## A Short History of Greek MathematicsJames Gow's A Short History of Greek Mathematics (1884) provided the first full account of the subject available in English, and it today remains a clear and thorough guide to early arithmetic and geometry. Beginning with the origins of the numerical system and proceeding through the theorems of Pythagoras, Euclid, Archimedes and many others, the Short History offers in-depth analysis and useful translations of individual texts as well as a broad historical overview of the development of mathematics. Parts I and II concern Greek arithmetic, including the origin of alphabetic numerals and the nomenclature for operations; Part III constitutes a complete history of Greek geometry, from its earliest precursors in Egypt and Babylon through to the innovations of the Ionic, Sophistic, and Academic schools and their followers. Particular attention is given to Pythagorus, Euclid, Archimedes, and Ptolemy, but a host of lesser-known thinkers receive deserved attention as well. |

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### Contents

PROLEGOMENA TO ARITHMETIC 121 | 1 |

Primitive expression of fractions 1314 | 13 |

GREEK ARITHMETIC 22122 | 21 |

Pebblesymbolism 2729 | 28 |

The Salaminian Table 3336 | 34 |

Earliest Greek written numerals 4041 | 40 |

SECTION PAOE | 41 |

Signs for fractions and compendia 4849 | 48 |

Bise of Alexandria 193195 | 194 |

Euclids life 195196 | 196 |

History of the text 199203 | 199 |

Modern history of the book 203209 | 203 |

SECTION PAGE 123 Other extant works of Euclid 209215 | 209 |

Life of Archimedes 221222 | 221 |

Catalogue of the works of Archimedes 223225 | 223 |

Geometry of Archimedes 225 233 | 225 |

Symbolism of Noviomagus | 64 |

Euclids Arithmetiea Book H of the Elements 7274 | 72 |

Theory of Combinations 8687 | 86 |

Theon Smyrnaeus 9596 | 95 |

PREHISTORIC AND EGYPTIAN GEOMETRY 123133 | 123 |

Connexion of Greek with Egyptian 131132 | 131 |

The antique style acc to Geminus 137138 | 137 |

6 The Ionic School SECTION PAGE 83 ThalesLife 138140 | 138 |

8486 His geometry 140145 | 140 |

Other Ionic geometers 145146 | 145 |

OBnopides of Chios 146147 | 146 |

c The Pythagoreans | 150 |

Life and teaching of Pythagoras 147149 | 153 |

Later Pythagoreans esp Archytas 157158 | 157 |

The insoluble problems 161162 | 161 |

Hippias and the quadratrix 162164 | 162 |

Theodoras of Cyrene and Hippocrates of Chios 164165 | 164 |

Quadrature of lunes by Hippocrates 165169 | 165 |

Duplicationproblem recast by Hippocrates | 169 |

Quadrature of circle by Antiphon and Bryson 170171 | 170 |

e The Academy 107 Plato and his mathematical teaching 173177 | 173 |

The method of analysis 177180 | 177 |

Platos solution of duplicationproblem etc 180181 | 180 |

Archytas 181188 | 181 |

Leodamas Theaetetus Neocleides Leon | 183 |

Menaechmus and the later Academics 185188 | 185 |

Aristotle 188189 | 188 |

115 Autolycus of Pitane 189190 | 189 |

Summary of the preEuolidean geometry 190191 | 190 |

Defects in Athenian culture | 192 |

Dimensio Circuli 233237 | 233 |

Mechanics and machines of Archimedes 237244 | 237 |

Eratosthenes 244246 | 244 |

Apollonius of Perga 246250 | 246 |

Summary of his Conies 250255 | 247 |

Method of duplication attributed to Apollonius 263264 | 263 |

GEOMETRY IN SECOND CENTUEY e g 265286 | 265 |

Nicomedes and the conchoid 266268 | 266 |

Diocles and the cissoid 268270 | 268 |

Perseus and his spirals 270271 | 270 |

Zenodorus onFigures of Equal Periphery 271272 | 271 |

Hypsicles and his works 272274 | 272 |

Hipparchus 274275 | 274 |

Heron of Alexandria 276280 | 276 |

Herons geometrical works 280284 | 280 |

Egyptian character of Herons work 284286 | 284 |

FEOM GEMINUS TO PTOLEMY 287301 | 287 |

Theodosius of Tripolis 288289 | 288 |

Serenus of Antissa 289291 | 289 |

Menelaus 291292 | 291 |

Trigonometry of Ptolemy 292299 | 292 |

Other geometrical work of Ptolemy 299301 | 299 |

LAST YEARS 302315 | 302 |

Pappus and his works 304305 | 304 |

Contents of the Malhematicae Collectiones 305308 | 305 |

Apergus of Pappus 308311 | 308 |

Greek Commentators on classical geometers 311313 | 311 |

Summary 313315 | 313 |

317 | |

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### Common terms and phrases

Ahmes Alexandria algebraical Almagest alphabet Apollonius Arabic Archimedes Archytas Aristotle arithmetical astronomical attributed Ave Maria Lane Bretschneider calculation called Cantor centre century Chasles chord circle cited College commentary cone conic conies contains cube curve Delambre Demy 8vo described diameter Diophantus edition Egyptian equal equations Eratosthenes Euclid Eudemian summary Eudemus Eudoxus Eutocius evidence extant fact figure fingers fractions Friedlein given Greek mathematics Hankel Heiberg Heron Hipparchus Hippocrates Hultsch Iamblichus introduced invented isosceles later lemmas Math mathematicians mathematics means mentioned method Nesselmann Nicomachus Notes numbers Pappus plane Plato Plutarch porism problem Proclus Professor proof Prop proportion propositions Ptolemy Pythagoras Pythagorean quoted ratio rectangle right angles says segment shews side similar solution sphere square number St John's College straight line Suidas symbolism Thales Theon theorem theory translation treatise triangle University of Cambridge University Press Warehouse Vorles writer