SUBJECT INDEX. 



803 



2 squares, 11, 15, 23, 



27, 32, 33, 36-38, 68, 

 225-257, 308, 317, 321, 

 322, 345, 348-9, 359, 364-5, 

 372, 373-4, 383, 385-7, 394, 

 399, 400, 405, 407, 533, 703, 

 716 



a square, 23, 190, 



446, 466, 483, 497, 527, 

 601-2, 613 (see right tri- 

 angle) 



^V, 234, 236, 



249, 253-7 



3 squares, 11, 15, 17, 



21, 23, 233, 244, 259-274, 

 276, 278-9, 282, 322, 335, 

 350, 385, 605, 718, 720 



a square, 222, 



249, 260-2, 265-9, 271-4, 

 443, 456, 502-5, 668-9 



a sum of two, 



244, 267-8, 272-274, 384, 

 434 



<#, 271-3 



4 squares, 6, 15, 18, 24, 



33, 233, 250, 261, 267, 270, 

 273, 275-303, 307-8, 310, 

 312, 314, 316-7, 320-2, 329, 

 330, 339, 428, 529, 649, 

 666, 718-9 



with given alge- 

 braic sum of roots, 25, 278 

 -9, 284, 289, 291-4, 319 



n squares, 17, 22, 



25-27, 32, 37, 253, 273-5, 

 305-323, 329, 331-2, 334-5, 

 339, 453, 544, 585, 660, 

 664, 705-712, 720 



a square, 318-323, 



425, 434, 509, 612 



, power of, 319, 



321-2 



squares a biquadrate, 



620-7, 665-7, 670 



Summation over divisors, 

 329-339 



Sums of 2 squares, two equal, 

 206, 225-7, 229, 232-3, 

 237, 245, 248, 252-4, 256-7, 

 268, 273, 283, 345, 347, 

 426-8, 436, 447, 450, 452, 

 455, 457, 492, 494-5, 497, 

 499, 500, 504, 525 



, quotient of, 

 252-3 



3 squares, two equal, 



260, 264, 267-9, 270-4, 284, 

 299 



, product of two, 



a sum of 3 squares, 263, 

 267-271, 273 



not a sum 



of 3 squares, 261 



4 squares, two equal, 



277-8, 284, 291-2, 298-9, 



303 



, product of two, 



a sum of 4 squares, 277, 



281, 283, 291, 293, 298, 



302-3, 530-1 

 n squares, product of 



two, 285, 318, 323 

 , quotient of two, 



314 

 Symbols, p' m , 1, 3; P r m , 2, 4; 



Ar. A(r), A, A' 6; A_ m , 16; 



Li, LJ, El, \*\, 6;/ r n, 7; 

 (?), 7; [n], 54; 0(x), 255; 

 (a/6) of Legendre and 

 Jacobi, 366, 370; (a, b, 

 . . . ) and {a, b, . . . } 

 in continued fractions, 49, 

 357; (0/6)4, 370; i, 705; 

 q(m), 768 



Symbolic, 30, 154, 722, 768, 

 773 



Symmetric function, 101, 122, 

 144-5, 154, 160 



Syzygy, 76, 161, 571, 643 



Table, 2, 12, 15, 20, 34, 38, 

 51, 104-5, 117, 125, 127-9, 

 133, 136, 141, 144, 155, 

 163, 179, 183, 189, 190, 

 192, 195-6, 198-200, 219, 

 225, 232-3, 236-7, 241, 

 251-2, 257, 271, 274-5, 

 290, 297, 353-358, 363, 

 366, 368-370, 373, 375, 



377, 379, 380, 386, 388, 

 389, 391, 394, 396, 398-400, 

 407, 435, 448, 459, 462, 

 464, 471, 473, 485, 494, 

 538-9, 541, 564, 573-4, 

 634-5, 650, 653, 656, 683, 

 688, 717, 719, 739, 722 



T'ai-yenrule, 57, 59, 60 

 Tangent method, 174, 558, 



576, 590-2, 595, 661 

 Tangential, 591-2 

 Tetradecagonal, 5 

 Tetragone, 7 



Tetrahedral, 4, 7, 23, 25, 36 

 Tetrahedron, 502 

 , rational, 220, 222-4 

 Theta functions, 113, 254, 



273-4, 300, 303, 314, 316, 



378, 398 



Toroid, 566 



Transversion, 137 



Triangle (see oblique, ra- 

 tional, right) 



of Pascal, 4, 9 



Tartaglia, 36 



Triangular number, 1-39, 

 103, 130, 152, 248, 260, 

 276, 289, 292, 342-4, 401, 

 407, 435, 574, 587, 664, 707 



equal to a difference of 



biquadrates, 35 

 cubes, 36, 



37 



a pentagonal 

 number, 18, 19, 22, 33, 35 



a square, 3, 7, 10, 



13, 16, 26, 27, 31, 32, 38 



of a trian- 

 gular number, 27, 36, 37 



not a biquadrate, 8, 10, 



17, 22, 25, 36 



- a cube, 10, 17, 25, 33 



numbers, consecutive, 2, 



27, 30, 33, 38 



, difference of, 9, 24, 26, 



33-35 

 , product of, 12, 29, 



31, 33-36, 38 

 , sum of squares of, 5, 



12, 23, 26, 27, 33 

 , sum of two, 2, 9, 11, 



12, 15, 24, 26, 27, 30-32, 34, 



36-38 

 three, 6, 11-13, 



15-18, 20, 24, 26, 28, 29, 



31, 33-35, 37, 38 

 four, 19, 20, 23-26, 



32 

 n, 4, 19, 22-24, 



28, 30, 32, 34-37, 130 



certain and 

 squares, 2, 5, 12, 15, 20, 23, 

 26, 36-38 



gives 



every number, 11, 15, 23, 

 24, 26 



Triangular-pyramid, 2, 4, 9 



Trianguli-pyramidal, 7 



Triangulo-triangular, 7 



Trigone, 7 



Trihedral angle, rational, 221, 

 224, 502 



Triple equation, 445 



Unicursal curve, 642, 676-7 



surface, 677 



Unit, 396, 399, 412, 536, 578, 

 594, 741-2, 755 



Variations, 140, 154 

 Virgins, 79, 106, 123 (see 

 Coeci) 



Waring's problem, 717-725 

 Wave, 119, 121, 124-5, 135, 



155, 159 

 Wilson's theorem, 56-7, 232, 



243, 255 

 Weierstrass' normal form of 



quartic, 224, 644 

 Wunder Zahl 666, 5, 6 



Zeta function, 725 



