An Introduction to the History of Algebra: Solving Equations from Mesopotamian Times to the Renaissance (Mathematical World) New ed. Edition
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This is not a comprehensive look at the developments in algebra during this period, nor is there any attempt to place algebra within the larger history of mathematics. What the book offers is an opportunity to see examples of how algebra was done before the use of modern notation and methods. Sesiano does not, however give attention to the evolution of algebraic notation.
For a finely detailed look at the subsequent period, from Cardano to Lagrange, 1545 to 1771, with a brief glance beyond that, see Jaqueline Stedall (2011): From Cardano's great art to Lagrange's reflections: filling a gap in the history of algebra. Of the two books, I find Stedall's book far more interesting, but Sesiano's book is worth spending some time with if you're interested in the history of algebra.
- Contents -
Chapter 1. Algebra in Mesopotamia
_ 1.1 Introduction
_ 1.2 Linear Systems
_ 1.3 Quadratic Equations and Systems
Chapter 2. Algebra in Ancient Greece
_ 2.1 Introduction
_ 2.2 Common Algebra
_ 2.3 Diophantine Algebra
Chapter 3. Algebra in the Islamic World
_3.4 The Geometric Construction of Solutions of the Quadratic Equation
_3.5 The Cubic Equation
Chapter 4. Algebra in Medieval Europe
_4.2 The Liber mahameleth
_4.3 Leonardo Fibonacci
_4.4 Later Developments
Chapter 5. Algebra in the Renaissance
_5.1 The Development of Algebraic Symbolism
_5.2 The Solution of the Cubic and Quartic Equations
_5.3 The Solution of the Cubic Equation in Italy
_5.4 Bombelli and Imaginary Numbers
_5.5 Casus irreducibles
Appendix A Mesopotamian Texts in Translation
Appendix B Greek and Latin Texts
Appendix C Arabic Texts
Appendix D Hebrew Text
Appendix E French, German, Italian, and Provencal Texts