SUBJECT INDEX. 



For classification of Diophantine equations, see Table of Contents. 



Abel's theorem, 501, 581 



Abelian integral, 641 



Abrade, 42, 348 



Additive, 41-3, 346-8 



Affected square, 348 



Algebraic numbers, 237, 253, 

 271, 314, 327, 393, 396, 398, 

 399, 412, 421, 477, 534, 

 536-8, 541-2, 546, 549, 550, 

 567, 569, 570, 573-4, 578-9, 

 593-5, 615,674,677-8,691, 

 696, 738-742, 745, 755, 757- 

 9, 761-5, 767-8, 77(>-l, 775 

 (see class, norm, unit) 



, conjugate develop- 

 ments of, 674 



Analytic functions, 162, 725 



Apocalyptic, 5 



Apocopation, 137 



Approximating fractions, 390, 

 412 



Approximation, 93-9, 361, 

 378 



to fractions, 47, 50, 93, 96, 

 98 



square roots, 341-2, 



346-7, 350-1, 354-6, 378, 

 390, 408 



Arithmetical progression, 1, 

 2, 6, 36, 47, 82, 107, 116, 

 124, 128, 143, 286, 322, 

 419, 440-1, 443-4, 446, 

 450, 452, 454, 456-8, 522, 

 582-8, 595, 602, 604-5, 

 612, 670, 680-1, 702, 710, 

 716, 762, 181 (see rational, 

 squares, sum) 



, sum of terms of, equal 



to o, 112, 118, 127, 130, 

 161, 166 



series of order n, 18 

 Astronomy, 41, 61-2 

 Asymptotic, 162, 172, 246, 



249, 253, 255-7, 272-3, 

 318, 725 (see limit, mean) 

 Augment, 41 

 Automedian, 205, 439 

 Automorph, 248, 297, 430, 

 594, 677 



Bachet's theorem, 275 



Ballots, 154 



Bernoullian function, 153 



numbers, 127, 161, 741-2, 

 744-5, 761, 768, 773, 775 



Bertrand's postulate, 679-681 



Bessel's functions, 256 



Bible, 5 



Bicursal curve, 676 



Bilinear form, 268 



Binomial coefficient, 4, 5, 7, 

 9, 18, 20, 39, 106-7, 114, 

 126, 127, 144-7, 149, 155, 



164, 599 (see figurate, tri- 

 angle of Pascal) 



, every number a sum 



of, 144 



Bipartition, 153 



Biquadrate, 437, 717 (see 

 difference, sum of squares) 



Biquadrates, relations be- 

 tween, 564, 647-657, 663 



and squares, 489, 



646-8, 656-660, 665 



, sum of 2, not a square, 

 615-620 



three, 38, 684, 753 



, two equal sums of two, 

 644-7 



Biquadratic residue, 370, 630 



Birational transformation, 

 568, 592, 676 



Bonds, 149 



between atoms, 131 



Cattle problem, 342-5 



Cecis (see Coeci) 



Chessboard, 162, 245 



Chinese problem of remain- 

 ders, 57-64 



Circle (see rational) 



Circulating function, 115, 

 117, 119, 161 



Circulator, 119-121, 159 



Class number, 550, 741, 745, 

 755, 763, 767-8, 775 



Coeci rule, 79-81 (see virgins) 



Colonne, 6 



Combinations, 114, 124, 128, 

 132-3, 144, 154-5, 163 



Combinatory analysis, 36, 

 141, 145, 151, 161-2 (see 

 partition) 



Complex number, 95, 97, 

 119, 121-2, 125, 162, 168, 

 170, 201, 231, 234, 237, 

 239-242, 247-9, 254-5, 274, 

 283, 287, 289, 296-7, 315, 

 371, 373-4, 376, 389, 397-8, 

 411, 431, 548, 572, 594, 

 620, 678, 684, 692, 716, 

 725,740,757 



Composite, 12, 15, 28, 229, 

 376 



Composition, 145, 147, 149, 

 151, 157 (see product) 



into squares, 296, 305 



of two forms x 2 ey 2 , 

 346-8, 355 



Concordant forms, 472-7 

 Configuration, 149, 592 

 Congruence, 19, 33, 87, 408, 

 673, 678, 684, 687, 692-3, 

 700, 758, 761, 766, 771-2, 

 775 (see lineor, quadratic) 



x n + 2/" + n = 0, 734, 



799 



736, 750, 753, 756-7, 762-5, 

 769, 770, 774 



l + g"> = g" } 739, 743, 75G 



Al m + Bu n + Cv l = 0, 

 749, 751, 764, 773-4 



Congruent number, 174, 435, 



459-472, 615 

 of order n, 472, 701-3 



to a sum, every number, 

 86,87 



Continuant, 183, 244, 254, 

 381 



Continued fraction, 19, 21, 

 32, 47^9, 51-54, 68, 72, 

 75, 93-94, 99, 149, 182, 

 198, 219, 233, 237-8, 240, 

 242-4, 250, 267-8, 295, 344, 

 350-3, 355-8, 361, 364-5, 

 367-372, 374-401, 408-412, 

 417-8, 473, 540, 587, 641, 

 673, 686, 762 



, bracket notation in, 



49, 149, 240, 357 



, negative, 379, 381 



Contra variant, 431 



Covariant, 120, 133, 161, 568 



Cremona transformation, 85, 

 320 



Cube, 6, 8, 23, 25, 28, 33, 35, 

 38, 177-180, 187, 246, 

 251-2, 255-7 (see differ- 

 ence, every, numbers, sum) 



not a sum of 2 cubes, 

 545-550 



of sum of n numbers plus 

 any one a cube, 607-12 



Cubes, equal sums of, 550- 



562 

 , relations between, 562-6, 



613 

 Cubic equation, 220, 545- 



613, 661 (see discriminant) 



form, binary, 538, 575, 662 



made a cube, 566-9 



a square, 569- 



572, 640 

 , ternary, 588-595, 695 



function made square, 457 



residues, 575 

 Cuttaca, 42, 58 



Cyclic method, 63, 346-8, 

 349, 386 



Cyclotomy, 243, 251, 295, 

 370-2, 376, 398, 736, 750, 

 753-4, 763, 765, 769, 770 



Decomposition into maxi- 

 mum squares, 309, 310 



triangular numbers. 



32 



powers, 686 



Definite polynomial, 720, 722, 

 723-4 



