Prolegomena to Arithmetic | p. 1 |
The Decimal Scale | p. 1 |
Aryan numerals | p. 1 |
Numerals in savage languages | p. 5 |
Etymology of Aryan numerals | p. 7 |
Primitive expression of fractions | p. 13 |
Egyptian Arithmetic | p. 15 |
Reasons for introducing the subject | p. 15 |
Ahmes and his table of submultiples | p. 16 |
Seqem-calculations | p. 18 |
Simple equations and series | p. 18 |
Summary | p. 20 |
Greek Arithmetic | p. 22 |
Calculation. Logistica | p. 22 |
Logistica opposed to Arithmetica | p. 22 |
Numerical symbolism | p. 24 |
Greek and Roman finger-symbols | p. 24 |
Pebble-symbolism | p. 27 |
Origin of the [characters not reproducible] | p. 29 |
The Roman abacus | p. 30 |
The Salaminian Table | p. 33 |
Combination of finger-symbolism and abacus | p. 36 |
The Apices | p. 37 |
Origin of written symbols | p. 39 |
Earliest Greek written numerals | p. 40 |
Greek alphabetic numerals | p. 42 |
Their origin | p. 43 |
Signs for fractions and compendia | p. 48 |
Greek multiplication | p. 49 |
Compound division | p. 51 |
Extraction of a square root | p. 53 |
Nomenclature of Archimedes | p. 57 |
Nomenclature and multiplication of Apollonius | p. 61 |
Symbolism of Noviomagus | p. 64 |
Greek arithmetical education | p. 64 |
Greek Theory of Numbers (Arithmetica) | p. 66 |
Pythagoras | p. 66 |
Pythagorean and Platonic Arithmetica | p. 68 |
Euclid's Arithmetica, Book II. of the Elements | p. 72 |
Books VII.-IX. | p. 74 |
Book X. Incommensurables | p. 78 |
Theory of Combinations | p. 86 |
Eratoshenes and Hypsicles | p. 87 |
Nicomachus Gerasenus | p. 88 |
Theon Symrnaeus | p. 95 |
Thymaridas | p. 96 |
Iamblichus | p. 97 |
Arithmetical epigrams | p. 98 |
Diophantus and Algebra | p. 100 |
Greek Geometry | p. 123 |
Prehistoric and Egyptian Geometry | p. 123 |
Origin of Geometry | p. 123 |
Geometry of Ahmes | p. 126 |
Later Egyptian Geometry | p. 129 |
Connexion of Greek with Egyptian | p. 131 |
Babylonian geometry | p. 132 |
Greek Geometry to Euclid | p. 134 |
Preliminary | |
The Eudemian summary | p. 134 |
The antique style acc. to Geminus | p. 137 |
The Ionic School | |
Thales' Life | p. 138 |
His geometry | p. 140 |
Other Ionic geometers | p. 145 |
Oenopides of Chios | p. 146 |
The Pythagoreans | |
Life and teaching of Pythagoras | p. 147 |
His geometry | p. 149 |
The regular solids | p. 153 |
The Pythagorean theorem | p. 155 |
Later Pythagoreans, esp. Archytas | p. 157 |
Eleatics and Atomists, esp. Democritus | p. 158 |
The Sophists | |
Rise of the Sophists | p. 160 |
The insoluble problems | p. 161 |
Hippias and the quadratrix | p. 162 |
Theodorus of Cyrene and Hippocrates of Chios | p. 164 |
Quadrature of lunes by Hippocrates | p. 165 |
Duplication-problem recast by Hippocrates | p. 169 |
Method of exhaustion and its origin | p. 169 |
Quadrature of circle by Antiphon and Bryson | p. 170 |
The Academy | |
Plato and his mathematical teaching | p. 173 |
The method of analysis | p. 177 |
Plato's solution of duplication-problem, etc. | p. 180 |
Archytas' solution of duplication-problem, etc. | p. 181 |
Leodamas, Theaetetus, Neocleides, Leon | p. 183 |
Eudoxus | p. 183 |
Menaechmus and the later Academics | p. 185 |
Aristotle | p. 188 |
Autolycus of Pitane | p. 189 |
Summary of the pre-Euclidean geometry | p. 190 |
Euclid, Archimedes, Apollonius | p. 192 |
Defects in Athenian culture | p. 192 |
Rise of Alexandria | p. 193 |
Euclid's life | p. 195 |
Style and structure of the Elements | p. 196 |
History of the text | p. 199 |
Modern history of the book | p. 203 |
Other extant works of Euclid | p. 209 |
Lost works of Euclid | p. 215 |
Life of Archimedes | p. 221 |
Catalogue of the works of Archimedes | p. 223 |
Geometry of Archimedes | p. 225 |
Dimensio Circuli | p. 233 |
Mechanics and machines of Archimedes | p. 237 |
Eratosthenes | p. 244 |
Apollonius of Perga | p. 246 |
Summary of his Conics | p. 250 |
Specimens of his Conics | p. 255 |
Chasles on Archimedes and Apollonius | p. 260 |
Lost works of Apollonius | p. 261 |
Method of duplication attributed to Apollonius | p. 263 |
Geometry in Second Century B.C. | p. 265 |
General criticism of the period | p. 265 |
Nicomedes and the conchoid | p. 266 |
Diocles and the cissoid | p. 268 |
Perseus and his spirals | p. 270 |
Zenodorus on 'Figures of Equal Periphery' | p. 271 |
Hypsicles and his works | p. 272 |
Hipparchus | p. 274 |
Heron of Alexandria | p. 276 |
Heron's geometrical works | p. 280 |
Egyptian character of Heron's work | p. 284 |
From Geminus to Ptolemy | p. 287 |
Geminus | p. 287 |
Theodosius of Tripolis | p. 288 |
Serenus of Antissa | p. 289 |
Menelaus | p. 291 |
Trigonometry of Ptolemy | p. 292 |
Other geometrical work of Ptolemy | p. 299 |
Last Years | p. 302 |
Sextus Julius Africanus | p. 302 |
Pappus and his works | p. 304 |
Contents of the Mathematicae Collectiones | p. 305 |
Apercus of Pappus | p. 308 |
Greek Commentators on classical geometers | p. 311 |
Summary | p. 313 |
Index | p. 317 |
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