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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
Parabola, sector      E.30 N.57
Parabola, sector, Lambert's th      J.16
Parabola, segment of      6078 A.26 29
Parabola, segment of, solid generated by it      N.42
Parabola, tangents      see "Conics"
Parabola, through 4 points, cn      4837 J.26
Parabola, triangle of 3 tangents      1237 1268 A.47 Me.75
Parabola, trigonometry of      CD.8
Paraboloid      5621 6126—6141 N.61 Q.13
Paraboloid of eight lines      C.84
Paraboloid of revolution      6134
Paraboloid, elliptic      5622 A.11 L.58 P.96
Paraboloid, generating lines of      5624
Paraboloid, hyperbolic      5623 A.11
Paraboloid, quadrature of      6127 An.55.
Paraboloid, segment of      6127—6133 A.29
Paradoxes of De Morgan      J.11 12 13 16
Parallel curves      J.55 ths32 LM.3 Q.11 Z.5
Parallel curves of ellipse      4960 A.39 An.60 N.44 Q.12
Parallel curves, closed      A.66
Parallel surface      C.54 LM.12
Parallel surface of ellipsoid      A.39 An.50 60 E.17 J.93
Parallel surface of surface of elasticity      An.57
Parallelogram of Watt      A.8 L.80
Parallelogram with sides through four given points      A.39
Parallelopipeds on a spherical base      N.45
Parallelopipeds on conjugate diameters      5648
Parallelopipeds, analogues of parallelograms      LM.2 Me.68
Parallelopipeds, diagonals, &c.      CM.1
Parallelopipeds, equality of      A.4
Parallelopipeds, system of      LM.8
Parallels      A.8 47 At.51 J.11 73 Mel.1 3 Mem.50 Z.21 22
Parallels in analytic geometry      A.44
Parallels, Thibaut's proof      A.15
Partial differences: question in analysis      J.16
Partial differential equations (P.D.E.)      3380—3445 C.3 11 16 78 95 96 thsCD.3 J.58 80 prs26 JP.7 10 11 L.36 80 83 M.11 Z.6 8 18
Partial differentials of $\frac{x}{x^{2}+y^{2}}$      J.11
Partial fractions      235 1915 A.30 66 C.46 49 78 CM.1 G.2 J.1 5 9 10 11 22 32 50 JP.3 L.46 Mem.9 N.45 64 69 Q.5
Partition of numbers      AJ.2 5 6 An.57 59 At.65 C.80 86 96 91 CP.8 J.13 61 85 M.14 Man.55 Me.78 79 Mem.13 geo.ap20 44 Mel.1 N.69 85 P.50 56 58 Pr.7 8 Q.1 2 7 15 Z.20 24 see "Indeterminate
Partition of numbers by Arbogast's derivatives      L.82
Partition of numbers by elliptic and hyper-elliptic functions      J.13
Partition of numbers into 10 triangular numbers      C.62
Partition of numbers into 2 cubes      L.70
Partition of numbers into 2 squares      An.50 52 54 C.87 J.49 LM.8 9 N.54 78 alg65
Partition of numbers into 2 squares, odd squares      Q.19
Partition of numbers into 3 squares      J.40 L.59 60
Partition of numbers into 4 cubes      N.77 N.79
Partition of numbers into 4 cubes, into 3 or 4 cubes      A.60
Partition of numbers into 4 squares      C.99 L.68 Pr.9 Q.1
Partition of numbers into 5 squares      C.97 98 J.35
Partition of numbers into maximum nth powers      C.95
Partition of numbers into p squares      C.39 90 L.61 N.54
Partition of numbers into p squares and an integer      L.57
Partition of numbers into parts, the sum of any two to be a sq.      Mem.9
Partition of numbers into sum or difference of 2 cubes      AJ.2
Partition of numbers into ten squares      C.60 L.66
Partition of numbers into the product of two sums of sqs.      L.57
Partition of numbers of n into 1, 2, 3, &c. different numbers      E.34
Partition of numbers of pentagonal numbers      C.96
Partition of numbers, $n^{12}-9m^{12}$ or its double into 2 cubes      N.81
Partition of numbers, $n^{3}-m^{3}$ into $3p^{2}+q^{2}$      N.49
Partition of numbers, 2 squares whose sum is a sq.      E.20 N.50
Partition of numbers, 2 sums of 8 sqs. into 8 sqs.      Me.78
Partition of numbers, 3 nos. whose sum is a cube, sum of sqs. a cube, and sum of cubes a sq.      E.26
Partition of numbers, 3 nos., the sum or diff. of two to be a sq.      Mem.18
