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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

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Предметный указатель
Isosceles figures      C.87 JP.30
Isotherms, families of      Z.26
Isotropic functions      C.26 27
Iterative functions      L.84
Jacobi — Bernoulli function      J.42
Jacobian      ths 1600—1609 AJ.3 thZ.10
Jacobian and polar opposites      Me.64
Jacobian of 3 conics      5023 LM.4
Jacobian, formulae      d.c.1471 J.84 Mo.84
Jacobian, function of several variables      Mo.82
Jacobian, function, one argument      G.2
Jacobian, modular eq. of 8th degree      M.15
Jacobian, sextic equation      Q.18
Jacobian, system, multiplicator      M.12
Kinematic geometry of similar plane figures      Z.19 20 23
Kinematic geometry of space      J.90
Kinematics      A.61 AJ.3 G.23 L.53 80 LM.th17 N.82 ths 84
Kinematics of a point      N.49 82
Kinematics of a point, barycentric method      Mel.5
Kinematics of plane curves      A.55 N.82
Kinematics of plane curves, caustics      Z.23
Kinematics of plane figures      Mel.26 N.78 80
Kinematics of plane figures, of a triangle      N.53
Kinematics of sliding and rolling solids      TA.2
Kinematics, paradox of Sylvester      Me.78
Knight's move at chess      C.31 52 74 CD.7 CM.3 E.41 N.54 Q.14
Knots      TE.28
Knots with 8 crossings      E.33
Kummer's 16-nodal quartic surface      C.92 J.84
Kummer's 16-nodal quartic surface, figures of      M.18
Kummer's 16-nodal quartic surface, lines of curv. of      J.98
Kummer's equation an analogous eq.      C.99
Kummer's equation, i.c.      2706
Kummer's equation, rational integrals of      M.24
Lagrange's theorem (d.c)      1552 C.60 77 CD.6 CM.3 Mel.2 gzC.96 Me.85 gzQ.2
Lambert's th. of a parabolic sector      A.16 33 48 Me.78 Q.15
Lambert's th. of elliptic sector      6114
Lame's equation      An.79 C.86 90 91 ths92
Lame's functions      C.87 J.56 60 62 M.18
Landen's th. of hyperbolic arc      6117 E.21
Laplace's coefficients or functions      see "Spherical harmonics"
Laplace's equation and its analogues      CD.7
Laplace's equation and quaternions      Q.1
Laplace's th. (d.c)      1556
Last multiplier, Jacobi's th., of      L.45
Lateral curves      A.58
Latus rectum      1160
Law of reciprocity      N.72
Law of reciprocity, d.e      3446
Law of reciprocity, ext. to numbers not prime      C.90
Least divisors, table of, from 1 to 99000      7
Least remainder (absolute) of real quantities      Mo.85
Least squares, method of      A.11 18 19 AJ.1 C.34 37 40 CP.8 11 G.18 J.26 L.52 53 67 75 Me.80 81 Mel.1 4 gzZ.18
Legal algebra (heredity)      N.63
Legendre's coefficient or function, $X_{n}$      2936 C.47 91 L.76 gz79 Me.80 Pr.27
Legendre's coefficient or function, $X_{n}$ and complete elliptic integral of 1st kind      Me.85
Legendre's coefficient or function, $X_{n}$, product of any two expressed by a series of the same functions      Pr.27
Legendre's coefficient or function, $X_{n}$, rth integral of and log integral of      Me.83
Legendre's symbol $\left ( \frac{a}{p} \right )$      Mel.4 5
Leibnitz's th. in d.c      1460 N.69
Leibnitz's th. in d.c, a formula      Mo.68
Lemniscate      5317 A.55 cn3 At.51 thsE.4 L.46 47 Me.68 N.45
Lemniscate, chord of contact, cn      Z.12
Lemniscate, division of perimeter      C.17 L.43
Lemniscate, division of perimeter, into 17 parts      J.75
Lemniscate, division of perimeter, irreducibility &c. of the partition equation      J.39
Lemniscate, tangents of      J.14 cnZ.12
Lemniscatic function, biquadratic theorem, multiplication and transformation of formulae      J.30
Lemniscatic geometry      Z.21
Lemniscatic geometry of nth order      J.83
Lemniscatic geometry, coordinates      Z.12
Lexell's problem      LM.2
Life annuities      A.42
Life annuities, cn of tables      P.59
Limacon      5327 C.98 N.81
Limited derivation and ap. thereof      Z.12
Limiting coefficients      C.37
