A History of Mathematical Notations Volume II, Notations Mainly in Higher Mathematics

Title page......Page 1 Table of contents (detailed)......Page 5 Illustrations......Page 13 Introduction......Page 15 Addenda......Page 17 Letters Representing Magnitudes......Page 19 The Letters pi and e......Page 26 The Evolution of the Dollar Mark......Page 33 Signs in the Theory of Numers......Page 47 Signs for Infinty and Transfinite Numbers......Page 62 Signs for Continued Fractions and Infinite Series......Page 66 Signs in the Theory of Combinations......Page 79 Determinant Notations......Page 105 Signs for Logarithms......Page 123 Signs of Theoretical Arithmetic......Page 133 Symbolism for Imaginaries and Vector Analysis......Page 144 Trigonometric Notations......Page 160 Survey of Mathematical Symbols Used by Leibniz......Page 198 1. Introduction......Page 214 2. Symbols for Fluxions, Differentials, and Derivatives......Page 215 3. Symbols for Integrals, Leibniz......Page 260 4. Early Use of Leibnizian Notation in Great Britain......Page 262 5. Symbols for Fluents: Later Notations in Integral Calculus......Page 264 6. Calculus Notations in the United States......Page 271 7. Symbols for Passing to the Limit......Page 272 8. Concluding Observations......Page 279 Finite Differences......Page 281 A. Symbols for Functions in General......Page 285 B. Symbols for Some Special Functions......Page 288 Symbols in Mathematical Logic......Page 299 1. Recent Geometry of Triangle and Circle, etc.......Page 333 2. Projective and Analytical Geometry......Page 337 A. The Teachings of History as Interpreted by Various Writers. Individual Judgments......Page 345 B. Empirical Generalizations on the Growth of Mathematical Notations......Page 354 C. Co-operation in Some Other Fields of Scientific Endeavor......Page 358 D. Group Action Attempted in Mathematics......Page 359 E. Agreements To Be Reached by International Committees: the Only Hope for Uniformity of Notations......Page 361 INDEX......Page 369