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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
Maximum or minimum, solids of max. vol. with given surface and of min. surface with given vol.      C.63
Maximum, ellipse touching 4 lines      A.12
Maximum, ellipsoid in a tetrahedron      Z.14
Maximum, polyhedron in ellipsoid      A.32
Maximum, solid of revolution      3074
Maximum, tetrahedron in ellipsoid      A.32
Maximum, tetrahedron, whose faccs have given areas      C.51 66 N.62
Maximum, volume with a given surface      3082
Mean centre of segments of a line crossing three others      A.40
Mean distance of lines from a point      Z.11
Mean error of observations      A.25 C.37 TI.22
Mean error of observations, in trigonometrical and chain measurements      A.46 Z.6
Mean proportionals between two lines      A.31 34
Mean values      C.18 20 23 26 27 L.67 LM.8 M.6 7 Z.3
Mean values and probabilities, geo      C.87 L.79
Mean values of a function of 3 variables      C.29
Mean values of a function of one variable      G.16
Measures of length &c.      4
Measures of length &c., exactitude of      Z.6
Measures of length &c., exactitude of, do. with chain      Z.1
Mechanical calculators      C.28 I.16 P.85
Mechanical calculators for "least squares"      Mel.2
Mechanical construction of $(a^{2}-x^{2})/y$      E.18
Mechanical construction of Cartesian oval      AJ.1
Mechanical construction of conformable figures      AJ.2
Mechanical construction of conics      An.52
Mechanical construction of cubic parabola      N.58
Mechanical construction of curves      M.6 N.56
Mechanical construction of curves for duplication of roots      A.48
Mechanical construction of ellipse      A.65 Z.1
Mechanical construction of lemniscate      A.3
Mechanical construction of surfaces of 2nd order and class      J.34
Mechanical construction of three      N.43
Mechanical division of angles      Q.4
Mechanical integrators      5450 C.92 94 95 Pr.24
Mechanical integrators for Xdx+Ydy      Me.78
Mechanical involution      AJ.4
Mechanical measurement of angles      A.61
Mechanical quadrature      3772 A.58 59 J.6 63 gzA.66 C.99
Mechanical solution of equations      Me.73 N.67
Mechanical solution of equations, cubic and biquadratic, graphically      A.1
Mechanical solution of equations, linear simultaneous      Pr.28
Mensuration of casks      A.20
Metamorphic method by reciprocal radii      N.54
Metamorphic transformation      N.46
Metrical properties of figures, transf. of      N.58 59 60 J.4
Metrical properties of surfaces      AJ.4
Metrical system      E.30
Meunier's theorem      5809 gzC.74
Minding's theorem, Quaternion proof      LM.10
Minimum surfaces      eqA.38 G.14 22 J.81 85 87 ext78 Mo.67 72
Minimum surfaces of a twisted quadric      At.52
Minimum surfaces, algebraic      M.3
Minimum surfaces, algebraic, lowest class-number      An.79
Minimum surfaces, arbitrary functions of the integral eq. of      C.40
Minimum surfaces, between 2 right lines in space      C.40
Minimum surfaces, generation of      L.63
Minimum surfaces, limits of (Calc. of Var.)      J.80
Minimum surfaces, limits of, determined by one of the edges of a twisted quadrilateral      Mo.65
Minimum surfaces, limits of, on a catenoid      M.2
Minimum surfaces, metric      M.15
Minimum surfaces, not algebraic and containing a succession of algebraic curves      C.87
