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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
Elliptic functions, quadriquadric curve      M.25
Elliptic functions, reduction of      An.64
Elliptic functions, reduction of, in canonical forms      J.53
Elliptic functions, relations      A.67 J.56
Elliptic functions, relations between $E^{'}(k)$ and $F^{'}(k)$      J.39
Elliptic functions, representation by power series      J.54
Elliptic functions, representation of quantities by sin am(u+w, k)      J.45
Elliptic functions, series      C.95
Elliptic functions, sn 8u, cn 8u, dn 8u in terms of sn u, tables      Pr.33
Elliptic functions, sn, cn, and dn of u+v+w      LM.13
Elliptic functions, spherical triangle of      Q.19
Elliptic functions, subsidiary, pm (u, k)      LM.15
Elliptic functions, substitution of 1st order      J.34
Elliptic functions, transformation      An.57 58 60 Ac.3 C.49 f79 f80 82 CD.3 5 J.3 34 35 f55 55 87 88 89 LM.9 11 M.14 19 22 Me.83 tr84 Pr.27 Q.13 20
Elliptic functions, transformation and division      J.76 M.25
Elliptic functions, transformation and of functions in theory of Catenary      A.2
Elliptic functions, transformation by roots of unity      J.6
Elliptic functions, transformation Hermite's; tables      J.72
Elliptic functions, transformation Jacobi's      LM.15 16 J.87
Elliptic functions, transformation of 11th order      At.5
Elliptic functions, transformation of 1st and 2nd kind as functions of the mod      L.40
Elliptic functions, transformation of 1st kind      A.33
Elliptic functions, transformation of 3rd order      J.60 Me.83
Elliptic functions, transformation of 7th order, square of mod      J.12 LM.13
Elliptic functions, transformation of a double integral, &c.      Me.75
Elliptic functions, transformation of rectangular coordinates      LM.15
Elliptic functions, transformation of the orders      11 13 17 19 J.12 16
Elliptic functions, transformation, cubic      C.64 Q.13
Elliptic functions, transformation, linear      J.91
Elliptic functions, transformation, modular, of Abel, ap to conics      C.79
Elliptic functions, transformation, modular, of Abel, ap to geom      C.58
Elliptic functions, transformation, modulus of in a function of the quotient of the two periods      An.70
Elliptic functions, transformation, pertaining to an even number      J.14
Elliptic functions, transformation, quartic      Q.12
Elliptic functions, triple division of and ap. to inflex. of cubics      A.70
Elliptic functions, Weierstrass's method      AJ.6
Emanents      1654
Empirical formulae, calculation of      Me.73
Engrenages      L.39 40
Envelope      5192 A.24 prs56 C.45 86
Envelope from ellipse and circle      LM.15
Envelope of a carried curve      5239
Envelope of a curve with n parameters      5194
Envelope of a plane      C.35
Envelope of a quadric      Q.11
Envelope of a right line      N.63 79 83 Q.13
Envelope of a right line, cutting two circles harmonically      N.85
Envelope of a right line, sliding on two rectangular axes      N.45
Envelope of a Simson line      E.29 34
Envelope of a sphere      C.67 J.33
Envelope of a sphere, touching 3 spheres      N.60
Envelope of a surface      CM.1 M.5
Envelope of a surface of revolution      L.65
Envelope of a surface, degree of      N.60
Envelope of chord of a closed curve      E.28
Envelope of chord of a closed curve, cutting of a constant area      E.31
Envelope of chords of a conic      N.48
Envelope of chords of a conic, subtending a constant angle at the focus      CM.3
