## Great Moments in Mathematics (after 1650)What a splendid addition this is to the Dolciani Mathematical Exposition series! This second set of lectures on great moments in mathematics (after 1650) is a fascinating collection of pivotal points in the historical development of mathematics...The four lectures devoted to the liberation of geometry and algebra are of particular interest. The lectures should be required reading for all teachers of mathematics. --Herbert Fremont, The Mathematics Teacher Eves is never less than tantalizing and usually inspiring...each 'great moment' has detailed exercises following it, as these have been carefully chosen to illustrate the depth of the ideas in question. --C. W. Kilmister, The London Times, Higher Education Supplement As is usual with Eves' work, the books are well written and entertaining. They give an historical background to many of the best known mathematical results, and, in addition, provide interesting pieces of information about the mathematicians involved. Eves includes relevant exercises at the end of each chapter. These are a good source of different, interesting problems, and when combined with the material in the chapter, could form the basis for a mathematical project...Eves' book provides an interesting, well-written, and enjoyable account. You won't be disappointed. --David Parrott, The Australian Mathematics Teacher |

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### Contents

LECTURE TWENTYTWO Moving pictures versus still pictures | 11 |

The invention of the differential calculus 16291680s | 25 |

LECTURE TWENTYFOUR Powerful series | 40 |

Copyright | |

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acute angle addition and multiplication applied arithmetic axiomatics branch of pure called Cantor cardinal number century complex numbers concept considered consistent constitutes convergence curve defined definition denote denumerable differential calculus discourse dyadic relation element elementary equal equation equivalent Euclid’s Euclidean geometry example exists Fermat finite number formula Fourier series given Godel number Hausdorff space Howard Eves hypothesis infinite sets interpretation invariant inverse lecture text Leibniz Lobachevskian logical lorotation machine mathe mathematicians ment method metric space MOMENTS IN MATHEMATICS natural number system Newton non-Euclidean geometry nonsingular transformations operation ordered pairs parallel postulate Pascal planar polynomial positive integers postulate set postulate system power series primitive terms problem projective geometry proof properties propositional function proved pure mathematics quaternions rational numbers real number system right angles Saccheri sequence set theory Show statements straight line symbol tangent tion transcendental transformation group triangle