P. HISTORY OF ' AATHEMATICAL - School of Mathematics

More documents

Recommendations

Info

188 A HISTORY OF MATHEMATICAL NOTATIONS 546. Plus, minU8.- Sign Meaning I Year Reference + ................. - ................. ± ................. ±,± ±,=F ) tt ......... (±), (±) ±, (±), «±» } ±, T, (T) .... (+)................ E1l. ................ -lor I............ + - Plus or minus The upper signs simultaneously, or the lower simultaneously Three independent ambiguities in sign Logical combination Logical combination "Minus one" (sign of quality) 1666 .... P 1666 .... P 1673 1684P 1684P ? ? 1684P 1684P ? ? ? ? V,15 V,15 0, 100, 126; I, 117 1,27 V, 222; VII, 56 VII, 145 VII, 139, 153 V,222 V,222 V, 169, 170 V,198 VII, 261, 285 V,370 547. MuUiplication.- Sign Meaning Year Reference ................... ,... ................. X ...........• · ,................... ................... ............................... i ... ················ * ................. Apposition Multiplication Multiplication Multiplication Multiplication Multiplication Multiplication aDd separation as in 2 1 ; 1.2.3 Multiplication 1710 ..•. P 1666P ? 1672 .... 1675 1677 1676 .... 1674 ...• 1710P 1676 ••.• 1684, 1691P 1713 1705 VII,219 V, 15, 20, 24, 25 VII,33,45,49,54,100,22O 1,29.156 E, 128. 138, 139 B,242 I. 117; B, 242 Cat. crit., No. 775; I, 100; VI,228 VII,219 I, 128; II, 196, 239; III, 36, 1110.341; IV, 211; V, Ill, 112; VII, 54, 103, 175 V, 129, 222; VII, 219 111,986 IV, 211 548. Division.- Sign Meaning Year Reference II ij .................. Fraction, division 1666 ••.. P V, 48, 49, 220 1673 •••. I, 46, 116; IV, 211; VII, 54, 170 v .....· ............ Division 1666P 1675 .••. ................... Division, ratio 1676 ...• 1684 .••• P V, 15,20 E, 134; IlI 526; VII, 91, 103 1,90, 128; kV, 211, 400; VII, 170 V, 131, 223, 228
SYMBOLS USED BY LEIBNIZ 189 Sign Meaning Year Reference : .. ............... : - ............... .",.. ................... Proportion Proportion a c /i-d········ .... ··· Proportion Continued proportion 1676 .... 1684P 1691 •••. 1694P 1710P 1696 .... 1710P 1710P I, 146; II, 44, 97, 121; V, 241; VII, 309, 310, 356, 364, 378: E, 150 V,225 II, 113, 118, 119, 196; III, 80, 84, 262, 288, 526; IV, 211; VII, 390, 17 (Wolf) V,315 VII,222 III, 262; IV, 211 VII,222 VII,222 549. Proportion.- Decimalfradions.- Sign Meaning Year Reference 3.14159, etc..•....•. .......................... 1682P V, 119, 120 ? VII,361 550. Greater or less.- n................. Greater fl ......·....·.... · Le•• ................. Greater - .................. Le.. > .................. Greater < .................. Less ":=1 ................ Greater c.. ................. Less 1679 .... 1679 .... 1710P 1710P 1749P 1749P 1863P 1863P V, 153; VII, 55, 81 V, 153, 198; VII, 55, 81 M i.cell. BerolinenBia. Ibid. ""'.0'''''. I' ., 2d ed. of ibid. n re!'nnt 0 VII, 222 f7~ole of VII,222 - Sign Meaning Year Reference
