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| Shiffer M.M., Bowden L. — Role of Mathematics in Science |
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| Предметный указатель |
 (pie) 25 59
(pie), Cusanus' calculation of 59
(pie), recursive formula for 59
Aaboe, Asger 15
Abraham 189
Absorption factor 30
Addition of velocities 160
Addition of velocities, relativistic 152 163 166
Addition, formulas 119 159 191
Addition, formulas for hyperbolIc functions 191
Addition, formulas of trigonometry 119 123 157
Additive function 173
Additive property 112 116
Admissible energy functions 178 ff
Affine maps 112
Algebra 104 131
Algebra of matnces 119 123
Algebra of vectors 107 108
Algebra, factor theorem of 143
Algebra, rules of 123
Algebraization of geometry 105
Allgaier — Hamppe 1
Analytic geometry 104
Angle of deflection 188
Angle of incidence 76 77 80 81 82
Angle of reflection 76 77 80
Angle of refraction 82
Angle of rotation 145 156
Apothem 64
Archimedes 1 3 4 6—9 11 12 15 16 24 59 169 199
Archimedes, "mechamcal method" of 15 16
Archimedes, axiom of 4
Archimedes, law of the lever 3 8 169
Archimedes, symmetry proof 80
Arithmetic progression 46
Arithmetic, -geometric mean 44
Arithmetic, -geometric mean, inequality 25 69—74
Arithmetic, average 34
Arithmetic, mean 44 69—74
Associative 115 118 164
Associative binary operation 164 167
Associative property 164
Attractors 52 56
Average see arithmetic mean
Beam(s) of light 94 100
Beam(s) of light, interfering 94
Bernoulli, James 33
Binary operation 164 165 166
Binary operation, infinitesimal 167
Binomial coefficients 32
Binomial theorem 32
Bohr, Niels 181
Bucherer 189
Calculus 91 99 162
Calculus of variations 91
Calculus, differential 87 98
Cartesian coordinates 110
Cassegram 101—103
Cauchy 70
Cavalieri 15
Center of gravity 12 14 19 20
Centroid 10 12 14 16
Clock readings 137
Collision, elastic 174
Collision, symmetic 170 174
Commule 112 194
Commutative 107 119 194
Component(s) 109 110 113 117 129
Component(s) transformation 130
Composile 117 123—126
Composition of linear maps 115
Composition of maps 115 118 123
Compound interest 30 31
Compounding continuously 33
Compounding inslantaneously 33
Congruence 124 125
Conic section 12 101—103
Conics 99
Conservalion law 183
Conservalion of energy 170 172 174 189
Conservalion of momentum 172
Continuous compounding 33
Continuous function 144 173
Continuous function, additive 174
Converge 52 56
Convergence 32 66 68
Coordinate(s) 105 129
Coordinate(s) axes 129
Coordinate(s) geometry 108
Coordinate(s) system 130 145
Coordinate(s) transformation 128
Coordinate(s), cartesian 110
Coperrucus 136
Corpuscular nature of light 95
Corpuscular theory of light 91 94
Correspondence principle 181 183—185 188
Cosines, Law of 110
Crooked lever 16 18—20
Cune 190
Cusanus 25 59 66
Cycle, stable 55 56
Cycle, steady 52 53
Cycle, steady, of period 2 52
Cyclotron 150
Darwin 46
Decimal fraction 21
Densily 22
Descarles 66 91
Differenlial calculus 87 98
Differenlial equalion(s) 44 45 178
Differenlial equalion(s), parlial 196
Differentiate 99 177 183
Displacement 105 106
Distance 124—127 130
Distance, preserving map 124—126 144
Distributive 107 110
Dot product 107 11 113 118 127 128
e (Euler's number) 32 33
Einstein's formula 163 189
Einstein's law for re1alivislic addilion of velocities 160 161
Einstein's principle of relativity 171
Einstein's space-lime transformation problem 132
Einstein's special theory of relativity 147
Einstein's theory of relativity 94
Einstein's time contraclion 150
Einstein's transformation equations 153
Einstein's transformation law 155
Einstein, Alberl 1 137 144 148 150 152 189 190 196 197 199
Elastic 170
Elastic collision 173
Electrodynamics 196
Electromagnetic theory 197
Electron(s) 188
Electron(s) beam 129
ellipse 12 82
Ellipse, foci of an 96
Ellipse, reflecting 99
Ellipse, tangent to an 95
Ellipsoidal cupola 99
Elliptical orbit 82
Energy 169 184—186 189 190
