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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
Continuants      AJ.1 Me.79
Continued fractions      160—187 A.18 33 55 69 An.51 gzC.99 CM.4 th G.10 15 J.6 8 11 ap 18 53 80 L.50 58 65 LM.5 Me.77
Continued fractions for $(m+\surd n)\div p$      N.45
Continued fractions for powers of binomials      CM.4 Mem.18
Continued fractions for Usin x+Vcos x+W, U, Y, W, polynomials in x      J.76
Continued fractions, $2+\frac{1}{2+}\frac{1}{2+}$ and $a+\frac{p}{q+}\frac{p}{q+}$      E.36 33
Continued fractions, $a+\frac{b}{a+1+}\frac{b+1}{a+2+\&c.} b>a+1$      Mel.1
Continued fractions, $x+\frac{1}{x+1+}\frac{1}{x+2+}$ and $2x+1+\frac{1}{2x+3+}\frac{1}{2x+5+}$      A.30
Continued fractions, $\frac{1}{a+}\frac{1}{a+}$ and $\frac{1}{a+}\frac{1}{b+}\frac{1}{a+}\frac{1}{b+}$      A.42 J.3
Continued fractions, algorithm $p_{n} = \alpha p_{n-1}+bp_{n-2}$      168 J.69 75
Continued fractions, ascending      A.60 Z.21
Continued fractions, combinator representation of the approximation      A.18
Continued fractions, development      Ac.4 C.87 Mem.9
Continued fractions, do. ap. to solution of trinomial eq      A.66
Continued fractions, do. of a cube root      A.8
Continued fractions, do. of an nth root      A.64
Continued fractions, Eisenstein's      TE.28
Continued fractions, for $e exp. a+bx+cx^{2}+$      C.87
Continued fractions, for $e^{x}$ and $\log{1+x}$      CM.4
Continued fractions, for $\frac{ x^{-1}-x^{-4}+x^{-9}+x^{-16}+}{ 1-x^{-1}+x^{-4}-x^{-9}+}$      J.27 28
Continued fractions, infinite      A.33
Continued fractions, Mem. ap to i.c      9 13 Mo.66 N.42 tr49 56 66 Q.4 geo
Continued fractions, numerical values      Q.13
Continued fractions, periodic      33 G.16 J.53 N.42 43 45 46
Continued fractions, periodic, 2 periods      A.19
Continued fractions, reduction of      J.46
Continued fractions, reduction of a square root to a      195 A.64 J.31
Continued fractions, Wallis's      Mem.15
Continuity, principle of      CP.8
Continuity, principle of, in relation to Taylor's and Maclaurin's theorems      L.47
Continuous functions      1401 A.15 Ac.5 C.18 20
Continuous functions and discontinuous      40
Continuous functions of integrals of d.e      23 TA.7
Continuous manifoldness of 2 dimensions      LM.8
Contragredients      1813
Contraposition      E.29
Contravariants      1814 G.12
Contravariants of 6th deg      19
Contravariants of two conics      4990 5027
Convergents      160—187 gzC.98 CD.5 J.37 57 58 N.46
Convex polygon, intersection of diags      N.80
Coordinate systems      4001—4031 5453 5501—5506 G.16 J.5 45 50 LM.12
Coordinate systems of a plane curve in space      LM.13
Coordinate systems, ap. to caustics      An.69
Coordinate systems, areal      4013 Me.80 82 gn
Coordinate systems, axial      N.84 85 Q.10
Coordinate systems, biangular      5453—5473 Q.9 8 13
Coordinate systems, bilinear      ap 5341 A.32
Coordinate systems, bipolar      N.82
Coordinate systems, bipunctual      AJ.1
Coordinate systems, Boothian      see "Tangential"
Coordinate systems, Cartesian      4001
Coordinate systems, Cartesian, dual inversion of c.c and t.c      Q.17
Coordinate systems, central      Z.20
Coordinate systems, curvilinear      A.34 An.57 64 68 70 73 C.48 54 CP.12 G.10
Coordinate systems, curvilinear and i.c      15 L.40 51 82 Mem.65 Q.19
Coordinate systems, curvilinear on a surface and in space, including any angle      J.58
Coordinate systems, curvilinear, on a surface and in space      An.69 71 73
Coordinate systems, eccentric values of      4275 5638 CM.4
Coordinate systems, elliptic      A.34 40 J.85 Q.7 Z.20
Coordinate systems, Fuchsian functions of a parameter      C.92
Coordinate systems, hyperelliptic coordinates      J.65
Coordinate systems, linear      Z.21
Coordinate systems, mixed coordinates      A.13
Coordinate systems, one-point intercept      4026
Coordinate systems, parabolic      C.50
Coordinate systems, parallel      N.84 85
Coordinate systems, pedal      Me.66
Coordinate systems, pentahedral      Me.66
Coordinate systems, polar      4003 sd5506 Me.76
Coordinate systems, polar linear in a plane      Z.21
Coordinate systems, quadrilinear      Me.62 64
Coordinate systems, quadriplanar or tetrahedral      sd5502 ap Q.4
