P. HISTORY OF ' AATHEMATICAL - School of Mathematics

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... vln TABLE OF CONTENTS ByzantineMaximus Planudes. Fourteenth Cent Italian-Leonardo of Pisa. Thirteenth Century French-Nicole Oresme. Fourteenth Century . Arabic-al.Qalasbdi. Fifteenth Century . . German-Regiomontanus. Fifteenth Century . Italian-Earliest Printed Arithmetic. 1478 . . French-Nicolas Chuquet. 1484 . . French-Estienne de la Roche. 1520 Italian-Pietro Borgi. 1484. 1488 Italian-Luca Pacioli. 1494. 1523 . . . Italian-F . Ghaligai. 1521. 1548. 1552 . . Italian-H . Cardan. 1532. 1545. 1570 . . . Italian-Nicolo Tartaglia. 1506-60 . . . . Italian-Rafaele Bombelli. 1572 . . German-Johann Widman. 1489. 1526 Austrian-Grammateus. 1518. 1535 German-Christoff Rudolff. 1525 . . . . Dutch-Gielis van der Hoecke. 1537 . . German-Michael Stifel. 1544. 1545. 1553 . . German-Nicolaus Copernicus. 1566 . German-Johann Scheubel. 1545. 1551 . . MalteseWil . Klebitius. 1565 . . German-Christophorus Clavius. 1608 . . . Belgium-Simon Stevin. 1585 LorraineAlbertGirard. 1629 . . German-Spanish-Marco Aurel. 1552 . . Portuguese-Spanish-Pedro Nuaez. 1567 . English-Robert Recorde. 1543(?). 1557 . . English-John Dee. 1570 . . . . . . English-Leonard and Thomas Digges. 1579 . English-Thomas Masterson. 1592 . . . . . . . . . . French-Jacques Peletier. 1554 French-Jean Buteon. 1559 French-Guillaume Gosselin. 1577 . . . . French-Francis Vieta. 1591 . . . . . . Italian-Bonaventura Cavalieri. 1647 . . English-William Oughtred. 1631. 1632. 1657 . English-Thomas Harriot. 1631 . . French-Pierre HBrigone. 1634. 1644 . . . ScobFrench-James Hume. 1635. 1636 . . French-Renk Descartes . . . . . . . English-Isaac Barrow . . . . . . . English-Richard Rawlinson. 1655-68 . . . Swiss-Johann Heinrich Rahn . . . . .
TABLE OF CONTENTS . . . . ix PARAQRAPAR English-John Wallis, 1655, 1657. 1685 195. 196 &tract from Acta eruditorum. Leipzig. 1708 197 . . . Extract from Miscellanea Berolinensial 1710 (Due to G . W . Leibniz) . . . . 198 Conclusions . . . . . . . . . . . . In9 . . . . . B . Topical Survey of the Use of Notations 200-356 Signs of Addition and Subtraction . . . . . . 200-216 Early Symbols . . . . . . 200 Origin and Meaning of the Signs . . . . . 201-3 Spread of the and Symbols 204 Shapes of the + Sign . . . . . . . 205-7 Varieties of . Signs . . . . . . . . 208, 209 Symbols for "Plus or Minus" 210. 211 . . . . . . . Certain Other Specialized Uses of + and . . . 212-14 . . . . . . . . . . Four Unusual Signs 215 Composition of Ratios 216 217-34 Signs of Multiplication . . . . . . . . Early Symbols . . . . . . . . . . 217 Early Uses of the St . Andrew's Cross. but Not as the Symbol of Multiplication of Two Numbers . . 218-30 The Process of Two False Positions . 219 Compound Proportions with Integers . 220 Proportions Involving Fractions . 221 Addition and Subtraction of Fractions . 222 Division of Fractions . . . . . . . 223 Casting Out the 9's. 7's. or 11's . 225 Multiplication of Integers . 226 Reducing Radicals to Radicals of the Same Order 227 Marking the Place for "Thousands" . 228 Place of Multiplication Table above 5 X 5 . . 229 The St . Andrew's Cross Used as a Symbol of Multiplication . . . . . . . . . . 231 Unsuccessful Symbols for Multiplication . 232 The Dot for Multiplication . 233 The St . Andrew's Cross in Notation for Transfinite Ordinal Numbers . . . . . . . . . . 234 Signs of Division and Ratio . . 235-47 Early Symbols . . . . . . . . . 235. 236 Fhhn's Notation . . . . . . . . . 237 Leibniz's Notations . . . . . . . . . . 238 Relative Position of Divisor and Dividend . 241 Order of Operations in Tenns Containing Both t andx . . . . . . . . . . . . 242 A Critical Estimate of : and + as Symboh . . 243
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Page 10 and 11: TABLE OF CONTENTS mx.&amms Notation
Page 12 and 13: TABLE OF CONTENTS PIRAQRAPER Crosse
Page 14 and 15: ILLUSTRATIONS PIQUBE 28 . REAL ESTA
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Abacus, 39, 75, 119 Abu Kamil, 273;
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ALPHABETICAL INDEX Birks, John, omi
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ALPHABETICAL INDEX 437 Curtze, M.,
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ALPWETICAL INDEX Fol!inus, H., 208,
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ALPHABETICAL INDEX Hindenburg, C. F
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ALPHABETICAL INDEX 443 Local value
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ALPWETICAL INDEX Oliver, Wait, and
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ALPHABETICAL INDFZ Rawlinson, H., 5
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Smith Eugene R.: area, 370; congrue
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ALPHABETICAL INDEX 451 Wachter, G.,
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h o ~ u c m TO o THE ~ SECOND VOL-
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TABLE OF CONTENTS PAEAQBbPHB Expone
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TABLE OF CONTENT'% Finite Differenc
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TABLE OF CONTENTS PIIIAQBAPBB C. Co
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INTRODUCTION TO THE SECOND VOLUME I
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TOPICAL SURVEY OF SYMBOLS IN ARITHM
