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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
"Ensembles", theory of      Ac.2
"Fifteen" puzzle      AJ.2
"Mouse-trap" at cards      Q.15
$E(x)\equiv integral\, part\, of\, x$      C.50 L.57
$e^{-\frac{1}{x^{2}}}$, &c.      CP.6
$e^{a+bx+cx^{2+}}$ in fractions      L.80
$e^{a+ib}$      A.33
$e^{DxD}e^{hx}$      E.37
$e^{ix}$      766 AJ.7
$e^{ix}$ in transformations      CM.4
$Sin\ \theta < \theta - \frac{\theta^{3}}{4}$      geo.N.75
$Sin^{-1} (x + iy)$      Q.15
$\Gamma(m)\Gamma(1-m)=\frac{\pi}{sin m\pi}$      2313 Ac.3
$\Gamma(n+1)=\surd(2\pi)e^{-n}n^{n+\frac{1}{2}}(1+e)$ (Stirling)      C.50
$\Gamma(x)=P(x)+Q(x)$      Ac.2
$\Gamma(x)\Gamma\left(x+\frac{n-1}{n}\right)$      2316 L.55 56
$\pi$      C.95 E.30 N.42 45 see
$\pi$, calculation of      A.6 18 E.27 G.2 cnJ.3 Me.73 74 N.50 56 66
$\pi$, calculation of, by equivalent surfaces      N.48
$\pi$, calculation of, by isoperimeters      N.46
$\pi$, calculation of, by logarithms      N.56
$\pi$, calculation of, to 200 decimal places      J.27
$\pi$, calculation of, to 208 decimal places      P.41
$\pi$, calculation of, to 333 decimal places      A.21
$\pi$, calculation of, to 400 decimal places      A.22
$\pi$, calculation of, to 500 decimal places      A.25
$\pi$, calculation of, to 607 decimal places      Pr.6 11 22
$\pi$, formulae for, or values of      A.12 J.17 L.46 M.20
$\pi$, formulae for, or values of, $\pi=3 + \frac{\surd 2}{10}$ approx.      Me.66
$\pi$, formulae for, or values of, $\pi=\frac{2}{z} log i$      J.9
$\pi$, functions of      p.6 A.1 C.56 74
$\pi$, functions of, $\pi^{-1}$      E.27
$\pi$, functions of, to 140 places      LM.4
$\pi$, hyperbolic logarithm of      LM.14
$\pi$, incommensurable      795
$\pi$, powers of $\pi$ and of $\pi^{-1}$      LM.8
$\pi$, series for      Q.12 TE.14
$\pi$, theorem on $\pi$ and e      Q.15
$\Pi(x)$ and imaginary triangles and quadrangles      A.51
$\Pi(x)\equiv 1(1+x)...\{1 + (n-1)x\}$      A.12 J.43 67
$\sum\frac{1}{\Gamma(x)}$      G.6
$\tan 120^{\circ}$      P.8 18
$\tan^{-1} (x + iy)$      Z.14
$\triangle^{'}$      1645
$\vartheta x = a^{2} (c - x) / \{ c (c - x) - b^{2} \}$      Q.15
Abacus of the Pythagoreans      L.39
Abel's formula for F(x+iy)+F(x-iy)      2705 Me.73
Abel's theorems      1572 C.94 J.9 24 61 90 LM.12 M.8 17 P.81 83 Pr.30 34
Abel's theorems, $\phi(x)+\phi(y)=\psi\{xf(y)+yf(x)\}$      An.57
Abelian cubics and symmetrical equations      Q.5
Abelian cubics and symmetrical equations of class $\surd{-31}$      Mo.82
Abelian equations      A.68 C.95 J.93 M.18 Mo.77 92
Abelian functions      see "Hyper-elliptic functions"
Abscissa      1160
Acceleration      Me.tr65
Algebra      1—380 A.tr20
Algebra, application to geometry      JP.4
Algebra, foundation, limitations      AJ.6 CP.7 8 Q.6
Algebra, history of, in Germany      Mo.67 70
Algebraic Calculus      N.81
Algebraic definitions      C.37
Algebraic forms      C.84 94 M.15
Algebraic forms in theory of cubics      M.8
Algebraic forms whose Hessian vanishes identically      M.10
Algebraic forms, coordination of      J.76
Algebraic formulae      G.12 Q.5
Algebraic functions      A.10 31 J.92 L.50 51 M.10 N.62
Algebraic functions as partial fractions      Z.9
Algebraic functions, applied to geometry      G.22 M.7
Algebraic functions, number of constants      J.64
Algebraic functions, rationalization of      A.69
Algebraic functions, representation by      J.77 78
Algebraic functions, resolution into factors      A.46
Algebraic functions, theorems      J.82 M.1 6
Algebraic synthesis      C.16
Algorithm of arithmetical functions      Gr.23
Algorithm of higher analysis      Mo.75
Algorithm redefinition of $(\frac{a}{b})$      J.27
