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Yates R.C. — Curves and Their Properties
Yates R.C. — Curves and Their Properties

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Название: Curves and Their Properties

Автор: Yates R.C.

Аннотация:

Some mathematical works of considerable vintage have a timeless quality about them. Like classics in any field, they still bring joy and guidance to the reader. Books of this kind, if no longer readily available, are being sought out by the National Council of Teachers of Mathematics, which has begun to publish a series of such classics. The present title is the fourth volume of the series.
A Handbook on Curves and Their Properties was first published in 1952 when the author was teaching at the United States Military Academy at West Point. A photo-lithoprint reproduction was issued in 1959 by Edwards Brothers, Inc., Lithoprinters, of Ann Arbor, Michigan. The present reprint edition has been similarly produced, by photo-offset, from a copy of the 1959 edition. Except for providing new front matter, including a biographical sketch of the author and this Foreword by way of explanation, no attempt has been made to modernize the book in any way. To do so would surely detract from, rather than add to, its value.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1974

Количество страниц: 258

Добавлена в каталог: 24.07.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
"e"      93 94
$y^{x} = x^{y}$      205
Addition of ordinates      188
Aeroplane design      48
Agnesi, Maria Gaetana      237
Alexander the Great      36
Alysoid      203
Apollonius      23 36 86 127 133
Arbelos      25
Archer's bow      204
Archimedes spiral      see "Spirals Archimedean"
Archimedes trammel      3 77 108 120 234
Astroid      1—3 63 73 78 84 109 111 126 140 156 157 163 169 174 234
Asymptotes      27 87 129 193 194 195 202 211 213
Auxiliary curves      190
Barrow      217
Bellavitis      127
Beltrami      221
bernoulli      1 12 65 67 68 69 81 93 143 152 175 206 221
Besant      108 175
Besicovitch      72
Boltzmann      106
Bouguer      170
Bowditch curves      203
Brachistochrone      68
Brianchon      48
Brocard      171
Bulbus      186
Bullet nose curve      203
Calculus of variations      80
Calyx      186
Cams      6 137 210
Cardioid      4—7 17 61 84 91 124 125 126 140 149 151 152 153 162 163 164 168 173 179 182 214 235
Carpenter's square      28 50 209 219
Cartesian oval      149 203
Cassinian curves      8—11 143 144
Catacaustic      see "Caustics"
Catalan's trisectrix      203 205
Catenary      12—14 20 63 80 87 117 124 126 174 177 182 183 203 222
Catenary of uniform strength      174 203
Catenary, elliptic      179 182 184
Catenary, hyperbolic      182 184
Caustics      5 15—20 69 71 73 79 81 87 149 152 153 160 163 207
Cayley      75
Cayley, sextic      97 153 163 214
Central force      8 145 212 214 215
Centrifugal pumps      210
Centrode      119
Cesaro      123 125 126
Chasles      85 119 138
circle      1 5 16 17 20 21—25 30 31 61 69 79 91 126 127 128 133 138 139 140 149 162 163 168 171 172 174 180 182 183 214 223 233 235
Cissoid      20 26—30 126 129 141 142 143 161 163 183 218 219
Clairaut      77
Clothoid      see "Spirals Euler"
Cochleoid      203
Cochloid      203
Cocked hat      203
Compass construction      128
Conchoid      30 31—33 108 109 120 121 141 142 148 203
cones      34—35 37 38 39
Conics      20 36—55 78 79 87 88 112 130 131 138 140 149 156 163 173 188 189 195 203
Convolvulus      186
Cornu's spiral      see "Spirals Euler"
Coronas      81
Cotes      212
Crane      204
Critical points      196
Cross curve      203
Crossed parallelogram      6 131 158 183
Cube root problem      26 31 36 204
