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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
Biquadratic equation and elliptic functions      C.57 L.58
Biquadratic equation and sextic eqs.in the theory of conics and quadrics      J.53
Biquadratic equation, cond. for two equal roots      E.44
Biquadratic equation, reduction to a reciprocal equation      L.63
Biquadratic equation, reduction to canonical form      G.5
Biquadratic equation, solution of      A.51 56 C.49 82 L.73 Q.19
Biquadratic equation, solution of, 4 variables      J.27
Biquadratic equation, solution of, numerical      C.61
Biquadratic equation, solution of, trigonometrical      A.19 70
Biquadratic equation, solution of, without eliminating the 2nd term      A.39
Biquadratic equation, values which make it a square      496 G.7 E.22
Biquadratic function with four variables      An.59
Biquadratic involutions      C.98
Biquaternions      AJ.7 LM.4
Biternary forms with contragrcdient variables      M.1
Bonnet, two formulae of      G.4
Borchardt's functions      J.82
Brachistochrone      3037 3044 L.48 Man.31 Me.80 Mem.22 N.77 80
Brahmins, trigonometrical tables of the      TE.4
Brianchon's theorem      4783 A.53 C.82 CM.4 G.2 J.84 93 gzN.82 Z.6
Brianchon's theorem and analogues      CD.7 Q.9
Brianchon's theorem and analogues on a quadric surface      C.98 E.19
Brianchon's theorem and analogues on a sphere      A.60
Brocard circle and Lemoine's point      4754c gzN.85
Burchardt's factor tables      p.7
Burchardt's factor tables, erratum      A.23
Burmann's theorem, d.c      1559
Calculating machine      Pr.37
Calculus of chemical operations      Pr.25
Calculus of direction and position      AJ.6 M.pr6
Calculus of enlargement      AJ.2
Calculus of equivalent statements      see "Logic"
Calculus of forms (Invariant theory)      CD.7 8 9
Calculus of infinitesimals, third branch of, viz., given y and $y_{x}$, to find x      TE.24
Calculus of limits, ap. to a system of d.e      C.15
Calculus of other subjects      see "The subject"
Calculus of Victorius      Z.16
Calculus, algebraic, which includes the calculus of imaginaries and quaternions      C.91
calendar      J.3 9 prs22
Calendar, Jewish      J.f28
Canal surfaces      A.1 10
Canon-arithmeticus of Jacobi      C.39 63 L.54
Cantor's theorem      M.22
Cardioid and ellipses      Pr.6
Cardioid, b=a in      5328 Fig.129 A.59 63 68 LM.4 Me.64 N.81
Carnot's theorem      4778
Cartesian oval      5341—5358 A.69 C.97 LM.1 3 99 Me.75 Q.1 Me.74 Q.12 cn
Cartesian oval through 4 points on a circle      LM.12
Cartesian oval with 2 imaginary axial foci      LM.3
Cartesian oval, area of      E.21
Cartesian oval, eq.with triple focus as origin      E.9 23
Cartesian oval, foci      E.7
Cartesian oval, functional images      Q.18
Cartesian oval, mechanically drawn      LM.5 6 Q.13
Cartesian oval, perimeter      E.21
Cartesian oval, rectific. by ellip. functions      C.80 87 LM.5
Cassinian oval      5313 Me.77 83 N.57
Cassinian oval, analogous surfaces      An.61
Cassinian oval, radial of      E.26
Cassinoid with n foci, rectif. of      L.48
Catacaustic and diacaustic of a sphere      JP.17
Catalecticant of a binary quantic      E.37 38
Catenary      5273 Me.64 66 68
Catenary by parabolic trigonometry      Pr.8
Catenary, revolving      E.22
Cauchy's formula i.c      2712
Cauchy's formula i.c, closed curve theorem      Mo.85
Cauchy's formula i.c, various formulae      C.27
Caustics      5248—5249 Ac.4 L.46 P.57 67 Pr.8 14 15 Q.1 2 3 cn8 9 12
Caustics by successive reflexion from spheres      J.13
Caustics of a cardioid      Me.83
Caustics of a circle      5248 CD.2
Caustics of a cycloid      A.30
Caustics of an ellipse, focus at centre      J.44
Caustics of infinitely thin pencils      J.98
Caustics of refraction at a plane surface      N.47
Caustics, identity with pedals      Z.14
