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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
Spherical trigonometry, geodetic reduction of a spherical angle      A.51
Spherical trigonometry, Legendre's th.      C.96 J.44 L.41 M.1 N.56 Z.20
Spherical trigonometry, Llhuillier's th.      905 A.20
Spherical trigonometry, Napier's eqs.      896 A.3 17 CM.3 LM.3 13
Spherical trigonometry, Napier's rules      881
Spherical trigonometry, supplement to, and geodesy      A.36
Sphero-conics      5655a
Sphero-conics, homofocal      C.50
Sphero-conics, mechanical cn      LM.6
Sphero-conics, tg.c      Q.8 9 Me.3 Z.6 23
Sphero-conjugate tangents      An.55
Sphero-cyclides      LM.16
Spheroidal trigonometry      J.43 M.22
Spheroidic transformation f. of Bessel      A.53
Spheroids      5604 6152
Spheroids, cubature      6158 A.2
Spieker's point      A.58
Spiral      A.28 L.69 N.79 Z.14
Spiral of Archimedes      5296 A.65 66
Spiral, conical      N.45
Spiral, equiangular      5288
Spiral, hyperbolic      5302
Spiral, involute, of 4th order      C.66
Spiral, involute, of circle      5306
squares      J.22
Squares whose diagonals are chords of given circles      A.64
Squares whose sides and diagonals are rational      J.37
Squares whose sides pass through 4 points      A.43
Squares, 64 transformed into 65, geo.      Me.77
Squares, maximum in a triangle      J.15
Squares, maximum with given sides      J.25
Squares, sum of four      L.57
Squares, sum of three      G.15
Standards of length      Pr.8 21
Statistics      Z.26
Steiner's ths. and prs.      A.53 J.13 14 16 18 23 25 36 71 73 N.48 56 59 62
Steiner's ths. and prs., Hexagon      A.6
Steiner's ths. and prs., Ray-systems      CD.6
Stereograms of surfaces      LM.2
Stereographic projection      A.39 JP.16 L.46
Stereometry      JP.1 thsA.10 31 43 57 J.1 5
Stereometry, multiplication      J.49
Stereometry, quadric and cubic eqs. and surfaces      J.49
Sternpolygon and sternpolyhedron      A.13
Stewart's geo.ths.      CM.2 L.48 TE.2 15
Stigmatics      see "Clinant"
Striction lines of conicoids      Z.28
Strophoids      AJ.7 N.75
Sturm's functions      506 A.62 C.36 62 68 G.1 20 J.48 L.46 48 67 Mo.58 78 N.43 46 52 54 66 67 81 Q.3
Sturm's functions and a quartic equation      A.34
Sturm's functions and addition th. for elliptic functions of 1st kind      Z.17
Sturm's functions and H. C. F.      Pr.6
Sturm's functions and their reciprocal relations      Mo.73
Sturm's functions, ap. to transcendental eqs.      J.33
Sturm's functions, ap. to transf. of binomial eqs.      L.42
Sturm's functions, ext. to simultaneous eqs.      C.35
Sturm's functions, remainders      J.43 48
Sturm's functions, tables      P.57 Pr.8
Subdeterminants of a symm. system      J.93 M.82
Subfactorial n      Me.78
Subinvariants $\equiv$ seminvariants to binary qualities of unlimited order      AJ.5
Subnormal      1160
Subsidiary angles      726 749
Substitutions      A.62 C.ths66 67 74 76 79 G.9 10 11 14 19 L.65 72 M.13
Substitutions and conjugate substitutions      C.21 22
Substitutions by approximation, of the ratio of the variables of a binary quantic to another function of the same degree      C.80
Substitutions of equidistant numbers in an integral function of a variable      N.51
Substitutions of n letters, geo. for n = 3, 4, 5, 6, and mystic hexagram      An.83
Substitutions of six letters      C.63
Substitutions of systems of equations      N.81
Substitutions of the form $\Theta (r) \equiv e (r^{n - 2} + ar^{\frac{n - 3}{2}})$      M.2
Substitutions which admit of a real inversion      J.73
Substitutions which do not alter the value of the function      C.21
Substitutions which lower the degree of an eq. in two variables and their use in Abelian integrals      C.15
Substitutions, a th. of Sylvester      AJ.1
Substitutions, ap. to functions of six or fewer variables      C.21
Substitutions, ap. to linear d.e      C.78
Substitutions, canonical forms of      L.72
Substitutions, linear      C.98 J.84 M.19 20
Substitutions, linear, and integral      M.24
