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| Sommerville D.M.Y. — The elements of non-Euclidean geometry |
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| Предметный указатель |
Nine-point circle Ex. iv. 25 26
Non-Euclidean geometry 14 20
Non-intersectors 12 31 40
Normal to conic 261
One-sided surface 92
Order 27
Orthaxis 54 141
Orthocentre 54 141
Orthogonal circles 219; Ex. vii. 4
Orthogonal points 89
Orthogonal trajectory 51
Orthopole Ex. iv. 13
Parabolas 258
Parabolic geometry 25
Parabolic geometry, inversion or radiation 240
Parabolic geometry, involution 97
Parallax 204
Parallel angle 30 35 58
Parallel lines 29 30;
Parallel planes 50
Parallel postulate Chap. i.; 27 203
Parataxy 108
Pasch axiom 29
Pasch, M. 193
Peano, G. 193
Pencil of circles 228 233
Pencil of lines 45 176
Pentagramma mirificum 65 68 118
Perimeter of triangle 104 163
Perpendicular to a line 28
Perpendicular to coplanar lines 12 40
Perpendicular to plane 43
Perpendicular to two lines in space 106 109
Perspective triangles 142
Perspectivity 95
Pieri, M. 193
Planes 42
Platonists 1
Playfair axiom 4 30
Playfair, J. 19
Poincare, H. 210
Polar system 92 98
Polar triangles 102 141
Pole and Polar 51 89 130;
Polygon, area 83 104
Polygon, regular 80 n; Ex. ii. 16—20
Polyhedra Ex. iii 7 8 12—15
Position-ratio 147
Postulates 2 3 27
Power of a line 216
Power of a point 212
Projection 95 148
Projection, gnomonic 170
Projection, stereographic 172
Projective geometry 93—98 135
Projective group 198
Projective metric 158
Pseudosphere 168
Pythagoras 1
Quadrangle-quadrilateral configuration 143
Quadrant 89 116
Quadrilateral, circumscribed Ex. 3
Quadrilateral, complete 148
Quadrilateral, inscribed Ex. ii. 2
Quadrilateral, of maximum area Ex. ii. 11 12
Quadrilateral, trirectangular 70 121
Quadrilateral-construction 96 199
Quaternions 251
Radian 28
Radiation and inversion 241; Ex. viii. 11
Radical axes 219 228
Radical centres 221
Radius of circle 51
Rationality, net of 96
Reciprocity of parallelism 32
rectangle 9 79 112
Reflexions 238 246
Reflexions, in Euc. Geom. 180
Reid, T. 208 n.
Relativity-principle 197 210
Reye, T. 94
Riemann, B. 25 194
Rigid figure 167 195
Rotation proof of parallel-postulate 6
| Rotations 185
Russell, B. 193
Saccheri, G. 11—13 15 18 24
Savile, H. 3
Schweikart, F. K. 14
Sections of sphere, etc. 53
Segments, congruence of 27
Self-corresponding elements 96
Semi-circular canals of the ear 208
Semi-hyperbola 257
Similar figures 7 13
Similar transformation 239 n
Simson, R. 42
Sommerville, D. M. Y. 24n.
Space-constant 58
Space-constant, construction for 77
Space-constant, physical measurement of 203
Space-fillings Ex. ii. 14 15 18- 15
Sphere 52 105
Sphere of infinite radius 15; see Horosphere
Sphere volume Ex. ii. 24; iii. 6
Spherical geometry 25 89 130 138
Spherical triangles 63
Spherical trigonometry 69 70 120
Square 2
Stackel, P. 11 n 13 23
Staudt, G. K. Ch. von 193 199
Stereographic projection 172
Straight line, as shortest path 17
Straight line, Euclid’s def. 2
Straight line, re-entrant 17 19
Superposition 8 27
Symmetry of space 28
Systems of circles 228 232
Tactual space 208
Tangents to a conic 261
Tangents to two circles 211
Taurinus, F. A. 15
tetrahedron Ex. iv. 7 8
Tetrahedron, desmic 144
Tetrahedron, radius of circumsphere Ex. iii. 7
Tetrahedron, with concurrent altitudes Ex. 24
Thales 1
Thibaut, B. F. 6
Thompson, T. Perronet 19 22
Tilly, J. M. de 196 n
Townsend, E. J. 27 n
Transformations, circular 181; Chap. viii.
Transformations, conformal 182; Chap. viii.
Transformations, congruent 158 238 245
Transformations, homographic 182 249
Transformations, infinitesimal 198
Transformations, of coordinates 245
Transformations, of inversion 180 183 241 252
Transitivity of parallelism 32 43
Transmissibility of parallelism 31
Transversal theorem 33
Triangle, angle-sum 5 10 12 13 15 16 18 20 21 77 104
Triangle, area 13 20 77—79 81 82 103—104
Triangle, associated 65 74 117
Triangle, exterior angle 17 19 29 34—35
Triangle, of maximum area 7 81
Triangle, perimeter 104 163
Triangle, perspective 142
Triangle, points connected with 139
Triangle, rectilinear and spherical 63
Triangle, right-angled 63 116
Triangle, side 29
Triangle, trigonometry of 66 116
Triangulation 203
Trigonometry 15 56 116
Trirectangular quadrilateral 36 70 121
Ultra-spatial elements 48
Unit of angle 28 160
Unit of area 79
Unit of length 13 15 58 160 162
Vanishing circle Ex. viii. 13
Veblen, O. 94 193
Visual space 208
volumes Ex. ii. 24; iii. 5 6
Wachter, F. L. 15
Wallis, J. 7
Weierstrass’ coordinates 127 129 171
Whitehead, A. N. 193 201
Young, J. W. 94
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