Energy and mailer 189
Energy and momenlum 181
Energy conservalion 170 172 174 189
Energy function 174—181
Energy function, admissible 174 178 181
Energy function, Newtonian 175
Energy, kinetic 170 189
Energy, Newtonian 181
Energy, relativistic 182
| Epidemic 29
Equilibrium 3 10—12 17—21 72
Equilibrium of the lever 3 80
Equiprobable 40
Error(s) 34 35
Error(s) in combinations of observations 43
Error(s), actual 35
Error(s), combination of 35
Error(s), Gauss' law of 35
Error(s), law of 34 36
Ether 94 163 189 196
Euclid 61 91
Euclid, law of reflection 91
Euclid, optics of 75
Euclidean motions 124
Even function 39
Events 38
Events, combined 38
Events, independent 38
Experimenlum cruds 93 94
Exponential 25
Exponential function 28
Exponential law of growth 25
Factor theorem of algebra 143
Feigenbaum, Mitchell J. 55
Fermat 16 91 93—95 98
Fermat law of refraction 90 91
Fermat quickest path principle 84 ff
Fitzgerald — Lorentz contraction 148 189
Fixed point 53—55 125
Fixed point of a function 53 54
Fixed point, stable 54
Fizeau 163 168
Focus (foci) 96 99 101
force 18 186—188
Force, magnetic 188
Force, moment of a 18
Frank, Philipp 199
Fresnel 163
Function 25 82
Function, additive 173
Function, continuous 144
Function, differentiable 165
Function, energy 174 ff
Function, energy, admissible 174 ff
Function, even 39
Function, exponential 28 34
Function, growth 25
Function, hyperbolic 157
Function, linear 142
Function, momentum 184
Function, vector 196 197
Functional equation 25 27 45 157
Galilei, Galileo 1 24 84 196
Gauss, Carl Friednch 34—36 42 43 72
Gauss, Carl Friednch, law of errors 42
Gauss, Carl Friednch, method of least squares 44 72
Geometric mean 69 ff
Geometric progression 45
Geometry, analytic 104
Geometry, coordinate 108
Gravitational field 169
Group 155 194
Growth 25
Growth, exponential law of 25
Growth, factor 49
Growth, functions 25 ff
Growth, law of 28 29
Growth, population 29 45 47
Growth, rate 45
Half-life 30
Half-life of muons 150
Half-life of radium 30
Heiberg 16
Heron of Alexandria 76—78 81 85 91
Heron of Alexandria, minimum principle 85
Heron of Alexandria, shortest path law of reflection 90
Hexagon 64
Hexagon, regular 64 67
Homogeneity 112
Homogeneous map 114
Huygens, Christian 94
Hyperbola 12 101 103
Hyperbolic cosine 159
Hyperbolic functions 157
Hyperbolic sine 159
Hyperbolic tangent 159
Identity 115 125 126
identity map 115
Image 105 106 113 117 125 127
Image mirror- 120 121
Image point 112
impact 170 173
Incident ray 76
Inclined plane 18 20—22 35
Independent events 38
Index of refraction 90
Inequality of arithmetic-geometric mean 25 69
Inertia 186
infinity 99
Intensity of light 30
Interest 30 31
Interest compound 30
Interest rate 30
Interest, simple 30
Interferometer 134
Invariance 196
Invariance of velocity of light 147
Invariance, laws of 169
Invariance, principle of 172
Inverse 106 115—117 119 122 126 154
Inverse of a displacement 106
Inverse of a Lorentz matrix 154
Inverse of a one-ta-one onto map 115 116
Isometry 124—128 130 144 145 156
Kaufmann 188
Kepler 82 83 90 91
Kepler, third law 84
Kinetic 35
kinetic energy 170 189
Kinetic theory of gases 35
Law(s) of (in)sufficient reason 3
Law(s) of conservation of energy 170
Law(s) of cosines 110
Law(s) of errors 34—36 42
Law(s) of invariance 169
Law(s) of the lever 3 10 11 14 16 169
Law(s), Verhulst's 47 48
Least squares 44
Least squares, Gauss' principle of 72
Leibniz 16 91
Lens, refracting 100
Lever 3 5—7 11 14
Lever, Archimedes' law of the 3
Lever, crooked 16
Lever, weightless 3
Lie, Sophus 167
Light, corpuscular theory of 91
Light, Iimit 15 67 69
Light, interfering beams of 94
Light, Newton's mechanistic theory of 91
Light, propagation of 81
Light, rays 75 94 133 134
Light, rays, bending of 81
Light, rectilinear propagation of 91 95
Light, relation 89
Light, speed of 137 152
Limiting value, tending to a 32
Linear 112
Linear functions 142 143
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