Coordinate systems, surface      C.65 81
Coordinate systems, tangential      4019 4870—4915 5030 Me.81 Pr.9 Q.2 8
Coordinate systems, tangential rectangular, or Boothian      4028
Coordinate systems, tetrahedral point coordinates      Z.8
Coordinate systems, triaxial      A.64
Coordinate systems, trigonal      G.14 Q.9
Coordinate systems, trilinear      4006 A.39 Me.62 64 N.63 Q.4 5 6
Coordinate systems, trilinear, conversion to tangential      4876
Coordinate systems, trimetrical point      A.67
Coordinate systems, two-point intercept      4025
Coordinates, transformation of      4048—4051 4871 5574—5581
Coplanation      Z.11
Coplanation of central quadric surfaces      Z.8
Coplanation of pedal surfaces      Z.8
Coresolvents      Q.6 10 14
Coresolvents, non-linear      TN.67
Correlation of planes      J.70 An.75 77 LM.5 6 8 10
Correlative figures, focal properties      LM.3
Correlative or reciprocal pencils      M.12
Correspondence for groups of n points and n rays      M.12
Correspondence of 2nd deg. between 2 simply infinite systems      An.71
Correspondence of algebraic figures      M.2 8
Correspondence of curves      C.62 P.68 Q.15
Correspondence of points      LM.2
Correspondence of points on a conic      Q.11
Correspondence of points on a curve      C.62
Correspondence of points on two surfaces      M.18
Correspondence of two planes      LM.9
Correspondence of two variables (2, 2)      Q.12
Correspondence, application to Bezout's th      C.81
Correspondence, application to curves      C.72
Correspondence, application to elimination      N.73
Correspondence, application to evolute and caustic      N.71
Correspondence, complementary theorem to      C.81
Correspondence, determination of no. of points of intersection of 2 curves at a finite distance      L.73 C.75
Correspondence, determination of the class of the envelope and of the caustic of a curve      C.72
Correspondence, determination of the degree of the envelope of a curve or surface of n parameters with n-2 relations      C.83
Correspondence, determination of the number of solutions of n simultaneous algebraic equations      C.78
Correspondence, determination of the order of a geometrical locus defined by algebraic conditions      C.82 84
Correspondence, forms      M.7
Correspondence, multiple in 2 dimensions      G.10
Correspondence, principle of      geo thAn.71 extC.78 80 ex83 85 N.46
Correspondent values, method of      P.1789
Corresponding points in some involutions      LM.3
Corresponding points on two curves      M.3
Corresponding points on two surfaces      C.70
Corresponding surface elements      M.11
Cosmography, graphic method      N.82 79
Cotes's theorem, analogous ths      CM.3
Cotes's theorem, areas      2995
Cotes's theorem, circle      821
Counter-pedal surface of ellipsoid      AJ.4
Coupures of functions      C.99
covariants      1629 4936—5030 C.80 81 th G.1 20 Q.5 16 J.47 87 90 thM.5 N.59
Covariants and contra variants of a system of simultaneous forms in n variables, to find the number of      C.84
Covariants and invariants      An.60
Covariants and invariants as criteria of roots of equations      An.68
Covariants and invariants of a binary octic, irreducible system      C.86 93
Covariants and invariants of a binary quintic      C.96
Covariants and invariants of a binary sextic      C.96
Covariants and invariants of binary forms      An.58 59 61 83 C.66 69
Covariants and invariants of binary forms, reciprocity law      C.86
Covariants of a binary quartic      J.53
Covariants of a binary quartic, quintics      An.60
Covariants of a septic, irreducible      C.87
Covariants of a system of 2 binary quadratic forms, number of      C.84
Covariants of a system of binary cubo-biquadra-tics, number of irreducible covariants      C.87
Covariants of binary forms      An.58 C.82 86 87 G.17 L.76 79 M.22
Covariants of binary quadrics, cubics, and quartics      An.65 J.50 Q.10
Covariants of binary quantics      E.31 Q.4 5 17
Covariants of quantics      An.58
Covariants of quantics, binary      Me.79
Covariants of ternary forms      G.19
Covariants of three conics      Q.10
Covariants of two conics      4989 5026
Covariants, ap to i.c      C.56
Covariants, binary      G.2
Covariants, sextic      G.19