Partition of numbers, 3 squares, the sum of every two being a sq.      E.17
Partition of numbers, 4 odd, or 2 even and 2 odd      Q.19 20
Partition of numbers, 4 squares, the sum of every two being a sq.      E.16
Partition of numbers, 5 biquadrates whose sum is a square      E.20
Partition of numbers, a cube into a sum of cubes      E.22 23
Partition of numbers, a quadric into a sum of squares      N.80 81
Partition of numbers, a series for the      AJ.6
Partition of numbers, a square into a sum of cubes      N.67
Partition of numbers, a sum of 4 sqs. into the product of 2 sums of 4 sqs.      TI.21
Partition of numbers, formation of numbers out of cubes      J.14
Partition of numbers, formula of verification      Pr.24
Partition of numbers, n nos. whose sum is a sq. and sum of sqs. a biquadrate      E.18 22 24
Partition of numbers, of complex numbers in Jacobi's th      C.96
Partition of numbers, tables, non-unitary      AJ.7
Partition of numbers, theorems      AJ.6 C.40 96 Me.76 80 83
Partition of numbers, theorems, pr. symm. functions      G.10
Partitions in planes and in space      J.1
Partitions in theory of alg. forms      G.19
Partitions, number of for n things      E.10
Partitions, Sylvester's theorem      Q.4
Partitions, trihedral of the X-ace and triangular of the X-gon      Man.58
Pascal lines      E.30
Pascal's theorem      4781 AJ.2 CD.3 4 CM.4 J.34 41 69 84 93 LM.8 Me.72 N.44 52 82 Q.1 4 5 9 Z.6 10
Pascal's theorem on a sphere      A.60
Pascal's theorem, ap. to geo. analysis      A.18
Pascal's theorem, extension of and analogues in space      C.82 98 CD.4 5 6 G.11 J.37 75 M.22 Me.85
Pascal's theorem, Steiner's "Gegenpunkte"      J.58
Pedal curve      A.35 36 52 J.48 50 M.6 Me.80 81 Q.11 Z.5 21
Pedal curve of a cissoid, vertex for pole      E.1
Pedal curve of a conic      A.20 LM.3 Z.3
Pedal curve of a conic, central      A.9 Me.83 N.71
Pedal curve of a conic, foci and vector eq.      LM.13
Pedal curve of a conic, negative central      E.20 29 TI.26
Pedal curve of a conic, negative focal      E.16 17 20
Pedal curve of a conic, nth and n-1th      E.18
Pedal curve of a parabola, focal and vector eqs.      LM.13
Pedal curve of evolute of lemniscate      E.30
Pedal curve which is its own pedal      L.66
Pedal curve, circle and radius of curvature      C.84 Z.14
Pedal curve, inversion and reciprocation of      E.21
Pedal curve, rectification of difference of arcs of      Z.3
Pedal surfaces      A.22 35 36 M.6 J.50 Z.8
Pedal surfaces, counter      AJ.5
Pedal surfaces, volumes of      C.55 A.34 An.63 J.62 Pr.12
Pentagon, ths      A.4 J.5 56 N.53
Pentagon, ths, diagonals of      A.57
Pentagonal dedecahedron      A.25
Pentahedron of given volume and minimum surface      L.57
Periodic continued fractions      A.62 68 C.96 J.20 33 53 N.68 Z.22
Periodic continued fractions with numerators not unity      C.96
Periodic continued fractions, closed form of      A.62
Periodic continued fractions, representing quadratic roots      A.43
Periodic functions      A.5 J.48 N.67 gzC.89 Mo.84
Periodic functions in theory of transcendents      J.11
Periodic functions of 2 variables with 3 or 4 pairs of periods      C.90
Periodic functions of 2nd species      M.20
Periodic functions of several variables      C.43 J.71
Periodic functions with non-periodic in def. integrals      C.18
Periodic functions, $cos x-\frac{1}{3} cos3x+ \frac{1}{5} cos5x$      CD.3
Periodic functions, 2n-ply, of n variables      Mo.69
Periodic functions, 4-ply, of 2 variables      J.13
Periodic functions, doubly      C.32 40 70 90 J.88 L.54
Periodic functions, doubly, expansion in trig. series      N.78
Periodic functions, doubly, monodromic and monogenous      C.40
Periodic functions, doubly, of 2nd kind      C.90 98 gzL.83
Periodic functions, doubly, of 3rd kind      C.97
Periodic functions, doubly, with essential singular points      C.89