Substitutions, linear, for reduction of elliptic functions of 1st kind      An.58
Substitutions, linear, of a determinant      An.84
Substitutions, linear, powers and roots of      C.94
Substitutions, linear, reduction of      C.90 JP.29
Substitutions, linear, successive      A.38
Substitutions, linear, which transform quadric functions into others which contain only the squares of the variables      J.57
Substitutions, no. of in a given no. of cycles      A.68
Substitutions, permutable amongst themselves      C.21
Sum and difference calculus      A.24
Sum of squares of lines drawn from a point to cut a curve in a given angle      J.11
Summation of series      3781 A.10—13 26 30 55 62 No.84 C.87 88 J.10 31 33 LM.4 7 Mem.20 30 P.1782 1784—1787 1791 1798 1802 1806 1807 1811 1819 Pr.14 see
Summation of series by $\psi (x)$      2757
Summation of series by definite integrals      A.4 6 38 J.17 38 42 46 74 Man.46 Mem.11
Summation of series by differences      264 Mem.30
Summation of series by differential formulae      L.31 Mem.15
Summation of series of arcs      A.63
Summation of series of derivatives and integrals      C.44
Summation of series of sines and cosines      J.4
Summation of series of terms of a high order      C.32
Summation of series of transcendents in alg. differentials      J.19
Summation of series, approximate      3820 J.5 I.24
Summation of series, Bernoulli's method      J.31
Summation of series, C (n, r) products of a, a + b, ... a + (n — 1) b      Q.18
Summation of series, Cauchy's th.      M.4
Summation of series, formulae      A.47 An.55 J.30
Summation of series, formulae, $f (\Delta, D) DF (n)$      Q.8
Summation of series, formulae, Lagrange's      J.34 P.60
Summation of series, formulae, Maclaurin's      C.86
Summation of series, formulae, Vandermonde's      L.41
Summation of series, Kummer's method      C.64
Summation of series, Lejeune Dirichlet's      CD.9
Summation of series, periodic      J.15
Summation of series, selected terms      Me.75
Summation of series, theorem re $\int_{a}^{b} X f (x, k) dx$      2708
Summation of series, trigonometrical and infinite      Me.64
Superposition      TE.21 23
Superposition of small quantities      1515
Supplement integrals      J.98
Supplementary angles      620
Supplementary chords      1201
Supplementary cones      thN.48
Supplementary curves      4917—4920 Man.54
Surds      108 N.47
Surds, $\surd (a \pm \surd b)$      121 A.3 13 J.17 20 Mem.10 N.46 48
Surds, $\surd (a^{2} + b^{2})$, $\surd (a^{2} - b^{2})$ approximately      J.13
Surds, ${3 \atop \surd} (a \pm \surd b)$      122
Surds, ${n \atop \surd} (a \pm \surd b)$      124
Surds, quadratic      see "Roots of numbers"
Surface curves      A.39 60 An.54 C.21 80 L.66 G.19 J.2 N.54 84
Surface curves and osculating sphere      C.73
Surface curves of intersection      M.2 N.68
Surface curves of intersection of 2 quadrics      A.16
Surface curves on a developable      An.57
Surface curves on a developable, the osculating plane making a constant angle with it      L.47
Surface curves on a one-fold hyperbola      CD.4
Surface curves on an ellipsoid      An.51 CD.3 geoL.50
Surface curves on cubic surfaces      M.21
Surface curves on quadrics      N.70
Surface curves on surfaces of revolution      Z.18 28
Surface curves, an an alg. surface      An.63
Surface curves, curvature of      N.65
Surface curves, groups of rational      M.3
Surface curves, multiple      G.14
Surface curves, multiple, singularities of      M.3
Surface curves, rectification of      A.36
Surface curves, relation to their tangents      C.82
Surface of centres      5774 A.68 An.57 C.70 71 E.30 L.41 58 LM.4 M.5 16
Surface of centres of a quadric      Q.2
Surface of centres of a quadric, bitangents of      Q.13
Surface of centres of a quadric, model of      Mo.62
Surface of centres of a quadric, principal axes of      N.48
Surface of centres, curvatures of the two, relation      C.74 79
Surface of centres, the two focal conics of a system of homofocal quadrics      C.53