Cribrum or sieve of Eratosthenes      N.43 49
Critical functions      see "Seminvariants"
Criticoids and synthetical solution      E.9 26 32
Cubature of solids      see "Volumes"
Cube numbers, graphic cn of      E.43 Me.85
Cube numbers, graphic cn of, tables to 12000      J.42
Cube root extraction      A.22 64 J.11 N.44 58 TI.1
Cube roots, table of (2 to 30)      p.6
Cube surfaces      Pr.17
Cubes of sums of numbers      N.71
Cubic and biquadratic equations      483—501 A.45 No.1780 An.58 C.geo41 90 JP.85 L.59 M.3 N.79 Z.8
Cubic and biquadratic equations, Arabic and Indian methods      15
Cubic and biquadratic equations, mechanical construction      LM.22
Cubic and biquadratic equations, Sturmian constants for      Q.4
Cubic and biquadratic problems      An.70
Cubic classes which belong to a determining quadratic class, number of      A.19
Cubic curves      An.73 AJ.5 15 27 C.37 thCD.7 CP.11 G.1 2 14 23 J.11 32 34 ths42 63 geo78 90 L.13 44 45 M.15 t.c Mo.geo56 N.50 67 geo72 P.57 58 Pr.8 9 Q.4 5 Z.geo15 22
Cubic curves and conics which touch them      J.36
Cubic curves and higher curves      A.70
Cubic curves and residual points      E.34
Cubic curves and right lines depending on given parameters      J.55
Cubic curves and surfaces      J.89
Cubic curves of third class with 3 single foci      Q.14 16
Cubic curves through 2 circular points at $\infty$      cnZ.14
Cubic curves through 8 points      Q.5
Cubic curves through 9 points      C.cn36 37 L.54
Cubic curves through 9 points, two cubics do.      CD.6
Cubic curves with a double point      M.6
Cubic curves with cusps      A.68
Cubic curves with double and single foci      Q.14
Cubic curves with two double points      M.3
Cubic curves, 16 cotangential chords of      Q.9
Cubic curves, 18 points on      E.4
Cubic curves, 48 coordinates of      P.81 ii
Cubic curves, classification of      Q.16
Cubic curves, coordinates, explicit functions of a parameter      J.82
Cubic curves, degeneration of      A.4 M.13 15
Cubic curves, derivation of points      LM.2
Cubic curves, Geiser's      J.77
Cubic curves, generation of      G.11 J.36 M.5 6
Cubic curves, generation of, by a conic pencil and a projective ray pencil      Z.23
Cubic curves, generation of, by a conic pencil and a projective ray pencil, linear      J.52
Cubic curves, inflexion points of      J.38 M.2 5 N.73 th83 85
Cubic curves, inflexion points of 12 lines on which they lie in threes      E.29
Cubic curves, mechanical construction of      LM.4
Cubic curves, nodal, tangents of      LM.12
Cubic curves, number of cubic classes which belong to a determining quadratic class      A.19
Cubic curves, rational      A.58 G.9
Cubic curves, referred to a tetrad of corresponding points      Q.15
Cubic curves, represented by elliptic functions      JP.34
Cubic curves, resolved into 3 right lines      M.14
Cubic curves, synthetic treatment      Z.21
Cubic curves, tangential of      P.58 Pr.9
Cubic curves, tangents to      cnE.25—27 ths28 LM.3 Q.3
Cubic curves, tangents with a double point or cusp      M.1
Cubic curves, tangents, forming an involution pencil      LM.13
Cubic curves, their intersections with cubics or conics      C.41 TI.26
Cubic curves, transformations of      C.91
Cubic equations      483—491 A.1 3—7 11 22 25 32 37 41 42 44 prs47 68 An.55 C.num46 85 CD.4 6 E.35 G.12 16 J.27 56 90 LM.8 M.3 Mem.26 N.45 th52 th56 64 66 70 75 78 81 84 TE.24 TI.7 see
Cubic equations and division of angles      A.15
Cubic equations in a homographic pr of Chasles      C.54
Cubic equations, irreducible case      A.30 39 41 42 No.1799 AJ.1 C.58 J.2 7 L.79 N.67
Cubic equations, irreducible case by continued fractions      A.2
Cubic equations, irreducible case in real values      A.49
Cubic equations, roots, condition of equality      E.30
Cubic equations, roots, definition of      thA.31
Cubic equations, roots, geometrical construction of      C.44 45
Cubic equations, roots, geometrical construction of Arab, m.s.s      J.40
Cubic equations, roots, integral      N.75
Cubic equations, roots, power-sums of      C.54 55
Cubic equations, roots, squares of differences of      An.56 Q.3
Cubic equations, solution of Cockle's      CM.2 3
Cubic equations, solution of, by $x=\frac{1}{z}+h$      C.60
