Differential equations, simultaneous system of, Hamiltonian Q.14
Differential equations, simultaneous system of, integration and inversion of the integrals C.23
Differential equations, simultaneous system of, Jacobi's CD.3
Differential equations, simultaneous system of, method of multipliers 3353
Differential equations, simultaneous system of, number of arbitrary constants Me.77
Differential equations, simultaneous system of, reduction of order 3350
Differential equations, simultaneous system of, reduction to a P.D. eq C.44
Differential equations, simultaneous system of, theorem analogous to Lagrange's in the Perturbation theory L.51
Differential equations, simultaneous system of, theorem of a new multiplier J.27
Differential equations, simultaneous system of, theorem of Abel C.24
Differential equations, simultaneous system of, transformation and integration of L.45
Differential equations, singular solution of 3169—3178 3301—3306 3401—3403 C.19 94 CM.2 JP.18 M.22 Man.83 84 Q.12 14
Differential equations, symbolic methods 3470—3636 CD.1 P.61 Q.3 17
Differential equations, symbolic methods to reduce a homog. eq. to the form 3585
Differential equations, symbolic methods to transform into the symbolic form, and the converse 3571 3573
Differential equations, symbolic methods to transform 3579—3580
Differential equations, symbolic methods, 3531
Differential equations, symbolic methods, 3535
Differential equations, symbolic methods, 3515
Differential equations, symbolic methods, 3558
Differential equations, symbolic methods, 3541
Differential equations, symbolic methods, 3575
Differential equations, symbolic methods, and similar 3522
Differential equations, symbolic methods, 3540
Differential equations, symbolic methods, exceptional case of the inverse process 3526
Differential equations, symbolic methods, reduction of an integral of the nth order 3530
Differential equations, symbolic methods, Reduction to the form 3546
Differential equations, synectic integrals of C.40
Differential equations, transformation of An.52 CD.9
Differential equations, transformation of, in curvilinear coords J.85
Differential equations, whose integrals are satisfied by the periodicity modulus of elliptic integrals of the first kind J.83
Differential equations, whose integrals satisfy relations of the form C.93
Differential expressions 1407 prAn.85
Differential expressions, algebraic An.79
Differential expressions, algebraic, by homog. cords M.9
Differential expressions, linear J.85
Differential expressions, transf. of J.85 Q.16 Mo.69
Differential formulae, theory of L.52
Differential functions, theory of C.60
Differential parameters of functions C.66 78
Differential quadratic forms An.84
Differential quadratic forms, transformation of A.16
Differential resolvents of Me.82
Differential resolvents of Q.17
Differential resolvents of &c. 3633—3636 Man.65
Differential resolvents of alg. eqs 3631—3637 An.83 C.91 LM.1 9 14 M.geo4 18 Me.75 82 Man.65 84 Q.6 11
Differentiants in terms of differences of roots of parent quantities AJ.1
Differentiation 1402—1482 CM.1 see
Differentiation by the method of "Rates" Me.75
Differentiation under the sign 2253 A.17
Differentiation when the function becomes infinite C.88
Differentiation, formulae 1411—1472 An.59 CD.2 CM.1 Pr.9
Differentiation, general, i.e., with any fractional or imaginary An.58 AJ.3 CD.3 4 5 J.12 JP.13 L.55 N.84 Q.3 4 TE.14 15 Z.16
Differentiation, general, i.e., with any fractional or imaginary, change of independent variable JP.15
Differentiation, successive A.20 Q.12
Digits, calculus of, Sbonimsky's th J.30
Digits, frequency of in numbers AJ.4
Digits, origin of L.39
Diophantine analysis see "Partition of numbers"
Direction ratios and cosines 5511—5514
Directive algebra N.68
Directrix of a conic 1160 gn.eq E.36 Me.80 t.c
Directrix of a curve A.20 J.2
Directrix of a parabola gn.eqE.29
Directrix of a quadric N.74 75
Directrix of in-parabola of a triangle Me.80
Discontinuity in curves CM.4 Z.26
Discontinuity in fractions Man.48
