P. HISTORY OF ' AATHEMATICAL - School of Mathematics

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434 A HISTORY OF MATHEMATICAL NOTATIONS Arc of circle, 370 Archibald, R. C., 218, 270, 376 Archimedes, 41, 384 Ardiiaer, Johann, 208,283; aggregation, 348; radical sign, 328, 332 Arithmetical progression, 248; arithmetical proportion, 249, 255 Amauld, Antoine, 249; equality, 266 Aryabhata, 76 Astronomical signs, relative position of planets, 358 Athelard of Bath, 81, 82 Attic signs, 33, 34, 35, 84 Auerbach, M., and C. B. Walsh: angle, 361; congruent in geometry, 372; is measured by, 383 Aurel, Marco, 165, 204, 327 Ayres, John, 225 Aztecs, 66 Babbage, Charles, 386; quoted, 386 Babylonians, 1-15; ideogram for multiphcation, 217; ideogram for division, 235 Bachet, C. G., 101, 339 Ba&za, L., 222 Bailey, M. A., 242 Baillet, J., 41 Bails, Benito, 249 Baker, Alfred, congruence in geometry, 374 Baker, Th.: parallel, 368; perpendicular, 364; use of star, 356 BakhshSili MS: survey of signs, 109; 106,200,217,235,250,260; equality, 260, 109; unknown quant~ty, 339 Btdam, R., 186,209,245,246,283,303; arithmetical proportion, 249 Balbontin, J. M., 239, 258 Ball, W. W. R., 96 Ballantine, J. P., 90 Bamberg arithmetic, 272 Barlaam, 40 Bar-le-Duc, I. Errard de. See Deidier, Dounot Barlow, Peter, 225, 286 Barreme, N., 91 Barrow, Isaac: SUNey of his signs, 192; 216, 237, 371, 384, 386; aggregation, 345, 354; equal~ty, 266; geometncal proportion, 251, 252; powers, 307 Bartholinus, E., 217 Bartjens, William, 52, 208 Barton, G. A., 9, 10, 12 Beaugrand, Jean de, 302 Beeckman, I., 340 Beauelin, Nic. de. 255 ~eidor, '~ernard' Forest de, 206, 248, 255. 257 ~ellaJitis, G., 268 Beman, W. W., 244. See alao Beman and Smith Beman, W. W., and D. E., Smith: angle, 360; right angle, 363; parallelogram, 365; similar, 372 Benedetti, J. B., 219 Banson, L. S., equivalence, 375 Berlet, Bruno, 148, 326 Bernhard, Max, angle, 362 Bernoulli, Daniel (b. 1700), parentheses, 351, 352 Bernoulli, Jakob I (James), 210, 255; aggregation, 348, 354; equality, 264, 267; radical signs, 334; as operator, 366 Bernoulli, Johann I (John), 233, 255, 258, 309, 310, 341; aggregation, 344; lettering figures, 376; "mem," 365; use of star, 356; radical expressions, 308; as operator, 366 Bernoulli, Johann I1 (b. 1710), 258; parentheses, 351, 352 Bernoulli, Johann I11 (b. 1744), 208, 365 Bernoulli, Nicolaus (b. 1687)) exponents, 313 Bertrand, Louis, 286 Bettini, Mario, 96, 226, 229 Betz, W., and H. E. Webb, congruent in geometry, 374 Beutel, Tobias, 208, 273, 283, 292 Beyer, J. H., 277, 283 Bezold, C., 358 BBzout, E., 91,241,248; geometry, 387 Bhakara: survey of his signs, 110-14; 109, 217, 295; unknown quantity, 339 Bianchini, G., 126, 138, 208, 318 Biart, L., 66 Biernatzki, 71 Billingsley's Euclid, 169, 251 Billy, J. de, 227, 249, 253, 254, 292; aggregation, 351; exponents, 307; use of B, 320 Binet, J., angle, 361 Biot, 71
ALPHABETICAL INDEX Birks, John, omicron-sigma, 307 Bjombo, A. A., 385 Blakelock, R., 386 BlaasiBre, J. J., 248, 249; circle, 367; parentheses, 351; similar, 372 Blundeville, Th., 91, 223 Bobynin, V. V., 22 Boethius, 59; apices, 81; proportions, 249, 250 Boeza, L., 273 Boissiere, Claude de, 229 Bolognetti, Pompeo, 145 Bolyai, John, 368 Bolyai, Wolfgang, 212, 268; angle, 361, 362; circle, 367; congruent In geometry, 374; different kinds of type, 378; equivalence, 376 Bombelli, Rafaele: survey of his signs, 144,145; 162, 164,190,384; aggregation, 344; use of R, 319, 199 Bomie, 258 Boncompagni, B., 91, 129, 131, 132, 219, 271, 273, 359 Boon, C. F., 270 Borel, E., angle, 361 Borgi (or Borghi) Pietro, survey of his signs, 133; 223, 278 or to lot ti, E., 47, 138, 145, 344, 351 Bosch, Klaas, 52, 208 Bosmans, H., 160, 162, 172, 176, 297 Boudrot, 249 Bouguer, P., 258 Bourke, J. G., 65 Braces, 353 Brackets, 347; in Bombelli, 351, 352 Brahmagupta: survey of his signs, 106- 8; 76, 80, 112, 114; unknown quantities, 339 Brancker, Thomas, 194, 237, 252, 307, 386; radical s~gn, 328, 333, unknown