A History of Mathematical Notations : Notations in Elementary Mathematics 〈1〉

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A History of Mathematical Notations : Notations in Elementary Mathematics 〈1〉

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  • 製本 Hardcover:ハードカバー版/ページ数 451 p.
  • 言語 ENG
  • 商品コード 9780548134085
  • DDC分類 500

Table of Contents

    I Introduction
II Numeral Symbols and Combinations of 99 (1)
Symbols
Babylonians 1 (15)
Egyptians 16 (11)
Phoenicians and Syrians 27 (2)
Hebrews 29 (3)
Greeks 32 (13)
Early Arabs 45 (1)
Romans 45 (17)
Peruvian and North American Knot Records 62 (4)
Aztecs 66 (2)
Maya 68 (1)
Chinese and Japanese 69 (5)
Hindu-Arabic Numerals 74 (26)
Introduction 74 (4)
Principle of Local Value 78 (3)
Forms of Numerals 81 (8)
Freak Forms 89 (1)
Negative Numerals 90 (1)
Grouping of Digits in Numeration 91 (1)
The Spanish Calderon 92 (2)
The Portuguese Cifrao 94 (1)
Relative Size of Numerals in Tables 95 (1)
Fanciful Hypotheses on the Origin of 96 (1)
Numeral Forms
A Sporadic Artificial System 97 (1)
General Remarks 98 (1)
Opinion of Laplace 99 (1)
III Symbols in Arithmetic and Algebra 100(257)
(Elementary Part)
A Groups of Symbols Used by Individual 101(99)
Writers
Greeks---Diophantus, Third Century A.D. 101(5)
Hindu---Brahmagupta, Seventh Century 106(3)
Hindu---The Bakhshali Manuscript 109(1)
Hindu---Bhaskara, Twelfth Century 110(5)
Arabic---al-Khowarizini, Ninth Century 115(1)
Arabic---al-Karkhi, Eleventh Century 116(1)
Byzantine---Michael Psellus, Eleventh 117(1)
Century
Arabic---Ibn Albanna, Thirteenth Century 118(1)
Chinese---Chu Shih-Chieh, Fourteenth 119(2)
Century
Byzantine---Maximus Planudes, 121(1)
Fourteenth Century
Italian---`Leonardo of Pisa, Thirteenth 122(1)
Century
French---Nicole Oresme, Fourteenth 123(1)
Century
Arabic---al-Qalasadi, Fifteenth Century 124(1)
German---Regiomontanus, Fifteenth 125(3)
Century
Italian---Earliest Printed Arithmetic, 128(1)
1478
French---Nicolas Chuquet, 1484 129(3)
French---Estienne de la Roche, 1520 132(1)
Italian---Pietro Borgi, 1484, 1488 133(1)
Italian---Luca Pacioli, 1494, 1523 134(5)
Italian---F. Ghaligai, 1521, 1548, 1552 139(1)
Italian---H. Cardan, 1532, 1545, 1570 140(2)
Italian---Nicolo Tartaglia, 1506-60 142(2)
Italian---Rafaele Bombelli, 1572 144(2)
German---Johann Widman, 1489, 1526 146(1)
Austrian---Grammateus, 1518, 1535 147(1)
German---Christoff Rudolff, 1525 148(2)
Dutch---Gielis van der Hoecke, 1537 150(1)
German---Michael Stifel, 1544, 1545, 151(6)
1553
German---Nicolaus Copernicus, 1566 157(1)
German---Johann Scheubel, 1545, 1551 158(2)
Maltese---Wil. Klebitius, 1565 160(1)
German---Christophorus Clavius, 1608 161(1)
Belgium---Simon Stevin, 1585 162(2)
Lorraine---Albert Girard, 1629 164(1)
German-Spanish---Marco Aurel, 1552 165(1)
Portuguese-Spanish---Pedro Nunez, 1567 166(1)
English---Robert Recorde, 1543(7), 1557 167(2)
English---John Dee, 1570 169(1)
English---Leonard and Thomas Digges, 170(1)
1579
English---Thomas Masterson, 1592 171(1)
French---Jacques Peletier, 1554 172(1)
French---Jean Buteon, 1559 173(1)
French---Guillaume Gosselin, 1577 174(2)
French---Francis Vieta, 1591 176(3)
Italian---Bonaventura Cavalieri, 1647 179(1)
English---William Oughtred, 1631, 1632, 180(8)
1657
English---Thomas Harriot, 1631 188(1)
French---Pierre H6rigone, 1634, 1644 189(1)
Scot-French---James Hume, 1635, 1636 190(1)
French---Rene Descartes 191(1)
English---Isaac Barrow 192(1)
English---Richard Rawlinson, 1655-68 193(1)
Swiss---Johann Heinrich Rahn 194(1)
English---John Wallis, 1655, 1657, 1685 195(2)
