A History of Mathematical Notations : Notations Mainly in Higher Mathematics 〈2〉

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A History of Mathematical Notations : Notations Mainly in Higher Mathematics 〈2〉

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  • Kessinger Pub(2007/07発売)
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  • 製本 Hardcover:ハードカバー版/ページ数 367 p.
  • 言語 ENG
  • 商品コード 9780548134092
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Table of Contents

Introduction To The Second Volume                  xi
I Topical Survey Of Symbols In Arithmetic And 1 (141)
Algebra (Advanced Part)
Letters Representing Magnitudes
Greek Period
Middle Ages
Vieta in 1591
Descartes in 1637
Different Alphabets
Astronomical Signs
The Letters π and e
Early Signs for 3.1415
First Occurrence of Sign π
Euler's Use of π
Spread of Jones's Notation
Signs for the Base of Natural Logarithms
The Letter e
B. Peirce's Signs for 3.141...and 2.718...
The Evolution of the Dollar Mark
Different Hypotheses
Evidence in Manuscripts and Early Printed
Modern Dollar Mark in Print
Signs in the Theory of Numbers
Divisors of Numbers, Residues
Congruence of Numbers
Prime and Relatively Prime Numbers
Sums of Numbers
Partition of Numbers
Figurate Numbers
Diophantine Expressions
Number Fields
Perfect Numbers
Mersenne's Numbers
Fermat's Numbers
Cotes's Numbers
Bernoulli's Numbers
Euler's Numbers
Signs for Infinity and Transfinite Numbers
Signs for Continued Fractions and Infinite
Continued Fractions
Tiered Fractions
Infinite Series
Signs in the Theory of Combinations
Binomial Formula
Product of Terms of Arithmetical Progression
Vandermonde's Symbols
Combinatorial School of Hindenburg
Kramp on Combinatorial Notations
Signs of Argand and Amp鑽e
Thomas Jarrett
Factorial n
Subfactorial N
Continued Products
Permutations and Combinations
Invariants and Covariants
Dual Arithmetic
Chessboard Problem
Determinant Notations
Seventeenth Century
Eighteenth Century
Early Nineteenth Century
Modern Notations
Compressed Notations
Cubic Determinants
Infinite Determinants
Matrix Notations
Signs for Logarithms
Abbreviation for "Logarithm"
Different Meanings of log x, lx, and Lx
Power of a Logarithm
Iterated Logarithms
Marking the Characteristic
Marking the Last Digit
Sporadic Notations
Complex Numbers
Dual Logarithms
Signs of Theoretical Arithmetic
Signs for "Greater" or "Less"
Sporadic Symbols for "Greater" or "Less"
Improvised Type
Modern Modifications
Absolute Difference
Other Meanings of ‾ and ‾
A Few Other Sporadic Symbols
Signs for Absolute Value
Zeroes of Different Origin
General Combinations between Magnitudes or
Symbolism for Imaginaries and Vector Analysis
Symbols for the Square Root of Minus One
De Morgan's Comments on square root of -1
Notation for a Vector
Length of a Vector
Equality of Vectors
Products of Vectors
Certain Operators
Rival Vector Systems
Attempts at Unification
II Symbols In Modern Analysis 142(173)
Trigonometric Notations
Origin of the Modern Symbols for Degrees,
Minutes, and Seconds
Signs for Radians
Marking Triangles
Early Abbreviations of Trigonometric Lines
Great Britain during 1602-18
European Continent during 1622-32
Great Britain during 1624-57
Seventeenth-Century English and Continental
Practices are Independent
England during 1657-1700
The Eighteenth Century
Trigonometric Symbols of the Eighteenth
Trigonometric Symbols of the Nineteenth
Less Common Trigonometric Functions
Quaternion Trigonometry
Hyperbolic Functions
Parabolic Functions
Inverse Trigonometric Functions
John Herschel's Notation for Inverse
Martin Ohm's Notation for Inverse Functions
Persistance of Rival Notations for Inverse
Inverse Hyperbolic Functions