Algorithmic geometry      N.57
Alternants of 4th order, co-factors of      AJ.7
Alternate numbers      LM.10
Alternating functions      AJ.7 C.12 22 J.83 Me.82 see
Altitudes, determination of      A.12 19 Mem.15 N.45
Amicable numbers      A.70
Anallagmatic curves and surfaces      C.87 N.64 see
Anallagmatic pavements      E.10
Analysis      A.1 An.50 C.3 11 12 J.f7 P.14 Q.6 7
Analysis, ap to geometry      G.23 JP.4
Analytical aphorisms      A.5 J.10
Analytical combination theorem      J.11
analytical functions      Ac.6 thsAn.82 trJP.3 see
Analytical functions, system of, and series from it      An.tr84
Analytical geometry      4001—6165 A.2 11 38 C.6 JP.9 L.72 M.2 Mem.13 Z.9 tr11 12
Analytical geometry of three dimensions      CM.4
Analytical geometry, plane and solid in homogeneous coordinates      Z.15 16
Analytical geometry, theorems and problems      A.8 52 J.46
Analytical metrics      Q.7 8
Analytical theorems      A.8
Analytical treatise      C.13
Angles division into n and n+1 parts      A.70
Angles of a central conic      4375
Angles of five circles or six spheres      Me.79
Angles of two circles      4180
Angles, conterminal      Me.74
Angles, problems on      P.1791
Angles, trisection of      5325 A.4 34 C.2 66 81 G.15 Me.72 N.56 76
Angles, two relations between five      A.20
Anharmonic pencils of conics      4809—4821
Anharmonic ratio      1052 4648 GM.12
Anharmonic ratio of 4 points in a plane      A.1 C.77
Anharmonic ratio of 5 lines in space      Me.76
Anharmonic ratio of a conic      Q.4
Anharmonic ratio of four tangents      4986
Anharmonic ratio, corresponding to roots of a biquadratic      N.60
Anharmonic ratio, sextic      LM.2 60 Q.37 38
Anharmonic ratio, systems      cnM.10
Anharmonics      LM.2 3
annuities      302 A.2 Ac.1 CP.3 J.83 1.1—24 P.1788 1789 1791 1794 1800—1810 N.47
Anticaustic (by refraction) of a parabola      N.83 85
Anticlastic surface      5623 5818
Aplanatic lines, lemniscates, caustics, &c.      thL.50 N.45
Apolarity of rational curves      M.21
Apollonius's problem      A.37 M.6
Approximation      J.13 N.66
Approximation of several variables      C.70
Approximation to functions represented by integrals      C.20
Approximation, algebraic      J.76
Approximation, successive      Mem.38
Apsidal surfaces      Q.16
Arabs, mathematics of      C.39 60
Arbitrary constants      C.15 L.80
Arbitrary constants in d.e and f.d.e      TI.13
Arc, area, &c., quantification of      1244 5205 5874 6015
Arc, area, &c., relations of      G.16 C.80 94 L.46
Arcs with a rectifiable difference and areas with a quadrable difference      L.46
Areas and volumes in t.c and q.c      4688 Q.2
Areas approximation by ordinates      2991—2997 C.78 CD.9
Areas between 3 lines      4038 Me.75
Areas between 3 lines, ext of meaning      CD.5
Arithmetic      A.5 18 L.59
Arithmetic mean      91 CD.6
Arithmetic mean of n quantities      332 L.39
Arithmetic of Ibn-Esra      trL.41
Arithmetic of Nicomaque de Gerase      An.57
Arithmetic, ancient      C.71 N.51
Arithmetic, degenre, ext. of the notion      C.94
Arithmetic, Higher      J.35
Arithmetic, history of      C.17
Arithmetical progression      79 thL.39 Pr.10
Arithmetical progression and g.p when n (the number of terms) is a fraction      A.35
Arithmetical progression when the terms are only known approximately      C.96
Arithmetical theorems      A.10 C.93 97 CD.6 G.7 18 L.63
Arithmetical theorems of I.c.m.      N.57 C.5
Arithmetical theory of algebraic forms      J.92 93
Arithmetico-geometric mean      Mo.58 Z.20
Arithmographe polychrome      C.51 53
Arithmometer      I.16—18
Aronhold, theorems of      gzJ.73
Associated forms and spherical harmonics      Me.85
