Mathematics From the Birth of NumbersA gently guided, profusely illustrated Grand Tour of the world of mathematics. This extraordinary work takes the reader on a long and fascinating journey--from the dual invention of numbers and language, through the major realms of arithmetic, algebra, geometry, trigonometry, and calculus, to the final destination of differential equations, with excursions into mathematical logic, set theory, topology, fractals, probability, and assorted other mathematical byways. The book is unique among popular books on mathematics in combining an engaging, easy-to-read history of the subject with a comprehensive mathematical survey text. Intended, in the author's words, "for the benefit of those who never studied the subject, those who think they have forgotten what they once learned, or those with a sincere desire for more knowledge," it links mathematics to the humanities, linguistics, the natural sciences, and technology. Contains more than 1000 original technical illustrations, a multitude of reproductions from mathematical classics and other relevant works, and a generous sprinkling of humorous asides, ranging from limericks and tall stories to cartoons and decorative drawings. |
Contents
I | 1 |
III | 3 |
IV | 5 |
V | 7 |
VI | 26 |
VII | 29 |
VIII | 31 |
IX | 32 |
CXXXI | 572 |
CXXXII | 582 |
CXXXIII | 595 |
CXXXVI | 596 |
CXXXVII | 598 |
CXXXVIII | 603 |
CXXXIX | 610 |
CXL | 621 |
X | 34 |
XI | 44 |
XII | 46 |
XIII | 48 |
XIV | 56 |
XV | 58 |
XVI | 61 |
XVII | 62 |
XVIII | 66 |
XIX | 69 |
XX | 70 |
XXI | 72 |
XXII | 77 |
XXIII | 82 |
XXIV | 84 |
XXV | 87 |
XXVI | 89 |
XXVII | 97 |
XXVIII | 98 |
XXIX | 101 |
XXX | 113 |
XXXI | 132 |
XXXII | 134 |
XXXIII | 150 |
XXXIV | 157 |
XXXV | 161 |
XXXVI | 168 |
XXXVII | 183 |
XXXIX | 184 |
XL | 186 |
XLI | 188 |
XLII | 196 |
XLIII | 199 |
XLIV | 201 |
XLV | 205 |
XLVI | 215 |
XLIX | 216 |
L | 219 |
LI | 220 |
LII | 225 |
LIII | 227 |
LIV | 229 |
LV | 231 |
LVI | 232 |
LVII | 233 |
LVIII | 242 |
LIX | 249 |
LX | 252 |
LXI | 257 |
LXII | 263 |
LXV | 264 |
LXVI | 266 |
LXVII | 270 |
LXVIII | 285 |
LXIX | 286 |
LXX | 289 |
LXXI | 295 |
LXXII | 297 |
LXXIII | 302 |
LXXIV | 307 |
LXXV | 308 |
LXXVI | 309 |
LXXVII | 312 |
LXXVIII | 316 |
LXXIX | 321 |
LXXX | 326 |
LXXXI | 331 |
LXXXIV | 332 |
LXXXVI | 344 |
LXXXVII | 351 |
LXXXVIII | 359 |
XCI | 360 |
XCII | 366 |
XCIII | 368 |
XCIV | 372 |
XCV | 373 |
XCVI | 374 |
XCVII | 377 |
XCVIII | 381 |
CI | 382 |
CIII | 401 |
CIV | 405 |
CV | 419 |
CVI | 451 |
CIX | 452 |
CX | 464 |
CXI | 471 |
CXII | 472 |
CXIII | 496 |
CXIV | 501 |
CXV | 510 |
CXVI | 522 |
CXVII | 527 |
CXX | 528 |
CXXI | 530 |
CXXII | 533 |
CXXIII | 535 |
CXXIV | 543 |
CXXVII | 544 |
CXXVIII | 545 |
CXXIX | 555 |
CXXX | 568 |
CXLII | 622 |
CXLIII | 623 |
CXLIV | 625 |
CXLV | 626 |
CXLVI | 627 |
CXLVII | 629 |
CXLVIII | 631 |
CXLIX | 633 |
CLII | 634 |
CLIII | 636 |
CLIV | 638 |
CLV | 642 |
CLVI | 650 |
CLVII | 655 |
CLVIII | 657 |
CLIX | 667 |
CLXII | 669 |
CLXIII | 670 |
CLXIV | 679 |
CLXVIII | 681 |
CLXIX | 685 |
CLXX | 691 |
CLXXI | 701 |
CLXXII | 706 |
CLXXIII | 712 |
CLXXIV | 717 |
CLXXVIII | 718 |
CLXXIX | 719 |
CLXXX | 749 |
CLXXXI | 752 |
CLXXXII | 761 |
CLXXXV | 762 |
CLXXXVI | 763 |
CLXXXVII | 767 |
CLXXXVIII | 771 |
CLXXXIX | 774 |
CXC | 775 |
CXCIII | 777 |
CXCIV | 778 |
CXCV | 783 |
CXCVIII | 784 |
CXCIX | 785 |
CC | 786 |
CCI | 787 |
CCII | 789 |
CCIII | 790 |
CCIV | 793 |
CCVII | 794 |
CCVIII | 811 |
CCIX | 818 |
CCX | 823 |
CCXIII | 825 |
CCXIV | 827 |
CCXV | 828 |
CCXVI | 831 |
CCXVII | 833 |
CCXX | 834 |
CCXXI | 838 |
CCXXII | 843 |
CCXXIII | 847 |
CCXXV | 848 |
CCXXVI | 856 |
CCXXVII | 863 |
CCXXVIII | 867 |
CCXXXI | 869 |
CCXXXIII | 873 |
CCXXXIV | 876 |
CCXXXV | 878 |
CCXXXVI | 880 |
CCXXXVII | 881 |
CCXXXVIII | 883 |
CCXXXIX | 887 |
CCXLII | 889 |
CCXLIII | 892 |
CCXLIV | 896 |
CCXLV | 897 |
CCXLVI | 900 |
CCXLVII | 903 |
CCL | 905 |
CCLI | 906 |
CCLII | 911 |
CCLIII | 914 |
CCLIV | 919 |
CCLVII | 921 |
CCLVIII | 922 |
CCLIX | 927 |
CCLX | 943 |
CCLXI | 957 |
CCLXIV | 958 |
CCLXV | 959 |
CCLXVI | 962 |
CCLXVII | 967 |
CCLXVIII | 970 |
CCLXIX | 972 |
CCLXX | 975 |
CCLXXI | 985 |
CCLXXII | 987 |
CCLXXIII | 990 |
CCLXXIV | 996 |
CCLXXV | 1011 |
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Common terms and phrases
algebraic angle arcsin arctan arithmetic axis calculation circle coefficients complex numbers convergence coordinate system cos2 cosh cube cubic equation curve decimal denoted derivative determine diagonal differentiation digits distance elements ellipse equal equation Euler factors formula fractions geometry graph Greek hyperbola hyperbolic imaginary unit infinite integer integral intersection interval inverse Latin Leibniz length Leonhard Euler logarithms magic square mathematician mathematics matrix method multiplication natural logarithm natural numbers notation origin orthogonal coordinate parabola parametric equations plane polynomial positive Pythagorean quartic equation radius real numbers roots secant sequence sides sine sinh solid of revolution solution solved spherical straight line subset subtraction symbols tangent theorem triangle trigonometric functions variable vector vertex vertices vigesimal x-axis y-axis zero π π ду дх