Discontinuity in maxima and minima CD.3
discontinuous functions A.7 C.15 28 G.19 J.7 10 LM.6 Man.48 TI.21
Discriminant 1627 1638—1639 1644 Ac.1 J.90 LM.2 M.12 N.59 Pr.14 Q.10 11
Discriminant of a binary sextic An.68
Discriminant of a quartic N.83
Discriminant of a ternary quadratic form Me.68
Discriminant of alg. eqs., resolution into factors M.24
Discriminant of alg. functions J.91
Discriminant of an algebraic d.e of 1st order in 4 variables, and of its complete primitive An.84
Discriminant of binary quantic An.56
Discriminant, applied to conics and quadrics A.58
Discriminating cubic 1849 5693 G.16 J.26 71
Discriminating cubic, proof of real roots 1850 A.29
Displacement of a figure, two of whose points slide on two curves C.82
Displacement of a solid L.40
Displacement of a solid, determination of the normals to the lines or surfaces described C.62
Displacement of a system of points C.78
Displacement of a system of points, virtual displacement J.11
Displacement of an invariable dihedron Me.85
Displacement of an invariable dihedron, infinitesimal ditto C.84
Displacement of an invariable figure C.51 52 66 92 JP.26 L.74 75
Displacement of plane figures C.80 N.73
Displacement, infinitesimal, of a parallelogram C.97
Displacement, infinitesimal, of an alg. surface C.70
Displacement, infinitesimal, of bodies only defined by 4 coordinates C.73
Displacement, theory of N.82
Distance between 2 points 4034—4035 t.c Q.7 sd5508 5510
Distance between 2 points, some relations G.9
Distance of a point from a line and from a plane A.57
Distance of a point from a plane in a given direction 5559
Distance, correspondences for quadric surfaces LM.16
Distance, relations Z.27
Distributive law 1488
Divisibility C.96 E.8 M.39 N.67 74
Divisibility of Me.79
Divisibility of a quotient by the powers of a factorial C.94
Divisibility of decadic numbers Z.22
Divisibility of numbers of the form Mel.5
Division prJ.47 prL.56
Division and transformation of plane figures A.4
Division by 73 or 47; rule for remainder E.22
Division of a rectilineal figure and of a spherical polygon J.10
Division of a right line into equal parts 950
Division of planes and spaces J.1 2
Division of trapeziums, pyramids, and spheres A.11
Division of triangles A.11 17
Division, abridged 28 arithj.31 N.45 46 52 54 57 81 algN.42
Division, effected by determinants 581
Division, Fourier's rule N.52
Divisors of L.49
Divisors of a polynomial with commensurable coefficients N.75
Divisors of an integer, number of 374 C.96 N.68
Divisors of integral rational functions Mem.57
Divisors, Newton's method of 459
Divisors, rational, of 2nd and 3rd degree N.45
Divisors, sum of 377 Ac.f4 L.56 57
Divisors, sum of powers of L.58
Double algebra LM.15
Double function, laws of change of higher order A.21
Double point, Clebseh's ths of these quantics C.84
Double points 5178
Double points in a locus defined by alg. conditions C.88
Double points in the projected intersection of 2 quadrics N.84
Double points of a pencil of curves An.64
Double points of plane curves in cubic space Z.28
Double points of tortuous curves M.3
Double points with M.2
Double points, n-tic with double points L.80
Double points, n-tic with C.60
Double relations A.60
Double tangents An.51 J.49 P.59 Q.4 Z.21
Double tangents of a Cartesian E.30
Double tangents of a quartic C.37 J.49 55 68 72 M.1 N.67 P.61 Pr.11
Double tangents of a quartic with a double point, reciprocity of 28 double tangents M.4 6
Double tangents of an n-tic M.7
Double tangents of an n-tic, J.40 63 N.53
Double tangents to the surface of centres of a quadric C.78
Drilling, shape of hole Pr.35
Dual relation between figures in space J.10
Duplication of the cube, approx. Pr.20
e 151 N.67 68 see
e and , numerical th Q.15
| e, combinatorial definition of A.1
e, geo meaning E.4 N.55
e, incommensurable 295 CM.2 L.40 Me.74
Edge of regression 5729 tg.eC.71
Edge of regression, radius of curvature of 5742
Eisenstein's theorem G.16
Elastic curve C.18 19 JP.34
Elementary calculation N.45
Eliminants 583 1626
Eliminants and associated roots LM.16
