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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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