Associated forms, systems of      gzAJ.1 C.86 CD.6
Astroid of a conic      A.64
Astronomical distances      p5
Asymptotes      5167 A.p.c 17 CM.4 M.11 N.68 thsN.48 73
Asymptotes of conics      1182 4490 t.c tg.c 4966 Me.71 Q.3 8
Asymptotes of imaginary branches of curves      CM.2
Asymptotes of intersections of quadrics      N.73
Asymptotic chords      A.12
Asymptotic cone of a quadric      5616 E.30 g.e
Asymptotic curves      5172
Asymptotic law of some functions      Mo.65
Asymptotic lines of surfaces      A.60 61 R.84
Asymptotic methods      M.82
Asymptotic planes and surfaces      CD.3
Asymptotic planes of a paraboloid      5625
Atomic theory and graphical representation of invariants and covariants of binary quantics      AJ.1
Attraction of a right line and of an elliptic arc      An.59 CD.8
Attraction of a ring and of elliptic and circular plates      G.21 Z.11
Attraction of confocal ellipsoids      Me.82
Attraction of ellipsoidal shell      J.12 JP.15 Q.17
Attraction of ellipsoids      CD.4 9 J.12 20 26 31 JP.15 L.40 45 M.10 N.76 Q.2 7 17
Attraction of paraboloids      L.57
Attraction of polyhedra      J.66
Attraction of solids of revolution, &c.      An.56 CD.2
Attraction of spheroids      J.12 JP.8 L.76 Mem.31 P.12 see
Attraction, solid of maximum      TE.6
Attraction, theorems      Q.4 17
Attraction, theory of      L.44 6
Auxiliary circle      1160
Averages      I.7 9
Axes of a conic      gn.eq 4687 A.30 E.36 G.12 Q.q.c t.c 8 15 20 Me.a.c 71 N.43 48 58 t.c
Axes of a quadric      5695 A.30 An.77 G.9 J.2 64 82 N.43 51 cn 69 74
Axes, cn. from conj. diameters      1253 A.13 20 Me.82 N.67 78
Axes, construction of      1252 Me.66
Axes, rectangular, nine direction cosines for two systems      5577—5578 L.44
Axis of perspective or homology      975
Axis of reflexion      1007
Axis of similitude      1046 4177
Axonometry and projective collineation in space      M.25 Z.12 21
Babbage's calculating machine      C.99
Barycentric calculus and right line construction      J.28
Battement de Monge      L.82
Beltrami's theorem      A.44
Bernoulli's numbers      1539 A.3 AJ.5 7 An.59 77 C.54 58 81 G.9 J.20 21 28 58 81 84 88 92 LM.4 7 9 Me.75 gzMem.83 N.76 Q.6 22
Bernoulli's numbers and interpolation      C.86
Bernoulli's numbers and secant series      A.1 3 35 C.4 32
Bernoulli's numbers and their first 250 logarithms      CP.12
Bernoulli's numbers, application to series      see "Series"
Bernoulli's numbers, bibliography of      AJ.5
Bernoulli's numbers, first 62      85
Bernoulli's numbers, indeterminate representation of      Z.19
Bernoulli's numbers, new theory of      C.83
Bernoulli's numbers, theorems on      E.2 8 N.77
Bernoulli's series      1510
Bessel's functions      J.75 M.3 4 9 14 16 Q.20 21 see
Bessel's functions, representation of arbitrary functions by      M.6
Bessel's functions, squares and products      M.2
Bessel's functions, tables      Z.2
Bicircular quartics      LM.3 99 P.77 Pr.25 Q.19 TI.24
Bicircular quartics, focal conics of      LM.11
Bicircular quartics, nodal, mechanical cn. of      LM.3
Bicircular quartics, with collinear triple and double foci      LM.12 14
Bifocal variable system      M.16
Bilinear forms      J.68 84 86 L.74 Mo.66 68 74
Bilinear forms, congruent transformation of      Mo.74
Bilinear forms, four variables      G.21 Mo.83
Bilinear forms, reciprocals      G.22
Bilinear forms, reduction of      C.78 92
Bilinear forms, relation between two and their quadric and quartic system      M.1
Bilinear functions      GM.11
Bilinear functions, polynomials      C.77
Bilinear functions, trilinear and quadrilinear systems      E.5
Billiards, theory of      L.83
Bimodular congruences      G.21
Binary and ternary quadratics      N.64 65
