|
|
 |
| Авторизация |
|
|
|
| Поиск по указателям |
|
|
|
|
|
|
|
 |
|
|
|
| Sommerville D.M.Y. — The elements of non-Euclidean geometry |
|
|
|
| Предметный указатель |
 28 76
 , ( ) 30 35 59;
Absolute geometry 22
Absolute Geometry, polar system 92
Absolute Geometry, space 197 210
Absolute unit, of angle 28
Absolute unit, of length 13 15 58 162
Absolute, the 46 98 154 198
Absolute, the, in Euc. Geom. 47 155 164
Absolute, the, its equation 127 129 174
Absorption of light 206
Actual points 46
Aether 197 201
Alembert, d’ 3
Altitudes of a tetrahedron Ex. iv. 24
Altitudes of a triangle 54 141
Anchor-ring 105 n
angle 28 121
Angle, dihedral 42
Angle, flat 28
Angle, formula 131
Angle, in a semicircle Ex. i. 1; ix. 5
Angle, logarithmic expression 157
Angle, of parallelism 30 35 58
Angle, right 28
Angle-sum of a triangle 5 10 12 15 16 18 21
Angle-sum of a triangle, and area 13 20 77 82 104
Antipodal points 55 89
Applicable surfaces 166
Archimedes, axiom of 17
Area, infinite 7—9 19 20
Area, of circle 80; Ex. ii. 23; 3
Area, of equidistant-curve Ex. ii. 22; iii. 4
Area, of plane 19; Ex. iii. 5
Area, of polygon 83 104
Area, of triangle 13 20 77—79 81 82 103—104
Area, of triangle, maximum 7 81
Area, unit of 79
Argand’s diagram 181 248
Aristotle 2
Astral geometry 15
Astronomy 203—207
Asymptotes 259
Asymptotic lines 10 39 42
Axioms 2 27
Axioms, of Archimedes 17
Axioms, of Pasch 29
Axis of a circle 52 104 136
Axis of a conic 258
Axis of a pencil of lines 48
Axis, radical 219 228
Ball, W. W. Rouse 201 n
Baltzer, H. R. 24
Beltrami, E. 202
Berkeley, G. 201
Bertranjd, L. 7
Bicircular quartic Ex. ix. 16
Bisectors of angles Ex. iii. 1; 139
Bolyai, J. 14 15 21—24
Bolyai, W. 7 14 21—24
Bonola, R. 24 n
Broad, C. D. 210 n
Bundle of circles 228
Bundle of lines 45 55 90
Camerer, J. W. 15
Carslaw, H. S. 24 n
Cayley, A. 158 192
Centre of circle 51 104
Centre of conic 258
Centre, homothetic 221
Centre, radical 221
Centroid 139
Ceva’s theorem 145
circle 51 104
Circle at infinity 164
Circle, circumference 76 114
Circle, equation 136 227 252
Circle, in Euc. Geom. 47 140
Circle, in relation to Absolute 136 258
Circle, of infinite radius 51; see also Horocycle
Circle, through three points 53 189
Circular functions 57 114
Circular functions, measure cf angle 57 81
Circular functions, points 47 156
Circular functions, transformations 181; Chap. viii
Circumcentre of triangle 54
Circumcircles of regular polygon Ex. ii. 17
Circumcircles of triangle 53 189; 13; 21 22
Circumscribed quadrilateral Ex. 3
Circumscribed sphere Ex. iii. 7 12
Clifford, W. K. 25 n 201
Clifford’s parallels 108
Clifford’s surface 106 112
Coaxal circles 222 232
Collinearity 135 145;
Collineation 180
Compass bearings 7
Complementary segments 63
complex numbers 181 248
Concurrency 135 145;
configurations 143
Confocal conics Ex. ix. 15
Conformal representation 172- 191
Conformal transformation 182; Chap. viii
Congruence 28 194—197
Congruence, of infinite areas 8
Congruent transformation 158 238 245
Conica 46 n 98;
Conjugate coaxal circles 232
Conjugate points 89
Conjugate, harmonic 95 148
Conjugate, isogonal 147
Consistency of N.-E. G. 202
Continuity 17 29 96
Convergent lines 42
Coolidge, J. L. 27 71
coordinates 125 199
Coordinates, homogeneous 135
Coordinates, line 128 172
Coordinates, polar 125
Coordinates, trilinear 172
Coordinates, Weierstrass’ 127 129 171 227
Corresponding points 32; Ex. ii. 8
Cross-ratio 147
cube Ex. iii. 8
Curvature, measure of 166
Curvature, of space 193 199
Curvature, surfaces of constant 168
Cyclic quadrilateral Ex. ii. 2
Cylinder 105
Defect of triangle 20 78
Definitions, Euclid’s 2
Degenerate cases in Euc. Geom. 11 47 75 92 139—141 155 161—162 217 226 244 259 261
Desargues’ theorem 142
Desmic system 144; Ex. iv. 23
Developable surfaces 166
Dihedral angles 42
Dimensions of space 208
Direction fallacy 6 20
Director points 259
Directrix 259
Displacement 179 196
Distance, absolute unit of 13 15
Distance, formula 129 132 158 186
Distance, in Euc. Geom. 75 156 161
Divergent lines 42
Duality 50 100 226
Egypt 1
Element of length 187 194;
ellipse 257
| Elliptic geometry 25 29 55; 208
Elliptic geometry, inversion or radiation 240
Elliptic geometry, involution 97
Empiricism 207
Engel, F. 11 n 13 21 68
Engel-Napier rules 67
Envelopes 104 129; 14
Equidistance 10 42
Equidistant-curve 12 52 105 258
Equidistant-curve, equation 136 228
Equidistant-curve, length of arc Ex. ii. 7 iii.