Page 1 and 2:
P. HISTORY OF ' AATHEMATICAL ound A
Page 3 and 4:
A HISTORY OF MATHEMATICAL NOTATIONS
Page 5:
PREFACE The study of the history of
Page 8 and 9:
... vln TABLE OF CONTENTS Byzantine
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
Page 16 and 17:
PIOURE 91 . RADICALS ILLUSTRATIONS
Page 18 and 19:
NUMERAL SYhlBOLS AND COMBINATIONS '
Page 20 and 21:
4 A HISTORY OF MATHEMATICAL NOTATIO
Page 22 and 23:
Page 24 and 25:
Page 26 and 27:
10 A HISTORY 6F' MATHEMATICAL NOTAT
Page 28 and 29:
12 A HISTORY OF MATHEMATICAL NOTATI
Page 30 and 31:
14 A HISTORY OF MATKEMATICAL NOTATI
Page 32 and 33:
Page 34 and 35:
18 A HISTORY OF MATHEMATICAL KOTATI
Page 36 and 37:
Page 38 and 39:
Page 40 and 41:
Page 42 and 43:
Page 44 and 45:
Page 46 and 47:
Page 48 and 49:
Page 50 and 51:
34 A HISTORY OF MATmMATICAL NOTATIO
Page 52 and 53:
Page 54 and 55:
Page 56 and 57:
Page 58 and 59:
Page 60 and 61:
Page 62 and 63:
Page 64 and 65:
Page 66 and 67:
Page 68 and 69:
Page 70 and 71:
Page 72 and 73:
- 56 A HISTORY OF MATHEMATICAL NOTA
Page 74 and 75:
Page 76 and 77:
Page 78 and 79:
Page 80 and 81:
Page 82 and 83:
Page 84 and 85:
Page 86 and 87:
Page 88 and 89:
Page 90 and 91:
Page 92 and 93:
Page 94 and 95:
Page 96 and 97:
Page 98 and 99:
82 A HISTORY OF MATmMATICAL NOTATIO
Page 100 and 101:
Page 102 and 103:
Page 104 and 105:
Page 106 and 107:
Page 108 and 109:
Page 110 and 111:
94 A HIETORY OF MATHEMATICAL NOTATI
Page 112 and 113:
Page 114 and 115:
Page 116 and 117:
100 A HISTORY OF MATHEMATICAL NOTAT
Page 118 and 119:
Page 120 and 121:
Page 122 and 123:
Page 124 and 125:
Page 126 and 127:
Page 128 and 129:
Page 130 and 131:
Page 132 and 133:
Page 134 and 135:
Page 136 and 137:
Page 138 and 139:
Page 140 and 141:
Page 142 and 143:
Page 144 and 145:
Page 146 and 147:
Page 148 and 149:
Page 150 and 151:
Page 152 and 153:
Page 154 and 155:
Page 156 and 157:
Page 158 and 159:
Page 160 and 161:
Page 162 and 163:
Page 164 and 165:
Page 166 and 167:
Page 168 and 169:
Page 170 and 171:
Page 172 and 173:
Page 174 and 175:
Page 176 and 177:
160 A HISTORY OF MATIIEMATICAL NOTA
Page 178 and 179:
Page 180 and 181:
Page 182 and 183:
Page 184 and 185:
Page 186 and 187:
Page 188 and 189:
Page 190 and 191:
Page 192 and 193:
176 A HISTORY OF MATEFEMATICAL NOTA
Page 194 and 195:
Page 196 and 197:
Page 198 and 199:
182 A HISTORY OF MATREMATICAL NOTAT
Page 200 and 201:
if54 A HISTORY OF MATHEMATICAL NOTA
Page 202 and 203:
Page 204 and 205:
Page 206 and 207:
' 1652 190 A HISTORY OF MATHEMATICA
Page 208 and 209:
......................... 192 A HIS
Page 210 and 211:
Page 212 and 213:
196 A HISTORY OF ,MATHEMATICAL NOTA
Page 214 and 215:
Page 216 and 217:
200 A HISTORY OF MATHEMATICAL 'NOTA
Page 218 and 219:
Page 220 and 221:
Page 222 and 223:
Page 224 and 225:
208 A HISTORY OF MATHJ3MATICAL NOTA
