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| Preface | |
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| Early Number Systems and Symbols | |
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| Primitive Counting | |
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| A Sense of Number Notches as Tally Marks | |
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| The Peruvian Quipus: Knots as Numbers | |
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| Number Recording of the Egyptians and Greeks | |
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| The History of Herodotus Hieroglyphic | |
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| Representation of Numbers Egyptian Hieratic Numeration | |
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| The Greek Alphabetic Numeral System | |
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| Number Recording of the Babylonians | |
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| Babylonian Cuneiform Script Deciphering Cuneiform: Grotefend and Rawlinson | |
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| The Babylonian Positional Number System Writing in Ancient China | |
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| Mathematics in Early Civilizations | |
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| The Rhind Papyrus Egyptian Mathematical Papyri A Key To Deciphering: The Rosetta Stone | |
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| Egyptian Arithmetic Early Egyptian Multiplication | |
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| The Unit Fraction Table Representing Rational Numbers | |
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| Four Problems from the Rhind Papyrus | |
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| The Method of False Position | |
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| A Curious Problem Egyptian Mathematics as Applied Arithmetic | |
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| Egyptian Geometry Approximating the Area of a Circle | |
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| The Volume of a Truncated Pyramid Speculations About the Great Pyramid | |
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| Babylonian Mathematics A Tablet of Reciprocals | |
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| The Babylonian Treatment of Quadratic Equations | |
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| Two Characteristic Babylonian Problems | |
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| Plimpton A Tablet Concerning Number | |
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| Triples Babylonian Use of the Pythagorean Theorem | |
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| The Cairo Mathematical Papyrus | |
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| The Beginnings of Greek Mathematics | |
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| The Geometric Discoveries of Thales Greece and the Aegean Area | |
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| The Dawn of Demonstrative Geometry: Thales of Miletos Measurements Using Geometry | |
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| Pythagorean Mathematics Pythagoras and His Followers Nichomachus'Introductio Arithmeticae | |
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| The Theory of Figurative Numbers Zeno's Paradox | |
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| The Pythagorean Problem Geometric Proofs of the Pythagorean Theorem | |
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| Early Solutions of the Pythagorean Equation | |
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| The Crisis of Incommensurable Quantities Theon's Side and Diagonal Numbers Eudoxus of Cnidos | |
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| Three Construction Problems of Antiquity Hippocrates and the Quadrature of the Circle | |
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| The Duplication of the Cube | |
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| The Trisection of an Angle | |
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| The Quadratrix of Hippias Rise of the Sophists Hippias of Elis | |
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| The Grove of Academia: Plato's Academy | |
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| The Alexandrian School: Euclid | |
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| Euclid and theElements A Center of Learning: The Museum Euclid's Life and Writings | |
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| Euclidean Geometry Euclid's Foundation for Geometry | |
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| Book I of theElements Euclid's Proof of the Pythagorean Theorem | |
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| Book II on Geometric Algebra Construction of the Regular Pentagon | |
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| Euclid's Number Theory Euclidean Divisibility Properties | |
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| The Algorithm of Euclid | |
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| The Fundamental Theorem of Arithmetic | |
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| An Infinity of Primes | |
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| Eratosthenes, the Wise Man of Alexandria | |
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| The Sieve of Eratosthenes Measurement of the Earth | |
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| TheAlmagestof Claudius Ptolemy Ptolemy's Geographical Dictionary | |
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| Archimedes The Ancient World's Genius | |
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| Estimating the Value ofp The Sand-Reckoner | |
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| Quadrature of a Parabolic Segment | |
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| Apollonius of Perga: theConics | |
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| The Twilight of Greek Mathematics: Diophantus | |
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| The Decline of Alexandrian Mathematics | |
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| The Waning of the Golden Age | |
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| The Spread of Christianity Constantinople, A Refuge for Greek Learning | |
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| he Arithmetica Diophantus's Number Theory Problems from theArithmetica | |
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| Diophantine Equations in Greece, India, and China | |
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| The Cattle Problem of Archimedes Early Mathematics in India | |
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| The Chinese Hundred Fowls Problem | |
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| The Later Commentators | |
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| TheMathematical Collectionof Pappus Hypatia, the First Woman Mathematician Roman Mathematics: Boethius and Cassiodorus | |
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| Mathematics in the Near and Far East | |
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| The Algebra of al-Khoworizm Ab Kamil and Thobit ibn Qurra Omar Khayyam | |
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| The Astronomers al-Tusi and al-Karashi | |
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| The Ancient ChineseNine Chapters Later Chine | |