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Carr G.S. — Formulas and Theorems in Pure Mathematics
Carr G.S. — Formulas and Theorems in Pure Mathematics



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Название: Formulas and Theorems in Pure Mathematics

Автор: Carr G.S.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Second Edition

Год издания: 1970

Количество страниц: 988

Добавлена в каталог: 07.05.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Curves algebraic of 3rd class and curves of 3rd order      J.38 L.78
Curves algebraic of 4th class with a triple and a single focus      Q.20
Curves algebraic of 6th class      Ac.2
Curves algebraic of class n and order m, two laws      C.85
Curves algebraic with a mid-point      J.47
Curves algebraic with axes of symmetry      N.80
Curves algebraic, common points, a system of      J.54
Curves algebraic, generation by right lines      J.42
Curves algebraic, lemniscatic      An.58
Curves algebraic, manifoldness of      M.10
Curves algebraic, mechanical construction of an n-tic      5407 LM.7
Curves algebraic, number of intersections      C.76 M.15
Curves algebraic, number of points of contact      C.82
Curves algebraic, projective involution      M.3
Curves algebraic, remarkable group of      M.16
Curves algebraic, represented by arcs of circles      JP.20
Curves algebraic, species determined      M.23
Curves algebraic, symmetrical expression of constants      Q.5
Curves algebraic, theorems, two metric      M.11
Curves algebraic, theorems, two metric, Maclaurin's      N.50
Curves and derived surfaces      An.59 61
Curves and surfaces      M.8 N.59 gn thsG.4
Curves and surfaces of same degree, a common property      G.8
Curves and surfaces, "arguisiane"      G.12
Curves and surfaces, algebraic      An.77 J.49 L.55
Curves and surfaces, curves having the same principal normals and the surface which the normals form      C.85
Curves and surfaces, satisfying conditions of double contact      C.89
Curves from Abel's functions, p = 2      M.1
Curves in a power-series of sines      J.3
Curves of "allineamento"      G.21
Curves of "raccordement"      JP.12
Curves of 2-point contact with a pencil of curves      M.3
Curves of 3-point contact with a triply infinite pencil of curves      M.10
Curves of 3-point contact with a triply infinite pencil of curves, 4-point do.      LM.8
Curves of a series of groups of points, ths      C.73
Curves of pursuit      5247 C.97 N.83
Curves of section      A.43
Curves of the species 1      C.97
Curves on surfaces      see "Surface curves"
Curves with a constant polar subtangent      N.62
Curves with branches, imaginary      CM.1 Q.7
Curves with branches, infinite      Q.3
Curves with multiple points      C.62 L.69
Curves with multiple points, n-tic with m.p of n-1th order      C.80 N.76
Curves with multiple points, with three of higher degrees      cn An.58
Curves with several "points d'arret"      N.60
Curves with similar evolutes      Me.66
Curves, $p+p_{2\psi}=s_{psi}$      E.11
Curves, $\int\frac{pdx}{R}$      J.1
Curves, $\phi_{2x}+\phi_{2y}=0, \rho\infty r^{2}$      Mem.24
Curves, $\phi_{2x}+\phi_{2y}=0, \rho^{n}=Asin\omega$      N.76
Curves, 2 characteristics defining a system of algebraic or transcendental curves      C.78
Curves, a family of      N.72
Curves, analytical method      LM.9 16
Curves, Aoust's problem      A.2 66
Curves, arcs of, compared with lengths      JP.23
Curves, argument of points on a plane curve      LM.15
Curves, bicursal      LM.4 7
Curves, class, diminution of      N.67
Curves, cutting others in given angles or in angles whose bisectors have a given direction      C.58 83
Curves, defined by a differential equation      C.81 90 93 98 L.81 82
