802 



SUBJECT INDEX. 



, number of ways a, 3, 



7,11 



of second order, 5, 10 

 , sum of powers of, 30, 34 

 - numbers, g.c.d. of two, 36 

 - of m sides, every num- 

 ber a sum of m, 6, 12-14, 

 16-18, 29-32, 309 



, sum of, 2, 5, 19, 20, 22, 



25, 26, 28, 29, 34, 35, 37 



residues, 33 

 Polyhedral, 16, 17, 24 

 Polynomial in a + b and 



ab equal to a" + b n , 737, 

 739, 745 (see equation) 

 Primes, 11, 36, 148, 234, 252, 



260-1, 264, 266, 396, 681 

 , sum of two, 282 289 

 Prize, 312, 641, 734, 742, 751, 



763 



Probability, 28, 158, 214 

 Product of 2 forms a like 

 form, 431, 470, 570, 594-5, 

 678, 691, 697, 727-8 

 consecutive integers, 



9, 56, 393, 679-682 



factors (x + l)/x, 687-8 



Products by twos plus n 



made squares, 513-520 

 Pronic, 5, 6, 232-3, 350, 407 

 Pulverizer, 41-44, 59, 348 

 Pyramid, rational, 221-4 

 Pyramidal number, 1-5, 7, 9, 



10, 14, 16-18, 20, 25, 30, 34 

 , central, 5 



, every number a sum 



of, 14, 23, 30 



, not a cube, 25, 34 



Pyramidi-pyramidal, 7 



Quadratic congruence, 19, 

 279, 280, 282-8, 295-7, 

 299-303, 325-7, 384, 408, 

 693, 749 



equation in x, y, 412, 485 

 (see equation) 



in n ^ 3 unknowns, 

 419-434 



Quadratic form, binary, 11, 

 17, 26, 94, 184, 233, 236, 

 239, 242, 247, 254, 260-3, 

 265, 269, 273-4, 331, 356, 

 359, 362, 364-5, 367, 370, 

 372, 374-9, 381, 386, 391-2, 

 398, 401-2, 404-6, 408, 

 410-1, 417-8, 430, 507, 

 536-7, 541-2, 549, 553-4, 

 559, 578-9, 619, 637, 657, 

 697, 699, 707, 712, 733, 

 741, 760 (see composition) 

 , ternary, 17, 260, 264-5, 

 272-3,282,287,291,294-5, 

 379, 422, 424, 429, 430-1 



in n ^ 4 variables, 

 263, 288, 308, 311, 313, 

 330, 332, 335-7, 387, 431, 

 433, 543, 724 (see every) 



function = cube, 28, 

 533-9 



= power, 533-544, 662, 



764 

 = square, 10, 13, 19, 



341-401, 404-7, 438, 445, 



459-532 

 = constant, 407-412 



residue, 231, 241, 253, 279, 

 282, 284, 287, 292, 296, 

 299, 301, 325-6, 365, 370-1, 

 378, 421-4, 432, 476, 630, 

 751, 766 



Quadrilateral, 201, 211, 216- 

 221, 223, 255, 449, 680 



Quartic equation, 465, 485, 

 615-671 



form a square, 567, 632, 

 627-644, 732, 746-8 



, 571 



Quaternion, 297 

 Quotity, 119 



Rational group of points, 



676-7 

 Rational oblique triangle, 



191-214, 220, 668 

 , circumscribed circle, 



191, 195-6, 200-1, 211 



, escribed circles, 

 195, 200-1, 213 



, Feuerbach's circles, 



201 



, inscribed circle, 

 194-7, 200-1, 208, 211, 

 215, 693 



, isosceles, 201, 211 



, Malfatti's circles, 



197 



, perimeter, 193, 

 195-7, 199, 200-1, 212 



, rational angle- 

 bisectors, 210-3 



medians, 207-9, 



212-3, 511 

 , sides in arithmetical 



progression, 192, 196-9, 



200-1, 214-5 

 Rectangles, ratio of area 



given, 485-7 

 Recurring series, 36, 75, 110, 



366, 391, 674, 695-6 

 Reduced multiplier, 41 

 Regular prime, 741, 745, 757, 



759, 762, 767, 775 

 Remainders, 57 

 Representation by squares, 



296, 305 

 Right triangle, 165-190, 273, 



459, 463 



, area given, 465, 615 



not a square, 462, 



615-620 



- formed from 2 num- 

 bers, 166 



, primitive, 166, 459 

 , problems involving 



area of, 166, 175-181, 



498, 533, 617, 634 



- sides, but not 



area, 184-8, 620-7 



, product of sides divis- 

 ible by sixty, 171 



, rational angle-bisec- 

 tors, 188-9 



triangles, areas in given 

 ratio, 174, 474, 494-5 



, number of, with given 



side, 172 

 , of equal area, 172-4, 



525 



hypotenuses, 225 



, tables of, 189, 190 



with given difference 



or sum of legs, 181-4 

 Roots of unity (see cyclot- 



omy) 



Satin, 87, 245 



Seminvariant, 124, 142, 571, 

 643 



Separations, 151, 156, 161 



Series of L. Pisano, 170 



Slide rule, 694 



Sophien, 769 



Spherical triangle, rational, 

 224 



Square, 1-4, 7, 8, 12, 16, 20, 

 26, 27, 31, 32, 176 (see 

 decomposition, differences, 

 every, number, sum) 



roots (see approximation) 

 Squares in arithmetical pro- 

 gression, 186, 435-440, 443, 

 446, 489, 492, 498, 527, 

 604, 617, 635 



geometrical progres- 

 sion, 441 



, sum of two less third a 

 square, 507-9 



, sums by twos squares, 

 497-502, 529 



, linear functions of, made 

 squares, 502-511 



Sum and difference of two 

 squares not squares, 618 



of any 2 of 4 integers a 

 cube, 561 



consecutive integers, 



139, 159, 160, 162 

 cubes of numbers in 



arithmetical progression a 



cube, 582-5, 685 

 a square, 



585-8, 685 

 2 cubes a square, 572, 



578-581, 587, 600, 752, 



758 

 3 cubes a square, 566, 



605-6 



- a sum of 2 



squares, 588 

 n cubes less g a square, 



607-612 

 divisors, 19, 24, 31, 



125, 140, 244, 246, 250, 



264, 266, 269, 285, 289, 



296, 305-317, 329-339 

 m m-gonal numbers 



(see polygonal) 