Caustics, radii of curvature      N.65
Caustics, surfaces and singularities      J.76
Cell structure      LM.16
Cells of bees      N.56 Q.2
Centimetre-gramme-second system      p.1
Centrals, theory of      J.24
Centre of a circle touching two      A.24
Centre of curves and surfaces      L.46 Q.10
Centre of geometrical figures      A.16
Centre of harmonic mean      J.3
Centre of mean distance of curves and surfaces      N.ths 85 Q.33
Centre of mean distance of points of contact of parallel tangents, ext. of th.      L.44
Centre of similarity      947
Centre of similitude      1037
Centre of similitude of 2 quadrics each of which circumscribes the same quadric      J.31
Centre of similitude of 3 circles      1046 4176
Centres, theory of      J.24
Centro-baric methods in anal. geometry      J.5
Centroid and its use in stereometre      A.39
Centroid of a dice      N.63
Centroid of a frustrum of a prism      L.39
Centroid of a frustrum of a pyramid      Me.79 N.76
Centroid of a gauche curve after development on a right line, locus of      C.88
Centroid of a perimeter      A.51
Centroid of a trapezium      Q.9
Centroid of a triangle      951 A.52 58
Centroid of algebraic curves and surfaces      An.68
Centroid of circular arc      6021 E.13
Centroid of common points of two conics      A.3
Centroid of frustrums      6048 &c. A.33
Centroid of oblique frustrum of a cone      E.33
Centroid of plane curves      5887 J.21 G.12
Centroid of spherical and other areas      5898 6051 J.50 L.39 42
Centroid of surface and solid of revolution      5896—5899 AJ.3 L.39
Centroid, formulae for      5884—5902 6015 JP.26 L.43
Change of independent variable      1760—1816 AJ.3 CM.1 G.2 L.40 58 Q.1 2 10 Z.17
Change of independent variable from x, y to r, $\theta$      1768
Change of independent variable from x, y, z to r, $\theta$, $\phi$      1783
Change of independent variable in a definite multiple integral      2774—2779 A.22 41
Change of independent variable in the theory of isotropic means      C.34
Change of independent variable in transcendent definite integrals      C.23
Characteristics      E.5 J.71 M.6
Characteristics of conic      A.1 C.67 72 76 83 JP.28 LM.9 M.15 N.66 71
Characteristics of conics of 5-point contact      E.27
Characteristics of cubic systems      C.74
Characteristics of curves and surfaces      C.73
Characteristics of quadrics      C.67 JP.28 N.68
Characteristics, relation between two characteristics in a system of curves of any degree      C.62
Characteristics, surface groups defined by two      C.79
Characteristics, surface groups defined by two, $\mu=1, \nu=1$      C.78
Chart construction      Mel.2 N.60 78
Chemico-algebraic theory      AJ.1
Chemico-graphs      AJ.1
Chess board, ths and prs      A.56 E.34 42 44
Chessmen, relative value of      E.39 Mel.3
Chinese arithmetic and algebra      C.51 N.63
Chord joining two points on a circle      4157 A.43 44 E.22
Chord of contact for two circle      4172
Chronology      J.26
circle      4136—4190 c.c A.1 3 th4 9 25 27 th47 C.94 J.14 17 Q.19 TE.th6
Circle and in-quadrilateral      733 CD.9
Circle and self-conj. triangle      A.41
Circle and triangle, ths and prs      A.30 57 LM.15 Q.4
Circle and two points; Alhazen's pr      AJ.4
Circle of curvature      1254 5134 A.31 63 J.45 p.cN.84
Circle, and sphere, geo.      Mo.82
Circle, approximate rectification and quadrature      6019 &c 6 geo13 14 43 J.32 Me.75 85 N.45 47 Q.4
Circle, arc of      see "Circular arc"
Circle, area of segment      6035 A.27 39 44
Circle, chord of      4157 4158
Circle, chord of contact      1017 4138 4172
Circle, cn. from 3 conditions      937 JP.9
Circle, coaxal      1021—1036 A.23
Circle, configuration of      C.93
Circle, Cotes's properties      821 A.11
Circle, Cotes's properties, ext. to ellipse      30 P.13 TI.7
Circle, cutting three at given angles      4185 LM.3 5 N.83
