## Mathematical Thought from Ancient to Modern Times:This comprehensive history traces the development of mathematical ideas and the careers of the mathematicians responsible for them. Originally published in 1972, it is now available as a three volume paperback edition. Volume 1 looks at the discipline's origins in Babylon and Egypt, the creation of geometry and trigonometry by the Greeks, and the role of mathematics in the medieval and early modern periods. Volume 2 focuses on calculus, the rise of analysis in the nineteenth century, and the number theories of Dedekind and Dirichlet. The concluding volume covers the revival of projective geometry, the emergence of abstract algebra, the beginnings of topology, and the influence of Gödel on recent mathematical study. |

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### Contents

I | 3 |

IV | 4 |

V | 5 |

VI | 7 |

VII | 8 |

VIII | 10 |

IX | 11 |

X | 13 |

LXIII | 183 |

LXVII | 188 |

LXVIII | 190 |

LXIX | 191 |

LXX | 195 |

LXXI | 197 |

LXXII | 200 |

LXXV | 201 |

XI | 15 |

XIV | 16 |

XV | 18 |

XVI | 21 |

XVII | 22 |

XVIII | 24 |

XIX | 25 |

XX | 27 |

XXI | 28 |

XXIII | 34 |

XXIV | 37 |

XXV | 42 |

XXVI | 48 |

XXVII | 51 |

XXVIII | 56 |

XXXI | 57 |

XXXII | 58 |

XXXIII | 60 |

XXXIV | 68 |

XXXV | 73 |

XXXVI | 77 |

XXXVII | 80 |

XXXVIII | 81 |

XXXIX | 86 |

XL | 88 |

XLI | 89 |

XLII | 101 |

XLIII | 103 |

XLIV | 105 |

XLV | 116 |

XLVI | 117 |

XLVII | 119 |

XLVIII | 126 |

XLIX | 131 |

L | 135 |

LI | 145 |

LII | 146 |

LIII | 147 |

LIV | 154 |

LV | 160 |

LVI | 162 |

LVII | 166 |

LVIII | 168 |

LIX | 171 |

LX | 173 |

LXI | 176 |

LXII | 177 |

LXXVI | 202 |

LXXVII | 203 |

LXXVIII | 205 |

LXXIX | 206 |

LXXX | 209 |

LXXXI | 211 |

LXXXII | 213 |

LXXXIII | 216 |

LXXXVI | 218 |

LXXXVII | 220 |

LXXXVIII | 221 |

LXXXIX | 223 |

XC | 227 |

XCI | 231 |

XCII | 234 |

XCIII | 236 |

XCIV | 237 |

XCV | 240 |

XCVI | 247 |

XCVII | 250 |

C | 251 |

CI | 259 |

CII | 263 |

CIII | 270 |

CIV | 274 |

CV | 278 |

CVI | 285 |

CIX | 286 |

CX | 288 |

CXI | 295 |

CXII | 299 |

CXIII | 302 |

CXV | 303 |

CXVI | 304 |

CXVII | 308 |

CXVIII | 317 |

CXIX | 325 |

CXX | 327 |

CXXI | 335 |

CXXII | 342 |

CXXIV | 344 |

CXXV | 356 |

CXXVI | 370 |

CXXVII | 380 |

CXXVIII | 381 |

CXXIX | 383 |

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### Common terms and phrases

angle Apollonius Arabs Archimedes Aristotle arithmetic and algebra Arithmetica astronomy axioms Babylonians became bodies Book calculation called Cardan century Chap chord circle classical concept cone conic sections construction coordinate geometry cube curves deductive definition Desargues Descartes Descartes's diameter Diophantus Dover reprint earth Egyptian ellipse equal equation Euclid Euclid's Elements Euclidean geometry Eudoxus example fact Fermat Figure fractions functions Galileo given Greek mathematics Hence Hindus Hipparchus History of Mathematics hyperbola ideas infinite integral irrational numbers Kepler knowledge Leibniz length magnitudes mathe mathematicians matics mechanics method method of exhaustion motion nature negative numbers Newton notation obtained Pappus parabola Pascal period philosophy physical plane Plato principles problems Proclus proof Proposition proved Ptolemy Pythagoreans quadratic quantities ratio rectangle roots says sides solve sphere spherical square straight line symbols tangent theorem theory of numbers triangle trigonometry University velocity Vieta volumes whole numbers wrote