. 59
The second editions: 1647 and 1648	p. 65
The third edition: 1652	p. 68
The fourth edition: 1667	p. 73
Wallis and the Clavis	p. 77
The final editions: 1693 onwards	p. 82
Rob'd of glories: Thomas Harriot and his Treatise on equations	p. 88
The Treatise on equations	p. 94
Harriot's Will and the writing of the Praxis	p. 97
The contents of the Praxis	p. 100
The Corrector and the Summary	p. 107
The fate of Harriot's material after 1631	p. 111
Wallis's account of Harriot's algebra	p. 117
Moving the Alps: uncovering the mathematics of John Pell	p. 126
An introduction to algebra	p. 135
Pell and Wallis	p. 139
Reading between the lines: John Wallis's Arithmetica infinitorum	p. 155
Squaring the circle	p. 156
Praise and criticism	p. 165
The enlargement of the mathematical empire	p. 173
Catching Proteus: the mathematics of William Brouncker	p. 183
Squaring the hyperbola and the circle	p. 185
The challenges from Fermat	p. 196
'Many pretty things worth looking into'	p. 208
Wallis's perspective on algebra	p. 212
Wallis's perspective on history	p. 215
Notes	p. 219
Bibliographies	p. 261
Primary sources: manuscripts	p. 261
Primary sources: printed books	p. 264
Secondary sources	p. 276
Index	p. 289
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