Envelope of conics, theorems      N.45
Envelope of curves in space      L.83
Envelope of directrix of a parabola      E.34
Envelope of geodesics      M.14 20
Envelope of pedal line of a triangle      Q.10
Envelope of pedal line of a triangle, do. of in-triangle of a circle      Q.8 9
Envelope of perpendiculars at extremities of diameter of an ellipse      N.46
Envelope of plane curves      G.11 12
Envelope of plane curves, singularities of      LM.2
Envelope of planes perpendicular to radiants of an ellipsoid at the surface      An.59 Pr.9
Envelope of planes which cut a quartic gauche curve of the 2° in 4 points of a circle      An.71
Envelope of polars of a curve      J.58
Envelope of tangent of 2 variable circles      N.51
Envelope, application to perspective      A.9
Envelope, class of (Chasles), th      C.85
Envelope, imaginary, of the conjugates of a plane curve      C.75
Envelope, p.d.e      CM.4 G.11 M.84 Me.64 72 N.44 59 68 74
Enveloping asymptotic chords and polars      A.14 16 17
Enveloping cone      5664—5672
Enveloping cone of a quadric      5697
Enveloping cone of a quadric, th of Jacobi      J.12 CD.3
Enveloping cone of a twisted hexagon, locus of vertex      A.10
Enveloping cone of an n-tic surface      CD.4
Enveloping line of class cubic, involution th      E.29
Epi- and Hypo-cycloids      5266—5272 LM.4 Z.18
Epi- and Hypo-cycloids and derived curves      Z.17
Epi- and Hypo-cycloids, tangential properties of      absPr.34
Epi- and Hypo-trochoids      5262—5265 LM.4
Epicycloids      J.1 Mem.20 N.45 46 60 TE.24 thsZ.15
Epicycloids, centre of curvature      N.59
Epicycloids, centre of curvature, plane and spherical      JP.14
Epicycloids, double generation of      N.69
Epicycloids, reciprocal polar of      geoE.19
Equality and similarity of figures      J.52
Equations      50—67 211—222 400—594 A.6 18 57 58 60 61 65 67 tr AJ.6 An.51 54 C.44 see
Equations (For Binomial, Biquadratic, Cubic, Cubic and biquadratic, Linear, Quadratic, Quintic, and Transcendental)      47 59 62 68 91 97 99 CM.3 CP.4 G.1 J.13 16 34 L.67 69 M.14 21 Me.76 Mo.79 f80 N.67 68 ths55 67 80 P.1799
Equations from observations      A.21
Equations in geo. mean of roots      N.45
Equations in one variable      45—58 214—216 400—550
Equations in one variable, approx      A.20
Equations in one variable, approx $x^{2n+1}-x-k=0$      An.59
Equations in one variable, approx, graphic solution      C.65
Equations in quotients of roots      N.45
Equations in sums of the C(n, 2) roots of another eq.      N.43
Equations in three variables, $(y-c)(z-b)=a^{2}, $ sym in x, y, z      219
Equations in three variables, $ax+by+cz=i, a^{'}x+b^{'}y+c^{'}z=i, x^{2}+y^{2}+x^{2}=1, $ by trigonometry      A.6
Equations in three variables, $x-yz=\pm\surd{(1-y^{2})(1-z^{2})} &c.$, sym      A.35
Equations in three variables, $x^{2}-yz=a^{2}, &c.$, sym, and x=cy+bz &c., sym      221—222
Equations in three variables, $y^{2}+z^{2}+yz= a^{2}, &c.$, sym      220
Equations in three variables, gn.sol      60 A.1 64 N.47 M.37
Equations in three variables, gn.sol by acubo-cycloid      C.69
Equations in two variables      59—67 211 217—218 A.20 25 CM.2 J.14 N.47 48 63 Pr.8 Q.18
Equations in two variables of any degree with a variable parameter      L.59
Equations in two variables, $x^{3}+y^{3}=a$ and $x^{2}y+xy^{2}=b$      A.48
Equations in two variables, implicit      Mem.30
Equations in two variables, numerical solution      Z.20
Equations of degree above the 4th not soluble      J.83
Equations of geometry      C.68
