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Index
DOVER SCIENCE BOOKS Title Page Copyright Page Dedication Table of Contents PREFACE THE GREEK ALPHABET 1 - EGYPTIAN MATHEMATICS
1-1 PREHISTORIC MATHEMATICS 1-2 THE EARLIEST WRITTEN MATHEMATICS 1-3 NUMERICAL NOTATION 1-4 ARITHMETIC OPERATIONS 1-5 MULTIPLICATION 1-6 FRACTIONS AND DIVISION 1-7 THE RED AUXILIARY NUMBERS 1-8 THE 2 ÷ n TABLE 1-9 THE LEATHER ROLL 1-10 ALGEBRAIC PROBLEMS 1-11 GEOMETRY REFERENCES
2 - BABYLONIAN MATHEMATICS
2-1 SOME HISTORICAL FACTS 2-2 BABYLONIAN NUMERICAL NOTATION 2-3 THE FUNDAMENTAL OPERATIONS 2-4 EXTRACTION OF ROOTS 2-5 BABYLONIAN ALGEBRA 2-6 A BABYLONIAN TEXT 2-7 BABYLONIAN GEOMETRY 2-8 APPROXIMATIONS TO π 2-9 ANOTHER PROBLEM AND A FAREWELL TO THE BABYLONIANS REFERENCES
3 - THE BEGINNING OF GREEK MATHEMATICS
3-1 THE EARLIEST RECORDS 3-2 GREEK NUMERATION SYSTEMS 3-3 THALES AND HIS IMPORTANCE TO MATHEMATICS 3-4 PYTHAGORAS AND THE PYTHAGOREANS 3-5 THE PYTHAGOREANS AND MUSIC 3-6 PYTHAGOREAN ARITHMETICA 3-7 PYTHAGOREAN NUMEROLOGY 3-8 PYTHAGOREAN ASTRONOMY 3-9 PYTHAGOREAN GEOMETRY 3-10 INCOMMENSURABLE SEGMENTS AND IRRATIONAL NUMBERS REFERENCES
4 - THE FAMOUS PROBLEMS OF GREEK ANTIOUITY
4-1 INTRODUCTION 4-2 HIPPOCRATES OF CHIOS AND THE QUADRATURE OF LUNES 4-3 OTHER QUADRATURES 4-4 HIPPOCRATES’ GEOMETRY 4-5 DUPLICATION OF THE CUBE 4-6 THE TRISECTION PROBLEM 4-7 HIPPIAS AND SQUARING OF THE CIRCLE 4-8 THE SOLUTIONS OF THE GREEK PROBLEMS REFERENCES
5 - EUCLID’S PHILOSOPHICAL FORERUNNERS
5-1 PHILOSOPHY AND PHILOSOPHERS 5-2 PLATO 5-3 ARISTOTLE AND HIS THEORY OF STATEMENTS 5-4 CONCEPTS AND DEFINITIONS 5-5 SPECIAL NOTIONS AND UNDEFINED TERMS REFERENCES
6 - EUCLID
6-1 ELEMENTS 6-2 THE STRUCTURE OF THE ELEMENTS OF EUCLID 6-3 THE DEFINITIONS 6-4 POSTULATES AND COMMON NOTIONS 6-5 THE MEANING OF A CONSTRUCTION 6-6 THE PURPORT OF POSTULATE III 6-7 CONGRUENCE 6-8 CONGRUENCE (CONTINUED) 6-9 THE THEORY OF PARALLELS 6-10 THE COMPARISON OF AREAS 6-11 THE THEOREM OF PYTHAGORAS 6-12 THE DIFFERENCE BETWEEN THE EUCLIDEAN AND THE MODERN METHOD OF COMPARING AREAS 6-13 GEOMETRIC ALGEBRA AND REGULAR POLYGONS 6-14 NUMBER THEORY IN THE ELEMENTS REFERENCES
7 - GREEK MATHEMATICS AFTER EUCLID. EUCLIDEAN VS. MODERN METHODS.
7-1 THE SPAN OF GREEK MATHEMATICS 7-2 ARCHIMEDES AND ERATOSTHENES 7-3 APOLLONIUS OF PERGA 7-4 HERON OF ALEXANDRIA AND DIOPHANTUS 7-5 PTOLEMY AND PAPPUS 7-6 REVIEW OF THE GREEK METHOD 7-7 OBJECTIONS TO THE EUCLIDEAN SYSTEM 7-8 THE MEANING OF DEDUCTION 7-9 EUCLID’S SYSTEM IS NOT PURELY DEDUCTIVE 7-10 HOW IS GEOMETRY BUILT UP PURELY DEDUCTIVELY? 7-11 A FOUR-POINT SYSTEM REFERENCES
8 - NUMERATION AND ARITHMETIC AFTER THE GREEKS
8-1 ROMAN NUMERALS 8-2 THE ABACUS AND TANGIBLE ARITHMETIC 8-3 THE HINDU-ARABIC NUMERALS 8-4 AN EARLY AMERICAN PLACE-VALUE NUMERATION SYSTEM 8-5 LATER DEVELOPMENTS IN POSITIONAL NOTATION 8-6 CONVERSIONS BETWEEN NUMERATION SYSTEMS 8-7 ADDITION AND SUBTRACTION ALGORITHMS IN NONDECIMAL BASES 8-8 MULTIPLICATION ALGORITHMS IN NONDECIMAL BASES 8-9 FRACTIONS, RATIONAL NUMBERS, AND PLACE-VALUE NUMERATION 8-10 IRRATIONAL NUMBERS 8-11 MODERN THEORETICAL FOUNDATIONS OF ARITHMETIC 8-12 MODERN NUMERATION REFERENCES
HINTS AND ANSWERS TO SELECTED EXERCISES INDEX A CATALOG OF SELECTED DOVER BOOKS IN ALL FIELDS OF INTEREST
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