Cubic equations, solution of, by continued fractions      A.10 39
Cubic equations, solution of, by differences of roots      J.42
Cubic equations, solution of, by logarithms      C.66
Cubic equations, solution of, Cardan's formula      484 A.14 40 gz22 Me.85
Cubic equations, solution of, mechanical      5429 C.79
Cubic equations, solution of, numerical      C.44
Cubic equations, solution of, trigonometrical      489 A.19 N.61 67 71 TE.5
Cubic forms      thsJ.27 see
Cubic forms, quaternary, division into five      J.78
Cubic forms, quaternary, transf      J.58 P.60 Pr.10
Cubic forms, ternary      J.28 29 JP.31 32
Cubic surfaces      Ac.3 5 thsAn.55 C.97 98 G.22 J.53 65 68 69 88 89 M.6 Mo.56 N.69 P.69 Z.20
Cubic surfaces in quaternions      AJ.2
Cubic surfaces with 4 double points      M.5
Cubic surfaces, "gobbe"      G.14 17 21
Cubic surfaces, 27 lines and 45 triple tangent planes of      An.84
Cubic surfaces, 27 lines and 45 triple tangent planes of, and 36 double sixers      Q.18
Cubic surfaces, 27 lines of      C.52 68 70 J.62 L.69 M.23 Q.2
Cubic surfaces, classification of      M.14
Cubic surfaces, double sixers of      Q.10
Cubic surfaces, hyperboloidal projection      G.2
Cubic surfaces, locus of centre of quadric through 8 points      Me.85
Cubic surfaces, model of      CP.12
Cubic surfaces, polar systems      M.20
Cubic surfaces, properties of situation      M.8
Cubic surfaces, reciprocal of Steiner's surface      N.72 73
Cubic surfaces, singular points of      P.63
Cubic surfaces, triple tangent planes      CD.4
Cubical parabola      Q.6 9
Cubical parabola, metrical properties      M.25
Cubo-biquadratic eqs., no. of irreducible forms      C.87
Curvature      1254—1258 5134 5174 A.1 28 43 J.81 Me.62 f64 72 75 N.th60 69 Q.t.c 12
Curvature at a cusp      5182 N.71
Curvature at a double point      5187 Q.3
Curvature at a multiple point      5187 C.68
Curvature of a plane section of a surface      C.78 Z.17
Curvature of an evolute of a surface      C.80
Curvature of higher multiplicity (Riemann)      Z.20 24
Curvature of higher order      5188—5191 M.7 16
Curvature of intersection of 2 quadrics      An.63
Curvature of orthogonal lines      JP.24
Curvature of surfaces      5818—5826 A.4 20 41 57 An.f ths61 64 C.th25 49 60 ths66 67 68 geo74 84 J.1 3 7 8 JP.13 L.44 72 p.c Mel.3 Q.12 Z.27
Curvature of surfaces and inflexion      trA.19
Curvature of surfaces and lines      An.53 59 L.41
Curvature of surfaces and orthogonal surfaces      P.73
Curvature of surfaces and pencils of normals      C.70
Curvature of surfaces of revolution      L.41 Z.21 22
Curvature of surfaces, approach of 2 axes of finite neighbouring curves      C.86
Curvature of surfaces, average, specific, integral, &c.      5826—5830
Curvature of surfaces, axis of curvature of envelope of a displaced plane      C.70
Curvature of surfaces, circular and spherical      see "Tortuous curves"
Curvature of surfaces, constant      J.88 G.3
Curvature of surfaces, constant, mean      C.76 L.41 53
Curvature of surfaces, constant, neg.      C.60 M.16
Curvature of surfaces, constant, pos.      G.20
Curvature of surfaces, constant, total      C.97
Curvature of surfaces, Euler's theorem      gzC.79
Curvature of surfaces, Gauss's      thC.42
Curvature of surfaces, Gauss's, analogy      M.21 Q.16
Curvature of surfaces, Gauss's, analogy, ap. to aneroid barometers      C.86
Curvature of surfaces, indeterminate      CD.7
Curvature of surfaces, integral      5826
Curvature of surfaces, mean = zero throughout      Mo.66
Curvature of surfaces, skew      Z.26
Curvature of surfaces, sphere of mean curvature of ellipsoid      A.43
Curvature of third order      C.26
Curvature, circle of      1254—1255 5134 A.cn30 37 J.68
Curvature, dual, evolute and involute      Q.10
Curvature, mean      C.92
Curvature, parabolic      5818
Curvature, spherical      A.25
CURVES      5100 A.2 16 32 66 An.53 54 C.geo72 91 J.14 31 34 63 64 70 L.38 44 ths57 ths61 M.16 N.p.c 71 77 85 cn see "Curves
Curves algebraic      C.99 ths60 ths80 CM.4 G.1 4 5 J.12 47 59 N.50 81 cn83 see
Curves algebraic and homothetic conics, ths      J.53
Curves algebraic of 2nd class and 2nd order      G.1
Curves algebraic of 3rd class and 4th order      G.4
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