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Coxeter H.S.M. Ч The Real Projective Plane
Coxeter H.S.M. Ч The Real Projective Plane



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Ќазвание: The Real Projective Plane

јвтор: Coxeter H.S.M.

язык: en

–убрика: ћатематика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1949

 оличество страниц: 203

ƒобавлена в каталог: 18.11.2012

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
Abscissa      30 150 153 181
Absolute involution      117 184Ч180 188
Addition of points      145Ч148
Affine coordinates, ISO      181
Affine geometry      1 85 98 145 158Ч159 180Ч188
Affinity      112
Altitudes of a triangle      118 128 184
Analytic geometry      30 168Ч188
angle      8 9 125Ч129 184
Angle bisector      126 131
Anharmonic ratio      (see Cross ratio)
Antiprojectivity      188
Apollonius      69Ч70 73 111Ч113 123Ч124 134 189
Archimedes      137Ч139
Area      2 10 5 108 115 125 181Ч182
Areal coordinates      182 183
Artin, Emil      105
Associative laws      14 1Ч14
Asymptotes of a hyperbola      4 110 113Ч116 183
Axiom of continuity      31 138
Axioms of incidence      12 14
Axioms of order      22 33
Axis of a conic      122 124
Axis of an elation or homology      54
Axis of conic      90 95
Axis on two lines      41
Biratio      (see Cross ratio)
Bisection of a segment      101 140
Bisection of an angle      126 131
Braikenridge, William      69Ч70 78Ч79 88
Branches of a hyperbola, S      110
Brianchon, C. J.      70 89 185
Bundle of lines and planes      5
Calculus of extension      169
Canonical form for a conic      175
Canonical form for a hyperbolic involution      153
Canonical form for a polarity      173
Canonical form for an elliptic involution      154
Cantor, Georg      103 138Ч142
Cartesian coordinates      148 150 183 185
Categoricalness      159Ч160
Center of a circle      119
Center of a conic      109Ч112
Center of a pencil      18
Center of an elation or homology      54
Center of an involution, on the affine line      103
Center on a conic      93
Centers of similitude      120Ч122
Central conics      110 123
Central inversion      105
Central of a triangle      122 182 186
Central projection      2Ч7
Chain on the complex line      187
Chaslcs, Michel      62 70 77Ч78 111Ч112 129 172 189
Chord of a conic      111
circle      3 53 69 92 119Ч124 183Ч186 188
Circuincircle of a triangle      119 122 185
Circular points at infinity      188
Circumrenter of a triangle      119 122 186
Classification of conics      109Ч110
Classification of polarities      70
Classification of projectivities      42 91
Collinear points      7 12 27 160Ч161
Collineation      36 52Ч58 67 91 167Ч170 Perspective
Common pair of two involutions      48 93
Commutative laws      145Ч148
complex numbers      187Ч188
Concentric circles      120 184
Concurrent lines      6 12 162
Cone      3 69 122
Configuration of Desargues      13 14 55 62 65Ч66 73 81
Configuration of inflexions of a cubic      188
Configuration of Pappus      40 42 66 163 174
Confocal conics      184
Congruence by a half-turn      106
Congruence by rotation      124
Congruence by translation      100 105
Congruent angles      126Ч129
Congruent transformation      129
conic      69Ч70 72Ч97 109Ч116 122Ч125 132Ч136 145Ч150 154 175Ч184 Center Construction Diameter Directrix Eccentricity Ellipse Focus Hyperbola Parabola Polarity Tangent Vertex
Conic through five points      77Ч79
Conjugate axis of a hyperbola      123
Conjugate diameters      111
Conjugate hyperbolas      112