Page 226 and 227:
Page 228 and 229:
Page 230 and 231:
Page 232 and 233:
216 ,A HISTORY OF MATHEMATICAL NOTA
Page 234 and 235:
Page 236 and 237:
no A HISTORY OF MATHEMATICAL NOTATI
Page 238 and 239:
Page 240 and 241:
Page 242 and 243:
Page 244 and 245:
n8 A HISTORY OF MATHEMATICAL NOTATI
Page 246 and 247:
Page 248 and 249:
Page 250 and 251:
Page 252 and 253:
Page 254 and 255:
Page 256 and 257:
Page 258 and 259:
2-12 A HISTORY OF MATHEMATICAL NOTA
Page 260 and 261:
Page 262 and 263:
Page 264 and 265:
Page 266 and 267:
Page 268 and 269:
Page 270 and 271:
Page 272 and 273:
Page 274 and 275:
Page 276 and 277:
Page 278 and 279:
Page 280 and 281:
Page 282 and 283:
Page 284 and 285:
268 A HISTORY OF MATEIEMATICAL NOTA
Page 286 and 287:
Page 288 and 289:
Page 290 and 291:
Page 292 and 293:
Page 294 and 295:
Page 296 and 297:
Page 298 and 299:
Page 300 and 301:
Page 302 and 303:
Page 304 and 305:
Page 306 and 307:
@ De 290 A HISTORY OF MATHEMATICAL
Page 308 and 309:
@ B. 292 A HISTORY OF MATHEMATICAL
Page 310 and 311:
Page 312 and 313:
Page 314 and 315:
298 A HISTORY OF MATEIEMATICAL NOTA
Page 316 and 317:
Page 318 and 319:
Page 320 and 321:
Page 322 and 323:
Page 324 and 325:
Page 326 and 327:
Page 328 and 329:
Page 330 and 331:
Page 332 and 333:
Page 334 and 335:
Page 336 and 337:
Page 338 and 339:
Page 340 and 341:
Page 342 and 343:
Page 344 and 345:
Page 346 and 347:
Page 348 and 349:
Page 350 and 351:
Page 352 and 353:
Page 354 and 355:
Page 356 and 357:
Page 358 and 359:
342 A HISTORY OF .MATHEMATICAL NOTA
Page 360 and 361:
Page 362 and 363:
Page 364 and 365:
Page 366 and 367:
Page 368 and 369:
Page 370 and 371:
Page 372 and 373:
Page 374 and 375:
358 A HISTORY OF MATBEMATICAL NOTAT
Page 376 and 377:
Page 378 and 379:
362 A HISTORY OF MATHE&lATICAL NOTA
Page 380 and 381:
Page 382 and 383:
Page 384 and 385:
Page 386 and 387:
Page 388 and 389:
Page 390 and 391:
Page 392 and 393:
Page 394 and 395:
Page 396 and 397:
Page 398 and 399:
Page 400 and 401:
Page 402 and 403:
Page 404 and 405:
Page 406 and 407:
Page 408 and 409:
Page 410 and 411:
Page 412 and 413:
Page 414 and 415:
Page 416 and 417:
Page 418 and 419:
Page 420 and 421:
@ G. 404 A HISTORY OF MATmMATICAL N
Page 422 and 423:
Page 424 and 425:
Page 426 and 427:
Page 428 and 429:
Page 430 and 431:
Page 432 and 433:
Page 434 and 435:
Page 436 and 437:
Page 438 and 439:
Page 440 and 441:
Page 442 and 443:
Page 444 and 445:
Page 446 and 447:
Page 449 and 450:
Abacus, 39, 75, 119 Abu Kamil, 273;
Page 451 and 452:
ALPHABETICAL INDEX Birks, John, omi
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
Page 461 and 462:
ALPWETICAL INDEX Oliver, Wait, and
Page 463 and 464:
ALPHABETICAL INDFZ Rawlinson, H., 5
Page 465 and 466:
Smith Eugene R.: area, 370; congrue
Page 467:
ALPHABETICAL INDEX 451 Wachter, G.,
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 .
