## Mathematics in Western CultureThis book gives a remarkably fine account of the influences mathematics has exerted on the development of philosophy, the physical sciences, religion, and the arts in Western life. |

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### Contents

Introduction True and False Conceptions | 3 |

The Rule of Thumb in Mathematics | 13 |

The Birth of the Mathematical Spirit | 24 |

The Elements of Euclid | 40 |

Placing a Yardstick to the Stars | 60 |

Nature Acquires Reason | 74 |

Interlude | 89 |

Renewal of the Mathematical Spirit | 99 |

The Newtonian Influence Religion | 257 |

The Newtonian Influence Literature and Aesthetics | 272 |

The Sine of G Major | 287 |

Mastery of the Ether Waves | 304 |

The Science of Human Nature | 322 |

The Mathematical Theory of Ignorance The Statistical Approach to the Study of Man | 340 |

Prediction and Probability | 359 |

Our Disorderly Universe The Statistical View of Nature | 376 |

The Harmony of the World | 110 |

Painting and Perspective | 126 |

Science Born of Art Projective Geometry | 144 |

A Discourse on Method | 159 |

The Quantitative Approach to Nature | 182 |

The Deduction of Universal Laws | 196 |

Grasping the Fleeting Instant The Calculus | 214 |

The Newtonian Influence Science and Philosophy | 234 |

The Paradoxes of the Infinite | 395 |

New Geometries New Worlds | 410 |

The Theory of Relativity | 432 |

Mathematics Method and Art | 453 |

473 | |

477 | |

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abstract algebra angle applied Archimedes Aristotle astronomical ball behavior believed calculate circle civilization co-ordinates concepts conclusions Copernicus curve deductive deductive reasoning Desargues Descartes distance Earth eighteenth century electromagnetic ematical equal equation Euclid Euclidean geometry example existence fact figure force formula frequency Galileo graph gravitation Greek heavenly bodies heliocentric theory Hence Hipparchus human ical ideas infinite Kepler knowledge laws of motion Leibniz Lobatchevsky logical mass mathe mathematical laws mathematicians matics matter means measure medieval method mind modern molecules moving nature Newton Newtonian non-Euclidean geometry objects observation obtain painting parabola parallel axiom path perspective phenomena philosophy physical world planets Plato position principle probability problems projective geometry Pythagoreans quantity rate of change rational reason relation religion Renaissance scientific scientists sine sound space speed sphere straight line surface theorems theory theory of relativity thought tion triangle truths tuning fork universe velocity waves