P. HISTORY OF ' AATHEMATICAL - School of Mathematics

More documents

Recommendations

Info

170 A HISTORY OF MATHEMATICAL NOTATIONS FIG. 76.-Leonard and Thomas Dimes, Strdiotiws (1579), p. 35, showing the unknown and its powers to 20.
INDIVIDUAL WRITERS 171 As stated by the authors, the symbols are simply the numerals somewhat disfigured and croszed out by an extra stroke, to prevent confusion with the ordinary figures. The example at the bottom of page 35 is the addition of 20x+30x2+25rc3 and 45x+16x2+13x3. It is noteworthy that in 1610 Cataldi in Italy devised a similar scheme for representing the powers of an unknown (5 340). The treatment of equations is shown on page 46, which is reproduced in Figure 77. Observe the symbol for zero in lines 4 and 7; this form is used only when the zero stands by itself. A little later, on page 51, the authors, without explanation, begin to use a sign of equality. Previously the state of equality had been expressed in words, "equal1 to," "are." The sign of equality looks as if it were made up of two letters C in these positions 3C and crossed by two horizontal lines. See Figure 78. This sign of equality is more elaborate than that previously devised by Robert Recorde: The Digges sign requires four strokes of the pen; the Recorde sign demands only two, yet is perfectly clear. The Digges symbol appeara again on five or more later pages of the Stratioticos. Perhaps the sign is the astronomical symbol for Pisces ("the Fishes"), with an extra horizontal line. The top equation on page 51 is xZ=6x+27. ENGLISH : THOMAS MASTERSON (1592) 171. The domination of German symbols over English authors of the sixteenth century is shown further by the Arithmeticke of Thomas Masterson (London, 1592). Stifel's symbols for powers are used. We reproduce (in Fig. 79) a page showing the symbols for radicals. FRENCH: JACQUES PELETIER (1554) 172. Jacques Peletier du Mans resided in Paris, Bordeaux, Beziers, Lyon, and Rome. He died in Paris. His algebra, De occvlta Parte Numerwvm, Quam Algebram vocant, Libri duo (Paris, 1554, and several other editions),' shows in the symbolism used both German and Italian influences: German in the designation of powers and roots, done in the manner of Stifel; Italian in the use of p. and m. for "plus" and "minus." All our information is drawn from H. Bosmane, "L'alghbre de Jacques Peletier du Mans," Extrait de la revue dea quatione scialijqua (Bruxelles: January, 1907), p. 1-61.
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:
A HISTORY OF MATHEMATICAL NOTATIONS
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: 120 A HISTORY OF MATHEMATICAL NOTAT
Page 176 and 177: 160 A HISTORY OF MATIIEMATICAL NOTA
Page 192 and 193: 176 A HISTORY OF MATEFEMATICAL NOTA
Page 198 and 199: 182 A HISTORY OF MATREMATICAL NOTAT
Page 200 and 201: if54 A HISTORY OF MATHEMATICAL NOTA
Page 206 and 207: ' 1652 190 A HISTORY OF MATHEMATICA
Page 208 and 209: ......................... 192 A HIS
Page 212 and 213: 196 A HISTORY OF ,MATHEMATICAL NOTA
Page 216 and 217: 200 A HISTORY OF MATHEMATICAL 'NOTA
Page 222 and 223: A HISTORY OF MATHEMATICAL NOTATIONS
Page 224 and 225: 208 A HISTORY OF MATHJ3MATICAL NOTA
Page 232 and 233: 216 ,A HISTORY OF MATHEMATICAL NOTA
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:
274 A HISTORY OF MATREMATICAL NOTAT
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:
416 A HISTORY OF MATREMATICAL NOTAT
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:
Page 619 and 620:
Page 621 and 622:
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 and 668:
SYMBOLS USED BY LEIBNIZ 187 544. Si
Page 669 and 670:
SYMBOLS USED BY LEIBNIZ 189 Sign Me
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?