Extract from Acta eruditorum, Leipzig, 197(1)
1708
Extract from Miscellanea Berolinensia, 198(1)
1710 (Duo to G. W. Leibniz)
Conclusions 199(1)
B Topical Survey of the Use of Notations 200(157)
Signs of Addition and Subtraction 200(1)
Early Symbols 200(1)
Origin and Meaning of the Signs 201(3)
Spread of the + and -- Symbols 204(1)
Shapes of the + Sign 205(3)
Varieties of -- Signs 208(2)
Symbols for "Plus or Minus" 210(2)
Certain Other Specialized Uses of + and 212(3)
--
Four Unusual Signs 215(1)
Composition of Ratios 216(1)
Signs of Multiplication 217(1)
Early Symbols 217(1)
Early Uses of the St. Andrew's Cross, 218(1)
but Not as the Symbol of Multiplication
of Two Numbers
The Process of Two False Positions 219(1)
Compound Proportions with Integers 220(1)
Proportions Involving Fractions 221(1)
Addition and Subtraction of Fractions 222(1)
Division of Fractions 223(2)
Casting Out the 9's, 7's, or Il's 225(1)
Multiplication of Integers 226(1)
Reducing Radicals to Radicals of the 227(1)
Same Order
Marking the Place for "Thousands" 228(1)
Place of Multiplication Table above 229(2)
5×5
The St. Andrew's Cross Used as a Symbol 231(1)
of Multiplication
Unsuccessful Symbols for Multiplication 232(1)
The Dot for Multiplication 233(1)
The St. Andrew's Cross in Notation for 234(1)
Transfinite Ordinal Numbers
Signs of Division and Ratio 235(1)
Early Symbols 235(2)
Rahn's Notation 237(1)
Leibniz's Notations 238(3)
Relative Position of Divisor and 241(1)
Dividend
Order of Operations in Terms Containing 242(1)
Both ÷ and ×
A Critical Estimate of: and ÷ as 243(1)
Symbols
Notations for Geometric Ratio 244(3)
Division in the Algebra of Complex 247(1)
Numbers
Signs of Proportion 248(1)
Arithmetical and Geometrical Progression 248(1)
Arithmetical, Proportion 249(1)
Geometrical Proportion 250(1)
Oughtred's Notation 251(1)
Struggle in England between Oughtred's 252(1)
and Wing's Notations before 1700
Struggle in England between Oughtred's 253(1)
and Wing's Notations during 1700-1750
Sporadic Notations 254(1)
Oughtred's Notation on the European 255(2)
Continent
Slight Modifications of Oughtred's 257(1)
Notation
The Notation: :: : in Europe and America 258(1)
The Notation of Leibniz 259(1)
Signs of Equality 260(1)
Early Symbols 260(1)
Recorde's Sign of Equality 261(1)
Different Meanings of = 262(1)
Competing Symbols 263(1)
Descartes' Sign of Equality 264(1)
Variations in the Form of Descartes' 265(1)
Symbol
Struggle for Supremacy 266(2)
Variation in the Form of Recorde's 268(1)
Symbol
Variation in the Manner of Using It 269(1)
Nearly Equal 270(1)
Signs of Common Fractions 271(1)
Early Forms 271(1)
The Fractional Line 272(2)
Special Symbols for Simple Fractions 274(1)
The Solidus 275(1)
Signs of Decimal Fractions 276(1)
Stevin's Notation 276(2)
Other Notations Used before 1617 278(1)
Did Pitiscus Use the Decimal Point? 279(3)
Decimal Comma and Point of Napier 282(1)
Seventeenth-Century Notations Used 283(2)
after 1617
Eighteenth-Century Discard of Clumsy 285(1)
Notations
Nineteenth Century Different Positions 286(3)
for Point and for Comma
Signs for Repeating Decimals 289(1)
Signs of Powers 290(1)
General Remarks 290(1)
Double Significance of R and l 291(2)
Facsimiles of Symbols in Manuscripts 293(1)
Two General Plans for Marking Powers 294(1)
Early Symbolisms: Abbreviative Plan, 295(1)
Index Plan
Notations Applied Only to an Unknown 296(1)
Quantity, the Base Being Omitted
Notations Applied to Any Quantity, the 297(1)
Base Being Designated
Descartes' Notation of 1637 298(1)
Did Stampioen Arrive at Descartes' 299(1)
Notation Independently?
