## Great Moments in Mathematics (before 1650)[V.1] Great moments in mathematics before 1650 is the product of a series of lectures on the history of mathematics given by Howard Eves. He presents here, in chronological order, 20 "great moments in mathematics before 1650," which can be appreciated by anyone who enjoys mathematics. These wonderful lectures could be used as the basis of a course on the history of mathematics, but can also serve as enrichment to any mathematics course. Included are lectures on the Pythagorean Theorem, Euclid's Elements, Archimedes (on the sphere), Diophantus, Omar Khayyam, and Fibonacci. |

### Contents

LECTURE TWO The greatest Egyptian pyramid | 8 |

LECTURE FOUR The first great theorem | 26 |

LECTURE FIVE Precipitation of the first crisis | 43 |

LECTURE SEVEN First steps in organizing mathematics | 62 |

LECTURE NINE The thinker and the thug | 83 |

LECTURE TEN A boost from astronomy | 96 |

LECTURE ELEVEN The first great number theorist | 110 |

LECTURE twelve The syncopation of algebra | 126 |

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### Common terms and phrases

abacus algebra algorithm altitude analytic geometry ancient angle Archimedes arithmetic base Book Cavalieri century chord circle compasses computing congruent construction counters cube cubic equation curve cylinder Descartes digit Diophantus divides divisor ellipse equal Euclid's Elements Eudoxian Fermat Fibonacci Figure formula Further Reading given golden ratio Greek Hindu Hindu-Arabic numeral system history of mathematics HOWARD EVES hypotenuse integers irrational number Kepler known later lecture legs length Liber abaci line segment logarithms mathematician method MOMENTS IN MATHEMATICS multiplication Napier obtain pair parallel perfect numbers plane polygon positive integers problem proof proposition Prove Ptolemy's Ptolemy's theorem pyramid Pythagorean theorem Pythagorean triple quadratic quadrilateral quartic equation radius rational number relatively prime right triangle roots Show side solid solution solve sphere spherical square straightedge symbols tangent tetrahedron tion triangle ABC trisection vertex volume whence