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| Hancock H. — Theory of Maxima and Minima |
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| Предметный указатель |
Abelian transcendents 169
Algebra, fundamental theorem of 165
Algebraic curve expressed through power series 36 53
Algebraic function at a singular point 180 et seq.
Algebraic function, its development in series 177
Algebraic structures 176 et seq. 181
Ambiguous case, the iv 27.
Analytic dependence 166 et seq. 169
Analytic function 73
Analytic function defined 138
Analytic structure 74 174
Appell 180
Area, maximum area 143
Asymptotic approach 138
Auxiliary variable 101 173
Baltzer 2
Bauer 107
Bertrand v 33
Biermann 136 155 168
Bocher 148
Bohlmann and Schepp iv
Bois-Reymond, Paul du 2 7 74
Bolzano 12 136
Borchardt 107
Boundary 136 et seq. 156
Brand 126 et seq.
Burnside 89 106
Calculus of variations iv 171
Cantor, Geschicte etc. 15
Cartesian oval 133
Cauchy 3 7 92
Cavalieri 27
Center of curvature 117 125
Christoffel 107
Complete differential quotient 6
Contact of indefinitely high order 36
Continuation of an analytic function 174
Continuous function 161 162
Convergence 166 167 168 172 178
Cremona 144
Curvature 117
Cusps, appearance of 30
Cylinder, trace of 31
Dantscher, method of 39 62 72
Dantscher, Victor von v 36 69
Definite form 19
Definite form, conditions for 91
Definite form, necessary condition 21 49 50 51 64 68 82 83 91 109 111 114;
Derivative, existence of a 161 162 166
Descartes iv 165
Determinant orthogonal 149
Determinant, the sign of the 25 et seq. 28 29 30 32 33 51 52 59 60 83 85 90 91 92 93 97 100 107 111;
Differentiation, one-sided iv 7 11
Dini 12 136 167
Distinctness as characteristic of an extreme 37 38 47 50
Double curve 54
Double point 101
Double point isolated 29 30 31
Double point with distinct tangents 29
Element of a complete structure 74
Equation of secular variations 107
Euclid iii 15 135
Euler 16 18 107
Euler, theorem of, for homogeneous functions 84 155
Exceptional cases involving a squared factor 54 58 68 97
Existence of an extreme, proof of 135 146
Extraordinary cases of extremes iv 19
Extraordinary maxima or minima 1 et 17 19 43 74
Extreme curves 53 54
Extreme, criteria for 4 6 26 92.
Extreme, or extreme value v 2 53
Failure of general criterion 55
Fallacious conclusions See Incorrectness of earlier theories
Fermat iii iv 15 132
Fermat, method of determining maximum and minimum iii
FORM See Definite form
FOURIER iii
Fourier series 74
Fractional powers 178 182
Fuchsian functions 171
Function many-valued 169
Function, one-valued 166
Function, rational 166
Function-element 138 174
Fundamental theorem of algebra 49
Gauss 19
Gauss, principle of 151 et seq.
Genocchi-Peano 1
Geometrical interpretations 6 24 31 46 69 71 97 125
Geometrical mechanics 139
Geometry of numbers 174
Gergonne 19
Goursat 6 28 27 29 31 126 170 177 180
Greatest value 1 48 94.
Hachette 107
hadamard 147 148 160
Hancock 123 166
hankel 74
Harkness 12
hermite 89 106 180
hilbert 170
homogeneous functions 49 155
Homogeneous quadratic forms 82 85 103
Homogeneous quadratic forms expressed as a sum of squares 86 89 91
Homogeneous quadratic forms with subsidiary conditions 114
Hudde 165
Huygens 16
Hypergeometric series 170
Improper maxima and minima See Maxima and minima
Incorrectness of earlier theories 33 et seq. 52
Indefinite form 19 49 50 51 64 68 82 106 116
Indeterminate coefficients 172
Inflection, point of 6
Integral rational function 168
Isolated point 29 31
jacobi 107
JORDAN 75
Koenigsberger 180
kronecker 106
Kummer 106 107
Lagrange iii v 4 18 22 26 38 43 77 86 92 99 107 114 127 131 148 172
Laplace iii 107
| Least squares 26
Least value 1 50 94.