Eliminants of two cubics J.64
Eliminants, degree of G.11
Eliminants, degree of, two eqs 12 J.22 31
Elimination 582—594 A.2 Ac.6 7 C.12 87 90 CD.3 6 CM.3 G.15 17 J.34 43 60 JP.4 L.41 44 LM.11 M.5 11 N.42 45 46 80 82 83 Q.7 th12 Z.23
Elimination of functions 3153 C.84 87 Me.73 76
Elimination of x between two equations 586—594 C.12 CM.2 J.15 27 Mo.81 N.43 76 77
Elimination of x between two equations by Bezout's method 586 A.79 J.53 Me.64 N.74 79
Elimination of x between two equations by cross multiplication CM.1
Elimination of x between two equations by h.c.f 593 JP.8
Elimination of x between two equations by indeterminate multipliers CM.1
Elimination of x between two equations by symmetrical functions 588
Elimination of x between two equations by the dialytic method 587 N.79
Elimination of x between two equations in geodetic operations Z.3
Elimination of x between two equations, degree of the final equation J.27 L.41
Elimination with linear differentials L.36
Elimination with linear equations At.53
Elimination with n variables CP.5
Elimination, ap to alg. curves M.4
Elimination, ap to in- and circum-conics of a polygon At.63
Elimination, calculation of Sturm's functions C.80
Elimination, problems C.84 97 J.58 M.12 Q.8 11
Elimination, problems in metrical geo A.63
Elimination, resultants, comparison of J.57
Elimination, resultants, comparison of, and interpolation J.57
Elimination, transformation and canonical forms CD.6
ellipse 1160 4250 cn1245 geoQ.9 see
Ellipse and hyperbola 1160 4250 A.24 28
Ellipse and hyperbola, sectors TE.14
Ellipse and hyperbola, theorems A.23 CM.3 N.85
Ellipse and triangle thQ.4
Ellipse as the projection of a circle 4921 N.75
Ellipse of maximum surface N.65
Ellipse, eq. r+r'=2a A.2
Ellipse, equal chords tg.eE.22
Ellipse, quadrature of 6108 6113 t.c A.46
Ellipse, quadrature of sector 6098 A.20
Ellipse, quadrature of segment 6103
Ellipse, rectification of 6083—6096 A.3 22 27 30 At.39
Ellipse, rectification of, graphic Mel.1 N.43 TE.4 Z.6
Ellipse, rectification of, graphic when e is very small TI.9
Ellipse, representation by a circle An.70
Ellipse, theorems A.30 47 prs49 N.76
Ellipse, theorems, Mc Cullagh's N.72
Ellipsoid 5600 6132 A.28 thCD.2 prC.20 L.38 cnM.20 P.9
Ellipsoid and enveloping cone 5664—5672 Q.6
Ellipsoid and plane of constant segment, th E.32
Ellipsoid of gyration 5930
Ellipsoid of inertia 5925—5939
Ellipsoid of revolution 5604
Ellipsoid of revolution, area N.42
Ellipsoid, a locus in space Q.16 17
Ellipsoid, centro-surface CP.12 LM.3
Ellipsoid, cubature of some derived surfaces A.12
Ellipsoid, generation of (Jacobi) CD.3
Ellipsoid, quadrature of 6143 J.17 Z.1
Ellipsoid, quadrature of zone A.22
Ellipsoid, volume 6144 6148 A.46
Ellipsoidal geometry A.10 LM.4
Ellipsoidal geometry, surfaces G.17
Elliptic functions 2125 A.1 12 16 21 35 48 trAc.5 6 ths7 An.61 84 C.46 50 90 96 97 CD.2 3 5 CM.3 E.23 G.1 J.2 3 4 6 8 16 26 27 30 32 35 37 39 46 72 83 JP.25 L.55 56 61 LM.7 10 29 M.3 11 12 pr25 Me.79 80 81 82 Mo.81 82 83 85 N.77 78 79 P.31 34 75 78 Pr.6 9 10 12 23 Q.11 17 19 Z.2 11 27
Elliptic functions and spherical trigonometry Q.17
Elliptic functions and theory of numbers L.58
Elliptic functions in complex regions Z.28
Elliptic functions of Me.85
Elliptic functions of first and second kind C.10
Elliptic functions of first and second kind, as functions of their amplitude JP.14
Elliptic functions of first and second kind, representation in a simple form Z.21
Elliptic functions of first and second kind, series by which they are computed J.16 17
Elliptic functions of first kind A.12 21 C.16 J.93 L.43
Elliptic functions of first kind with complementary moduli extension of a theorem of Lagrange An83
Elliptic functions of first kind, normal forms of 3rd and 5th degree M.17
Elliptic functions of first kind, replaced by one of second kind J.55
Elliptic functions of first kind, represented by gauchebiquadratics C.83
Elliptic functions of second and third kind, expression by function Z.10
Elliptic functions of second kind J.93
