434 A <strong>HISTORY</strong> <strong>OF</strong> MATHEMATICAL NOTATIONS Arc <strong>of</strong> 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 <strong>of</strong> planets, 358 Athelard <strong>of</strong> 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 <strong>of</strong> star, 356 BakhshSili MS: survey <strong>of</strong> 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 <strong>of</strong> 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 <strong>of</strong> 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 <strong>of</strong> 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 <strong>of</strong> 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 <strong>of</strong> type, 378; equivalence, 376 Bombelli, Rafaele: survey <strong>of</strong> his signs, 144,145; 162, 164,190,384; aggrega- tion, 344; use <strong>of</strong> 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 <strong>of</strong> 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 <strong>of</strong> 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 <strong>of</strong> 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 <strong>of</strong> 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 <strong>of</strong> 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 <strong>of</strong> 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 <strong>of</strong> his signs, 140, 141; 152, 161, 176, 166, 177, 384; aggregation, 343, 351; equality, 140, 260; use <strong>of</strong> R, 199,319; use <strong>of</strong> 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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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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IMAGINARIES AND VECTOR ANALYSIS 129
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and laws of combination, without gi
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IMAGINARIES AND VECTOR ANALYSIS 133
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IMAGINARIES AND VECTOR ANALYSIS 135
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IMAGINARIES AND VECTOR ANALYSIS 137
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IMAGINARIES AND VECTOR ANALYSIS 139
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IMAGINARIES AND VECTOR ANALYSIS 141
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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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258 A HISTORY OF MATHEMATICAL NOTAT
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260 A HISTORY OF MATHEMATICAL NOTAT
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262 A HISTORY OF MATHEMATICAL NOTAT
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264 A HISTORY OF MATHEMATICAL NOTAT
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266 . A HISTORY OF MATHEMATICAL NOT
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268 A HISTORY OF MATHEMATICAL NOTAT
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270 A HISTORY OF MATHEMATICAL NOTAT
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272 A HISTORY OF MATHEMATICAL NOTAT
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274 A HISTORY OF MATHEMATICAL NOTAT
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'* 276 A HISTORY OF MATHEMATICAL
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280 A HISTORY OF MATHEMATICAL NOTAT
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282 A HISTORY OF MATHEMATICAL NOTAT
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366 A mSTORY OF MATHEMATICAL NOTATI