Equations of geometry, homogeneous      N.64
Equations of nth degree with two real roots      C.98
Equations of payments      A.34 36 CD.1 CM.2
Equations with integral coefficients      503 C.24 J.53
Equations with integral, complex coefficients      J.53
Equations with only one positive root      411 C.98
Equations, $(1+x)^{m}(1+bx)=0$ when x is small      A.2
Equations, $(x-1)!+1=x^{m}$      L.56
Equations, $(x^{p}-a^{p})\psi (x)=0$      N.82
Equations, $ax^{2m+n}+bx^{m+n}+cx^{n}+d=0$      G.14
Equations, $x^{2n}+qx^{n}+p^{n}=0$ and derivatives      N.65
Equations, $x^{m}-px+q=0$: number of real roots      C.98
Equations, $x^{n-1}+x^{n-2}+...+1=0$ irreducible if n be a prime      L.56
Equations, Abel's properties      C.91
Equations, algorithms for solving      M.3
Equations, derived      424—431 A.22
Equations, derived in d.e      1708—1712
Equations, developments      An.61
Equations, differential operators in      LM.14
Equations, Eisenstein's theorem      LM.7
Equations, extension of theory of      C.58
Equations, fundamental principles or theorems      A.1 11 C.96 97 L.39 40 J.23
Equations, Galois' theory      C.60 G.12 M.18 23
Equations, generic      Q.4 5
Equations, Hariot's law of      J.2 extC.98
Equations, homogeneous, reduction of a principal function which verifies a characteristic homog. eq.      C.13 14
Equations, identical      J.27
Equations, impossible      Man.51
Equations, insolubility of quintics, &c.      J.1
Equations, irrational      Man.51
Equations, irreducible      An.51 Mo.80
Equations, irreducible, of prime degrees      AJ.7
Equations, linear      see "Linear equations"
Equations, miscellaneous      214
Equations, numerical      C.10 12 32 78 81 G.13 J.10 L.36 38 41 83
Equations, numerical and commensurable quadratic factors      L.45
Equations, reciprocal      466 A.44 C.16
Equations, reciprocal of a quartic      N.66
Equations, reduction of      C.97 CD.6
Equations, reduction of, to reciprocal eqs.      A.35
Equations, relation to linear d.e and f.d.e      L.36
Equations, simultaneous      59 211 582 C.25 LM.6 thsN.48 81 see "Equations
Equations, simultaneous, deducible the one from the other      C.22
Equations, simultaneous, of the form $x^{m}+y^{m}+z^{m}=a$      N.46
Equations, simultaneous, quadratics      N.60
Equations, solution by approximation      506—533 A.30 Ac.4 C.11 17 45 60 79 82 E.4 G.8 J.14 22 Me.68 N.51 62 78 80 84 No.58 P.5 Q.3 TI.7 Z.23
Equations, solution by continued fractions      J.33
Equations, solution by definite integrals      Me.81 P.64 Z.3
Equations, solution by diminishing the powers of the roots      C.41
Equations, solution by elimination of integers      N.70
Equations, solution by geometry      C.87
Equations, solution by imaginary values      J.20
Equations, solution by infinite series      J.33
Equations, solution by interpolation      C.5
Equations, solution by logarithms      C.95
Equations, solution by radicals      C.58 Q.15
Equations, solution by series      An.57 C.49 52 J.6 Mem.33
Equations, solution by transcendents      An.63 Q.5
Equations, solution by trigonometry      480 A.1
Equations, solution of      45 54 59 211 466—533 582 A.64 trAn.52 C.3 5 62 64 J.4 27 87 Mo.56 61
Equations, solution of a nonic eq. which has this characteristic: A given rational symmetrical function $\theta(\alpha, \beta)$ of two roots, gives a third root $\gamma$, such that $\alpha=\theta(\beta, \gamma), \beta=\theta(\gamma, \alpha), \gamma=\theta(\alpha, \beta)$      J.34
