This is a source book of the history of mathematics focusing on algorithms. With the development of computing has come an awakening of interest in algorithms. Often neglected by historians and modern scientists, more concerned with the nature of concepts, algorithmic procedures turn out to have been instrumental in the development of fundamental ideas: practice led to theory just as much as the other way round. The purpose of this book is to offer a historical background to contemporary algorithmic practice. Each chapter centres around a theme, more or less in chronological order, and the theory is told through the reading of over 200 original texts, faithfully reproduced.

Contents:

0. Introduction;

1. Algorithms for arithmetic operations;

2. Magic squares;

3. Methods of false position;

4. Euclid s algorithm

5. From measuring the circle to calculating (geometric and analytic approaches);

6. Newton s methods (the tangent method, Newton s polygons);

7. Solving equations by successive approximations (extraction of square roots, polynomials equations);

8. Algorithms in arithmetic (factors and multiples, tests for primality, factorisation algorithms, the Pell-Fermat equation);

9. Solving systems of linear equations;

10. Tables and interpolation;

11. Approximate quadratures;

12. Approximate solutions of differential equations;

13. Approximation of functions (uniform approximation and mean quadratic approximation);

14. Acceleration of convergence;

15. Toward the concept of algorithm (recursive functions and computable functions, machines).