History of Mathematics, Vol. II

Volume 2 of an unusually clear and readable 2-volume history from Egyptian papyri and medieval maps to modern graphs and diagrams. Evolution of arithmetic, geometry, trigonometry, calculating devices, algebra, calculus, more. Includes problems, re-creations and applications.

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