Curves, defined by a differential equation, $\phi_{2x}+\phi_{2y}=0$      Pr.15
Curves, defined by a differential equation, do. algebraic and an analogous space theorem      L.76
Curves, defined by intersecting conics      C.37
Curves, derived from an ellipse      A.10
Curves, determination from property of tangents      A.51
Curves, determination from their curvature      P.83 84
Curves, determination of the number of curves of degree r which have a contact of degree n<mr, with an m-tic, and which satisfy $\frac{1}{2}r(r+3)-n$ other conditions, and similar problems      C.63
Curves, diameters of      L.49 N.71
Curves, diameters of, and surface      C.60
Curves, eq obtained from tangent      N.45
Curves, equidistant, tangents to      cnZ.28
Curves, extension to space      C.85
Curves, four, with two common points      Q.9
Curves, generation of      geoJ.58 71 M.18
Curves, generation of, by collinear ray-systems      Z.19
Curves, generation of, by intersections of given curves      Z.14
Curves, geometrical      A.37
Curves, geometrical, "gobbe" of zero kind      G.11
Curves, geometrical, "gobbe", rational      G.9 12
Curves, geometrical, two laws      C.84
Curves, geometrical, two laws, relation to harmonic axes      C.73
Curves, higher plane      A.70 L.61 63
Curves, homofocal      N.81
Curves, intrinsic equation      CP.8 Q.5
Curves, joining two points      pr L.63
Curves, least chord through a given point      A.23
Curves, network of      C.67
Curves, pencils of      A.65
Curves, pencils of, of 3rd order      Z.13
Curves, rational      A.56 G.th15 16 M.9 18
Curves, rational, generation of      G.12
Curves, re lines drawn at all points of a curve at the same inclination to it      C.74
Curves, reciprocal of      J.42
Curves, sextactic points of      P.65
Curves, singularities of      5187 An.71 C.78 80 CP.9 J.64 JP.7 L.37 45 LM.6 M.8—10 16 N.50 80 81 Q.2 7
Curves, singularities of, higher singularities      J.64 L.70
Curves, systems of      An.61 G.13 Mo.82
Curves, systems of, theory      C.63 94
Curves, systems of, theory and surfaces      A.73 Ac.7 L.65
Curves, tangential polar eq of      Q.1
Curves, theorems or problems      A.pr1 31 prs 42 G.1 J.1 M.14 Q.3
Curves, theorems or problems, re arc CP and chords CP, PM, CM      Mem.10
Curves, theorems or problems, to describe curves which shall have equal arcs cut off by a fixed pencil of lines      Mem.10
Curves, tracing apparatus      LM.4
Curves, transformation of      CD.8 LM.1
Curves, transformation of 14-ics which cut a quartic in the points of contact of its double tangents      J.52
Curves, transformation of scalene      Q.13 M.4 20 21
Curves, transformation of, and transversals      J.47
Curves, transformation of, under given conditions      P.68
Curves, whose arcs and coordinates are connected by a quadratic equation      J.62
Curves, whose arcs are expressible by elliptic or hyperelliptic functions of the 1st kind      Z.25
Curves, whose coordinates are functions of a variable parameter      Me.85
Curves, whose coordinates are functions of a variable parameter, elliptic      J.64 N.68
Curves, whose equations are $r\phi = asin\phi$      A.48
Curves, whose equations are $v^{3}=u(u-1)(u-x)(u-y)$, x and y constants      C.93
Curves, whose equations are $y=\Gamma (x)$      2323
Curves, whose equations are $y=\sqrt[n]{x}$      A.14 16
Curves, whose equations are linear functions of the coordinates      N.65
Curves, whose evolute and involute are equal      C.84
Curvilinear angles, ths      L.44 45
Curvilinear triangles      A.61 N.45
Curvital functions      C.60
Curvo-graph      A.1
Cusps      5181 Mem.22 Q.10
Cusps, construction of 8 cusps of 3 quadric surfaces when 7 are given      J.26
Cusps, keratoid      5182
Cusps, ramphoid      5183
