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Sommerville D. — An introduction to the geometry of N dimensions
Sommerville D. — An introduction to the geometry of N dimensions



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Название: An introduction to the geometry of N dimensions

Автор: Sommerville D.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1959

Количество страниц: 203

Добавлена в каталог: 11.11.2012

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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 $V^{2}_{n-1}$      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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