Conjugate lines      59 61 73 93 172
Conjugate points      59 61 73 171
Consistency      158Ч159
Construction for a conic      76 79
Construction for a diameter      111
Construction for a focus      133Ч134
Construction for a polarity      64
Construction for a projectivity      89 41
Construction for a tangent      74 79
Construction for an involution      50 93
Construction for the invariant points of a projectivity      92
Continuity      22 103 138 165
Coolidge, J. L.      52 95 126 189
Coordinate axes      180
Coordinate transformation      169 176 183
coordinates      (see Affine coordinates Areal Barycentric Cartesian Envelope Homogeneous Trilinear
Correlation      52 57Ч64 170Ч171
Correspondence      18 159 Opposite Ordered
Coxeter, H. S. M.      5 26 131 189
Cremona, Luigi      2 52 61 92 189
cross      (see Angle)
Cross ratio of four points on a line      165
Cross ratio of two points and two lines      166
Cubic curve      188
Cyclic order      22Ч24
De la Hire      (see La Hire)
Dedekind, Richard      22 137 143Ч144
Degenerate conic      81Ч82 97 176Ч177
Degenerate involution      47 49 60 147 148 177
Degenerate polarity      173Ч174 184Ч185
Dehn, Max      41 109 189
Dense set      140
Desargues involution theorem      77 81 87 118 178
Desargues two-triangle theorem      6Ч7 12 17 41 55 62 65 73 80
Desargues, Girard      8 70 103Ч104 126
Descartes, Ren      6 69
Diagonal triangle      14 73Ч74
Diameter of a circle      120
Diameter of a conic      110Ч116
Dietrich, V. E.      121
Dilatation      105
Direct correspondence      28 130
Direct projectivity      42
Directed angle      8Ч9 127
Directrix      134Ч136
Dissection of a polygon      106Ч109
Distance      101 181
Distributive law      149
Divergent sequence      167
Division of a segment      102Ч103
Double contact      77 87 124
Double point      (see Invariant point)
Du Val, Patrick      61
Duality      13Ч16 66
Duplication of the cube      69
Durell, C. V.      121 180
Eccentric ellipse      120
Eccentricity      119 135Ч136
Elation      54Ч56 105 170
Elements of Euclid      1 4 6 120
ellipse      109Ч110 120 134
Elliptic involution      47 03 111
Elliptic polarity      70
Elliptic projeetivily      42 91
Enriques, Federigo      22 36 44 52 54 50 62 70 72 88 92 137 143Ч144 189
Enumerable separation set      112
Envelope      72 77Ч78 175Ч177
Envelope coordinates      157 160
Equation for a conic      175
Equation for a line      15 5 1 50
Equation for a point      157 100
Equivalent polygons      107
Erdos, Paul      27
Euclid      4 6 69 101 119 122 131
Euclidean geometry      1 4 52 98 117Ч13 5 158Ч159 183Ч18 5
Eudoxus      138
Euler, Leonhard      2 122 180
Excenter      128
Fermat, Pierre      60
Focal distances      136
Focus      132 13 5 184
Forder      11
Fractional distance      103
Fregier point.      119
Fundamental theorem      38 142Ч143
Gallai      (see Griinwald)
Generalized perspectivity      86
Gergonne, J. D.      13Ч14 59 66 70
Glide reflection      132
Gnomonic projection      50
Godel, Kurt      159
Grassmann, Robert      169
Graustein, W. C.      78 162 189
Griinwald, T. (alias Gallai)      26
Half-turn      105 129
Hamilton, Sir W. R.      187
Hardy, G. II.      5 189
Harmonic conjugate      16Ч17 29 101 162
Harmonic homology      56Ч57 66 92 105
Harmonic mean      105
Harmonic net      139Ч143 152
Harmonic set      16 30Ч21 37 104Ч105 152
Heffter, Lothar      1 5 5 189
Hesse, L. O.      60 175 189
Hexagon of lirianchon      80 89
Hexagon of Pappus      40
Hexagon of Pascal      80 88 95 147 150
