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| Sommerville D. — An introduction to the geometry of N dimensions |
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| Предметный указатель |
Absolute, the 32—33
Absolute, the, point-equations 79—81 87
Absolute, the, tangential equation 83
Allomorphic polytopes 101
Analysis situs 100
Analysis situs, chap ix. 161
Angle between two hyperplanes 39
Angle between two hyperplanes in oblique co-ordinates 82
Angle between two hyperplanes in rectangular co-ordinates 77
Angle between two lines, oblique co-ordinates 81
Angle between two lines, rectangular coordinates 76
Angle, n-dimensional 152—154
Angle, solid and dihedral 150
Angle-constituents of a polytope 100 166
Angle-sum of a polytope 150—152 157—159
Angle-sum of a spherical polygon 142 154
Angles between two linear spaces 45—48
Angles between two planes 41—45
Angles between two planes, analytical 90—91
Angular regions of a simplex 154—157
Axioms 2—4 5 19
Baker, H.F. 95
Bertini, E. vii 72
Brueckner, M. 117
Canonical equation of (n - 1)-flat 77 82
Canonical equation of quadric 62
Categoricalness of a set of axioms 2
Cauchy, A.L. 160
Cayley, A. v 21 72 102
Clifford, W.K. v vi 72
Co-ordinates of a hyperplane 56
Co-ordinates of a plane 83
Co-ordinates, rectangular 75
Co-ordinates, rectangular, general cartesian 80
Co-ordinates, rectangular, Grassmann 92
Co-ordinates, rectangular, homogeneous 51 75
Co-ordinates, rectangular, metrical 73
Co-ordinates, rectangular, Pluecker 83
Co-ordinates, rectangular, projective 51
Complementary boundaries of a simplex 115
Completely orthogonal 31
Completely orthogonal, analytical conditions 89
Completely parallel 27
Completely parallel, analytical conditions 88
Complex of lines 10 86
Complex polytopes 98
configurations 97—98
Configurations, polyhedral 161 166
Congruence 19
Congruence of lines 10 86
Conjugate points 59
Connectivity 144—146
Conservation of number 11
Consistency of axioms 2
Constant-number, def. 9
Content of orthogonal projections 50
Content, chap viii
Convex polytope 99 143
Correlations 60
Correspondence 56
Correspondence, dualistic 56 60
Cotes, R. 140
Cross-ratio co-ordinates 55 73
Cullis, C.E. 72
Degenerate quadrics 67
Degrees of freedom 7 9
Degrees of incidence 9
Degrees of orthogonality 36
Degrees of parallelism 26
Dehn, M. 160
Desargues' theorem 5
Direction 24
Direction-angles and cosines 76
Direction-angles and cosines, ratios 81
Directrices of a congruence 86
Distance between non-intersecting flats 40
Distance between parallel flats 40
Distance between two points 76 80
Distance from a point to a hyperplane 77 82
Duality 9 56
Duality in enumerative geometry 12
Dyck, W. 191
Ebbrhard v. 117
Elliptic geometry, angle-sums 159
Elliptic geometry, honeycombs 166 186—191
Elliptic geometry, measurement of angle 152—154
Elliptic geometry, networks 163—165
Elliptic geometry, the absolute in 32
Elliptic geometry, trigonometry 163
Enumerative geometry 10—19
Equations of a p-flat 52 82
Equations of a quadric 59
Equations, parametric 51 56—57
Euclidean geometry, angle-sums 159
Euclidean geometry, incidence of planes 5
Euclidean geometry, measurement of angle 152
Euclidean geometry, parallel lines 4
Euclidean geometry, the absolute 32
Euler's polyhedral formula 97
Euler's polyhedral formula, chap ix
Euler, L. 160
Eulerian polyhedra 146
Existence-postulates 3
Face-constituents of a polytope 99 165
Flat space 8
Forder, H.G. 20 21
Freedom of a p-flat in a  69
Freedom, degrees of 7 9
Frustum of a simplex 103—106
Fundamental numbers of a homogeneous polyhedron 162
Fundamental numbers of a polytope 167 187
Fundamental points of co-ordinate system 55
Grassmann co-ordinates 92
Grassmann, H. v. 95
Half-orthogonal 34
Half-orthogonal, analytical condition 89
Half-parallel 25
Half-parallel, analytical condition 89
Heegaard, P. 160
Hilbert, D. 3 20 21
Homaloid 72
Homogeneous co-ordinates 51 75
Homogeneous parameters 51
Homogeneous polyhedra 161
Homogeneous polytopes 165
Honeycombs 166
Hyperbolic geometry, angle-sums 159
Hyperbolic geometry, honeycombs in four dimensions 187—191
Hyperbolic geometry, honeycombs in three dimensions 166
Hyperbolic geometry, networks 163—164
Hyperbolic geometry, parallel lines 22
Hyperbolic geometry, the absolute in 32