Elliptic functions of second kind, mechanical representation Me.75
Elliptic functions of second kind, reduction to first kind from same modulus A.56
Elliptic functions of third kind C.94 96 CD.8 J.14 47 LM.13
Elliptic functions, Me.75
Elliptic functions, J.37
Elliptic functions, addition of A.47 geo64 AJ.7 C.59 78 J.35 41 44 54 88 90 LM.13 M.17 Me.80 84 Q.18 Z.1
Elliptic functions, addition of 1st kind Z.26
Elliptic functions, addition of 2nd kind by q series Me.83
Elliptic functions, addition of 3rd kind Me.81
Elliptic functions, application of C.85 86 89 90 93 94
Elliptic functions, application of, to algebra J.7
Elliptic functions, application of, to arithmetic C.98 L.62
Elliptic functions, application of, to confocal conics Z.7
Elliptic functions, application of, to geometry G.12 J.38 53
Elliptic functions, application of, to in- and circum-circles of a polygon L.45
Elliptic functions, application of, to rectification L.45
Elliptic functions, application of, to spherical conics Z.22
Elliptic functions, application of, to spherical curves and quadrature An.50
Elliptic functions, application of, to spherical polygons with in- and circum-circles L.46
Elliptic functions, application of, to spherical trigonometry Q.20
Elliptic functions, approximation to 2127—2132 P.60 62
Elliptic functions, arg sn a and 2, as def. integrals Q.19
Elliptic functions, arithmetical consequences Ac.5
Elliptic functions, arithmetico-geometric mean J.58 85 89
Elliptic functions, development of 2127—2132 J.81
Elliptic functions, development of 1st and 2nd kind C.92
Elliptic functions, development of 1st and 2nd kind with respect to the modulus of and their powers C.86
Elliptic functions, development of an imaginary period when the modulus is small enough An.70
Elliptic functions, differentiation by periods and invariants J.92
Elliptic functions, discriminant of modular equations M.8 9
Elliptic functions, double substitution J.15
Elliptic functions, eqs. for the division of Mo.75
Elliptic functions, formulae AJ.5 J.15 36 50 LM.13 Me.78 80 85
Elliptic functions, formulae for sn, cn, dn, of u+v+w Me.82
Elliptic functions, formulae from confocal conics LM.14
Elliptic functions, formulae, differential Me.82
Elliptic functions, formulae, Jacobi Mel.1 Q.16 19
Elliptic functions, Galois' resolvent M.18
Elliptic functions, geo. problems M.19
Elliptic functions, geo. properties L.43 45 P.52 54
Elliptic functions, geo. representation A.22 61 An.60 61 At.53 C.19 21 J.63 L.44 78
Elliptic functions, geo. representation in solid geo M.9
Elliptic functions, geo. representation of 1st kind An.53 C.70 CD.1 JP.28 L.43 45 46 78
Elliptic functions, geo. representation of 3rd kind A.24
Elliptic functions, identities Me.77
Elliptic functions, imaginary periods AJ.6
Elliptic functions, infinite double products A.14
Elliptic functions, infinite double products with elliptic functions as quotients J.35
Elliptic functions, inversion of J.4 JP.34 L.69
Elliptic functions, modular equations C.47 J.58 LM.9 10 M.12
Elliptic functions, modular functions A.11 13 G.12 J.72 83 L.40 M.17 18
Elliptic functions, modular functions, differentiation for modulus of am LM.13
Elliptic functions, modular functions, expansion in powers of modulus J.41
Elliptic functions, modular functions, formulae L.64
Elliptic functions, modular functions, relation between the modulus and the invariant of a binary quartic Z.18
Elliptic functions, multiplication of C.88 J.14 39 41 74 76 81 86 88 M.8 Mo.57 83
Elliptic functions, multiplication of, and division Z.7
Elliptic functions, multiplication of, complex M.25 Mo.62 Q.19 20
Elliptic functions, multiplication of, formulae trA.36 C.59 J.39 48
Elliptic functions, multiplication of, mod. J.48
Elliptic functions, periodicity moduli of hyper-elliptic integrals as functions of a parameter J.71 91
Elliptic functions, products of powers Mem.71
Elliptic functions, q-formula for sin am LM.11
Elliptic functions, q-series f85
Elliptic functions, q-series for coeffs. Q.21
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