## The Rainbow of Mathematics: A History of the Mathematical SciencesHe charts the growth of mathematics through its refinement by ancient Greeks and then medieval Arabs, to its systematic development by Europeans from the Middle Ages to the early twentieth century. This book describes the evolution of arithmetic and geometry, trigonometry and algebra; the interplay between mathematics, physics, and mathematical astronomy; and "new" branches such as probability and statistics. Authoritative and comprehensive, The Rainbow of Mathematics is a unique account of the development of the science that is at the heart of so many other sciences. Originally published under the title The Norton History of the Mathematical Sciences. |

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This magnificent work covers mathematics from its recorded beginnings to the end of World War I. It provides remarkable insight into the development of the various branches of mathematics, and into the connections between mathematical and scientific ideas. Readers will find a wealth of interesting and useful information, including a superb bibliography. Highly recommended!

### Contents

Previewing the rainbow | 3 |

Invisible origins and ancient traditions | 18 |

from the early Middle | 104 |

The calculus and its consequences | 257 |

Analysis and mechanics at centre stage | 303 |

Institutions and the profession after | 347 |

Mathematical analysis | 364 |

The expanding world of algebras | 409 |

Mechanics and mathematical physics | 439 |

International mathematics but the rise | 479 |

The new century to the Great | 654 |

Revie wing the rainbow | 719 |

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### Common terms and phrases

aether algebra angles applied Arabic Archimedes arithmetic astronomy axioms became Bernoulli body calculus Cantor's Cauchy Cauchy's centre century Chap circle coefficients complex concern continued Crelle's journal curves defined Descartes developed differential equations differential geometry early Ecole edition especially Euclid Euclid's Elements Euclidean geometry Euler example expressed figures finite followed formula Fourier Fourier series French functions Gauss geometry German given Grattan-Guinness Greek important innovation integers integral Kepler Klein known Lagrange Lagrange's Laplace Laplace's later Leibniz linear logic major mathe mathematical analysis mathematicians matics mechanics methods motion Newton non-Euclidean geometry notation number theory optics orbits paper Pappos physics plane Poincar polynomial potential theory principle probability probability theory problem proof properties published ratios Riemann roots rotation set theory solutions square surface theorem tion topology translation triangle trigonometry values variables various velocity Weierstrass