Minimum surfaces, projective      M.14
Minimum surfaces, representation of by elliptic functions      J.99
Minimum surfaces, variation of surface, capacity of      Mo.72
Minimum value of $\int \surd (dx^{2}+dy^{2}+\ldots)$ when the variables are connected by a quadric equation      J.43
Minimum value of $\int_{-1}^{1} (A+Bx+Cx^{2}+\&c.)dx$      N.73
Minimum, theory of      L.56 prM.20
Minimum, theory of, angle between two conj. tangents on a positive curved surface      A.69
Minimum, theory of, area      J.67
Minimum, theory of, area of a hexagonal "alveole", pr      N.43
Minimum, theory of, area of circum-polygon      CD.3
Minimum, theory of, circum-conic of a quadrilateral      A.13 An.54
Minimum, theory of, circum-tetrahedron of an ellipsoid      Z.25
Minimum, theory of, circum-triangle of a conic      Z.28
Minimum, theory of, circum-triangle of an ellipse      Z.25
Minimum, theory of, curves on surfaces      J.5 see
Minimum, theory of, distance of 2 right lines      G.4
Minimum, theory of, distance of a point, ths      A.8
Minimum, theory of, ellipse through 3 points and ellipsoid through 4      L.42
Minimum, theory of, ellipsoid, th      Mo.72
Minimum, theory of, N.G.F. of a binary septic      AJ.2
Minimum, theory of, numerical value of a linear function with integral coefficients of an irrational quantity      C.53 54
Minimum, theory of, perimeter enclosing a given area on a curved surface      J.86
Minimum, theory of, questions relating to approximation      Mel.2 Mem.59
Minimum, theory of, sum of distances from two points      920 921
Minimum, theory of, sum of squares of distances of a point from three right lines      Z.12
Minimum, theory of, sum of squares of functions      N.79
Models      LM.39
Models of ruled surfaces      Me.74
Modular equations      An.79
Modular equations of 8th degree      59 C.48 49 66 M.1 2 Mo.65 see
Modular factors of integral functions      N.24
Modular functions and integrals      An.51 J.18 19 20 21 23 25 M.20
Modular indices of polynomials, which furnish the powers and products of a binomial eq      N.25
Modular relations      At.65
Modular, degradation of      M.14
Modulus of functions, principal      N.20
Modulus of series      N.17
Modulus of transformations      1604 A.17
Moment of inertia      5903 An.63 At.43 M.23
Moment of inertia by geometry of 4 dimensions      Q.16
Moment of inertia of a quadrilateral      5951 Q.11
Moment of inertia of a tetrahedron      5957
Moment of inertia of a triangle      5944 Me.4 Q.6
Moment of inertia of a triangle, polar      N.83
Moment of inertia of ellipsoid      6150 CD.8 J.16
Moment of inertia of solid rings of revolution      Q.16
Moment of inertia of various laminae and solids      6015—6165
Moment of inertia, principal axes      5926 5967 5972 At.43
Momental ellipse      5953
Momental ellipsoid      5925 5934
Momental ellipsoid for a plane      5936
Monge's theory "des Deblais et des Remblais"      LM.14
Monocyclic systems and related ones      J.98
Monodrome functions      C.43 G.18
Monogenous functions (Laurent's th)      Ac.4 C.32 43
Monothetic equations      C.99
Monotypical functions      C.32
Mortality      A.39
Movements      JP.15
Movements of "ahnlich - veraenderlicher" and "affin-veraenderlicher" systems      Z.24 19
Movements of a plane figure      thAn.68 JP.20 28 LM.3