Limits of ${\left ( 1 + \frac{1}{x} \right )}^{x}$ when $x=\infty$      L.40 N.85 Q.5
Limits of functions of two variables      M.11
Limits, theory of      Me.68
Linear associative algebra      AJ.4
Linear construction      Man.51
Linear coordinates in space      M.1
Linear dependency of a function of one variable      J.55
Linear dependent point systems      J.88
Linear equations      A.51 70 Ac.4 C.81 th94 G.14 J.30 JP.29 L.f39 66 Mo.84 N.51 75 80 Z.15 22
Linear equations with real coefficients      M.6
Linear equations, analogous to Lame's      C.98
Linear equations, similar      N.45
Linear equations, solution by roots of unity      C.25
Linear equations, symbolic solution in connexion with the theory of permutations      C.21
Linear equations, systems of      582 A.10 22 52 57 Gr.15 C.81 96 L.58 N.46
Linear equations, systems of, in one unknown      C.90 Gr.9
Linear equations, systems of, of nth order      J.15
Linear equations, systems of, standard solution      582 Q.19
Linear equations, systems of, standard solution, gen. th      A.12
Linear equations, whose number exceeds the number of variables      N.46
Linear forms      L.84
Linear forms, with integral coefficients      J.86 88
Linear function of n variables      G.14
Linear geometry, th      M.22
Linear identities between square binary forms      M.21
Linear systems, calculus of      JP.25
Linear, $U^{2}=V^{2}$ where U, V are products of n linear functions of two variables      CD.5
Lines of curvature      5773 A.34 37 An.53 C.74 CD.5 L.46 M.2 3 76 N.79 Q.5
Lines of curvature and conics, analogy      5854 Me.62
Lines of curvature and geodesies of developables      L.59
Lines of curvature and shortest distance of 2 normals one of which passes through an umbilic      L.55
Lines of curvature and triple orthogonal systems      M.3
Lines of curvature of a quadric      5833—5834 C.22 49 51 G.11 J.26 Me.1 N.63 Pr.32 TI.14
Lines of curvature of a quadric, pd constant along it      5836
Lines of curvature of a quadric, projected from an umbilic into confocal Cartesians      E.19
Lines of curvature of a quadric, quadratic for $y_{x}$, giving the directions      5810
Lines of curvature of an ellipsoid      A.38 48 An.70 ths CM.2 3 4 JP.1 N.81
Lines of curvature of an ellipsoid and of its pedal surfaces      Q.12
Lines of curvature of an ellipsoid, comparison of arcs of, by Abel's th      An.69
Lines of curvature of an ellipsoid, projection of      Z.2
Lines of curvature of an ellipsoid, rectification of      An.73
Lines of curvature of an equilateral paraboloid      N.84
Lines of curvature of quartic surfaces      C.59 L.76
Lines of curvature of ruled surfaces      C.78
Lines of curvature of surface of the 4th class, correlatives of cyclides which have the circle at infinity for a double line      C.92
Lines of curvature of the tetrahedral surfaces of Lame, &c      C.84
Lines of curvature of two homofocal quadrics      L.45
Lines of curvature, dividing a surface into squares      C.74 LM.4 Mo.83
Lines of curvature, generation of surfaces by      J.98 N.77
Lines of curvature, near an umbilic      5822 A.70 Q.10
Lines of curvature, of alg. surfaces      Z.24
Lines of curvature, osculating plane of      5835
Lines of curvature, plane or spherical      An.57 C.46 JP.20 L.53
Lines of curvature, plane, condition for      5843 An.68 C.36 42 96 G.22 Me.64
Lines of curvature, spherical      C.36 42
Lines of greatest slope      A.29
Lines of greatest slope and with vertical osculating planes      C.73
Lines, "de faits et de thalweg" in topography      L.77
Lines, alg. representation of      C.76
Lines, generated by a moving plane figure      C.86
Lines, loxodromic      J.11
Lines, six coordinates of      CP.11
Linkage and linkwork      5400—5431 E.28 30 Me.75 N.75 78
Linkage and linkwork for constructing $x^{2}$ and $x^{m}$      AJ.1 3
Linkage and linkwork for constructing a lemniscate      AJ.1
Linkage and linkwork for constructing a limacon      5427 Me.76
