## Great Moments in Mathematics (after 1650) |

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### Contents

PREFACE ix | 16 |

LECTURE TWENTYTHREE Like opening and closing a door | 31 |

Formal axiomatics early twentieth century LECTURE THIRTYFIVE Some remarkable definitions | 38 |

Copyright | |

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### Common terms and phrases

acute angle addition algebra analysis angles appeared applied arithmetic associative assume assumptions basic branch calculus called carries century commutative complex numbers concept considered consistent constitutes contains convergence correspondence curve defined definition denote differential early element equal equation equivalent established Euclid's Euclidean example Exercises exists field Figure finite four Fourier function Further given hold hypothesis idea important infinite integers interpretation interval invariant inverse known later lecture length limit logical mathematicians mathematics matrices means method multiplication natural numbers obtain operation ordered original pairs parallel postulate plane positive possible postulate set problem proof properties propositions proved published pure real number regarded relation remarkable result right angles sequence Show shown space statements straight line symbol theorem theory tion transformation triangle University values York