Movements of a point on an ellipsoid      AJ.1 J.54
Movements of a right line      C.89 N.63
Movements of a solid      JP.21
Movements of an invariable system      C.43
Movements, elliptic and parabolic      JP.30
Movements, groups of      An.69
Movements, relative      JP.19
Movements, relative, of a point      L.63
Movements, transmission of and the curves resulting      JP.3
Multinomial theorem      137 Me.62
Multiple curves of alg. surfaces      An.73
Multiple Gauss sums      J.74
Multiple integrals      1905 2825 A.64 An.52 C.8 11 thsCD.1 thE.36 J.69 L.39 43 45 46 th48 56 LM.8 Me.76 Z.1 3
Multiple integrals $\int \int \int \epsilon \ exp(-x^{2}-y^{2}-z^{2}), x^{p}y^{q}z dx dy dz$      N.54
Multiple integrals $\int \int \int \ldots \phi (ax^{\alpha} + by^{\beta} + \&c.)x^{p}y^{q} \ldots dxdy \ldots$ with limits 0 to $\infty$ in each case (Pfaff)      J.28
Multiple integrals $\int \int \ldots \frac{dxdy\ldots}{\{ (a-x)^{2}+(b-y)^{2}+\ldots \}^{n}}$by discontinuous functions      TI.21
Multiple integrals $\int\int \ldots F(x,y,z \ldots)PQdxdydz\ldots$ where $P=(1 - x)^{a-1}(1 - y)^{b-1}\ldots Qy^{a}z^{a+b}t^{a+b+c}\ldots$      L.59
Multiple integrals of theory of attraction      CD.7
Multiple integrals which are unaltered in form by transformation of the variables      J.15 91
Multiple integrals, $\int \int \int F(ax+by+cz, a^{'}x+b^{'}y+c^{'}z, a^{''}x+b^{''}y+c^{''}z)dxdydz$, limits $\pm \infty$      A.30
Multiple integrals, $\int \int \int \ldots dxdydz \ldots$      Q.23
Multiple integrals, $\int \int \int \ldots x^{l-1}y^{m-1}z^{n-1}\ldots dxdydz\ldots $ with different limiting equations      2825 CM.2 L.51
Multiple integrals, arising from (2604), viz: $\int_{0}^{\infty} \epsilon \ exp(-x^{2}-\frac{a^{2}}{x^{2}})dx$      Pr.42
Multiple integrals, do. with $n=\frac{m}{2}$ and with a numerator $(a-x)F(\frac{x^{2}}{h^{2}}+\frac{y^{2}}{k^{2}}+\ldots)$      CM.3
Multiple integrals, double      2710 2734—2742 A.13 Ac.5 An.70 J.27 G.10 L.58 Mem.30
Multiple integrals, double, $\frac{1}{\pi^{2}} \int_{0}^{2\pi} \int_{0}^{2\pi} \frac{\cos ix \cos jx dx dy}{\surd \{ 1+a^{2}+2a(\mu \cos a+\nu \cos y) \}}$      C.96
Multiple integrals, double, $\int \int F(a+bx+cy)dx dy$      A.37
Multiple integrals, double, $\int \int F^{'} (x+iy)dx dy$      J.42
Multiple integrals, double, $\int \int \frac{(x^{'}-x)(dydz^{'}-dzdy^{'})+sym}{\surd \{(x^{'}-x)^{2}+\ldots \}^{3}}=4mn$      C.66
Multiple integrals, double, $\int \int \frac{F(u,t,z)}{G(u,t,z)}dt du$      C.96
Multiple integrals, double, $\int_{0}^{b} \int_{b}^{c} \frac{(x^{2}-y^{2}) dx dy}{\surd \{ (x^{2}-b^{2})(c^{2}-x^{2})(b^{2}-y^{2})(c^{2}-y^{2}) \}}=\frac{\pi}{2}$      L.38
Multiple integrals, double, $\int_{0}^{\infty} \int_{0}^{\infty} \phi (ax^{m}\pm by^{n})x^{p-1}y^{q-1}dxdy$      J.37
Multiple integrals, double, approximation to      J.6
Multiple integrals, double, Cauchy's theory, ext. of      C.75
Multiple integrals, double, change of order of integration      2775 A.19
Multiple integrals, double, expressing an arbitrary function      J.43
Multiple integrals, double, reduction of      J.45 Z.9
Multiple integrals, double, residues of      C.75
Multiple integrals, double, same with log of numerator      L.50
Multiple integrals, double, transf. of $\int \int \frac{d\phi d\psi}{\surd (\sin^{2}\nu - \sin^{2}\phi \cos^{2}\psi)}$      J.20
Multiple integrals, evaluation      A.5