Surface or surfaces      5770 A.14 f32 41 59 60 62 An.51—53 55 60 61 65 71 At.57 C.17 33 37 49 ths58 61 64 67 69 80 86 99 G.3 21 J.9 ths13 58 63 64 85 98 JP.19 24 25 33 L.44 47 51 60 M.2 4 7 9 cn19 Mo.82 83 84 N.53 65 68 72 TI.14 Z.7 8 20
Surface or surfaces and p. d. e      C.13 CD.2 Z.7
Surface or surfaces and plane curves      J.54 72 M.7
Surface or surfaces and point at $\infty$ on it      J.65
Surface or surfaces and point moving on it      L.76 77
Surface or surfaces and transversal, th.      N.49
Surface or surfaces of corresponding points      M.4
Surface or surfaces of elliptic cone      An.51
Surface or surfaces of equal slope      C.98 N.65
Surface or surfaces of even order      A.70
Surface or surfaces of minimum area      C.57 J.8 13 L.59 Q.14
Surface or surfaces of normals      N.59
Surface or surfaces of nth order      cnM.23
Surface or surfaces of nth order, 2nd, 3rd and 4th      Mel.6
Surface or surfaces of revolution      C.86 G.4
Surface or surfaces of revolution in perspective      JP.20
Surface or surfaces of revolution of a conic about any axis in space      JP.23 L.63
Surface or surfaces of revolution of constant mean curvature      L.41
Surface or surfaces of revolution of reg. polygon about a side, vol.      A.57
Surface or surfaces of revolution, areas and volumes      5877—5879 A.48
Surface or surfaces of revolution, meridian and contour curves of      Z.21
Surface or surfaces of revolution, meridian of, a lemniscate      G.21
Surface or surfaces of revolution, meridian of, generation of      C.85
Surface or surfaces of revolution, oblique      Q.6
Surface or surfaces of revolution, passing through a given line, tangent plane of      N.84
Surface or surfaces of revolution, quadric      A.55 L.60
Surface or surfaces of revolution, shortest line on      A.38
Surface or surfaces of revolution, superposable      C.80 N.81
Surface or surfaces which cuts the curve of intersection of two alg. surfaces in the point of contact of the stationary osculating planes      L.63
Surface or surfaces whose coordinates are Abelian functions of two parameters      C.92 M.19
Surface or surfaces whose normals all touch a sphere or conical surface      JP.4
Surface or surfaces, $\frac{x^{n}}{a} + \frac{y^{n}}{b} + \frac{z^{n}}{c} = 1$      A.35
Surface or surfaces, $\frac{x^{n}}{a} + \frac{y^{n}}{b} + \frac{z^{n}}{c} = 1$, a = b = c = 1      A.21
Surface or surfaces, areas of      G.22 N.52
Surface or surfaces, argument of points on      LM.16
Surface or surfaces, complex      M.5
Surface or surfaces, complex of 4th order and class      M.2
Surface or surfaces, cut orthogonally by spheres      3393 C.36
Surface or surfaces, deficiency of      M.3
Surface or surfaces, definitions      5770
Surface or surfaces, determined from two surfaces of centres      A.68
Surface or surfaces, Dirichlet's problem      An.71
Surface or surfaces, do. for surface of revolution      JP.5
Surface or surfaces, doubly circumscribing an n-tic surface      J.54
Surface or surfaces, Dupin's theorem      C.74 CM.4 Q.12
Surface or surfaces, equation of      gn5780 A.3
Surface or surfaces, equation of, for points near origin      5803
Surface or surfaces, families of      C.70 Me.72
Surface or surfaces, flexure of      J.18
Surface or surfaces, Gaussian theory of      LM.12 N.52
Surface or surfaces, generation of      C.94 97 G.9 J.49 L.56 83 M.18
Surface or surfaces, implexes of      C.79 82
Surface or surfaces, number under 9 conditions      C.62
Surface or surfaces, octic of zero kind      G.12
Surface or surfaces, one-sided      A.57
Surface or surfaces, order determined      Me.83
Surface or surfaces, parabolic points of      CD.2
Surface or surfaces, relation of in Riemann's sense      M.7
Surface or surfaces, representation of      J.83
Surface or surfaces, representation of, on a plane      An.68 71 76
Surface or surfaces, representation of, one upon another      An.77
Surface or surfaces, Riemann's symmetrical and periodicity modulus of the related Abelian integral of the 1st kind      Z.28
Surface or surfaces, ruled octic with 5 quartic curves      C.61