Page 485 and 486:
LETTERS REPRESENTING MAGNITUDES 5 d
Page 487 and 488:
LETTERS REPRESENTING MAGNITUDES Y'
Page 489 and 490:
LETTERS n AND e 9 William Oughtred1
Page 491 and 492:
LETTERS r AND e 11 he began to use
Page 493 and 494:
LETTERS r AND e 13 mate ratio of th
Page 495 and 496:
DOLLAR MARK 15 The use of the lette
Page 497 and 498:
DOLLAR MARK 17 "dollar" and to have
Page 499 and 500:
DOLLAR MARK 19 lines being marks of
Page 501 and 502:
DOLLAR MARK 21 Ivan Vasquez de Sern
Page 503 and 504:
DOLLAR MARK 18, 19 are from the Dra
Page 505 and 506:
DOLLAR MARK 25 tion of the conventi
Page 507 and 508:
DOLLAR MARK 27 114 and 115. It will
Page 509 and 510:
THEORY OF NUMBERS 29 405. Conclusio
Page 511 and 512:
THEORY OF NUMBERS complex integers
Page 513 and 514:
THEORY OF NUMBERS 33 +'(n) is half
Page 515 and 516:
THEORY OF NUMBERS 35 deux. Ce signe
Page 525 and 526:
INFINITY AND TRANSFINITE NUMBERS 45
Page 527 and 528:
INFINITY AND TRANSFINITE NUMBERS 47
Page 529 and 530:
CONTINUED FRACTIONS, INFINITE SERIE
Page 531 and 532:
Page 533 and 534:
Page 535 and 536:
Page 537 and 538:
Page 539 and 540:
Page 541 and 542:
THEORY OF COMBINATIONS 61 438. The
Page 543 and 544:
THEORY OF COMBINATIONS 63 expansion
Page 545 and 546:
THEORY OF COMBINATIONS 65 in the po
Page 547 and 548:
THEORY OF COMBINATIONS 67 The polyn
Page 549 and 550:
THEORY OF COMBINATIONS 69 0, 1, ...
Page 551 and 552:
THEORY OF COMBINATIONS 2;""3 C, •
Page 553 and 554:
THEORY OF COMBINATIONS 73 A new des
Page 555 and 556:
THEORY OF COMBINATIONS 75 universal
Page 557 and 558:
THEORY OF COMBINATIONS 77 Of course
Page 559 and 560:
THEORY OF COMBINATIONS 79 ubi k nat
Page 561 and 562:
THEORY OF COMBINATIONS 81 the eleme
Page 563 and 564:
THEORY OF COMBINATIONS 83 applying
Page 565 and 566:
THEORY OF COMBINATIONS brevity, ~(n
Page 567 and 568:
DETERMINANTS 87 DETERMINANT NOTATIO
Page 569 and 570:
DETERMINANTS 89 rum bb-ac, a cuius
Page 571 and 572:
DETERMINANTS 91 Jacobi! chose the r
Page 573 and 574:
DETERMINANTS and failure to represe
Page 575 and 576:
DETERMINANTS 95 side the array. The
Page 577 and 578:
DETERMINANTS 97 and in general the
Page 579 and 580:
DETERMINANTS 99 may be written! (~,
Page 581 and 582:
DETERMINANTS 101 Sheppard' follows
Page 583 and 584:
DETERMINANTS 103 The notation for f
Page 585 and 586:
LOGARITHMS 105 Most general single-
Page 587 and 588:
LOGARITHMS 107 The capital letter "
Page 589 and 590:
LOGARITHMS 109 in Napier's Descript
Page 591 and 592:
LOGARITHMS 111 Morgan states that "
Page 593 and 594:
LOGARITHMS 113 en general, aNsera l
Page 595 and 596:
THEORETICAL ARITHMETIC 115 stand fo
Page 597 and 598:
THEORETICAL ARITHMETIC 117 argues t
Page 599 and 600:
THEORETICAL ARITHMETIC 119 485. Imp
Page 601 and 602:
THEORETICAL ARITHMETIC 121 er." Pro
Page 603 and 604:
THEORETICAL ARITHMETIC 123 Littlewo
Page 605 and 606:
THEORETICAL ARITHMETIC 125 494. Gen
Page 607 and 608:
IMAGINARIES AND VECTOR ANALYSIS 127
Page 609 and 610:
Page 611 and 612:
and laws of combination, without gi
Page 613 and 614:
Page 615 and 616:
Page 617 and 618: IMAGINARIES AND VECTOR ANALYSIS 137
Page 623 and 624: TRIGONOMETRY 143 512. A different d
Page 625 and 626: TRIGONOMETRY 145 Gioseppe' uses Gra
Page 627 and 628: TRIGONOMETRY 147 A novel mark is ad
Page 629 and 630: TRIGONOMETRY 149 tion (p. 47) a str
Page 631 and 632: TRIGONOMETRY 151 (P. 360) Rad. sin.