Multiple integrals, evaluation by Fourier's th      CM.4
Multiple integrals, expansion of      Q.8
Multiple integrals, Frullanian      LM.15
Multiple integrals, limits of      LM.16
Multiple integrals, reduction of      An.57 L.41 39
Multiple integrals, reduction of, $\int^{n} F(x^{2}+y^{2}+\ldots)\phi(ax + by+\ldots)dxdy$      L.57
Multiple integrals, reduction of, by transf. of coordinates      C.13
Multiple integrals, some other integrals evaluated by $\Gamma$ functions      2826 2834
Multiple integrals, transformation of      2774 A.10 An.53 No.47 CM.4 Mel.2 Mem.38 Q.4 12
Multiple integrals, transformation of, $y_{1}dx_{1}+ \ldots +y_{n}dx_{n}$      LM.11
Multiple integrals, transformation of, a triple integral      2774 2779 J.45
Multiple integrals, transformation of, an indef. double      J.8 10
Multiple integrals, triple      2774 A.30 J.45
Multiple integrals, volume integral of $(\frac{x}{a})^{p}+(\frac{y}{b})^{q}+(\frac{z}{c})^{r}$      Z.14
Multiple points      5178 CM.2 thG.15 Me.2 Q.2 6
Multiple points on a surface      J.28
Multiple points on algebraic curves      An.52 L.42 N.51 59 81
Multiple points on algebraic curves at $\infty$      64
Multiple points on two curves having branches in contact      C.77
Multiple-centres, geo. theory      L.45
Multiplication      28 J.49
Multiplication by fractions      Me.68
Multiplication, abridged      N.79
Multiplicator equations      M.15
Multiplicity or manifoldness      J.84 86 thAc.5 Z.20
MUSIC      E.27 28 Pr.37
Nasik squares and cubes      Q.8 15
Navigation, geo. prs. of use in      A.38
Negative in geometry      No.1792
Negative quantities      At.55 N.44 67 TE.1788
Nephroid      LM.10
Net surfaces      J.1 2 M.1
Net surfaces and series      C.62
Net surfaces, any order      An.64
Net surfaces, having a 3-point contact with the intersection of two algebraic surfaces      G.9
Net surfaces, quadric      J.70 82 M.11
Net surfaces, quartic      M.7
Net surfaces, trigonometrical      Z.14
Newton, autograph m.s.s of      TE.12
Nine-point circle      954 4754 A.41 E.7 30 th35 pr39 G.1 ths4 Me.64 68 Q.5—8
Nine-point circle and 12-point sphere, analogy      N.63
Nine-point circle, an analogous circle      A.51
Nine-point circle, contact with in- and ex-circles      959 Me.82 Q.13
Nine-point conic of a tetrahedron      Me.71
Nodal cones of quadrinodal cubics      Q.10
Node cusps      Q.6
Nodes, two-plane and one-plane      M.22
Non-uniform functions      C.88
Nonions (analogous to Quaternions)      C.97 98
Normals      1160 4122—4123 5122 A.13 53 LM.9 p.eMe.66 Z.cn2 3
Normals of a surface      5771 5785 C.52 CD.3 CM.2 L.39 47 72 M.7
Normals of a surface, coincident      L.48
Normals of envelopes      Me.80
Normals of rational space curves      J.74
Normals, plane of a surface      5772
Normals, principal      5722
Normals, principal, condition for being normals of a second curve      C.85
Normals, section of ellipsoid (geodesy)      A.40
Normals, transformation of a pencil of      C.88
Notation A, B, C, F, G, H      1642 see
Notation for some developments      C.98
Notation, $(a_{1}b_{2}c_{3})$      554
Notation, $(n) (\frac{b}{a})$, Jacobi's function      see "Functions"
Notation, $(\frac{n}{r})\equiv$ $r$th coeff. of nth power of (1+x) also Jacobi's function      see "Functions"
Notation, $a+\frac{1}{b}+\frac{1}{c}$      160