Binary cubics      1631 A.17 C.92 G.17 J.27 53 41 Q.1 11
Binary cubics, and quadratic forms      G.21
Binary cubics, automorphic transf. of      LM.14
Binary cubics, resultant      Q.6
Binary cubics, system of two      E.7 G.17 LM.13 M.7
Binary cubics, tables and classification of      A.31
Binary cubics, transformation by linear substitution      J.38
Binary forms      An.56 77 At.65 G.2 3 10 16 J.74 M.2 3 20 Q.14
Binary forms and their covariants, geo.      M.23
Binary forms in a cubic space-curve      J.86
Binary forms in two conjugate indeterminates      C.97
Binary forms, (q) groups of      M.23
Binary forms, ap. to anal. geometry      L.75
Binary forms, ap. to elliptic functions      AJ.5
Binary forms, ap. to Euler's integrals      C.47
Binary forms, canonical      J.54 M.21
Binary forms, evectant      Q.11
Binary forms, geo. interpretation or ap.      C.78 G.17 M.9 22
Binary forms, having similar polar forms      M.8
Binary forms, having the same Jacobian      C.94
Binary forms, most general case of linear equations in      C.99
Binary forms, transference of, when not of a prime degree      M.21
Binary forms, transformation of      M.4 9
Binary forms, typical representation of      An.68 69
Binary forms, with related coefficients      M.12
Binary homographics represented by points in space, applied to the rotation of a sphere      M.22
Binary nonics, ground forms      AJ.2
Binary octics      thC.96 M.17
Binary quadrics      C.47 G.3 J.27 L.59 77 M.15 17
Binary quadrics for a negative determinant      No.81 L.57 M.17 21 25
Binary quadrics for a negative determinant, table      C.60
Binary quadrics, construction of, through a symbolical formula      C.57
Binary quadrics, indeterminate, integral sol.      J.45
Binary quadrics, partition table      AJ.4
Binary quadrics, representing the same numbers      L.59
Binary quadrics, transformation of      C.41
Binary quadrics, with two conjugate indeterminates      C.96
Binary qualities      1636 An.56 C.52 CD.9
Binary qualities in two polynomials U, V, prime to each other and of the same degree      N.85
Binary qualities, (2n-1)-ic, canonical form of      Q.20
Binary qualities, derivatives of      Q.15
Binary qualities, discriminant of      1638 Q.10
Binary qualities, reduction of      J.36 L.52 Q.7
Binary qualities, transformation of      CM.1 thE.28
Binary quartics and ternary cubic, correlation between      An.76
Binary quartics and their invariants      A.18 G.14 J.41 M.19 Q.7
Binary quartics or quintics, with three equal roots or two pairs of equal roots      P.68
Binary quartics, condition for perfect square      E.36
Binary quintic      G.14
Binary quintic, canonical form for      Q.19
Binary sextics      taAJ.4 C.64 87 96 G.14 M.2 76 77
Binary sextics, syzygies of      AJ.7
Binet's function      L.75
Binodal quartic with elliptic function coordinates      AJ.5
Binomial coefficients      283 366—367 A.1 2 G.14 Mem.24 N.th60 61 70 85 Z.25
Binomial coefficients, sum of selected      Me.85
Binomial equations      480 A.10 At.65 68 C.10 44 G.5 10 L.57 LM.11 12 16
Binomial equations, $x^{p}-1=0$      see "Roots of unity"
Binomial equations, irreducible factors of      An.69
Binomial equivalences to any modulus      C.25
Binomial theorem      125—136 A.8 geo.61 C.45 CD.7 CM.3 G.12 J.1 4 5 28 55 Me.71 N.42 47 50 71 78 P.16 16 95 96 TI.12
Binomial, generalization of      J.1 N.57
Binormal      5723
Bipartite functions and determinants      LM.16
Bipartition, repeated      Mel.4
Biquadratic equation      492—501 A.1 12 16 23 31 39 40 41 45 69 A CM.1 46 47 G.5—7 13 21 J.90 Me.62 N.44 58 59 60 63 78 81 83 Q.7 28 Z.6 8 18 see
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