Cyclic and hyperbolic functions      37
Cyclic curves      A.37 Z.cn2 26 27
Cyclic functions      A.69
Cyclic interchanges (higher algebra)      Man.62
Cyclic projective groups of points      M.13 20
Cyclic projective groups of points, number of do. in a space transf.      C.90
Cyclic surfaces      Z.14
Cyclic systems      C.76
Cyclides      N.66 70 Pr.19 Q.9 12
Cyclides and sphero-quartics      P.71
Cyclides, reducible      LM.2
Cycloidal curves      Z.9
Cycloids      5250 A.13 N.52 82
Cycloids and trochoids on surface of sphere      Mem.22 Q.19
Cycloids, surface of, th of Archimedes      Me.84
Cyclosis in lines      LM.2
Cyclotomic functions      C.90
Cylinder, frustrum of      6048
Cylinder, frustrum of, and cones, intersection by spheres, ths      J.54
Cylinder, frustrum of, and hemisphere      P.12
Cylinder, frustrum of, circumscribing a torus of revolution      C.45
Cylindrical functions      A.56 An.73 M.5 16
Cylindrical functions and d.i      M.8
Cylindrical functions of 1st and 2nd class      M.1
Cylindrical functions, J(x) analogous to the spherical function $P^{n}(cos\theta)u$      M.3
Cylindrical functions, representing a function of 2 variables      M.5
Cylindrical surfaces      5591 LM.3
Cylindrical surfaces, quadrature of      A.9
Cylindroids      At.19 39 Me.80 Z.25
De Moivre's theorem      756 A.6 11
Decimal fractions, approximation by      N.51
Decimal fractions, error in addition of non-terminating      C.40 N.56
Decimal fractions, repeating      A.16 33 56 G.9 Me.85 Mel.5 N.42 49 74
Decimal fractions, repeating, $\frac{1}{p}$ where p is one of the first 1500 primes      A.3
Definite integrals      see "Integrals"
Deformation of a cache-pot      3ST.81
Deformation of a one-fold hyperboloid      E.30
Deformation of conics      Z.25
Deformation of surfaces      C.68 70 G.16 JP.22 L.60
Demonstrations, reduction to simplest form      C.83
Derivation of a curve      An.52
Derivation of analytical functions, gz      G.22
Derivation, applied to geo prs      An.54
derivatives      see "Differential coefficient"
Derivatives, Arbogast's      1536 CD.6 I.12 L.82 extMe.78 P.61 Pr.11 Q.4 7
Derivatives, Schwarzian      CP.13
Descriptive geometry      An.63 L.39 N.52 56
Detached coefficients      28
Determinants      554 A.44 56 65 apAn.57 J.22 tr51 72 73 74 89 C.86 CP.8 G.1 4 8 9 10 L.84 LM.10 Me.62 78 79 83 N.51 69 ap Pr.8 Q.8 TE.28 Z.16
Determinants and algebraic "clefs"      C.36
Determinants and duadic disynthemes      AJ.22
Determinants for verifying a system of d.e      C.23
Determinants in conics      J.89 92
Determinants of alternate numbers      LM.11
Determinants of binomial coefficients      Z.24
Determinants of Cauchy ("aleph")      G.17
Determinants of definite integrals      L.52 Z.11
Determinants of even order, analogy between a class of      J.52
Determinants of figurate numbers      G.9
Determinants of lower determinants      J.61
Determinants of minors of given determinant      C.86
Determinants of powers      AJ.4
Determinants of rational fractions      Me.82
Determinants of sixth order      Me.84
Determinants of squares of distances of points      Q.11
Determinants of the 16 lines joining the vertices of two tetrahedrons      J.62
Determinants with a diagonal of zeros      Me.73
Determinants with continued fractions      J.69
Determinants with polynomial elements      Me.85
Determinants, application to algebra and geometry      A.51 50 53
Determinants, application to contact of circles and spheres      N.60
Determinants, application to cylindrical surfaces      A.58
Determinants, application to equations      Q.19
Determinants, application to geometry      J.40 49 77
Determinants, application to surfaces of revolution      A.58
Determinants, arithmetical      G.23 LM.10 Me.78 Pr.15