Notation, $a^{b}$ or $a^{n/b}$      2451
Notation, $B_{2^{n}$, Bernoulli's nos.      1539
Notation, $d^{2}y$, $dx^{3}$, $\frac{dy}{dx}$,&c.      1407
Notation, $f^{'}(x)f^{n}(x)$      424 1405
Notation, $Gu_{x}$      3732
Notation, $n\equiv n^{(n)} \equiv n!$      94 3713
Notation, $sin^{-1}$, &c.      626
Notation, $S_{m}$, $S_{m,p}$      534
Notation, $S_{n}$      2940
Notation, $u_{n}$      3499
Notation, $\frac{d(uvw)}{d(xyz)}$      1600
Notation, $\phi(\alpha \beta \gamma)\equiv u$      4656
Notation, $\Phi(\lambda \mu \nu)$ or U      4665
Notation, $\pi$ as operator      3500
Notation, $\psi(x)$ or $Z^{'}(x) \equiv d_{x} log \Gamma (x)$      2743
Notation, $\Sigma$      3781—3783
Notation, $\triangle$      582 1641 3701
Notation, ( I ) and ( X )      1620
Notation, A.P., G.P., H.P.      79 83 87
Notation, algebraic      CP.3
Notation, C(n,r) or $C_{n,r}$      96
Notation, D      3489
Notation, D, $d_{x}$, $d_{nx}$, &c.      1405
Notation, E      902 3735
Notation, f(x)      400 1400
Notation, f(x), $f^{-2}(x)$      430
Notation, H(n,r)      98
Notation, J      1600
Notation, P(n,r) or $P_{n,r}\equiv n^{(r)}$      95
Notation, R, r, $r_{a}$      909—913
Notation, sinh, &c.      2180
Notation, subfactorial      Me.78
Notation, suggestions      Me.73
Numbers      349 A.2 16 26 58 59 Ac.2 AJ.4 6 C.f12 43 44 45 f60 CM.1 G.16 32 J.9 39 40 48 77 tr 27 28 29 JP.9 L.37—39 41 45 58 59 60 LM.4 Mem.22 24 tr(Euler) 30 N.44 62 79 Q.4 TE.23 see "Indeterminate
Numbers of $\Gamma$ function      No.81
Numbers of infinitesimal analysis      J.19 21
Numbers, 4m+1 and 4m+3 divisors of a number      LM.15
Numbers, ap. of algebra      JP.11
Numbers, approximation to $\surd N$      E.17
Numbers, approximation to functions of large numbers      C.82
Numbers, binomial eqs. with a prime mod      C.62
Numbers, cube      Q.4
Numbers, cubic binomials: $x^{3} \pm y^{3}$      C.61
Numbers, determined by continued fractions      LM.29
Numbers, digits terminating a power      A.58 N.46
Numbers, digits, calculus of, th      J.30
Numbers, Dirichlet's f. for class numbers as positive determinants      L.57
Numbers, Dirichlet's th. $\Sigma^{\theta} \left ( \frac{m}{D^{2}} \right )=\zeta (m)$      L.57
Numbers, division of      A.26 J.13 Mel.3 Pr.7 10
Numbers, division of, by $mx^{2}+ny^{2}$      Mem.15 P.17 88 Q.19 20
Numbers, division of, by 7 and 13      A.25 26
Numbers, divisors arising from the division of the circle      L.60
Numbers, divisors of $y^{2}+Az^{2}$ when A=4n+3 a prime      J.9
Numbers, factors of      Mem.41
Numbers, formulae      L.64 65
Numbers, Gauss's form      L.56
Numbers, integral quotients and remainders      An.52
Numbers, large, analysis of      A.2 C.2 29
Numbers, method with continuous variables      J.41
Numbers, multiples of      C.2
Numbers, non-pentagonal th      J.31
Numbers, number of integers prime to n in $n! \equiv \phi (n)$      L.57
Numbers, odd      A.1
Numbers, odd and prime to all squares      C.67
Numbers, Pellian equation      prA.49 LM.15
Numbers, Pellian equation, sol. by ell. functions      Mo.63
Numbers, perfect      C.81 N.79
Numbers, polygonal, Fermat's th. of      P.61
Numbers, polynomials having determinate prime divisors      C.98
Numbers, powers of, 12 theorems      N.46
Numbers, prime to and < N      A.3 29 E.28 J.31 N.45
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