## Classical Mathematics from Al-Khwarizmi to DescartesThis book follows the development of classical mathematics and the relation between work done in the Arab and Islamic worlds and that undertaken by the likes of Descartes and Fermat. ‘Early modern,’ mathematics is a term widely used to refer to the mathematics which developed in the West during the sixteenth and seventeenth century. For many historians and philosophers this is the watershed which marks a radical departure from ‘classical mathematics,’ to more modern mathematics; heralding the arrival of algebra, geometrical algebra, and the mathematics of the continuous. In this book, Roshdi Rashed demonstrates that ‘early modern,’ mathematics is actually far more composite than previously assumed, with each branch having different traceable origins which span the millennium. Going back to the beginning of these parts, the aim of this book is to identify the concepts and practices of key figures in their development, thereby presenting a fuller reality of these mathematics. This book will be of interest to students and scholars specialising in Islamic science and mathematics, as well as to those with an interest in the more general history of science and mathematics and the transmission of ideas and culture. |

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### Contents

the fifth book of Apolloniuss | |

The founding acts and main contours of Arabic mathematics | |

Fermat and algebraic geometry | |

the beginnings of combinatorial analysis | |

The first classifications of curves | |

Thābit ibn Qurra and amicable numbers | |

Fibonacci and Arabic mathematics | |

Fibonacci and the Latin extension of Arabic mathematics | |

AlYazdī and the equation | |

Fermat and the modern beginnings of Diophantine analysis | |

The Archimedeans and problems with infinitesimals | |

The traditions of the Conics and the beginning of research | |

The continuous drawing of conic curves and the classification | |

Simplicius On the Euclidean definition of the straight line | |

Descartess ovals | |

Descartes and the infinitely small | |

ARITHMETIC | |

Algorithmic methods | |

Algebra and its unifying role | |