SUBJECT INDEX. 



801 



108, 111, 113, 115-6, 119, 

 120, 127, 137, 140-1, 143, 

 146, 148-9, 155, 160, 162-3, 

 235-6, 240, 243, 245, 254, 

 262, 265, 277, 283, 285, 

 292, 297, 305, 313, 333, 

 337-8, 380, 399, 403, 411, 

 562, 714-6 



Integration, 51, 256, 266, 

 566, 685, 722-3, 749, 751 



Invariant, 92, 433, 571, 592-3, 

 643-4 



Inverse tangent, 395, 716 



Irrational, 93-99 



Irreducible, 674, 695 



Isobaric function, 132 



Jacpbi symbol (see Legendre) 

 Julian period, 61, 62 



Knots, 144 



Latin square, 154 



Lattice, 51, 52, 66, 68, 87, 



95, 98, 160, 162, 168, 236, 



241, 245, 257, 724 

 Legendre-Jacobi symbol 



(m/n), 248, 253, 263-4, 



305, 308-9, 312-4, 325-7, 



370, 372, 386, 431 

 Lemniscate, 389, 398 

 Like powers, relations be- 

 tween, 585, 648, 682-6, 



705-716 

 Limit, 97, 155, 158, 254, 272, 



377, 399, 400, 404, 675, 686, 



723 

 Linear congruence in one 



unknown, 47, 52, 54-64, 



693 

 , improper or 



imaginary solutions of, 55 

 in several unknowns, 



86-88 



congruences in n un- 

 knowns, 83, 88-93, 423-4, 

 426 



difference equation, 107- 

 111, 115, 158, 368 



differential equation, 144, 

 393 



Linear equation in 2 un- 

 knowns, 41-71, 91 



, number of 



solutions, 50-1, 64-71, 130 



in 3 unknowns, 52, 55, 



71-73 



, number of 



solutions, 121, 126, 128, 

 130, 132, 141,145, 152, 160 

 (101-164, implicitly) 



in n unknowns, 41, 43, 



73-77, 133, 143, 161 



, number of 



solutions, 109, 114, 119, 

 122, 125-7, 130-1, 134, 

 140, 142, 155-6, 164 



Linear equations, system of, 

 in 2 unknowns, 66-8 



- in n unknowns, 

 73, 77-86, 150, 342 (see 

 multipartite) 



, number 



of solutions, 106, 123, 144, 

 149 



, fun- 

 damental solution, 75-6, 

 83-4 



, irreduc- 

 ible solution, 85 

 - form, 93-99 



forms, system of, 84-86, 

 90, 93-98 



, sum of powers of, 95, 



96 



functions made squares, 

 440, 443-458 



, product of, 677-9 



inequality, 52, 135, 153, 

 156, 161 



Logarithms, 714-6, 741,744-5 

 Lucas' u n , v n , 542-3, 698 



Magic square, 6, 118, 134, 



154, 156, 163 

 Malfatti's circles, 197 

 Matrix, 82-85, 90, 91, 95, 134, 



139, 153 



, augmented, 83, 84, 90 

 , rank of, 84, 90, 91, 95 

 Mean value, 28, 32, 140, 234, 



246, 311, 411, 751 (see 



asymptotic) 

 Minimum, 94-99, 288, 364, 



374, 408, 540, 673 

 Mobius' function n, 701 

 Modul of Dedekind, 92 

 Modular equation, 389 



system, 85, 91 

 Multipartite, 123, 145, 147, 



150-2, 160-2, 163 



Node, 139 



Norm, 283, 296, 373, 398, 570, 



593-4, 677-8, 740 

 Number and its square sums 



of 2 consecutive squares, 



477, 488-9, 670 

 Number of divisors, 67, 129, 



139, 142, 162, 235-6, 238-9, 



242-3, 248, 250, 265, 297, 



313, 403-4 



Fibonacci, 439 



form 4a6 (a 2 - 6 2 ), 459 



, quotient a 

 square, 474, 494-5, 661 



sets of k integers < x 



and prime to x, 701 

 solutions of Ui ... Uk 



= n, 157, 403, 679 

 Ax a + By b = n, 



751 

 Numbers a sum of 2 rational 



cubes, 572-8, 729 

 cubic functions, 



578 

 unlike powers, 



725-6 



Oblique triangle, 214-6 (see 

 rational) 



, autornedian, 205, 439 

 , linear relation between 

 angles of, 213-4 



, rational angle-bisec- 

 tors, 209-213 



- medians, 202-9, 212, 

 428 



Octahedral, 16, 23 

 Optic formula 1/z + l/y = 



I/a, 688-691 



Orthogonal substitutions, 

 530-2 



Pack of cards, 157 



Parallelogram, rational sides 

 and diagonals, 205-6 



, Heron, 207 



s, ratio of areas given, 

 486 



Parallelepiped, 267, 487, 502, 

 613, 670 



Partition, 101-164, 250, 270 

 (see bipartition, circulating, 

 circulator, combinations, 

 combinatory, composition, 

 distributions, generating, 

 multipartite, permutation, 

 separations, symmetric, 

 variations, wave) 



, compound, 123, 141 



, conjugate, 121, 124, 136, 

 139, 154, 163 



, double, 123 



, graph of, 118, 134, 137, 

 139, 141, 142, 147, 151-4, 

 158, 160 



into squares, 296 

 , modulo M , 88 



, new definition of, 161 



, perfect, 143, 145 



, regularized, 139, 141-2, 

 152 



, self -con jugate, 136-7, 141 



Pell equation, 341-400 



, upper limits for solu- 

 tions, 399, 400 



in polynomials, 389, 



390, 393-4, 397, 743 



Pentagon inscribed in circle, 

 202, 221 



Pentagonal, 1, 2, 5, 6, 8, 10, 

 11,13,16,18-20,22,23,25, 

 26, 28, 29, 31, 33-35, 37, 

 113, 147 



Permutation of letters, 114, 

 131, 147, 155, 157, 162 



Pile of bullets, 25 



Planude, problem of, 485-7 



Polygon, 56, 147, 386, 543, 

 688 



, rational inscribed, 221 



Polygonal divisors, 32 



number, 1-7, 9-22, 24, 28- 

 39, 117, 147 



, central, 5, 10, 12, 16 



equal square, 3, 10, 11, 



13, 38 



