A short history of Greek mathematics.
Gow, James, 1854-1923.
[Rev.]. --
New York : Chelsea Pub. Co., [1968]
xii, 325 p. ; 21 cm.
More Details
New York : Chelsea Pub. Co., [1968]
general note
Reprint of the 1884 ed.
catalogue key
Bibliographical footnotes.
A Look Inside
Main Description
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. Book jacket.
Table of Contents
Prolegomena to Arithmeticp. 1
The Decimal Scalep. 1
Aryan numeralsp. 1
Numerals in savage languagesp. 5
Etymology of Aryan numeralsp. 7
Primitive expression of fractionsp. 13
Egyptian Arithmeticp. 15
Reasons for introducing the subjectp. 15
Ahmes and his table of submultiplesp. 16
Seqem-calculationsp. 18
Simple equations and seriesp. 18
Summaryp. 20
Greek Arithmeticp. 22
Calculation. Logisticap. 22
Logistica opposed to Arithmeticap. 22
Numerical symbolismp. 24
Greek and Roman finger-symbolsp. 24
Pebble-symbolismp. 27
Origin of the [characters not reproducible]p. 29
The Roman abacusp. 30
The Salaminian Tablep. 33
Combination of finger-symbolism and abacusp. 36
The Apicesp. 37
Origin of written symbolsp. 39
Earliest Greek written numeralsp. 40
Greek alphabetic numeralsp. 42
Their originp. 43
Signs for fractions and compendiap. 48
Greek multiplicationp. 49
Compound divisionp. 51
Extraction of a square rootp. 53
Nomenclature of Archimedesp. 57
Nomenclature and multiplication of Apolloniusp. 61
Symbolism of Noviomagusp. 64
Greek arithmetical educationp. 64
Greek Theory of Numbers (Arithmetica)p. 66
Pythagorasp. 66
Pythagorean and Platonic Arithmeticap. 68
Euclid's Arithmetica, Book II. of the Elementsp. 72
Books VII.-IX.p. 74
Book X. Incommensurablesp. 78
Theory of Combinationsp. 86
Eratoshenes and Hypsiclesp. 87
Nicomachus Gerasenusp. 88
Theon Symrnaeusp. 95
Thymaridasp. 96
Iamblichusp. 97
Arithmetical epigramsp. 98
Diophantus and Algebrap. 100
Greek Geometryp. 123
Prehistoric and Egyptian Geometryp. 123
Origin of Geometryp. 123
Geometry of Ahmesp. 126
Later Egyptian Geometryp. 129
Connexion of Greek with Egyptianp. 131
Babylonian geometryp. 132
Greek Geometry to Euclidp. 134
The Eudemian summaryp. 134
The antique style acc. to Geminusp. 137
The Ionic School
Thales' Lifep. 138
His geometryp. 140
Other Ionic geometersp. 145
Oenopides of Chiosp. 146
The Pythagoreans
Life and teaching of Pythagorasp. 147
His geometryp. 149
The regular solidsp. 153
The Pythagorean theoremp. 155
Later Pythagoreans, esp. Archytasp. 157
Eleatics and Atomists, esp. Democritusp. 158
The Sophists
Rise of the Sophistsp. 160
The insoluble problemsp. 161
Hippias and the quadratrixp. 162
Theodorus of Cyrene and Hippocrates of Chiosp. 164
Quadrature of lunes by Hippocratesp. 165
Duplication-problem recast by Hippocratesp. 169
Method of exhaustion and its originp. 169
Quadrature of circle by Antiphon and Brysonp. 170
The Academy
Plato and his mathematical teachingp. 173
The method of analysisp. 177
Plato's solution of duplication-problem, etc.p. 180
Archytas' solution of duplication-problem, etc.p. 181
Leodamas, Theaetetus, Neocleides, Leonp. 183
Eudoxusp. 183
Menaechmus and the later Academicsp. 185
Aristotlep. 188
Autolycus of Pitanep. 189
Summary of the pre-Euclidean geometryp. 190
Euclid, Archimedes, Apolloniusp. 192
Defects in Athenian culturep. 192
Rise of Alexandriap. 193
Euclid's lifep. 195
Style and structure of the Elementsp. 196
History of the textp. 199
Modern history of the bookp. 203
Other extant works of Euclidp. 209
Lost works of Euclidp. 215
Life of Archimedesp. 221
Catalogue of the works of Archimedesp. 223
Geometry of Archimedesp. 225
Dimensio Circulip. 233
Mechanics and machines of Archimedesp. 237
Eratosthenesp. 244
Apollonius of Pergap. 246
Summary of his Conicsp. 250
Specimens of his Conicsp. 255
Chasles on Archimedes and Apolloniusp. 260
Lost works of Apolloniusp. 261
Method of duplication attributed to Apolloniusp. 263
Geometry in Second Century B.C.p. 265
General criticism of the periodp. 265
Nicomedes and the conchoidp. 266
Diocles and the cissoidp. 268
Perseus and his spiralsp. 270
Zenodorus on 'Figures of Equal Periphery'p. 271
Hypsicles and his worksp. 272
Hipparchusp. 274
Heron of Alexandriap. 276
Heron's geometrical worksp. 280
Egyptian character of Heron's workp. 284
From Geminus to Ptolemyp. 287
Geminusp. 287
Theodosius of Tripolisp. 288
Serenus of Antissap. 289
Menelausp. 291
Trigonometry of Ptolemyp. 292
Other geometrical work of Ptolemyp. 299
Last Yearsp. 302
Sextus Julius Africanusp. 302
Pappus and his worksp. 304
Contents of the Mathematicae Collectionesp. 305
Apercus of Pappusp. 308
Greek Commentators on classical geometersp. 311
Summaryp. 313
Indexp. 317
Table of Contents provided by Ingram. All Rights Reserved.

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