quantity, 341 Brandis, 88 Brasch, F. E., 125 Brasser, J. R., 343 Briggs, H., 261; decimal fractions, 283; use of 1 for root, 322 Brito Rcbello, J. I., 56 Dronkhorst, J. (Noviamagus), 97 Brouncker, W., 264 Brown, Richard, 35 Briickner, Mac, angle, 362 Brugs~h, H., 16, 18, 200 Bryan, G. H., 334, 275 Bubnov, N., 75 Budden, E., similar, 374 Biihler, G., 80 Biirgi, Joost, 278, 283; powers, 296 '~urja, Abel, radical sign, 331 Bush, W. N., and John B. Clarke: angle, 363; congruent in geometry, 372; =, 374 Buteon, Jean: survey of his signs, 173; 132, 204, 263; equality, 263 Byerly, W. E.: angle, 360; pardelogram, 365; right angle, 363 f Byrne, 0.: an e, 362; edition of Euclid, 386; rig t angle, 363 Cajori, F., 75, 92 Ca_lk!lus, differential and integral, 365, 54 l Calderdn (Span. sign), 92 Callet, Fr., 95; similar, 374 Cambuston, H., 275 Campanus' Euclid, 385 Camus, C. E. L., 372 Cantor, Moritz, 27, 28, 31-34, 36, 38, 46, 47, 69, 71, 74, 76, 81, 91, 96, 97, 100, 116, 118, 136, 144,201, 238, 263, 264, 271, 304, 324, 339; per mllle, 274; lettering of figures, 376 Capella, Martianus, 322, 386 Cappelli, A., 48, 51, 93, 94, 208, 274 Caramuel, J., 91, 92; .decimal separatrix, 262, 283; equal~ty, 265; powen, 303, 305, 366; radical signs, 328; unknowns, 341 Cardano (Cardan), Hieronimo: survey of his signs, 140, 141; 152, 161, 176, 166, 177, 384; aggregation, 343, 351; equality, 140, 260; use of R, 199,319; use of round parentheses once, 351 Carlos le-Maur, 96 Carrnichael, Robert, calculus, 348 Carnot, L. N. M.: angle, 705; geometric notation, 379 Carra de Vaux, 75 Carr6, L., 255, 266; parentheses, 351 Cartan, E., 247 Casati, P., 273, Casey, John: angle, 360; congruent in geometry, 374 Cassany, F., 254 Castillon, G. F., 286; radical signs, 330
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P. HISTORY OF ' AATHEMATICAL ound A
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A HISTORY OF MATHEMATICAL NOTATIONS
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PREFACE The study of the history of
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... vln TABLE OF CONTENTS Byzantine
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TABLE OF CONTENTS mx.&amms Notation
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TABLE OF CONTENTS PIRAQRAPER Crosse
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ILLUSTRATIONS PIQUBE 28 . REAL ESTA
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PIOURE 91 . RADICALS ILLUSTRATIONS
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NUMERAL SYhlBOLS AND COMBINATIONS '
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4 A HISTORY OF MATHEMATICAL NOTATIO
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......................... 192 A HIS
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Page 449: Abacus, 39, 75, 119 Abu Kamil, 273;
Page 453 and 454: ALPHABETICAL INDEX 437 Curtze, M.,
Page 455 and 456: ALPWETICAL INDEX Fol!inus, H., 208,
Page 457 and 458: ALPHABETICAL INDEX Hindenburg, C. F
Page 459 and 460: ALPHABETICAL INDEX 443 Local value
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Page 463 and 464: ALPHABETICAL INDFZ Rawlinson, H., 5
Page 465 and 466: Smith Eugene R.: area, 370; congrue
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Page 471 and 472: h o ~ u c m TO o THE ~ SECOND VOL-
Page 473 and 474: TABLE OF CONTENTS PAEAQBbPHB Expone
Page 475 and 476: TABLE OF CONTENT'% Finite Differenc
Page 477 and 478: TABLE OF CONTENTS PIIIAQBAPBB C. Co
Page 479 and 480: INTRODUCTION TO THE SECOND VOLUME I
Page 481 and 482: TOPICAL SURVEY OF SYMBOLS IN ARITHM
Page 483 and 484: LE I'TERS REPRESENTING MAGNITUDES .
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Page 489 and 490: LETTERS n AND e 9 William Oughtred1
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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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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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