Hyperbolic geometry, trigonometry 163
Hypercones 64—66
Hyperplane at infinity 26
Hyperplane, co-ordinates of 56
Hyperplane, def. 7
Hyperplane, equation of 52
Hypersphere at infinity 79
Hypersphere, content 135—137
Hypersphere, equation of 78
Incidence of linear spaces 10—19
Incidence, Axioms of 3
Incidence, degrees of 9
Incomplete polytopes 146—147
Indefinables 2
Independence of axioms 2
| Independent hyperplanes 55
Independent points 8 54
Inertia, law of 64
Infinity, hyperplane at 26 74
Infinity, hypersphere at 79
Infinity, points, lines and planes at 24—25 31
Interior points of a polytope 144
Interior points of a simplex 20—21
Isocline planes 44
Isocline planes, analytical condition 90
Isomorphic polytopes 100
Jessop, C.M. 95
Joachimsthal's formulae 78
Jordan, C. 50
Klein, F. 95
Legendre proof of Euler's Theorem 142
Legendre, A.M. 160
Lhuilier proof of Euler's Theorem 142
Lhuilier, S.A.J. 160
Linear space, def. 8
Linearly independent points 8 54
Linearly independent points, hyperplanes 55
Listing, J.B. 160
Manning, H.P. 21
Matrix 52—54
Mensuration, chap viii
Meyer, W.F. 18 21
Motion 19
Mueller, E. 95
networks 162—165
Normal curves 57
Normal curves, varieties 58
Normal to a hyperplane 30
Normal to a hyperplane, common to two non-intersecting flats 41
Null system 61
Order of a curve 57
Order of a variety 56
Order or sequence 19 20
Orientation 24
Orthogonality, analytical conditions 76 81 82 89
Orthogonality, chap iii
Orthotope, configurational numbers 113
Orthotope, content 118
Orthotope, def. 49
Orthotope, projection 59
Orthotope, regular 171 177 182 190
Pappus' theorem 139
Parallel, half or semi 26
Parallelism, degrees of 26
Parallelotope 28—29
Parallelotope, content 119—123
Parallelotope, projection 49
Parametric equations 51 56 57
Pentahedron 103
Perpendicularity see "Orthogonality"
Pliicker's co-ordinates 83 91
Pluecker, J. 95
Poincare, H. 160
Pointing 102
Polar allomorphism 101
Polar isomorphism 101
Polar system 61
Polar with regard to a quadric 59 66
Polar with regard to a quadric, absolute 32
Polyacron 102
Polycorypha 102 150
Polytope, def. 96
prism 113
Prism, content 118
Prismoid 115—117
Prismoid, content 135
Prismoidal figure 131 135
Prismoidal formulae 131—135
Projection 48
Projection, orthogonal 49—50
Projection, parallel 48
Projective geometry 4 22
Projective geometry, analytical 51
Pyramid 106 111—113
Pyramid of second and higher species 126—130
Pyramid, content 123—124
Pyramidoid 115
Quadric varieties 59—72
Radian angular measure 152—154
Radius vector 75 80
Rank of a matrix 53
Rational curve 57
Rational curve, variety 58
Reciprocal poly topes 101
Reciprocity or duality 9
Regular polyhedra 161 177 179
Regular polytopes, chap x
Regular simplex, content of 125
Regulus 86
Ring-shaped polygons 144
Ring-shaped polyhedra 145
Schilling, M. 191
Schlaefli, L. v 140 191
Schlegel diagram 100
Schlegel, V. v 117
Schoute, P.H. vii 27 29 117 191
Schubert, H. 11 19 21 95
Sections of a simplex 103—106 114
Sections of parallel spaces 27
Segment 20
Segre, C. 21
Self-reciprocal polytopes 101
Simple polytope 98
Simplex of reference 55
Simplex regions 21 154—157
Simplex regions, complementary boundaries 115
Simplex regions, configurational numbers 96
Simplex regions, content 124—126
Simplex regions, sections and frusta 103—106
Simplex-polycorypha 102 150
Simplex-polytope 102 149—150 157
Simplotope 113—115
Simplotope, content 130
Simply-connected regions 144—145
Simpson, T. 140
Sine of n-dimensional angle 121
Singular correlation 61
Sommerville, D.M.Y. vii 38 44 160 191
Specialisation, principle of 11
Spherical geometry 153 see
Staudt proof of Euler's Theorem 143
Staudt, G.C.K. von 160
Steggall, J.E.A. 191
Steiner proof of Euler's Theorem 142
Steiner, J. 160
Steinitz, E. 117
Stereographic projection of rational varieties 59 70
Stereographic projection of spherical networks 165
Stratification 26
Stringham, W.I. 191
Surface-content of hypersphere 136
Sylvester, J.J. v 64 72
Tangent to quadric 59 67
Total configurational numbers 101
Triangular polyhedron 102 148
Trihedral polyhedron 102 148
truncating 102
Unit-point of co-ordinate system 55
Varieties 56
Varieties of revolution 137—138
Vertex-constituent of polytope 99 166
Virtual hypersphere 79 quadric 64
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