Equations, solution of the one by the other      C.72 L.71
Equations, solution of, Horner's method      533 P.19
Equations, solution of, Lagrange's method      525 C.91
Equations, solution of, Newton — Fourier method      527—528 AJ.4 G.2 Me.66 N.46 56 60 69 79
Equations, solution of, Weddle's method      Z.7 8
Equations, symbolic, non-linear      C.22
Equations, systems of      C.67 G.11 18 LM.2 8 Q.11 M.19 Z.14 18 see
Equations, transformation of      C.64
Equations, whose coefficients are rational functions of a variable      J.74
Equations, whose degree is a power of a prime      An.61 C.48 L.68
Equiangular spiral      5288 Me.62 N.69 70
Equilateral hyperbolic paraboloid and derived ray-system      Z.23
Equimultiples in proportion      G1
Equipollences, method of      N.69 70 73 74
Equipotential curves      Me.82 Pr.24
Equipotential surfaces      G.20 geoJ.42 M.8
Equipotential surfaces of ellipsoid      L.82
Equivalence of forms      C.88 90 JP.29
Equivalent representation      Z.23
Equivalents, theory of      A.44
Eratosthenes' crib or sieve      N.43 49
Error in final digit of decimals      C.40 Me.74 N.56
Errors of constants      Mo.83
Errors of observation      A.18 19 An.58 C.93 JP.13 N.56 P.70 TE.24
Euclid, enunciations      p.xxi
Euclid, enunciations, axiom 11      J.1 I.47
Euclid, enunciations, axiom 11, new proof      C.60
Euclid, enunciations, II 12 and 13, new proof      Q.9
Euclid, enunciations, II. 12 and 13      Me.80 VI.7 Q.11
Euclid, enunciations, XI., &c.      Me.71 XI.28 A.10
Euclid, enunciations, XII., &c.      G.9
Euclid, enunciations, XII., criticism on      Q.7 9
Euler's algorithms      A.67
Euler's constant      2744 Pr.15 16 18 19 20 Table
Euler's constant and Binet's function      C.77 L.75
Euler's equation      N.72
Euler's equation, integration of it by the lines of curvature of a ruled hyberboloid      N.75
Euler's equations of motion solved by elliptic integrals      Q.14
Euler's formula for $(1+x)^{n}$      L.44
Euler's integrals      2280—2323 A.41 Ac.1 2 An.54 C.9 17 94 95 th96 J.15 21 45 fL.43 Me.83 Z.9
Euler's integrals, $\Gamma(n)$      see "Gamma function"
Euler's integrals, ap. to series and functions of large numbers      JP.16
Euler's integrals, B(l, m)      2280 An.69 G.9
Euler's integrals, sum formula and quadratic residues      An.52
Euler's numbers      AJ.5 An.77 C.66 83 J.79 89 prsL.44 Me.78 80
Evectant of Hessian of a curve      E.32
Even and odd functions      1401
Evolute      5149—5159 5165 An.53 61 C.30 Q.3 11
Evolute and involute in one      L.41
Evolute of a catenary      5159
Evolute of a cubic curve      Q.11
Evolute of a cycloid      A.30
Evolute of a parabola      4549 4959 Q.5 N.65
Evolute of a tortuous curve      5731 A.25
Evolute of a tortuous curve, angle of torsion of evolute      5754
Evolute of a tortuous curve, integrable equations      L.43
Evolute of an ellipse      4547 4958 C.84 N.52 63
Evolute of an evolute, in inf.      L.59 Me.80
Evolute of negative focal pedal of a parabola      E.29
Evolute of surfaces      C.74
Evolute of symmetrical bicircular quartics      Q.18
Evolute of the limacon, rectif. and quadr. of      E.40
Evolute, analogous curves      L.76
Evolute, oblique, direct and inverse of different orders      C.85
Evolute, rectification and quadrature of      A.4
Evolution      35
Ex-circle of a triangle      711 953 4749 A.54 thN.60
Ex-circle of a triangle, focus of centre, th      Q.9
Expansion of $(1+ax)^{\frac{1}{n}}$ in an integral series      A.65
Expansion of $(1+ax+bx^{2})^{n}$      Q.18
