A Short History of Greek Mathematics [NOOK Book]

Overview

Authoritative and highly readable, this history of Greek mathematics focuses on the contributions of major figures such as Euclid, Archimedes, and Ptolemy, but also explores fascinating aspects of works by many lesser-known scholars and thinkers. Mathematicians will find accounts here of every extant Greek mathematical book, in addition to many proofs translated directly from ancient texts. Greek scholars will encounter a full treatment of nomenclature and arithmetical symbols. Students of history, even those ...
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A Short History of Greek Mathematics

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Overview

Authoritative and highly readable, this history of Greek mathematics focuses on the contributions of major figures such as Euclid, Archimedes, and Ptolemy, but also explores fascinating aspects of works by many lesser-known scholars and thinkers. Mathematicians will find accounts here of every extant Greek mathematical book, in addition to many proofs translated directly from ancient texts. Greek scholars will encounter a full treatment of nomenclature and arithmetical symbols. Students of history, even those without a particular interest in Greek or mathematics, will be able to extract from these pages a chronicle of the development of mathematical science. Contents include discussions of the decimal scale; Egyptian and Greek arithmetic; the Greek theory of numbers and Greek geometry; prehistoric and Egyptian geometry; and the works of Euclid, Archimedes, Apollonius, and their successors.
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Product Details

  • BN ID: 2940026473199
  • Publisher: University press
  • Sold by: Barnes & Noble
  • Format: eBook
  • Edition description: Digitized from 1884 volume
  • File size: 756 KB