Equidistant-surface 53 105
Escribed circles Ex. ii. 13
Euclid 1 2
Euclidean geometry 30 47 75 79 90 92 134 139—141 155—161 175 226 259 261
Excess of a triangle 104
Exterior angle, theorem 17 19 29 34—35
Focal distance property 260 262
Focal lines 259
foci 259; Ex. ix. 1 3 4 5
Focus-directrix property 262
Four dimensions of space 42 n 193 199
Frankland, W. B. 4 n 206
Free mobility 167 168 195—199
Fundamental theorem of projective geometry 96
Gauss pentagram 68 n
Gauss, C. F., on area of triangle 7 82—83
Gauss, C. F., on curved surfaces 168
Gauss, C. F., on parallels 14 22 24
Geodesics 166
Geometry on curved surface 166
Geometry on equidistant-surface 56
Geometry on horosphere 15 56 84 165;
Geometry on imaginary sphere 13 15 165
Geometry on plane at infinity 135 165
Geometry on sphere 56 165
Geometry origins 1
Geometry with hyperbolic or parabolic measure of angle 162 164
Geometry with projective metric 160
Geometry, absolute 22
Geometry, analytical Chap. iv
Geometry, Astral 15
Geometry, Bizarre 162 164
Geometry, differential 194
Geometry, elliptic Chap. iii
Geometry, Euclidean q.v
Geometry, hyperbolic Chap. ii
Geometry, Imaginary 21
Geometry, in the infinitesimal 76 114
Geometry, Log.-spherical 15
Geometry, non-Euclidean 14 20
Geometry, of a bundle 55 90
Geometry, on Clifford’s surface 113
Geometry, Parabolic 25
Geometry, projective 93—98
Geometry, spherical 25 89 130 138
Gergonne, J. D Ex. i. 5
Greek geometry 1
Greenstreet, W. J. 210 n
Gronau, K. T. E. Ex. i. 7
groups 197 250
Halsted, G. B. 11 n 21 23
Harmonic range 95
Hart’s circle Ex. iv. 25
Hauff, J. K. F. Ex i. 6
Hausdorff, F. 229 n
Heath, T L. 2
Heiberg, J. L. 2
Helmholtz, H. von 195—197 199
Herodotus 1
Hilbert, D. 27 41 193
Hinton, C. H. 201 n
Hippocrates 1
Ho el, J. 24
Holgate, T. F. 94
Homocentric circles 224
Homographic transformation 182 249
Homography 94
Homothetic centres and axes 221
Horocycle 51 258
Horocycle equation 137 228
Horocycle, length of arc 57; Ex. ii. 4
Horosphere 52
Horosphere, geometry on 15 56 84 165;
Hyperbolas 257
Hyperbolic functions 15 63
Hyperbolic geometry Chap. ii.; 25 30
Hyperbolic inversion or radiation 240
Hyperbolic involution 97
Ideal elements 47 154
Imaginary points 97 133 154
Indefinables 2 27
Inequalities 28
Infinite areas 7—9 19 20
Infinite vs. unbounded 194
Infinitesimal domain 76 114
Infinitesimal transformation 198
Infinity, points at 46
Inscribed circles of a regular polygon Ex. ii. 17
Inscribed circles of a triangle 54 139; 13; 19 20
Inscribed quadrilateral Ex. ii. 2
Intersection of circles 211 228
Intersection of lines 132
Intersection, angle of, of circles 218
Intuition 2 207
inversion 241 252
Inversion, in Euc. Geom. 180 183 244
Inversion, quadric 244; Ex. viii. 12
Involution 97
Involutory transformation 241
Isogonal conjugates 147
Isosceles triangle 28
Ivory, J. 19
Kaestner, A. G. 21
Kant, I. 14 207
Klgel, G. S. 22
Klein, F. 25 159 192
Laguerre, E. 156 n
Lambert, J. H. 13—14 15 20
Legendre, A. M. 16—19 Ex.
Leslie, J. 19
Lie, S. 197
Liebmann, H. 24 n 229
Limiting lines 225
Limiting points 223
Line-coordi nates 128
Line-element 187 194;
Linear systems of circles 226
Lobachevsky, N. I. 15 20—21 23 24 68 243
Loci Ex. iv. 14; ix. 5—9 12 13
Logarithmic expression for distance and angle 157
Logarithmic-spherical geometry 15
Ludlam, W. 4
M bius’ sheet 91
Manifold 194
Marginal images 229
Maximum quadrilateral Ex. ii. 11 12
Maximum triangle 7 81;
Medians 139
Meikle, H. 19 22
Menelaus’ theorem 145
Middle point of segment 138
Milne, W. P. 262 n
Minimal lines 134; Ex. iv. 2
monodromy 195
Motions 28 179 185 196 246
Napier rules 68 74 119 122
Napier, J. 68 n
Net of rationality 96
networks Ex. ii. 14 15 18—20;
|
|
|
| Реклама |
|
|
|
|
|
О проекте