Linkage and linkwork for constructing an ellipse      5426
Linkage and linkwork for constructing root of a cubic equation      5429
Linkage and linkwork, 3-bar      5430 E.34
Linkage and linkwork, 4-bar      Me.76
Linkage and linkwork, conjugate 4-piece      LM.9
Linkage and linkwork, Hart's      5417 LM.6 8
Linkage and linkwork, Kenipe's      5401 Pr.23
Linkage and linkwork, Peaucellier's      5410 E.21 LM.6 N.82
Linkage and linkwork, the Fan of Sylvester      E.33
Linkage and linkwork, the Invertor      5419
Linkage and linkwork, the Multiplicator      5407
Linkage and linkwork, the Pentograph      5423
Linkage and linkwork, the Plagiograph      5424
Linkage and linkwork, the Planimeter      5452
Linkage and linkwork, the Proportionator      5423
Linkage and linkwork, the Quadruplane      5422
Linkage and linkwork, the Reciprocator      5419
Linkage and linkwork, the Reversor      5407
Linkage and linkwork, the Translator      5407
Linkage and linkwork, the Versor-invertor      5422
Linkage and linkwork, the Versor-proportionator      5424
Lissajons' curves      A.70 M.8
Lituus      5305
Loci, classification of      C.83 85 P.78 Pr.27
Locus of a point of intersection of common tangents to a conic and circle      N.63 79
Locus of a point of intersection of curves      CM.2
Locus of a point on a moving curve      Mem.18
Locus of a point on a moving right line      L.49
Locus of a point, at which 2 given lengths subtend equal angles      A.68
Locus of a point, ditto of two revolving curves      N.64
Locus of a point, dividing a variable line in a constant ratio      gzAJ.3
Locus of a point, the centre of a circle cutting 3 circles in equal angles      N.53
Locus of a point, the centre of collineation between a quadric surface and a system of spherical surfaces      A.65
Locus of a point, the product of 2 tangents from which, to 2 equal circles is constant      An.64
Locus of a point, whose distances from 2 curves have a constant ratio      An.58
Locus of a point, whose distances from 2 curves have a constant ratio or satisfy a given relation      A.33 symbolic f.
Locus of a point, whose sum of distances from 2 lines is constant      N.64
Locus of a point, whose sum of distances from 3 lines is constant      A.17 46
Locus of a point, whose sum of distances from lines or planes is constant      A.19 prs31 ths31
Locus of pole of one conic with respect to another      N.42
Locus of remarkable points in a plane triangle      A.43
Locus of vertex of constant angle touching a given curve      N.61
Locus of vertex of quadric cone passing through 6 points      N.63
Logarithmic curve      5284
Logarithmic curve, quadrature      N.45
Logarithmic integral      A.93 19 J.17 Z.6
Logarithmic integral of a rational differential      J.3
Logarithmic integral, numerical determination      A.11
Logarithmic parabola      CD.7
Logarithmic potentials      M.3 4 8 13 16 Z.20
Logarithmic rational fractions      A.6
Logarithmic systems      A.14
Logarithmic transcendents      P.14
Logarithmic waves      LM.2
Logarithms      142 P.1792 1787 1806 17 TE.26
Logarithms and anti-logarithms, cn      I.12 24
Logarithms and circular functions from definite integrals      A.65
Logarithms of 2, 3, 5, 10 and e to 205 places      Pr.6 20
Logarithms of 2, 3, 5, 7, 10 and e all to 260 decimal places      Pr.27
Logarithms of different orders of numbers      L.45
Logarithms of negative numbers      No.1784
Logarithms of primes from 2 to 109, table viii.      p.6
Logarithms of sum and difference of 2 numbers      A.45
Logarithms with many decimal places      N.67
Logarithms, calculation of      688 A.24 27 42 LM.1 5 Me.74 N.51 Pr.31 32 TE.6 14 TI.6 8
Logarithms, calculation of, Huyghen's method      C.66 68
Logarithms, common or Briggean      A.24
Logarithms, constants in integral      J.60
Logarithms, higher theory of      trA.15
Logarithms, impossible      CM.1
Logarithms, natural, base of      see "e."