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LE I'TERS REPRESENTING MAGNITUDES .
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LETTERS REPRESENTING MAGNITUDES 5 d
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LETTERS REPRESENTING MAGNITUDES Y'
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LETTERS n AND e 9 William Oughtred1
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LETTERS r AND e 11 he began to use
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LETTERS r AND e 13 mate ratio of th
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DOLLAR MARK 15 The use of the lette
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DOLLAR MARK 17 "dollar" and to have
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DOLLAR MARK 19 lines being marks of
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DOLLAR MARK 21 Ivan Vasquez de Sern
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DOLLAR MARK 18, 19 are from the Dra
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DOLLAR MARK 25 tion of the conventi
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DOLLAR MARK 27 114 and 115. It will
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THEORY OF NUMBERS 29 405. Conclusio
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THEORY OF NUMBERS complex integers
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THEORY OF NUMBERS 33 +'(n) is half
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THEORY OF NUMBERS 35 deux. Ce signe
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INFINITY AND TRANSFINITE NUMBERS 45
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INFINITY AND TRANSFINITE NUMBERS 47
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CONTINUED FRACTIONS, INFINITE SERIE
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THEORY OF COMBINATIONS 61 438. The
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THEORY OF COMBINATIONS 63 expansion
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THEORY OF COMBINATIONS 65 in the po
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THEORY OF COMBINATIONS 67 The polyn
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THEORY OF COMBINATIONS 69 0, 1, ...
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THEORY OF COMBINATIONS 2;""3 C, •
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THEORY OF COMBINATIONS 73 A new des
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THEORY OF COMBINATIONS 75 universal
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THEORY OF COMBINATIONS 77 Of course
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THEORY OF COMBINATIONS 79 ubi k nat
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THEORY OF COMBINATIONS 81 the eleme
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THEORY OF COMBINATIONS 83 applying
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THEORY OF COMBINATIONS brevity, ~(n
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DETERMINANTS 87 DETERMINANT NOTATIO
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DETERMINANTS 89 rum bb-ac, a cuius
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DETERMINANTS 91 Jacobi! chose the r
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DETERMINANTS and failure to represe
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DETERMINANTS 95 side the array. The
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DETERMINANTS 97 and in general the
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DETERMINANTS 99 may be written! (~,
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DETERMINANTS 101 Sheppard' follows
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DETERMINANTS 103 The notation for f
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LOGARITHMS 105 Most general single-
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LOGARITHMS 107 The capital letter "
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LOGARITHMS 109 in Napier's Descript
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LOGARITHMS 111 Morgan states that "
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LOGARITHMS 113 en general, aNsera l
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THEORETICAL ARITHMETIC 115 stand fo
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THEORETICAL ARITHMETIC 117 argues t
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THEORETICAL ARITHMETIC 119 485. Imp
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THEORETICAL ARITHMETIC 121 er." Pro
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THEORETICAL ARITHMETIC 123 Littlewo
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THEORETICAL ARITHMETIC 125 494. Gen
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IMAGINARIES AND VECTOR ANALYSIS 127
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and laws of combination, without gi
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TRIGONOMETRY 143 512. A different d
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TRIGONOMETRY 145 Gioseppe' uses Gra
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TRIGONOMETRY 147 A novel mark is ad
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TRIGONOMETRY 149 tion (p. 47) a str
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TRIGONOMETRY 151 (P. 360) Rad. sin.
