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Mathematics in Mesopotamia | |

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Where Did Mathematics Begin? | |

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Political History in Mesopotamia | |

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The Number Symbols | |

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Arithmetic Operations | |

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Babylonian Algebra | |

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Babylonian Geometry | |

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The Uses of Mathematics in Babylonia | |

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Evaluation of Babylonian Mathematics | |

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Egyptian Mathematics | |

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Background | |

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The Arithmetic | |

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Algebra and Geometry | |

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Egyptian Uses of Mathematics | |

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Summary | |

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The Creation of Classical Greek Mathematics | |

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Background | |

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The General Sources | |

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The Major Schools of the Classical Period | |

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The Ionian School | |

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The Pythagoreans | |

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The Eleatic School | |

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The Sophist School | |

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The Platonic School | |

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The School of Eudoxus | |

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Aristotle and His School | |

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Euclid and Apollonius | |

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Introduction | |

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The Background of Euclid's Elements | |

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The Definitions and Axioms of the Elements | |

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Books I to IV of the Elements | |

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Book V: The Theory of Proportion | |

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Book VI: Similar Figures | |

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Books VII, VIII, and IX: The Theory of Numbers | |

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Book X: The Classification of Incommensurables | |

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Books XI, XII, and XIII: Solid Geometry and the Method of Exhaustion | |

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The Merits and Defects of the Elements | |

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Other Mathematical Works by Euclid | |

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The Mathematical Work of Apollonius | |

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The Alexandrian Greek Period: Geometry and Trigonometry | |

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The Founding of Alexandria | |

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The Character of Alexandrian Greek Mathematics | |

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Areas and Volumes in the Work of Archimedes | |

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Areas and Volumes in the Work of Heron | |

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Some Exceptional Curves | |

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The Creation of Trigonometry | |

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Late Alexandrian Activity in Geometry | |

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The Alexandrian Period: The Reemergence of Arithmetic and Algebra | |

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The Symbols and Operations of Greek Arithmetic | |

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Arithmetic and Algebra as an Independent Development | |

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The Greek Rationalization of Nature | |

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The Inspiration for Greek Mathematics | |

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The Beginnings of a Rational View of Nature | |

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The Development of the Belief in Mathematical Design | |

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Greek Mathematical Astronomy | |

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Geography | |

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Mechanics | |

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Optics | |

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Astrology | |

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The Demise of the Greek World | |

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A Review of the Greek Achievements | |

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The Limitations of Greek Mathematics | |

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The Problems Bequeathed by the Greeks | |

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The Demise of the Greek Civilization | |

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The Mathematics of the Hindus and Arabs | |

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Early Hindu Mathematics | |

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Hindu Arithmetic and Algebra of the Period A.D. 200-1200 | |

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Hindu Geometry and Trigonometry of the Period A.D. 200-1200 | |

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The Arabs | |

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Arabic Arithmetic and Algebra | |

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Arabic Geometry and Trigonometry | |

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Mathematics circa 1300 | |

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The Medieval Period in Europe | |

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The Beginnings of a European Civilization | |

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The Materials Available for Learning | |

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The Role of Mathematics in Early Medieval Europe | |

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The Stagnation in Mathematics | |

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The First Revival of the Greek Works | |

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The Revival of Rationalism and Interest in Nature | |

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Progress in Mathematics Proper | |

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Progress in Physical Science | |

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Summary | |

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The Renaissance | |

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Revolutionary Influences in Europe | |

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The New Intellectual Outlook | |

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The Spread of Learning | |

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Humanistic Activity in Mathematics | |

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The Clamor for the Reform of Science | |

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The Rise of Empiricism | |

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Mathematical Contributions in the Renaissance | |

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Perspective | |

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Geometry Proper | |

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Algebra | |

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Trigonometry | |

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The Major Scientific Progress in the Renaissance | |

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Remarks on the Renaissance | |

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Arithmetic and Algebra in the Sixteenth and Seventeenth Centuries | |

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Introduction | |

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The Status of the Number System and Arithmetic | |

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Symbolism | |

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The Solution of Third and Fourth Degree Equations | |

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The Theory of Equations | |

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The Binomial Theorem and Allied Topics | |

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The Theory of Numbers | |

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The Relationship of Algebra to Geometry | |

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The Beginnings of Projective Geometry | |

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The Rebirth of Geometry | |

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The Problems Raised by the Work on Perspective | |

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The Work of Desargues | |

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The Work of Pascal and La Hire | |

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The Emergence of New Principles | |

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Coordinate Geometry | |

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The Motivation for Coordinate Geometry | |

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The Coordinate Geometry of Fermat | |

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Rene Descartes | |

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Descartes's Work in Coordinate Geometry | |

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Seventeenth-Century Extensions of Coordinate Geometry | |

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The Importance of Coordinate Geometry | |

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The Mathematization of Science | |

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Introduction | |

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Descartes's Concept of Science | |

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Galileo's Approach to Science | |

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The Function Concept | |

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The Creation of the Calculus | |

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The Motivation for the Calculus | |

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Early Seventeenth-Century Work on the Calculus | |

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The Work of Newton | |

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The Work of Leibniz | |

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A Comparison of the Work of Newton and Leibniz | |

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The Controversy over Priority | |

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Some Immediate Additions to the Calculus | |

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The Soundness of the Calculus | |

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List of Abbreviations | |

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Index | |