Notations Used by Descartes before 1637 300(1)
Use of Herigone's Notation after 1637 301(1)
Later Use of Hume's Notation of 1636 302(1)
Other Exponential Notations Suggested 303(4)
after 1637
Spread of Descartes' Notation 307(1)
Negative, Fractional, and Literal 308(1)
Exponents
Imaginary Exponents 309(3)
Notation for Principal Values 312(1)
Complicated Exponents 313(1)
D. F. Gregory's (+)r 314(1)
Conclusions 315(1)
Signs for Roots 316(1)
Early Forms, General Statement 316(2)
The Sign R, First Appearance 318(1)
Sixteenth-Century Use of R 319(2)
Seventeenth-Century Use of R 321(1)
The Sign l 322(1)
Napier's Line Symbolism 323(1)
The Sign √ 324(1)
Origin of √ 324(3)
Spread of the √ 327(1)
Rudolff's Signs outside of Germany 328(1)
Stevin's Numeral Root-Indices 329(3)
Rudolff and Stifel's Aggregation Signs 332(1)
Descartes' Union of Radical Sign and 333(1)
Vinculum
Other Signs of Aggregation of Terms 334(1)
Redundancy in the Use of Aggregation 335(1)
Signs
Peculiar Dutch Symbolism 336(1)
Principal Root-Values 337(1)
Recommendation of the U.S. National 338(1)
Committee
Signs for Unknown Numbers 339(1)
Early Forms 339(1)
Crossed Numerals Representing Powers of 340(1)
Unknowns
Descartes' z, y, x 340(1)
Spread of Descartes' Signs 341(1)
Signs of Aggregation 342(1)
Introduction 342(1)
Aggregation Expressed by Letters 343(1)
Aggregation Expressed by Horizontal 344(4)
Bars or Vinculums
Aggregation Expressed by Dots 348(1)
Aggregation Expressed by Commas 349(1)
Aggregation Expressed by Parentheses 350(1)
Early Occurrence of Parentheses 351(2)
Terms in an Aggregate Placed in a 353(1)
Vertical Column
Marking Binomial Coefficients 354(1)
Special Uses of Parentheses 355(1)
A Star to Mark the Absence of Terms 356(1)
IV Symbols in Geometry (Elementary Part) 357
A Ordinary Elementary Geometry 357(28)
Early Use of Pictographs 357(3)
Signs for Angles 360(4)
Signs for "Perpendicular" 364(1)
Signs for Triangle, Square, Rectangle, 365(1)
Parallelogram
The Square as an Operator 366(1)
Sign for Circle 367(1)
Signs for Parallel Lines 368(1)
Signs for Equal and Parallel 369(1)
Signs for Arcs of Circles 370(1)
Other Pictographs 371(1)
Signs for Similarity and Congruence 372(3)
The Sign for Equivalence 375(1)
Lettering of Geometric Figures 376(4)
Sign for Spherical Excess 380(1)
Symbols in the Statement of Theorems 381(1)
Signs for Incommensurables 382(1)
Unusual Ideographs in Elementary 383(1)
Geometry
Algebraic Symbols in Elementary Geometry 384(1)
B Past Struggles between Symbolists and 385
Rhetoricians in Elementary Geometry
Index