Surface or surfaces, ruled, with generators part of a linear complex      C.84
Surface or surfaces, screw, parallel projection of      cnZ.18
Surface or surfaces, section of, homogeneous eq.      LM.15
Surface or surfaces, self-reciprocal      LM.2
Surface or surfaces, self-reciprocal, quadric      E.36
Surface or surfaces, sextic of first species      M.21
Surface or surfaces, singularities of      A.25 An.79 CD.7 CM.2 J.72 M.9 N.64 Q.9
Surface or surfaces, singularities of, 16 singular points      C.92
Surface or surfaces, singularities of, cubics      M.4
Surface or surfaces, singularities of, cubics and quadrics      A.17
Surface or surfaces, solutions by infinites of 3rd order      geoC.80
Surface or surfaces, Steiner's      LM.5 14 M.5
Surface or surfaces, touching a fixed surface always      G.20
Surface or surfaces, touching a plane along a curve      CD.3 CM.2
Surface or surfaces, transformation of      M.19
Surface or surfaces, trapezoidal problem      Z.14
Surface or surfaces, two series of      prsAn.73
Surface or surfaces, web-system      J.82
surveying      N.50
Surveying, geo. th.      A.37
Symbolic geometry      CD.1—4 see
Symbolical language      E.28
Symmedian line      E.42 N.83—85 Q.20
Symmedian point      4754c
Symmetrical conics of triangles      A.59
Symmetrical connections by generating functions      J.53
Symmetrical expressions      219
Symmetrical figures      J.44
Symmetrical functions      C.76 J.69 93 98 LM.13 Q.20 Z.4
Symmetrical functions of any number of variables      C.82
Symmetrical functions of the common sol. of several eqs.      An.58
Symmetrical functions, Brioschi's th.      C.98
Symmetrical functions, multiplication of      Me.85
Symmetrical functions, simple and complete      M.18 20
Symmetrical functions, tables of      AJ.5
Symmetrical functions, tables of, of 12-ic      AJ.5
Symmetrical points of 1st order      A.60 cnA.64
Symmetrical points of a triangle      A.58
Symmetrical points of tetrahedrons      A.60
Symmetrical products      P.61 Pr.11
Symmetrical products with prime roots of unity      Me.85
Symmetrical tetrahedral surfaces      Z.11
Symmetry, plane and in space      N.47
Synthesis      C.18
Synthetic division      28
Synthetic division, evolution      Me.68
Syntractrix      5282
Tables for empirical formulae      AJ.5
Tables in theory of numbers      Q.1
Tables of $e^{x}$, $e^{-x}$, $\log_{10} e^{x}$, $\log_{10} e^{-x}$      CP.13
Tables of Bernoulli's nos., logarithms, &c., calculation of      J.2
Tables, mathematical      xi
Tac-loci      Me.83
Tamisage      LM.14
tan nx, f. in      N.53
tan x as a continued fraction      Z.16
tan x as a continued fraction, do. tan nx      Me.74
Tangencies (circles, points, and lines)      937 Pr.9 Q.2 8
Tangent cone at a singular point      5783
Tangent planes      5770—5782 p.c5790 CM.4 N.45
Tangent planes and surface, intersection of      5786—5789 L.58
Tangent planes to equidistant surfaces      cnZ.28
Tangent planes, triple      C.77
Tangential eq. with the intercept and angle of inclination for coordinates of the line      P.77
tangents      1160 cnA.4 33 J.56 73 N.42 Z.23
Tangents and contact-point in loci and envelopes      C.85 cnN.57
Tangents and normals      5100
Tangents and normals, relations      A.51
Tangents at a multiple point, cn.      JP.13
Tangents of a surface      5781
Tangents of a surface at singular points      5783 M.11 15
Tangents, conjugate (and Dupin's th.)      An.60
Tangents, construction of      M.22 N.80
Tangents, cut by lines at a constant angle      A.43
Tangents, double      Q.3
Tangents, eq. of, to find it      4120—4132 Me.66
Tangents, faisceaux of      N.50
Tangents, locus of intersections of three      LM.15
Tangents, parallel      N.45
Tangents, segments of      4307
Tangents, segments of, equality of      C.81
tanh S      2213
tantochrone      L.44 An.53
Taylor's theorem      1500 1520 1523 A.8 13 AJ.4 ext1 C.58 CM.1 J.11 L.37 38 45 58 gz64 M.21 23 Me.72 73 75 Mem.20 N.52 63 70 74 79 TA.7 8 Z.gz 25
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