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TRIGONOMETRY 153 As far as the form
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TRIGONOMETRY 155 lettering is emplo
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TRIGONOMETRY 157 edition of the boo
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TRIGONOMETRY 159 also his Trigonome
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TRIGONOMETRY 161 During the latter
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TRIGONOMETRY 163 his lack of assert
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TRIGONOMETRY 165 We close with a re
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••••••••••• .
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21. J. A. Segner, Cur.... matMmatic
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TRIGONOMETRY 171 9. G. U. A. Vieth,
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TRIGONOMETRY 173 J. Houel! in 1864
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TRIGONOMETRY 175 tan [(ct>, x)] =ta
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TRIGONOMETRY 177 for the calculus,
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TRIGONOMETRY 179 formula "4 sin.f1=
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SYMBOLS USED BY LEIBNIZ 181 sponded
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SYMBOLS USED BY LEIBNIZ 183 by two
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SYMBOLS USED BY LEIBNIZ 185 desuetu
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SYMBOLS USED BY LEIBNIZ 187 544. Si
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SYMBOLS USED BY LEIBNIZ 189 Sign Me
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SYMBOLS USED BY LEIllNIZ 191 552. P
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SYMBOLS USED BY LEIBNIZ 193 558. Fu
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SYMBOLS USED BY LEIBNIZ 195 BC, or
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DIFFERENTIAL CALCULUS 197 2. SYMBOL
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DIFFERENTIAL CALCULUS 199 few other
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DIFFERENTIAL CALCULUS 201 duced Flu
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DIFFERENTIAL CALCULUS 203 admirable
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DIFFERENTIAL CALCULUS 205 did he su
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DIFFERENTIAL CALCULUS 207 Here the
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DIFFERENTIAL CALCULUS 209 1797 edit
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DIFFERENTIAL CALCULUS 211 Kramp say
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DIFFERENTIAL CALCULUS 213 580. S. F
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DIFFERENTIAL CALCULUS 215 Nor had L
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DIFFERENTIAL CALCULUS 217 The varia
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DIFFERENTIAL CALCULUS 219 the book
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DIFFERENTIAL CALCULUS 221 l'Hospita
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DIFFERENTIAL CALCULUS 223 different
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DIFFERENTIAL CALCULUS 225 x and y,
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DIFFERENTIAL CALCULUS . 'l2.7 shoul
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DIFFERENTIAL CALCULUS 229 represent
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DIFFERENTIAL CALCULUS 231 cannot be
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DIFFERENTIAL CALCULUS 233 607. M. O
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DIFFERENTIAL CALCULUS 235 610. Cauc
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DIFFERENTIAL CALCULUS 237 values ac
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DIFFERENTIAL CALCULUS 239 "The stud
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DIFFERENTIAL CALCULUS 241 618. T. M
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INTEGRAL CALCULUS 243 In Leibnizens
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INTEGRAL CALCULUS 245 nizian notati
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INTEGRAL CALCULUS 247 In Newton's P
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INTEGRAL CALCULUS 249 624. A. L. Cr
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INTEGRAL CALCULUS 251 claiming for
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INTEGRAL CALCULUS 253 6. CALCULUS N
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INTEGRAL CALCULUS 255 and "Lim. ~~.
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INTEGRAL CALCULUS 257 limit, when .
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INTEGRAL CALCULUS 259 introduced th
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INTEGRAL CALCULUS 261 Diderot's Enc
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FINITE DIFFERENCES 263 FINITE DIFFE
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FINITE DIFFERENCES 265 Wide accepta
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THEORY OF FUNCTIONS 267 introductio
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THEORY OF FUNCTIONS 269 1747 D'Alem
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THEORY OF FUNCTIONS 271 by Cauchy'
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THEORY OF FUNCTIONS 273 Hence this
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THEORY OF FUNCTIONS 275 where the a
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THEORY OF FUNCTIONS 277 he employed
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THEORY OF FUNCTIONS 279 in a series
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