Determinants, catalogue of papers and treatises      Q.18
Determinants, combination of      CD.8
Determinants, combinatory analysis of      C.86
Determinants, composite      555 J.88 89
Determinants, compound      555 AJ.6 LM.14 Me.82
Determinants, cubic      G.6 LM.13
Determinants, cubic and higher      11
Determinants, cycle of equations      G.11
Determinants, development of      An.58 N.85
Determinants, development of and ap to resultant of 2eqs      G.21
Determinants, development of, in binomials      G.10
Determinants, development of, in polynomials      G.13 15
Determinants, ditto of negative dets.      J.37 L.60 M.22 Mo.62 75
Determinants, division problems      A.59
Determinants, double orthosymmetric      Z.26
Determinants, elements of      G.10 15
Determinants, equation in which $a_{pq}=a_{qp}$      C.41
Determinants, function in analysis for a certain determinant of n quantities      C.70
Determinants, functional      CD.9 J.22 69 70 77 84 M.1 18 Me.80 Q.1
Determinants, functional of a system of functions      L.51
Determinants, functional of binary forms      C.92
Determinants, gauche $(a_{pq}=-a_{qp})$      C.88 89 CD.9 J.32 38 50 th55 L.54
Determinants, involving $\sqrt[3]{1}, &amp;c.$      Q.15 16 17
Determinants, minor      554 G.1
Determinants, multiplication of      562 570 A.14 59 L.52
Determinants, number of terms in      LM.10
Determinants, partial      C.97
Determinants, persymmetric      Me.82
Determinants, quadratic forms of      J.53 89 L.56 N.52
Determinants, resolution into quadratic factors of a det. formed from two circulants      Me.82
Determinants, signs of the terms      557 E.29 Me.80
Determinants, skew      Q.8 18
Determinants, Sylvester's det. and Euler's resultant      An.59
Determinants, symmetrical      G.1 J.82 M.16 th Q.14 18
Determinants, symmetrical, and Lagrange's interpolation      LM.13
Determinants, symmetrical, ap to a pr in geo      Z.20
Determinants, symmetrical, of nth order and n-1th power $\times$ sq. of a similar determinant      AJ.4
Determinants, theorems and problems      AJ.3 An.pr60 G.2 4 6 12 16 J.pr66 pr84 L.51 54 M.13 Me.79 N.65 Q.1 pr2 15 Z.7 prs18
Determinants, transformation of      An.73 G.10 f16
Determinants, transformation of product      L.60
Determinants, unimodular, cn      Z.21
Developable cylinders, motion of      Man.84
Developable surfaces      A.69 M.18 Me.77 Q.6
Developable surfaces of a conical screw      A.69
Developable surfaces of first 7 degrees      J.64
Developable surfaces of surfaces having principal lines of curvature plane      C.36
Developable surfaces, circumscribing 2 quadrics      C.67 ths54 gz63 CD.5
Developable surfaces, circumscribing given surfaces      Z.13 15
Developable surfaces, edge of regression      L.72
Developable surfaces, mutual      J.19
Developable surfaces, quintic      C.54 CD.5 G.3
Developable surfaces, through a gauche curve      C.97
Developable surfaces, through a given curve which develops into a circular arc      L.56
Development of tortuous curves      prs Mem
Di-polar geometry      Z.27
Diacaustic of a plane      N.75
Diagonal scales      LM.6
Diametral curves      CM.2
Diametral curves of constant sectional area, prs      N.43
Didon, proposition of      C.86
Differences and differential quotients      A.49 53 N.69
Differences, equations of mixed      JP.6 N.85
Differences, parameters of functions      C.95
Differential calculus      1400—1868 J.11 12 13 14 15 16 Me.66 Q.4
Differential Calculus, reciprocal methods      CD.7 8
Differential coefficients or differential quotients or derivatives      1402 1422—1446 Pr.12 see
Differential coefficients or differential quotients or derivatives of $x^{a}$ and $a^{x}$      N.53