Expansion of $(1+ax+bx^{2}+...lx^{n-1})^{-1}$      AJ.6
Expansion of $(1+x)(1+2x)...(1+\bar{n-1}x)$      C.25 J.43
Expansion of $(1-2ax+x^{2})^{-\frac{1}{2}}$      L.37
Expansion of $(1-2ax+\alpha^{2}a^{2})^{-\frac{2l+1}{2}}$      C.86
Expansion of $(1-ax-bx^{2})^{-m}$      J.43
Expansion of $(1-x)(1-x^{2})(1-x^{3})...$      C.92 J.21 L.42
Expansion of $(1-x)(1-x^{2})(1-x^{4})(1-x^{8})...$      Me.80
Expansion of $(1-\mu cos\phi)^{-1}=\sum a_{n}cos 2n\phi$      A.21
Expansion of $(a+b cos\phi+c cos\phi^{'})^{-n}$ in cosines of multiples of $\phi$ and $\phi^{'}$      J.15
Expansion of $(ae^{x}-1)^{-1}$      At.57
Expansion of $(a^{2}+b^{2}-2abcos\phi)exp.-(m+\frac{1}{2})$      TE.5
Expansion of $(x+y)^{(n)}$      CM.3
Expansion of $(x-z)^{m}$ in powers $x^{2}-1$      C.86
Expansion of $(\frac{1-\surd(1-4t)}{2})^{2}$ in powers of t, when $y=\frac{x}{1+\surd(1-x^{2})}$      1565
Expansion of $a^{x} sin x$ in differences of sin x      3749
Expansion of $cos k cos^{-1}(cos\omega+a)$      C.15
Expansion of $cot^{-1}(m-1)-cot^{-1}(m+1)$      A.47
Expansion of $e exp. a sin^{-1}x$      1535
Expansion of $e exp. log(z+xsiny)$      1557
Expansion of $e exp. sin x$      1529
Expansion of $e exp.(\lambda x+\frac{\mu}{x})$      Z.3
Expansion of $e exp.-\phi(x, y, z...)$      C.58
Expansion of $e=limit\, of\, (1+x)^{\frac{1}{x}}$      1590 A.3 23 Q.7
Expansion of $e^{ax}cos bx$      798
Expansion of $e^{ay}$ in powers of $ye^{by}$      1571
Expansion of $e^{x}$      C.30 N.48
Expansion of $f\{z+x\phi(y)\}$ in powers of x (Lagrange)      1552
Expansion of $f\{z+x\phi(y)\}$ in powers of x (Lagrange), Laplace's th      1556
Expansion of $f\{\psi^{-1}(x)\}$ and $\psi^{-1}(x)$      1561—1563
Expansion of $log(1+2acos x+a^{2})$      2922
Expansion of $log(1+ncos x)$      2933
Expansion of $log(1\pm x), log\frac{1+x}{1-x}, &c.$      155—159
Expansion of $log(a+bx+cx^{2}+...)$      1537
Expansion of $log2{cos \atop sin}\left(\frac{x}{2}\right)$      2927
Expansion of $log\Gamma(1+x)$      2294 2773
Expansion of $sin n\theta$ and $cos n\theta$ in powers of $sine$ or $cosine$, $cos n\theta$ in powers of cos $\theta$      780 Q.12
Expansion of $sin n\theta$ and $cos n\theta$ in powers of $sine$ or $cosine$, $cos^{n}ax$      A.11
Expansion of $sin n\theta$ and $cos n\theta$ in powers of $sine$ or $cosine$, $sin^{-1}$      1528 1564 J.25 N.74
Expansion of $sin n\theta$ and $cos n\theta$ in powers of $sine$ or $cosine$, $sin^{-1}$, remainder      Z.1
Expansion of $sin n\theta$ and $cos n\theta$ in powers of sine or cosine      758 775—779 1533 C.82 CM.2 Me.76 Mem.13 15 18 N.73 83 Q.4
Expansion of $sin n\theta$ and $cos n\theta$ in powers of sine or cosine, convergency of the series      J.4
Expansion of $sin^{n}\theta$ and $cos^{n}\theta$ in sines or cosines of multiple arcs      772—774 A.24 55 C.12 CD.3 J.1 5 14 N.71 TI.7
Expansion of $tan n\theta$      760
Expansion of $tan^{-1}$      791
Expansion of $u_{nx}$ in differences of u      3752
Expansion of $u_{x+n}$      3740
Expansion of $u_{x+n}$, $\delta^{n}u$      3761
Expansion of $\delta^{n}u_{x}$ and $\delta^{n}u_{0}$      3741—3742
Expansion of $\delta^{n}u_{x}$ and $\delta^{n}u_{0}$ in differential coefficients of u      3751
Expansion of $\delta^{n}x^{m}$ and $\delta^{n}0^{m}$      3743—3734
Expansion of $\frac{1}{\phi(x)}$ (Cayley)      1555
Expansion of $\frac{e^{ax}-e^{-ax}}{e^{a\pi}-e^{-a\pi}}$      2962
Expansion of $\frac{f^{n}(x)}{n!}$, by Taylor's th      CM.4
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