Table of Contents

CHAPTER I. DEVELOPMENT OF THE ARITHMETICA 1. GENERAL SURVEY 2. THE SEVEN LIBERAL ARTS 3. EARLY WRITERS ON NUMBER THEORY 4. NAMES FOR ARITHMETIC 5. ELEMENTARY CLASSIFICATIONS OF NUMBER 6. UNITY 7. LATER DEVELOPMENTS TOPICS FOR DISCUSSION II. LOGISTIC OF NATURAL NUMBERS 1. FUNDAMENTAL OPERATIONS 2. READING AND WRITING NUMBERS 3. ADDITION 4. SUBTRACTION 5. MULTIPLICATION 6. DIVISION 7. ROOTS 8. CHECKS ON OPERATIONS TOPICS FOR DISCUSSION III. MECHANICAL AIDS TO CALCULATION 1. THE ABACUS 2. FINGER RECKONING 3. MODERN CALCULATING MACHINES TOPICS FOR DISCUSSION IV. ARTIFICIAL NUMBERS 1. COMMON FRACTIONS 2. SEXAGESIMAL FRACTIONS 3. DECIMAL FRACTIONS 4. SURD NUMBERS 5. NEGATIVE NUMBERS 6. COMPLEX NUMBERS 7. TRANSCENDENTAL NUMBERS TOPICS FOR DISCUSSION V. GEOMETRY 1. GENERAL PROGRESS OF ELEMENTARY GEOMETRY 2. NAME FOR GEOMETRY 3. TECHNICAL TERMS OF EUCLIDEAN GEOMETRY 4. AXIOMS AND POSTULATES 5. TYPICAL PROPOSITIONS OF PLANE GEOMETRY 6. TYPICAL PROPOSITIONS OF SOLID GEOMETRY 7. THE THREE FAMOUS PROBLEMS 8. ANALYTIC GEOMETRY 9. MODERN GEOMETRY 10. PERSPECTIVE AND OPTICS 11. INSTRUMENTS IN GEOMETRY 12. THE PROBLEM OF EARTH MEASURE TOPICS FOR DISCUSSION VI. ALGEBRA 1. GENERAL PROGRESS OF ALGEBRA 2. NAME FOR ALGEBRA 3. TECHNICAL TERMS 4. SYMBOLS OF ALGEBRA 5. FUNDAMENTAL OPERATIONS 6. CONTINUED FRACTIONS 7. THE WRITING OF EQUATIONS 8. THE SOLUTION OF EQUATIONS 9. DETERMINANTS 10. "RATIO, PROPORTION, AND THE RULE OF THREE" 11. SERIES 12. LOGARITHMS 13. "PERMUTATIONS, COMBINATIONS, PROBABILITY" TOPICS FOR DISCUSSION VII. ELEMENTARY PROBLEMS 1. MATHEMATICAL RECREATIONS 2. TYPICAL PROBLEMS 3. COMMERCIAL PROBLEMS 4. APPLICATIONS OF ALGEBRA 5. MAGIC SQUARES TOPICS FOR DISCUSSION VIII. TRIGONOMETRY 1. GENERAL DEVELOPMENT OF TRIGONOMETRY 2. TRIGONOMETRIC FUNCTIONS 3. TRIGONOMETRIC TABLES 4. TYPICAL THEOREMS TOPICS FOR DISCUSSION IX. MEASURES 1. WEIGHT 2. LENGTH 3. AREAS 4. CAPACITY 5. VALUE 6. METRIC SYSTEM 7. TIME TOPICS FOR DISCUSSION X. THE CALCULUS 1. GREEK IDEAS OF A CALCULUS 2. MEDIEVAL IDEAS OF THE CALCULUS 3. MODERN FORERUNNERS OF THE CALCULUS 4. NEWTON AND LEIBNIZ TOPICS FOR DISCUSSION INDEX