Left-hand differential quotient 7 11
legendre 135
Leibnitz 3 15
Limitation expressed through an equation 150
Lipschitz 2 74
Lower limit 63 See
Lueroth See Dini
Maclaurin iii 3 4 15 22 77
Maxima and minima (see also Extreme value), one of the most admirable applications of fluxions iv
Maxima and minima, absolute 2
Maxima and minima, condition for improper extremes 41 42 140
Maxima and minima, condition for proper extremes 40 42
Maxima and minima, conditions for iv 4 40 99
Maxima and minima, criteria for 4 7—12 et 48 51 55 64 67 68 77 80 81 82 92 100 102 115 116
Maxima and minima, criteria for relative maxima and minima 115
Maxima and minima, erroneous criteria 33
Maxima and minima, extraordinary (see under Extraordinary etc.)
Maxima and minima, geometrical interpretation of 6
Maxima and minima, improper 2 5 23 26 31 50 59 60 63 75 140 164
Maxima and minima, inaccuracies in v
Maxima and minima, maximum defined 1
Maxima and minima, minimum 1
Maxima and minima, ordinary (see under Ordinary etc.)
Maxima and minima, proper 2 5 17 23 26 44 45 60 61 63 74 75
Maxima and minima, relative 2 21 96
Mayer iv v 2 79
Mechanics, derivation of the ordinary equations of 152
Mechanics, problems in 139 150
Minimal surfaces 123
Minkowski 174
Morley See Harkness
Neighborhood of, in the 65 173
Newton, discoverer of the calculus iii
One-sided differential quotient 7 11
Orbits of planets 107
Order of a curve 54
Ordinary maxima and minima 1 et seq. 17
Osculating circle 117
Osgood 167 170
Panton See Burnside
Pappus 15 164
Pascal, Exercici etc. 11
Pascal, Repertorium etc. 130
Peano iv v 2 6 21 31 33 34 62 61 68 94
Pendulum 150
Petzval 107
Picard 170 180
Pierpont 3 7 15 34 37 177
Poincare 170 180
Poison 107
Polygon See Regular polygon
POSITION 135 et seq.
Power-series 171 et seq. 175 179
Proper maxima or minima See Maxima and minima
Puiseux 180
Quadratic form 19
Quadratic form, application of 92 et seq. See Homogeneous quadratic forms
Quadratic form, expressed as a sum of squares 86 et seq. 89
Radius of curvature 117
realm 135 174
Reflection of a ray of light 126 et seq.
Refraction of a ray of light 131 et seq.
Regiomontanus 16
Region of convergence 167 168
Regular function 73
Regular point 177
Regular polygon 140 142 147
Relative maxima and minima See Maxima and minima
Reversion of series 153 et seq.
Richelot 106
Right-hand differential quotient 7 11
Roots of unity 180
Salmon 107 120 122
Scheeffer v 19 27 35 36 39 46 48 50 62 70
Scheeffer's method 37
Scheeffer's theorem 43 46 55 59 60 61 62 70 72
Scheeffer's theory 43 et seq.
Schepp See Bohlmann ; see also Dini
Secular variations, equation of 107
Semi-axes of a central section 165
Semi-definite case iv
Semi-definite form 19 49 50 51 52 64 65 68 70 82 83 92 93 106 116
Serret v 33 104 106 136
Severus 16
Shortest distance to a given surface v 101 123
Simple point 177
Simpson 16
Singular point 164 177 180 183 184
Sluse, Rene F. W. de 16
Smallest value 1
Smith, Edward 107
Spherical triangle 136
Squared factor See Exceptional cases
Stolz v 2 6 11 43 45 46 60 60 70 79 91 100 136 166 164 180 181 187 189
Stolz's added theorem 46 60
Stolzian theorems 39 et seq. 66 68 70 72
Structure of the first kind etc. 175
Sturm's theorem 61 106
Surfaces of second degree 107
Sylvester 89 107
System of m equations, solution of 171 et seq.
Tangent, common to two curves 34 35 36
Tangent, parallel to x-axis 6
Tangential plane 28 31
Tartaglia 16
Taylor's development in series v 4 5 9 10 19 24 33 75 79 80 97 152 159
Taylor-Lagrange theorem 43 47 77
Todhunter 33
Transcendental curves 36
Transcendental functions 167 169
uniform See Convergence
Upper and lower limits 2 12 55 57 94 104 136 137
Variations, calculus of iv 171
Von Dantscher See Dantscher
Voss 2
Weierstrass iv 73 79 86 107 138 167 168 169 174 181
Wilson, E. B. 12
Wirtinger 148
Zajaczkowski 106
Zenodorus 142 147
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