Periodic functions, integrals between imaginary limits      A.23
Periodic functions, multiply      C.57 58
Periodic functions, real kind of      Mo.66 84
Periodicity theory      M.18
Periods cyclic, of the quadrature of an algebraic curve      C.80 84
Periods in reciprocals of primes      Me.73
Periods of integrals      see "Integrals"
Periods of the exponential $e^{x}$      C.83
Periods, law of      C.96
permutations      94 A1 C.22 CD.7 L.39 61 LM.15 Me.64 66 79 N.44 71 76 81 Q.1 Z.10
Permutations of 3q and 2q letters, 2 and 2 alike      N.74 75
Permutations of n things      C.95 N.83
Permutations of n things in groups      L.65
Permutations with star arrangements      Z.23
Permutations, alternate      L.81
Permutations, ap. to differentiation and integration      A.21
Permutations, number of values of a function through the permutations of its letters      C.20 21 46 47 L.65
Permutations, successive ("battement de Monge")      L.82
Perpendicular from a point upon a line: length of      4094 t.c4624 eq4086 t.c4625 sd5530
Perpendicular from a point upon a plane      5554
Perpendicular from a point upon tangent of a conic      4366—4373
Perpendicular from a point upon tangent plane of a quadric      5627
Perpendicular from a point, ditto for any surface      5791—5793
Perpetuants      AJ.7
Perspective      1083 A.69 G.3 thsL.37 Me.75 81
Perspective of coordinate planes      CM.2
Perspective, analytical      A.11
Perspective, drawing      1083—1086
Perspective, figures of circle and sphere      A.57
Perspective, isometrical      CP.1
Perspective, oblique parallel      Z.16
Perspective, projection      A.16 70
Perspective, relief      A.36 70 N.57
Perspective, triangles      974 E.29 J.89 M.2 16
Perspective, triangles in a conic      A.1
Petersburg problem      A.67
Pfaff's problem      A.60 C.94 J.61 82 M.17
Pfaff's problem, th of Jacobi      J.57
Pfaffians, ths on      Me.79 81
Piles of balls and shells      N.72
Pinseux's theorem      Mo.84
Plane      J.20 45 Mem.22
Plane and line, problems      CD.2 J.14
Plane coordinate geometry      4001—5473
Plane, cond. for intersection of two planes touching a quadric      5703
Plane, condition for touching a cone      5700
Plane, condition for touching a cone, ditto for a quadric      5635 5701
Plane, Equations of      5545 q.c p.c Z.1
Plane, equations of, under given conditions      5560—5573
Plane, figures, relation between      A.55 J.52 M.3
Plane, kinematics of      Q.16
Plane, motion of      JP.2 LM.7
Plane, point-systems      J.77
Plane, point-systems, perspective      Z.17
Plane, representing a quadric      N.71
Planimeter      A.58 Mel.2 3
Planimeter, Amsler's      5452 C.77
Planimeter, polar      A.51 N.80
Planimeter, Trunk's      A.44
Planimetrical theorems      A.37 60
Pluecker's complex surfaces      M.7
Plueckerian characteristics of a curve discriminant      Q.12
Plueckerian numbers of envelopes      C.78
Point-pair, absolute on a conic      Q.8
Point-pair, absolute on a conic, harmonic to two such      Z.13
Point-plane system      M.23
Points at infinity on a quadric      N.65
Points in a plane, relation between four      A.2 26
Points in a plane, relation between four, tg.eq of two      4669 4913
Points in space, represented by triplets of points on a line      LM.2
Points of equal parallel transversals      A.61
Points on a circle and on a sphere      N.82
Points, four, or lines, ths      CD.8
Points, roots in a closed curve      N.68
Points, systems      JP.9 M.6 25 N.58
Points, systems, of cubic curves      Z.15
Points, three, coordinates of      N.42
Points, three, pr      A.8
polar      1016 4124 A.28 J.58 gzLM.2 Me.64 66 N.72 79
Polar curves, tangents of      N.43
Polar line of two points with respect to a quadric      5685
Polar of 3 right lines      A.1