Hilbert, David      106 138 145 180
History of conics      60
Hodge, W. V. I      39 180
Holgate, T. F.      8 5 04 119 133 135 180
Homogeneous coordinates      154Ч157 160Ч188
Homol belie      105
Homology      52 54 57 00 57 84Ч85 170
Hyperbola      109 110 133 181Ч183
Hyperbola, branches of a      3 110
Hyperbolic involution      28 46 93 111 146 151
Hyperbolic polarity      70
Hyperbolic projectivity      42 19 151Ч152
Ideal elements      4Ч5
Identity      18
Ilessenberg, Gerhard      41Ч42 145 189
Incenter of a triangle      128 184 186
incidence      11 160
Incircle of a triangle      185
Inflexions of a cubic      188
Interior of a conic      72
Interior of a triangle      100 167
Interior of an interval      24
Intermediacy      99
Internal convexity      188
Intersection      11
interval      24
Invariant point      27 81Ч33 42 91Ч92 153 170
Inverse correspondence      18
inversion      53 124 179
Involution      46Ч50 77 81 103Ч104 145Ч154 172 Elliptic Hyperbolic Orthogonal
Involution on a conic      93
Involutory collineation      56Ч57
Involutory correlation      (see Polarity)
Jenkins, James      95
Johnson, R, A.      8 127 189
Join      11
Kepler, Johann      4 69Ч70
Kronecker, Leopold      168
La Hire, Philippe de      52 70 99 111 132
Lehmer, D. N      99 189
Leibniz, G. W.      88
Leisenring, Kenneth      90 180
Length      106 124
Levi, F. W.      42 189
Liiroth, Jakob      142
LIMIT      137Ч143 152
Line      10 160
Line at infinity      5 98 182 184
Line coordinates      157 160
Linear fractional transformation      151
Linear homogeneous transformation      167
Maclaurin, Colin      40 69Ч70 78
Major axis of an ellipse      124
Mathews, G. B.      49 75 142 189
Maurolycus      13
Median class of a set of points      142
Medians of a triangle      101
Menaechmus      69
Menger, Karl      14
Meobius, A. F.      52 169
Mid-point      101 140
Minkowski, Hermann      1
Minor axis of an ellipse      124
Model      158Ч159
Monotonic sequence      137Ч143 147 165 167
Moore, J. C.      135
Multiplication of points      148Ч150
Mydorge, Claude      70
Net of rationality      139 143 152
Newton, Sir Isaac      52 69
Nine-point center      122 18
Nine-point circle      121 186
Nine-point conic      84 85 110 11 5
Non Ч Euclidean geometry      1 189
Normal to a conic      119
Oblique triangle      117Ч118
One-dimensional geometry      22Ч34 42 41 145Ч154
Opposite correspondence      28 130
Opposite projectivity      42
Order in a pencil      34
Order on a conic      86
Order on a line      22Ч34 150
Ordered correspondence      27Ч32 142Ч144
orthocenter      118 121Ч122 135Ч136 186
Orthogonal involution      117
OТHara, C. W.      40 145 189
Pappus      40Ч42 66 69 88 91 109 135 145 169 174
parabola      3 78 109Ч110 122 133Ч135 181 183
Parabolic projectivity      42 45 50 91 100Ч101 111 151Ч152
Parallel lines      2 4 98 103
Parallel projection      1 99
Parallelogram      98 107
Parameter for a point on a conic      176
Pascal, Blui.se      70 86 88Ч91 95 147 150 178
Pasch, Moritz      41 109 189
Pedal triangle      118 128
Pedoe, Daniel      39 189
Pencil of conics      83 85 177
Pencil of lines      18 31
Pencil of parallel linos      4
Pencil of polarities      66Ч67 81 83 174
Pentagon      04
Perfect set      139
Periodic projectivity      45 170
Perpendicular lines      117 181Ч18 5
Perspective ollincation      54Ч57
Perspectivily      19 39
Picken, IX K.      8 1 27
Pieri, Mario      12 33 142 104 189
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