## The Works of Archimedes |

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### Contents

INTRODUCTION | xv |

Manuscripts and principal editionborder | xxiii |

Relation op Archimedes to his predecessors | xxxix |

Arithmetic in Archimedes | lxviii |

On the problems known as NEY2EI2 | c |

Cobic equations | cxxiii |

Anticipations by Archimedes of the inte | cxlii |

The terminology of Archimedes civ | clv |

ON CONOIDS AND SPHERODDS | 99 |

ON SPIRALS | 151 |

ON THE EQULLIBBIUM OF PLANES BOOK L | 189 |

BOOK II | 203 |

THE SANDRECKONER | 221 |

QUADRATURE OF THE PARABOLA | 235 |

ON FLOATING BODIES BOOK 1 | 253 |

BOOK II | 263 |

ON THE SPHERE AND CYLINDEB BOOK 1 | 1 |

MEASUREMENT OF A CIRCLE | 91 |

BOOK OF LEMMAS | 301 |

THE CATTLEPROBLEM | 319 |

### Common terms and phrases

Apollonius Apollonius of Perga Archimedes axes axis base equal bisecting centre of gravity chord circle circumference circumscribed figure cone cone whose base conic sections conics conoid Conoids and Spheroids cubic equation curve cutting plane cylinder or frustum described diameter draw drawn ellipse equal height Euclid Eutocius fluid follows geometrical given ratio gnomon greater Greek height is equal Hence hyperboloid hypothesis immersed portion inscribed figure intersection Join lemma length less magnitudes mean proportionals meet method middle point Pappus parabola parabolic segment paraboloid parallel parallelogram perpendicular polygon problem produced proof Prop Proposition proved pyramid radius rectangle regular polygon respectively revolution rhombus right angles sector segment ABB semicircle side similar Similarly solid solution solved Sphere and Cylinder spheroid spiral straight line Suppose surface term theorems tlie touch trapezium triangle vertex volume whence