## A Manual of Greek Mathematics |

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### Contents

1 | |

11 | |

36 | |

THE EARLIEST GREEK GEOMETRY THALES | 73 |

PYTHAGOREAN GEOMETRY | 92 |

PROGRESS IN THE ELEMENTS DOWN TO PLATOS TIME | 112 |

SPECIAL PROBLEMS | 139 |

FROM PLATO TO EUCLID | 171 |

ARCHIMEDES | 277 |

CONIC SECTIONS APOLLONIUS OF PERGA | 347 |

THE SUCCESSORS OF THE GREAT GEOMETERS | 377 |

TRIGONOMETRY HIPPARCHUS MENELAUS AND PTOLEMY | 393 |

MENSURATION HERON OF ALEXANDRIA | 415 |

PAPPUS OF ALEXANDRIA | 434 |

ALGEBRA DIOPHANTUS OF ALEXANDRIA | 466 |

COMMENTATORS AND MINOR WRITERS | 510 |

### Common terms and phrases

Alexandria algebra Apollonius Archimedes Archytas Aristotle arithmetic astronomy axis base bisected Book centre of gravity chord circle circumference circumscribed commentary cone conics construction contained cube curve cylinder deﬁned deﬁnition diameter Diophantus divided draw earth Elements equal equations equivalent Eratosthenes Eucl Euclid Eudemus Eudoxus Eutocius ﬁgure ﬁnd ﬁnding ﬁrst ﬁve ﬁxed ﬂuid geometry given straight line gives gnomon Greek Heron HERON OF ALEXANDRIA Hipparchus Hippocrates hyperbola inscribed irrational isosceles lemmas length loci magnitudes mathematics mean proportionals measure method method of exhaustion moon multiplied namely Nicomachus Pappus parabola parallel parallelogram pentagon perpendicular plane Plato Porisms problem Proclus proof Prop propositions proved Ptolemy pyramid Pythagoras Pythagoreans quadrature radius rectangle regular solids respectively right angles right-angled triangle says segment semicircle sides similar solution solved sphere spiral square number surface tangent Thales Theaetetus Theon theorem theory tion translation treatise triangular number

### Popular passages

Page 3 - ... certain definite stages in its development, with the intervals separating them. In Thales's time (about 600 B. c.) we find the first glimmerings of a theory of geometry, in the theorems that a circle is bisected by any diameter, that an isosceles triangle has the angles opposite to the equal sides equal, and (if Thales really discovered this) that the angle in a semicircle is a right angle.

Page 2 - To be a Greek was to seek to know; to know the primordial substance of matter, to know the meaning of number, to know the world as a rational whole. In no spirit of paradox one may say that Euclid is the most typical Greek : he would fain know to the bottom, and know as a rational system, the laws of the measurement of the earth.