Table of Contents

Part I. Prolegomena to Arithmetic 1
Chapter I. The Decimal Scale 1
Section 1, 2 Aryan numerals 1
Section 3-5 Numerals in savage languages 5
Section 6-9 Etymology of Aryan numerals 7
Section 10 Primitive expression of fractions 13
Chapter II. Egyptian Arithmetic 15
Section 11 Reasons for introducing the subject 15
Section 12 Ahmes and his table of submultiples 16
Section 13 Seqem-calculations 18
Section 14 Simple equations and series 18
15, 16 Summary 20
Part II. Greek Arithmetic 22
Chapter III. Calculation. Logistica 22
Section 17 Logistica opposed to Arithmetica 22
Section 18 Numerical symbolism 24
Section 19, 20 Greek and Roman finger-symbols 24
Section 21 Pebble-symbolism 27
Section 22 Origin of the [characters not reproducible] 29
Section 23 The Roman abacus 30
Section 24 The Salaminian Table 33
Section 25 Combination of finger-symbolism and abacus 36
Section 26, 27 The Apices 37
Section 28 Origin of written symbols 39
Section 29 Earliest Greek written numerals 40
Section 30 Greek alphabetic numerals 42
Section 31-33 Their origin 43
Section 34 Signs for fractions and compendia 48
Section 35 Greek multiplication 49
Section 36 Compound division 51
Section 37, 38 Extraction of a square root 53
Section 39, 40 Nomenclature of Archimedes 57
Section 41 Nomenclature and multiplication of Apollonius 61
Section 42 Symbolism of Noviomagus 64
Section 43 Greek arithmetical education 64
Chapter IV. Greek Theory of Numbers (Arithmetica) 66
Section 44 Pythagoras 66
Section 45-46 Pythagorean and Platonic Arithmetica 68
Section 47 Euclid's Arithmetica, Book II. of the Elements 72
Section 48-50 Books VII.-IX. 74
Section 51-53 Book X. Incommensurables 78
Section 54 Theory of Combinations 86
Section 55 Eratoshenes and Hypsicles 87
Section 56-60 Nicomachus Gerasenus 88
Section 61 Theon Symrnaeus 95
Section 62 Thymaridas 96
Section 63 Iamblichus 97
Section 64 Arithmetical epigrams 98
Section 65-72 Diophantus and Algebra 100
Part III. Greek Geometry 123
Chapter V. Prehistoric and Egyptian Geometry 123
Section 73, 74 Origin of Geometry 123
Section 75, 76 Geometry of Ahmes 126
Section 77, 78 Later Egyptian Geometry 129
Section 79 Connexion of Greek with Egyptian 131
Section 80 Babylonian geometry 132
Chapter VI. Greek Geometry to Euclid 134
(a) Preliminary
Section 81 The Eudemian summary 134
Section 82 The antique style acc. to Geminus 137
(b) The Ionic School
Section 83 Thales' Life 138
Section 84-86 His geometry 140
Section 87 Other Ionic geometers 145
Section 88 Oenopides of Chios 146
(c) The Pythagoreans
Section 89, 90 Life and teaching of Pythagoras 147
Section 91, 92 His geometry 149
Section 93 The regular solids 153
Section 94 The Pythagorean theorem 155
Section 95 Later Pythagoreans, esp. Archytas 157
Section 96 Eleatics and Atomists, esp. Democritus 158
(d) The Sophists
Section 97 Rise of the Sophists 160
Section 98 The insoluble problems 161
Section 99 Hippias and the quadratrix 162
Section 100 Theodorus of Cyrene and Hippocrates of Chios 164
Section 101 Quadrature of lunes by Hippocrates 165
Section 102 Duplication-problem recast by Hippocrates 169
Section 103-106 Method of exhaustion and its origin 169
Section 104 Quadrature of circle by Antiphon and Bryson 170
(e) The Academy
Section 107 Plato and his mathematical teaching 173
Section 108 The method of analysis 177
Section 109 Plato's solution of duplication-problem, etc. 180
Section 110 Archytas' solution of duplication-problem, etc. 181
Section 111 Leodamas, Theaetetus, Neocleides, Leon 183
Section 112 Eudoxus 183
Section 113 Menaechmus and the later Academics 185
Section 114 Aristotle 188
Section 115 Autolycus of Pitane 189
Section 116 Summary of the pre-Euclidean geometry 190
Chapter VII. Euclid, Archimedes, Apollonius 192
Section 117 Defects in Athenian culture 192
Section 118 Rise of Alexandria 193
Section 119 Euclid's life 195
Section 120 Style and structure of the Elements 196
Section 121 History of the text 199
Section 122 Modern history of the book 203
Section 123 Other extant works of Euclid 209
Section 124 Lost works of Euclid 215
Section 125 Life of Archimedes 221
Section 126 Catalogue of the works of Archimedes 223
Section 127 Geometry of Archimedes 225
Section 128 Dimensio Circuli 233
Section 129 Mechanics and machines of Archimedes 237
Section 130 Eratosthenes 244
Section 131 Apollonius of Perga 246
Section 132 Summary of his Conics 250
Section 133 Specimens of his Conics 255
Section 134 Chasles on Archimedes and Apollonius 260
Section 135 Lost works of Apollonius 261
Section 136 Method of duplication attributed to Apollonius 263
Chapter VIII. Geometry in Second Century B.C. 265
Section 137 General criticism of the period 265
Section 138 Nicomedes and the conchoid 266
Section 139 Diocles and the cissoid 268
Section 140 Perseus and his spirals 270
Section 141 Zenodorus on 'Figures of Equal Periphery' 271
Section 142 Hypsicles and his works 272
Section 143 Hipparchus 274
Section 144 Heron of Alexandria 276
Section 145 Heron's geometrical works 280
Section 146 Egyptian character of Heron's work 284
Chapter IX. From Geminus to Ptolemy 287
Section 147 Geminus 287
Section 148 Theodosius of Tripolis 288
Section 149 Serenus of Antissa 289
Section 150 Menelaus 291
Section 151 Trigonometry of Ptolemy 292
Section 152 Other geometrical work of Ptolemy 299
Chapter X. Last Years 302
Section 153 Sextus Julius Africanus 302
Section 154 Pappus and his works 304
Section 155 Contents of the Mathematicae Collectiones 305
Section 156 Apercus of Pappus 308
Section 157 Greek Commentators on classical geometers 311
Section 158 Summary 313
Index 317
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