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Sommerville D.M.Y. — The elements of non-Euclidean geometry
Sommerville D.M.Y. — The elements of non-Euclidean geometry



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Название: The elements of non-Euclidean geometry

Автор: Sommerville D.M.Y.

Аннотация:

The present work is an extension and elaboration of a course of lectures on Non-Euclidean Geometry which I delivered at the Colloquium held under the auspices of the Edinburgh Mathematical Society in August, 1913.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1919

Количество страниц: 287

Добавлена в каталог: 12.07.2013

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Предметный указатель
$\pi$      28 76
$\Pi$, ($p$)      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$\ddot{u}$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
Kl$\ddot{u}$gel, 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$\ddot{o}$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;
1 2
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