Powers of Trigonometric Functions
Survey of Mathematical Symbols Used by Leibniz
Tables of Symbols
Remarks on Tables
Differential and Integral Calculus
1 Introduction
2 Symbols for Fluxions, Differentials, and
a Total Differentiation during the
Seventeenth and Eighteenth Centuries.
Newton, Leibniz, Landen, Fontaine,
Lagrange (1797), Pasquich, Gr on,
Arbogast, Kramp
b Criticisms of Eighteenth-Century
Notations. Woodhouse, Lacroix, Lagrange
c Total Differentiation during the
Nineteenth Century. Barlow, Mitchell,
Herschel, Peacock, Babbage, Crelle,
Cauchy (1823, 1829), M. Ohm, Cauchy and
Moigno (1840), B. Peirce, Carr, Peacock,
d Partial Differentials and Partial
Derivatives. Euler, Karsten, Fontaine,
Monge, Condorcet, Legendre, Lagrange
(1788), Lacroix, Da Cunha, L'Huilier,
Lagrange (1797), Arbogast, Lagrange
(1801), Crelle, Barlow, Cauchy, M. Ohm,
W.R. Hamilton, W. Bolyai, Cauchy and
Moigno, C.G.J. Jacobi, Hesse, B. Peirce,
Strauch, Duhamel, Carr, Wray, Muir,
3 Symbols for Integrals, Leibniz
4 Early Use of Leibnizian Notation in Great
5 Symbols for Fluents: Later Notations in
Integral Calculus. Newton, Reyneau, Crelle,
Euler, Fourier, Volterra, Peano, E.H.
Moore, Cauchy's Residual Calculus
6 Calculus Notations in the United States
7 Symbols for Passing to the Limit.
L'Huilier, Weierstrass Oliver, Riemann,
Leathem, Dirichlet, Pringsheim, Scheffer,
Peano, W.H. Young
8 The Sign 0/0
9 Concluding Observations
Finite Differences
Early Notations
Later Notations
Symbols in Theory of Functions
A Symbols for Functions in General
B Symbols for Some Special Functions
Symmetric Functions
Gamma and Beta Functions
Elliptic Functions
Theta Functions
Zeta Functions
Power Series
Laplace, Lam  and Bessel Functions
Logarithm-Integral, Cosine-Integral, etc
Symbols in Mathematical Logic
Some Early Symbols
The Sign for "Therefore"
The Sign for "Because"
The Program of Leibniz
Signs of:
H. Lambert
G.J. von Holland
G.F. Castillon
J.D. Gergonne
A. de Morgan
G. Boole
W.S. Jevons
C.S. Peirce
Ladd-Franklin and Mitchell
R.G. Grassmann
E. Schroeder
J.H. MacColl
G. Frege
G. Peano
A.N. Whitehead
E.H. Moore
Whitehead and Russell
P. Poretsky
L. Wittgenstein
Remarks by Rignano and Jourdain
A Question
III Symbols In Geometry (Advanced Part) 315(12)
1 Recent Geometry of Triangle and Circle, etc
Signs for Polyhedra
Geometry of Graphics
2 Projective and Analytical Geometry
Signs for Projectivity and Perspectivity
Signs for Harmonic and Anharmonic Ratios
Descriptive Geometry
Analytical Geometry
Pl ker's Equations
The Twenty-seven Lines on a Cubic Surface
The Pascal Hexagram
IV The Teachings Of History 327(24)
A The Teachings of History as Interpreted by
Various Writers. Individual Judgments
Review of D. Andr 
Quotations from A. de Morgan

Quotations from J.W.L. Glaisher

Quotations from D.E. Smith

Quotations from A. Saverien

Quotations from C. Maclaurin

Quotations from Ch. Babbage

Quotations from E. Mach

Quotations from B. Branford

Quotations from A.N. Whitehead

Quotations from H.F. Baker

Quotations from H. Burckhardt

Quotations from P.G. Tait

Quotations from O.S. Adams

Quotations from A British Committee

B Empirical Generalizations on the Growth of

Mathematical Notations

Forms of Symbols

Invention of Symbols

Nature of Symbols

Potency of Symbols

Selection and Spread of Symbols

State of Flux

Defects in Symbolism

Individualism a Failure

C Co-operation in Some Other Fields of

Scientific Endeavor

Electric Units

Star Chart and Catalogue

D Group Action Attempted in Mathematics

In Vector Analysis

In Potential and Elasticity

In Actuarial Science

E Agreements To Be Reached by International

Committees the Only Hope for Uniformity of


Alphabetical Index 351