Polar of a quartic      L.57
Polar of conics      4762 thsN.58
Polar of cubic curves      J.89 L.57 Mel.5 Q.2
Polar plane      Q.2 Z.22
Polar plane of a quadric      5678 5687 An.71
Polar plane of a quadric, of four      LM.13
Polar subtangent      5133
Polar surface of a cubic      J.89
Polar surface of a cubic, twisted      Z.23 24
Polar surface of a plane      C.60 N.66
Polar surface of a point      N.65
Polar surface of a triangle      A.59
Polar surface of a triangle, perspective      J.65
Polar surface, tetrahedron      J.78 N.65 Z.13
Polar, developable      5728
Polar, inclined      N.59
Pole and Polar      1016 4124
Pole of chords joining feet of normals of conic drawn from points on the evolute      N.60
Pole of similitude      5587
Pole of the line $\lambda \alpha +\mu \beta +\nu \gamma $      4671
Political arithmetic      trA.36—38
Pollock's geo. theorems      Q.1
Poloids of Poinsot      CD.3
Polyacrons, $\Delta -faced$      Man.62
Polydrometry      A.38 39
Polygonal numbers      287 Pr.10 11 12 13
Polygonometry      thsAn.52 J.2 47 Mem.30
POLYGONS      An.cn53 63 JP.4 9 N.74 Z.11 see
Polygons of circular arcs, cn      A.3 J.76
Polygons of even number of sides      LM.1
Polygons of n+2n sides, numbers related to      A.62
Polygons of Poncelet, metrical properties      L.79
Polygons, area of      748 4042 J.24 N.48 52
Polygons, articulated and pr. of configuration, tr      An.84
Polygons, centroid      N.77
Polygons, classification      Q.2
Polygons, division into triangles      A.1 8 L.38 39 LM.13 Pr.8
Polygons, family of      N.83
Polygons, maximum with given sides      J.26
Polygons, semi-regular      JP.24
Polygons, semi-regular, star      A.59 L.79 80
Polygons, sum of angles of      A.52 N.50
Polygons, theorems      A.1 2 C.26 prsCD.5 Mel.2 N.58
Polyhedral function (Prepotentials)      CP.13
Polyhedrons      906 C.46 60—62 J.3 JP.4 9 15 24 L.66 Man.55 N.83 P.56 57 Pr.8 9 11 12 Q.7 Z.11 14
Polyhedrons, classification of      C.51 52
Polyhedrons, convex, angles of      C.74
Polyhedrons, convex, regular      A.59
Polyhedrons, diagonals, number of      N.63
Polyhedrons, Euler's theorem      J.8 14 Mem.13 Z.9
Polyhedrons, F+S=E+2      906 A.24 E.20 27
Polyhedrons, maximum, for a given surface      M.2 Mel.4
Polyhedrons, maximum, regular      C.61
Polyhedrons, minimum surfaces of      A.58
Polyhedrons, regular, ellipsoidal      C.27
Polyhedrons, regular, self-conj.      A.62
Polyhedrons, regular, star      A.62 thsC.26
Polyhedrons, surface of      A.53
Polyhedrons, surface of, volume      J.24 N.52
Polyhedrons, symmetrical      J.4 L.49
Polyhedrons, theorems      E.39—42 J.18 N.43
Polynomials of two variables-analogous to Jacobi's      A.16
Polynomials, determined from its partial differential      A.4
Polynomials, geometry of      JP.28 thQ.14
Polynomials, product of two      N.44
Polynomials, system of      L.56
Polynomials, value when the variable varies between given limits      C.98
Polyzonal curves, $\surd U + \surd V=0$      TE.25
Porisms      L.59 P.1798 Q.11 TE.3 4 9
Porisms of Euclid      C.29 48 56—59 L.55
Porisms of in- and circum-polygon      Me.83 P.61
Porisms of in- and circum-triangle      LM.6 9 Q.1
Porisms of two circles      Me.84
Porisms, Fermat's fourth      A.46
Poristic equations      LM.4 5
Poristic relations between two conics      LM.8
Position, pr. relating to theory of numbers      Mel.2
Potential      thsAn.82 C.88 G.15 J.20 32 63 70 th81 85 M.2 3 N.70 Z.17
Potential of a circle      J.76
Potential of a right solid      J.58
Potential of a sphere      Me.81
Potential of a sphere, surface of      Me.83 Q.12 Z.7
Potential of cyclides      C.83 J.61
Potential of cyclides, elliptic      Me.78
Potential of ellipsoids      J.98 Me.84 Q.14
Potential of ellipsoids, two homog.      J.63 70
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