Differential coefficients or differential quotients or derivatives of $\{f(x)\}^{n}$      M.3
Differential coefficients or differential quotients or derivatives of $\{f(x)\}^{n}, of y exp(z^{x})$      A.22
Differential coefficients or differential quotients or derivatives of a composite function      1420 nth G.13
Differential coefficients or differential quotients or derivatives of a function of a function      1415 A.9
Differential coefficients or differential quotients or derivatives of a function of a function, in terms of derivative of inverse function      Mem.57
Differential coefficients or differential quotients or derivatives of a function of two independent variables      1815
Differential coefficients or differential quotients or derivatives of algebraic functions      Mel.1
Differential coefficients or differential quotients or derivatives of exponentials and logarithms      1422—1427 A.11 N.50 52 85
Differential coefficients or differential quotients or derivatives of irrational functions      P.16
Differential coefficients or differential quotients or derivatives of log x and $a^{x}$      A.1
Differential coefficients or differential quotients or derivatives of nth order with x=0 in the result, $(1+x^{2})^{\pm\frac{m}{2}}{sin \atop cos}m\tan^{-1}x$      2883—2887
Differential coefficients or differential quotients or derivatives of nth order with x=0 in the result, $tan^{-1}x, sin^{-1}x, (sin^{-1}x)^{2}$      2865—2869
Differential coefficients or differential quotients or derivatives of nth order with x=0 in the result, $\frac{sin(x\, or\, y)+cos x}{1+2y cos x+y^{2}}$      A.3
Differential coefficients or differential quotients or derivatives of nth order with x=0 in the result, $\frac{x}{e^{x}-1}$, $x^{p}e^{ax}cos bx$      2889—2891
Differential coefficients or differential quotients or derivatives of nth order with x=0 in the result, ${cos \atop sin}msin^{-1}x, {cos \atop sin}cos^{-1}x$      2871—2877
Differential coefficients or differential quotients or derivatives of products whose factors are consecutive terms of a series      Me.31
Differential coefficients or differential quotients or derivatives, calculated from differentials      AJ.16
Differential coefficients or differential quotients or derivatives, ratio to the function at the limit $\infty$      J.74
Differential coefficients or differential quotients or derivatives, successive or of nth order      1405 1460—1472 2852—2891 A.1 4 7 An.57 G.18 M.4 Z.3
Differential coefficients or differential quotients or derivatives, successive or of nth order, $(1-x^{2})^{ n-\frac{1}{2} }(Jacobi)$      1471 A.4
Differential coefficients or differential quotients or derivatives, successive or of nth order, $(a+bx+cx^{2})^{n}$      2858
Differential coefficients or differential quotients or derivatives, successive or of nth order, $(x^{2}+ax+b)^{-m}$      A.8
Differential coefficients or differential quotients or derivatives, successive or of nth order, $cos^{m}x$      A.9
Differential coefficients or differential quotients or derivatives, successive or of nth order, $e^{ax^{2}}$      2861 A.30
Differential coefficients or differential quotients or derivatives, successive or of nth order, $e^{ax}, e^{ax}y$      1463—1464
Differential coefficients or differential quotients or derivatives, successive or of nth order, $e^{ax}cos bx$      1465
Differential coefficients or differential quotients or derivatives, successive or of nth order, $e^{ax}x^{m}$      CM.2
Differential coefficients or differential quotients or derivatives, successive or of nth order, $e^{xcos a}cos(xsina)$      2856
Differential coefficients or differential quotients or derivatives, successive or of nth order, $sin^{-1}x$      2854—2855
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