Cubic parabola      56—59 89 186 197
Cubic, l'Hospital's      203 205
Cubic, Tschirnhausen      203 205 214
Curtate cycloid      65 69 see
Curvature      53 60—64 86 167 172 180 181 184 197 207 213 215 223
Curvature, construction of center of      54 55 145 150 213
Cusp      20 27 90 192 197 199 200 202
Cycloid      1 4 63 65—70 80 89 92 122 125 126 136 137 138 139 172 174 176 177 179 180 181 182 183 see
Cylinder      229 230
da Vinci, Leonardo      170
Damping factor      190
De Moivre      93
Deltoid      71—74 84 126 140 164 169 174 203
Desargues      175
Descartes      65 98 205 206 207
Deviation, standard      96
Devil curve      203
Diacaustic      see "Caustics"
Differential equation      75 77
Diffraction of light      215
Diodes      26 129
Directional curves      190
Discontinuous curves      100—107
Discriminant      39 57 76 189
Double generation      81
Duality      48
Duerer      175 233
Elastic spring      215
ellipse      2 19 27 36—55 63 78 79 88 109 111 112 120 139 140 149 157 158 164 169 173 178 179 180 182 183 184 189 195 202 230 234 299
Elliptic catenary      179 182 184
Envelopes      2 3 15 50 72 73 75—80 85 87 91 108 109 110 111 112 135 139 144 153 155 160 161 175 180 181 234 235
Epi      203
Epicycloid      4 5 63 81—85 87 122 126 139 152 163 169 174 177 180 182 183
Epitrochoids      see "Trochoids"
Equation of second degree      39 188
Equiangular spiral      see "Spirals equiangular"
Equitangential curve      see "Tractrix"
Eudoxus, Hippopede of      203
Eudoxus, Kampyle of      174 204
Euler      67 71 82
Euler form      94 116 226
Evolutes      2 5 15 16 19 20 57 66 68 72 79 85 86—92 135 139 149 152 153 155 173 187 197 204 207
Exponential curves      20 93—97
Fermat      237
Fermat's spiral      see "Spirals parabolic"
Festoon      204
Flex point      10 56 87 90 196 198
Flower pot      204
Folium      72
Folium of Descartes      98—99 193 205
Folium, simple, double, tri-, quadri-      73 140 163 164 174 203
Fourier development      232
Fucia      186
Functions with discontinuous properties      100—107
Galileo      12 65 66 81
Gaussian curve      95
Gears      1 69 81 137 233
Gerono's lemniscate      203
Glissettes      50 108—112 121 122 138 139 149 216
Goblet      204
Grandi      237
Graphical solution of cubics      57 58
Great circle route      230
Gregory      238
Growth, law of      94
Gudermann      113
Gudermannian      115
Guillery      69
Halley      207
Harmonic analysis      230
Harmonic motion      6 67 229
Harmonic section      42
Hart      131
Hathaway      171
Helix      69 203 209 211 229
Helmet      204
Helmholtz      203
hessian      99
Hillock      204
Hippias, quadratrix of      204
Hippopede of Eudoxus      203
Hire      138 175
Horopter      203 204 205
Huygens      15 66 67 86 135 152 155 186 221
Hyacinth      186
Hyperbola      19 27 36—55 63 78 79 88 101 112 115 116 129 130 139 140 144 149 157 163 164 168 169 173 182 184 189 195 205 214 219
Hyperbolic catenary      182 184
Hyperbolic functions      113—118
Hyperbolic spiral      see "Spirals reciprocal"
Hypocycloid      1 63 71 81—85 87 122 126 140 163 169 177 180 182
Hypotrochoids      see "Trochoids"
Ingram      127
Instantaneous center of rotation      3 15 29 32 66 73 85 119—122 155 158 176 209
Intrinsic equations      92 123—126 180
inversion      63 127—134
Involutes      13 20 66 68 85 87 125 126 135—137 155 156 164 176 182 183 208 209 222
Ionic volute      213
Isolated point      192 197 200 202
Isoptic curves      69 85 121 138—140 213
Jones      210
Kakeya      72
Kampyle of Eudoxus      174 204
Kappa curve      174 204 205 222
Kelvin      127 141 142
Kieroid      29 33 141—142 219
Kite      158
L'Hospital      68