Circle, Division of      A.27 37 41 At.19 E.1 31 G.6 C.85 93 J.27 54 56 N.53 54
Circle, division of and theory of numbers      J.30 84 87 N.56
Circle, division of, ths. on sum of sqs. of perpendiculars, &c.      1094—1098
Circle, eight circles touching three, cn      4189 Mel.3 Q.5
Circle, eight through 6 points of intersection of 3 conics      Q.10
Circle, equation of      4136—4148 p.c Pr.27 TI.26
Circle, equation of, general eq. t.c      4691 4751
Circle, equation of, general eq. tg.c      4906
Circle, Euler's th. extended to ellips      A.51
Circle, five-point th.      E.5
Circle, four pairs of circles through 6 points common to 3 circle      Q.9
Circle, four points concyclic, condition      A.44 N.84
Circle, geometry of      A.67 Z.24
Circle, groups of points on      A.14
Circle, in tri-metric point-coordinates      Z.27
Circle, lines of equi-different powers in two circles      A.19
Circle, polar of x'y'      4138 4164
Circle, prs.      1049 At.19 L.46 see
Circle, rectangles of      Z.14
Circle, ring of, touching two fixed      J.39 Me.78
Circle, six points th.      Q.8
Circle, system through a point on a plane or sphere      G.16
Circle, tangents      4137—4143 4160 L.56 P.14
Circle, tangents, common to a circle and conic      cnA.69
Circle, tangents, common to two circles      953 4171 cnA.34
Circle, tangents, locus of a point, the tangents from which to two circles have a given ratio      geo.965 966
Circle, three      997—999 1036 1046—1051 4183—4187
Circle, through 3 points      4156 4738
Circle, through 3 points on a conic      A.2 J.39
Circle, through mid-points of sides of a triangle      see "Nine-point circle"
Circle, touching 3 circles, cn      946 1049 A.24 26 28 35 An.68 C.60 Me.62 N.63 65 66 84 Q.8
Circle, touching a conic twice      J.56 N.65
Circle, touching the 4 circles which touch the sides of a spherical triangle      A.4
Circle, two; eq. for angle of intersection      4180 4181
Circle, two; theorems      984—1045 Q.11 see "Coaxal
Circulants of odd order      Q.18
Circulants, final expansion of      Me.85
Circular and elliptic functions in continued fractions      CD.4
Circular, arc, length centroid with real tangents      Z.1
Circular, arc, length centroid, &c.      6019
Circular, arc, length centroid, graphic rectification and transposition of      Z.2
Circular, cubics, involution of      LM.1 7
Circular, cubics, involution of, chord of curvature of      E.cn36
Circular, functions      606 A.17 J.16
Circular, points at infinity      see "Imaginary ditto"
Circular, relation of Mobius      LM.8 N.76 Q.2
Circular, segment: arc, chord and area      6035 N.63
Circulating functions      P.18
Circum cubic of a complete quadrilateral      G.10 Q.5
Circum-centre of a triangle      4642 tg.
Circum-circle of a polygon      746—748 A.19
Circum-circle of a quadrilateral      733 N.79
Circum-circle of a triangle      713 4738 tg. A.51 58
Circum-circle of a triangle and in conic      N.79
Circum-circle of a triangle, coordinates of centre      4642
Circum-circle of a triangle, hypocycloidic envelope of Ferrers      N.70
Circum-cone of a quadric, locus of vertex      N.52
Circum-conic of a quadrilateral      4697 At.54
Circum-conic of a quadrilateral, locus of centre      E.1
Circum-conic of a triangle      4724 tg. An.57
Circum-parallelogram of an ellipse      4367
Circum-pentagon of a conic      M.5 N.67
Circum-polygon of a circle      746—748 CD.1 Me.80 N.66
Circum-polygon of a conic      M.25
Circum-polygon of a cuspidal cubic      LM.13
Circum-polygon of a cuspidal cubic, ditto quartic      LM.14
Circum-polygon of a parabola      CM.2
Circum-quadrilateral of a circle      E.35 N.48
Circum-quadrilateral of two circle      N.67
Circum-rhombus of an equil. triangle      A.45
Circum-triangle of a conic      N.70
Circum-triangle of a conic, locus of vertex      4800 E.35
