## A History of MathematicsOriginally published in 1893, this book was significantly revised and extended by the author (second edition, 1919) to cover the history of mathematics from antiquity to the end of World War I. Since then, three more editions were published, and the current volume is a reproduction of the fifth edition (1991). The book covers the history of ancient mathematics (Babylonian, Egyptian, Roman, Chinese, Japanese, Mayan, Hindu, and Arabic, with a major emphasis on ancient Greek mathematics). The chapters that follow explore European mathematics in the Middle Ages and the mathematics of the sixteenth, seventeenth, and eighteenth centuries (Vieta, Decartes, Newton, Euler, and Lagrange). The last and longest chapter discusses major mathematics events of the nineteenth and early twentieth centuries. Topics discussed in this chapter include synthetic and analytic geometry, algebra, analysis, the theory of functions, the theory of numbers, and others. In one concise volume, the author presents an interesting and reliable account of mathematics history. Cajori has mastered the art of incorporating an enormous amount of material into a smoothly flowing narrative. The review of the volume's third edition in Mathematical Reviews ends with the following words: "Chaque mathematicien devrait lire ce livre!" |

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### Contents

THE BABYLONIANS | 1 |

THE EGYPTIANS | 9 |

THE GREEKS | 15 |

Greek Arithmetic and Algebra | 52 |

THE ROMANS | 63 |

THE MAYA | 69 |

THE CHINESE | 71 |

THE JAPANESE | 78 |

Descartes to Newton | 173 |

Newton to Euler | 190 |

Euler Lagrange and Laplace | 231 |

THE NINETEENTH AND EARLY TWENTIETH CENTURIES | 278 |

Synthetic Geometry | 286 |

Analytic Geometry | 309 |

Algebra | 329 |

Analysis | 367 |

THE HINDUS | 83 |

THE ARABS | 99 |

EUROPE DURING THE MIDDLE AGES | 113 |

Translation of Arabic Manuscripts | 118 |

The First Awakening and its Sequel | 120 |

EUROPE DURING THE SIXTEENTH SEVENTEENTH AND EIGHTEENTH CENTURIES | 130 |

Vieta to Descartes | 145 |

### Common terms and phrases

A. L. Cauchy algebra analysis analytical angles applied Arabic Archimedes arithmetic astronomical Berlin Bernoulli C. G. J. Jacobi calculus called Cambridge Cantor Cayley century circle coefficients contains convergent cubic curve Descartes determine developed differential equations Diophantus discovery edition elliptic functions Euclid Euler Fermat finite fluxions formula fractions gave geometry given gives Greek groups hased Hindu infinite integral invention investigations J. J. Sylvester Johann Bernoulli K. F. Gauss known Lagrange later Leibniz Leipzig linear logarithms magic squares Math mathematicians mathematics matics memoir method motion N. H. Abel Newton notation P. G. Tait P. S. Laplace Paris plane Poincare principle problem professor prohability proof proved published Pythagorean quadratic quadrature researches Riemann roots sexagesimal solution solved square surface symbols synthetic geometry tangents theorem theory of numbers tion treatise triangle trigonometry University variables Weierstrass writings wrote