Page 633 and 634: TRIGONOMETRY 153 As far as the form
Page 635 and 636: TRIGONOMETRY 155 lettering is emplo
Page 637 and 638: TRIGONOMETRY 157 edition of the boo
Page 639 and 640: TRIGONOMETRY 159 also his Trigonome
Page 641 and 642: TRIGONOMETRY 161 During the latter
Page 643 and 644: TRIGONOMETRY 163 his lack of assert
Page 645 and 646: TRIGONOMETRY 165 We close with a re
Page 647 and 648: ••••••••••• .
Page 649 and 650: 21. J. A. Segner, Cur.... matMmatic
Page 651 and 652: TRIGONOMETRY 171 9. G. U. A. Vieth,
Page 653 and 654: TRIGONOMETRY 173 J. Houel! in 1864
Page 655 and 656: TRIGONOMETRY 175 tan [(ct>, x)] =ta
Page 657 and 658: TRIGONOMETRY 177 for the calculus,
Page 659 and 660: TRIGONOMETRY 179 formula "4 sin.f1=
Page 661 and 662: SYMBOLS USED BY LEIBNIZ 181 sponded
Page 663 and 664: SYMBOLS USED BY LEIBNIZ 183 by two
Page 665 and 666: SYMBOLS USED BY LEIBNIZ 185 desuetu
Page 667: SYMBOLS USED BY LEIBNIZ 187 544. Si
Page 671 and 672: SYMBOLS USED BY LEIllNIZ 191 552. P
Page 673 and 674: SYMBOLS USED BY LEIBNIZ 193 558. Fu
Page 675 and 676: SYMBOLS USED BY LEIBNIZ 195 BC, or
Page 677 and 678: DIFFERENTIAL CALCULUS 197 2. SYMBOL
Page 679 and 680: DIFFERENTIAL CALCULUS 199 few other
Page 681 and 682: DIFFERENTIAL CALCULUS 201 duced Flu
Page 683 and 684: DIFFERENTIAL CALCULUS 203 admirable
Page 685 and 686: DIFFERENTIAL CALCULUS 205 did he su
Page 687 and 688: DIFFERENTIAL CALCULUS 207 Here the
Page 689 and 690: DIFFERENTIAL CALCULUS 209 1797 edit
Page 691 and 692: DIFFERENTIAL CALCULUS 211 Kramp say
Page 693 and 694: DIFFERENTIAL CALCULUS 213 580. S. F
Page 695 and 696: DIFFERENTIAL CALCULUS 215 Nor had L
Page 697 and 698: DIFFERENTIAL CALCULUS 217 The varia
Page 699 and 700: DIFFERENTIAL CALCULUS 219 the book
Page 701 and 702: DIFFERENTIAL CALCULUS 221 l'Hospita
Page 703 and 704: DIFFERENTIAL CALCULUS 223 different
Page 705 and 706: DIFFERENTIAL CALCULUS 225 x and y,
Page 707 and 708: DIFFERENTIAL CALCULUS . 'l2.7 shoul
Page 709 and 710: DIFFERENTIAL CALCULUS 229 represent
Page 711 and 712: DIFFERENTIAL CALCULUS 231 cannot be
Page 713 and 714: DIFFERENTIAL CALCULUS 233 607. M. O
Page 715 and 716: DIFFERENTIAL CALCULUS 235 610. Cauc
Page 717 and 718: DIFFERENTIAL CALCULUS 237 values ac
Page 719 and 720:
DIFFERENTIAL CALCULUS 239 "The stud
Page 721 and 722:
DIFFERENTIAL CALCULUS 241 618. T. M
Page 723 and 724:
INTEGRAL CALCULUS 243 In Leibnizens
Page 725 and 726:
INTEGRAL CALCULUS 245 nizian notati
Page 727 and 728:
INTEGRAL CALCULUS 247 In Newton's P
Page 729 and 730:
INTEGRAL CALCULUS 249 624. A. L. Cr
Page 731 and 732:
INTEGRAL CALCULUS 251 claiming for
Page 733 and 734:
INTEGRAL CALCULUS 253 6. CALCULUS N
Page 735 and 736:
INTEGRAL CALCULUS 255 and "Lim. ~~.