l'Hospital, cubic      203 205
Lagrange      15 67 75
Lambert      113
Lame curve      87 164 204
Law of growth (or decay)      94
Law of Sines      225
Least area      72
Leibnitz      56 68 155 175 186 221 238
Lemniscate, Bernoulli's      9 10 63 130 143—147 157 163 168 205 214
Lemniscate, Gerono's      203
Light rays      15 86
Limacon of Pascal      5 7 16 31 108 110 121 130 139 140 148—151 163 234 235
Line motion      84 132 158 210 234
Linkages      6 9 28 51 132 146 151 158 183
Liouville      221
Lissajous curves      see "Bowditch curves"
Lituus      169 212 213
Logarithmic spiral      see "Spirals equiangular"
Loria      186
Lucas      171
Maclaurin      143 160 163 182 205 213
Mapping      118 223 230
Maxwell      136 175
Mayer      113
Mechanical inversors      131
Mechanical solution of cubic      57
Mechanism, quick return      183
Menaechmus      36
Mercator      118 230
mersenne      65 81
Minimal surfaces      13 183
Monge      56
Montucla      69
Morley      171
Motion, harmonic      6 229
Motion, line      84 132 158 210 234
Mueller      225
Multiple point      20 192 197 199 200 202
Napier      95
Napkin ring      17
Nasir      234
Nautilus, septa of      208
Neil      186
Nephroid      17 75 84 87 126 152—154
Newton      28 51 56 60 67 68 81 175
Nicomedes, chonchoid of      31—55 108 142
Node      192 197 199 200
Normal curve      95 96
Normals      91
Optics      40 203
orthocenter      22
Orthogonal trajectory      223
Orthoptic      3 75 138 139 149
Orthotomic      15 20 87 160
Osculating circle      60 63
Osculinflexion      198 199 200 202
ovals      131 149 203
Palm stems      204
Paper folding      50 78
Pappus      25
parabola      5 12 13 19 20 27 29 36—55 61 64 75 76 79 80 87 88 91 111 112 129 136 138 139 140 149 156 157 161 163 164 168 169 173 176 182 183 187 189 214 216 219
Parallel curves      79 155—159
Parallelogram, crossed      6 131 158 183
Pascal      36 65 148
Pascal, theorem of      45 ff.
Pearls of Sluze      56 204
Peaucellier cell      10 28 52 131
Pedal curves      5 9 15 29 63 72 79 85 136 138 144 149 160—165 167 179 182 203 207 209 214 219
Pedal equations      162 166—169 177 213
Pendulum, cycloidal      68
Pilaster      204
pink      186
Piriform      204
Pivot, Schiele's      222
Poinsot's spiral      204
Points, singular      192 199 200 202
Polars      41 42 43 44 133
Polynomial curves      64 89 194 198
Polynomial curves, semi-      61 87 201
Power of a point      21
Probability curve      95
Projection, Mercator's      118
Projection, orthogonal      229
Projection, orthographic      211
Projection, stereographic      207 219
Prolate cycloid      65 69 see
Pseudo-sphere      223
Pseudo-witch      238
Pursuit curve      170—171
Pyramid      204
Quadratrix of hippias      204
Quadrifolium      140 163
Quetelet      15 127 160
Quick return mechanism      183
Radial curves      69 73 172—174 222
Radical axis      22
Radical center      22
Reflection      see "Caustics"
Refraction      69 see
Rhodcneae      see "Roses"
Rhumb line      118
Riccati      113
Ridolphi      235
Roberval      65 66 148
Roemer      1 81 233
Roses      85 163 174 216 235 see
Roulettes      13 29 65 73 79 110 135 136 175—185 207 212 222 233 235 see
Sacchi      169
Sail, section of      14
Schiele's pivot      222
Secant property      21
Semi-cubic parabola      61 87 157 186—187 192 201
Semi-polynomials      61 87 201
Semi-trident      204
Septa of the Nautilus      208
Series      117 227 228 232 238
Serpentine      204
Shoemaker's knife      25
Sierpinski      107
Similitude      22
Simson line      72
Sine curve      225 229 230 231 232
Sines, law of      225
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