Circum-triangle of a triangle      J.30
Cissoid      5309—5312 A.62 69 N.43 85
Cissoid, tangents of      LM.2
Cissoidal curves      A.56
Clairaut's function and equations      Pr.25
Clinant geometry      Pr.10 11 12 15
Closed curves      Me.77 geo
Closed curves and moving chord, Holditch's th      5244 gzMe.78 Q.2
Closed curves and moving chord, Holditch's th, ext. to surfaces      Me.81
Closed curves, $\int\!\!\!\int \frac{\sin\theta}{tt^{'}}dxdy, t=0, t^{'}=0$ being the tangents from xy      LM.2
Closed curves, quadrature of      A.61 N.43
Closed curves, quadrature, Crofton's ths      A.55 C.65 68 E.36
Closed curves, rectification of      5204
Closed surfaces      JP.21
Coaxal circle      1021—1036 4161—4170 Q.5
Coaxal circle, Poncelet's limiting points      4165 thJ.86
Coaxal circle, reciprocated      4558
Coaxal conics      Q.10
Cochleoid, $(x^{2}+y^{2})tan^{-1}\frac{y}{x}=\pi ry$      A.70
Coefficients detached      28
Coefficients, differential      1402
Coefficients, indeterminate      232
Cogredients      1653
Collinear and concurrent systems of points and lines      967 A.69 G.21
Collineation and correlation      M.22 prM.10
Collineation and correlation and reciprocity      M.23
Collineation and correlation of plane figures, ground forms      J.74
Collineation and correlation, "gleichstimmigkeit" of, in space      Z.24 28
Collineation and correlation, multiple c. of two triangles      A.2 70
Collineation and correlation, paradox      Z.28
Combinations      94—107 trA.15 CP.8 G.18 J.5 13 21 34 38 th53 M.5 Z.2
Combinations of 1, 2, ...n, each c. having a sum $\leqq a$      G.19 20
Combinations of dominoes      An.73
Combinations of Euler and its use in an eq.      L.39
Combinations of n dice each with p faces      TE.21
Combinations of n points in space      L.40
Combinations of observations      L.50
Combinations of planes through a system of points      N.57
Combinations, $C(m+m^{'}, p) = \sum_{0}^{p}C(m, r).C(m, p-r)$      L.42
Combinations, ap. to determinants      JP.28
Combinations, C(n, r) = C(n-1, r-1)+C(n-1, r)      102
Combinations, C(n, r) an integer      366 L.42
Combinations, C(n, r) when n is fractional      A.70
Combinations, complete, i.e., with repetitions      C.92 N.42 74
Combinations, compound      Man.79
Combinations, problem or theorem      105—107 A.21 C.97 CD.2 4 7 8 I.5 J.3 45 56 L.38 Mem.11 N.53 73 Z.15
Combinatorial products      A.34
Combinatorial systems      L.56
Combinatory analysis      A.2 50 70 J.11 22 Mem.50 N.80
Commensurable quadratic divisors      N.47
Commensurables      TE.23
Commutative law      1489
Companion to the cycloid      5258
Complanation formula      A.48
Complementary functions      C.19 J.11
Complete functions      C.86 J.48
Complete numbers      Mo.62
Complete primitive      3163
Complex axes of a quadric      Z.19
complex numbers      A.28 C.90 99 G.11 J.22 35 67 93 L.54 75 80 M.22 Mo.70 Q.4
Complex numbers from the 31st roots of unity      Mo.70
Complex numbers from the nth roots of unity      J.40 Mo.70
Complex numbers from the roots of unity; class numbers      J.65 Mo.61 63 70
Complex numbers in theory of residues of 5th, 8th and 12th powers      L.43
Complex numbers, index and base of a power, geo      Z.5
Complex numbers, prime and from roots of unity      J.35 taMo.75
Complex numbers, prime and from the 5th roots of unity      Mo.ta 59
Complex numbers, resolution of $A^{n}+B^{n}+C^{n} = 0$, and when n=5      L.47
Complex roots of an algebraical eq      M.1 N.44
Complex roots of an algebraical eq, of $x^{n}=1$      Mo.57
Complex unities      C.96 99 J.53
Complex unities, Klein's groups      J.50
Complex variables, functions of      An.59 68 71 82 83 G.3 6 J.54 73 83 M.19 Z.8 10
Complex variables, functions of, especially of integrals of d.e      J.75 76
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