Page 737 and 738:
INTEGRAL CALCULUS 257 limit, when .
Page 739 and 740:
INTEGRAL CALCULUS 259 introduced th
Page 741 and 742:
INTEGRAL CALCULUS 261 Diderot's Enc
Page 743 and 744:
FINITE DIFFERENCES 263 FINITE DIFFE
Page 745 and 746:
FINITE DIFFERENCES 265 Wide accepta
Page 747 and 748:
THEORY OF FUNCTIONS 267 introductio
Page 749 and 750:
THEORY OF FUNCTIONS 269 1747 D'Alem
Page 751 and 752:
THEORY OF FUNCTIONS 271 by Cauchy'
Page 753 and 754:
THEORY OF FUNCTIONS 273 Hence this
Page 755 and 756:
THEORY OF FUNCTIONS 275 where the a
Page 757 and 758:
THEORY OF FUNCTIONS 277 he employed
Page 759 and 760:
THEORY OF FUNCTIONS 279 in a series
Page 761 and 762:
Page 763 and 764:
Page 765 and 766:
Page 767 and 768:
Page 769 and 770:
266 . A HISTORY OF MATHEMATICAL NOT
Page 771 and 772:
Page 773 and 774:
Page 775 and 776:
Page 777 and 778:
Page 779 and 780:
'* 276 A HISTORY OF MATHEMATICAL
Page 781 and 782:
Page 783 and 784:
Page 785 and 786:
Page 787 and 788:
Page 789 and 790:
Page 791 and 792:
Page 793 and 794:
Page 795 and 796:
Page 797 and 798:
Page 799 and 800:
Page 801 and 802:
Page 803 and 804:
Page 805 and 806:
Page 807 and 808:
Page 809 and 810:
Page 811 and 812:
Page 813 and 814:
Page 815 and 816:
Page 817 and 818:
Page 819 and 820:
Page 821 and 822:
Page 823 and 824:
Page 825 and 826:
322 A HISTORY OF MATHEJ\lATICAL NOT
Page 827 and 828:
Page 829 and 830:
Page 831 and 832:
328 A HISTOHY OF MATHEMATICAL NOTAT
Page 833 and 834:
Page 835 and 836:
332 A HISTORY m' :\L\THEMATICAL NOT
Page 837 and 838:
Page 839 and 840:
Page 841 and 842:
Page 843 and 844:
Page 845 and 846:
Page 847 and 848:
Page 849 and 850:
346 A HlfTORY OF MATHEMATICAL NOTAT
Page 851 and 852:
Page 853 and 854:
Page 855 and 856:
Page 857 and 858:
Page 859 and 860:
Page 861 and 862:
Page 863 and 864:
Page 865 and 866:
Page 867 and 868:
Page 869 and 870:
366 A mSTORY OF MATHEMATICAL NOTATI
show all

P. HISTORY OF ' AATHEMATICAL - School of Mathematics

Create successful ePaper yourself

Delete template?

Save as template?