Logarithms, natural, modulus of      148 A.3
Logarithms, natural, of commensurable numbers or of algebraic irrationals      C.95
Logarithms, natural, or Napierian, or hyperbolic      A.25 26 57
Logarithms, new kind of      J.70
Logarithms, powers of      CM.2
Logarithms, tables of log sines, &c. cn      Q.7
Logic of numbers      AJ.4
Logic, algebra or calculus of      A.6 AJ.3 7 CD.3 M.12 Man.71 76 82 Q.11
Logic, algebra or calculus of equivalent statements      LM.11
Logocyclic curve      Pr.9 Q.3
Longimetry applied to planimetry      J.52
Loto, game of      L.42
Loxodrome      eqA.21 N.61 Z.5
Loxodrome of a surface of revolution      N.74
Loxodrome of cylinder and sphere      A.2
Loxodrome of ellipsoid and sphere      A.32
Loxodrome of paraboloid of rotation      A.13
Loxodromic triangle upon an oblate spheroid      A.27
Lucas's analogous f.      G.13
Lucas's th      G.14
Ludolphian number      Mo.82
Lunes      J.21
Maclaurin's th. (d.c)      1507 A.12 CM.3 J.84 N.70
Maclaurin's th., symbolic form      CM.4
Maclaurin-sum-formula      J.12
Magic cubes      Q.7 CD.1
Magic cyclovolute      TA.5 9
Magic parallelopiped      A.67
Magic rectangles      A.65 66
Magic squares      A.21 57 66 CD.1 CM.4 E.8 J.44 Me.73 Pr.15 16 Q.6 10 11 TA.5 9
Magical equation of tangent      Q.6
Malfatti's problem, to inscribe 3 circles in a triangle touching each other      A.15 16 20 55 J.10 45 76 77 84 89 LM.7 M.6 P.52 Pr.6 Q.1 TE.24 Z.21
Malfatti's resolvents of quintic eqs      A.45
Malm's surfaces, th      J.84 88
Mannheim, two theorems      G.8
Martin's measure of distance      A.19
Matrices      E.42 LM.4 16 thMe.85 P.58 66 Pr.9 14
Matrices of 2nd order, linear eq.      C.99
Matrices of 2nd order, quadratic      Q.20
Matrices of any order, linear eq.      C.99
Matrices, $^{(a,b)}_{\mid c,d \mid}$ and function $f(x)=\frac{ax+b}{cx+d}$      Me.80
Matrices, Cayley's th      LM.16 Me.85
Matrices, equation, px=xq      C.99
Matrices, notation of      J.50
Matrices, persymmetrical, th      E.34
Matrices, product of      G.5 11
Matrices, roots of a unit matrix      C.94
Matrices, whose terms are linear functions of x      J.50
Maximum of $ax+by+\&c$., when $x^{2}+y^{2}+\&c.=1$      N.46
Maximum of $\frac{\sin x}{x}$      A.36
Maximum of $\sqrt[x]{x}$, &c.      A.42
Maximum of a factorial function      Me.73
Maximum of a product      N.44
Maximum of a sphere, th      N.53
Maximum or minimum      58 1830 A.4 13 22 35 49 53 60 70 C.17 24 J.48 JP.25 Me.1 geo5 72 76 81 83 N.43 Z.13
Maximum or minimum by interpolation, f      A.25
Maximum or minimum of $\iint F(x, y, z) dS$, &c., to find S      3078 3080
Maximum or minimum of $\int F(x,y)ds$, &c., to find s      3070 3072
Maximum or minimum of a definite integral      Z.21
Maximum or minimum of figures in plane and in space      CM.3 L.41 J.24 Z.11
Maximum or minimum of in- and circum-polygon of a circle      A.29 30
Maximum or minimum of in- and circum-polygon of ellipse, and analogous th. for ellipsoid      An.50
Maximum or minimum of multiple definite integrals      Mel.4
Maximum or minimum of single integrals between fixed limits      J.54 69 M.25
Maximum or minimum of the sum of the distances of a point from given points, lines, or planes      J.62
Maximum or minimum of the sum of the values of an integral function and of its derivatives      L.68
Maximum or minimum, continuous      1866
Maximum or minimum, discontinuity in      CD.3
Maximum or minimum, distances between points, lines, and surfaces, geo      At.65
Maximum or minimum, duplication of results      Me.80
Maximum or minimum, ellipse which can pass through 2 points and touch 2 right lines      A.14
Maximum or minimum, elliptic function method      Mel.5
Maximum or minimum, functions of 2 variables      1841 Mem.31 Q.5 6
Maximum or minimum, functions of 2 variables, Lagrange's condition      CM.2
Maximum or minimum, functions of 3 variables      1852 CD.1 prs 1865
Maximum or minimum, functions of n variables      1862 L.43 Mem.59 Q.12
Maximum or minimum, functions of n variables, symmetrical      Mel.2
Maximum or minimum, functions of one variable      1830
Maximum or minimum, functions of one variable, ditto. with an infinity of max. and min. values      J.63
Maximum or minimum, in-polygon (with given sides) of an ellipse      A.30
Maximum or minimum, indeterminates      CM.4
Maximum or minimum, method of substitution      A.23
Maximum or minimum, of an arc as a function of the abscissa      J.17
Maximum or minimum, planimetrical groups of      A.2
Maximum or minimum, problems on      1835 1840 1847 A.2 geo19 38 39 geoL.42 Mem.11
Maximum or minimum, problems on, a paradox      N.63
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