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| Baker H.F. — Principles of geometry (Vol. 2) |
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| Предметный указатель |
Absolute conic, by projection from a quadric 196
Absolute conic, properties relative to 166
Angle between two circles interpreted on a quadric 193
Angle properties for a circle 75
Angular intervals for a triangle 177 180 181
Anharmonic, example of 210
Anharmonic, or cross-ratio, symbol for four points 166
Apolar triads 114 117 124 147
Asymptotes of a conic 77
Auxiliary circle of a conic 85 88 119 133
Axes and foci of a conic 77 160
Axis of relation, or axis of homography 16
Bauer 235
Bipunctual conic, in regard to a triad of points 123
Bolyai — Lobatschewsky geometry, angle of parallelism 182
Bolyai — Lobatschewsky geometry, circle 182
Bolyai — Lobatschewsky geometry, equidistant curve 183
Bolyai — Lobatschewsky geometry, horocycle 183
Bolyai — Lobatschewsky geometry, interpretation with minimal lines as circles 203
Boscovich 88
Brianchon's theorem 25 235
Burnside 186
Caporali 236
Castelnuovo 236
Cayley — Salmon lines 227
Cayley's measure of interval deduced from Laguerre's 195—197
Centre and axes of a conic, equation referred to 118
Centres of similitude of two circles 112
Centroid of three pomts 64
Circle, after Lobatschewsky 182
Circle, angle between two circles interpreted on a quadric 193
Circle, angle properties for 76
Circle, auxiliary circle of a conic 85 88 119 133
Circle, circle through centres of similitude of two circles, with centre on line of centres 132
Circle, circles at right angles, or cutting orthogonally 66
Circle, circles determined by threes of four points meet in a point, and their centres lie on a circle 71 72
Circle, coaxial circles 66
Circle, common chords of circle and conic 79
Circle, definition and centre 65
Circle, equation of 107 108
Circle, inversion in regard to 67
Circle, limiting points and radical axis 66
Circle, Miquel's theorem 70
Circle, through three points whose joins touch a parabola, contains the focus 81
Cone, circular sections and focal lines 209
configurations see also “Note II”
Configurations, a primary theorem 218
Configurations, some examples of 212
Confocal conies 79 119
Confocal conies, intersection of tangents at right angles describes a circle 133
Confocal conies, polars of fixed point in regard thereto, touch a parabola 90
Conic constructed, given self-polar triad and pole and polar 46
Conic constructed, given self-polar triad and two points 46
Conic constructed, given three points and two pairs of conjugate points 165
Conic constructed, having two triads, lying on another conic, as self-polar triads 45
Conic, absolute 166 196
Conic, first properties, conic outpolar to another 33
Conic, first properties, conies through two points containing the threes of four given points 61
Conic, first properties, definition 10
Conic, first properties, degenerate 10
Conic, first properties, dual definition 22
Conic, first properties, dual of this 41
Conic, first properties, four through two points to touch three lines 39
Conic, first properties, Maclaurin's definition of 13
Conic, first properties, Pascal's theorem 13 16
Conic, first properties, polar lines 20
Conic, first properties, Related ranges and involution on 14
Conic, first properties, symbols applied to 16 97
Conic, first properties, tangent of 11 14
Conic, first properties, triangularly circumscribed 48
Conic, first properties, two through four points to touch a line 24
Conies associated with a triad 53 121 see “Nine “Bipunctual”
Conies associated with a triad, conic harmonically conjugate to a given one 122
Conies through four points, conjugate points in regard thereto 38
Conies through four points, cut an arbitrary line in pairs of points in involution 12
Conies through four points, poles of a line in regard thereto 41
Conies through four points, Poncelet's porism 55
Conies through four points, their common self-polar triad 23
Conies through four points, two such, whose eight tangents at the common points meet in two points 42
Conies touching four lines, director circles are coaxial 80
Conies touching four lines, tangents from a point are in involution 25
Conies, two, reduced equations 146
Conjugate diameters of a conic 77
Conjugate lines 26 31
Conjugate points 28 31
Conjugate points, conjugate imaginary points 158
Conjugate points, conjugate points in regard to conies through four points 38
Conjugate points, conjugate points, lying on two conies, envelope of join of 127
Conjugate points, given three points of a conic, line conjugate to one join meets other joins in conjugate points 28
Contact, point of, of conic, with one of five given tangents 25
Coordinates of a point 97
Coordinates of a point, of a line 99
Correspondence of two points in regard to conies through four points 39
Correspondence of two points in regard to conies through four points, of foci of conic touching three lines 77
Correspondence of two points in regard to conies through four points, of points of a conic 135
Cremona 219 235 236
Cross-ratio, or anharmonic ratio, for four points 166
Cross-ratio, or anharmonic ratio, for four points, example of 210
Cubic surface with node, applied to Pascal's figure by Cremona 229
Curve of third order 229
Delambre's formulae in spherical trigonometry 205
Desmic tetrads 213 233
Director conic of a conic 26
Director conic of a conic, director circle 80 95 125 127 151
Directrix of a parabola 81
Discussion of a turning point in the logical theory 153
Distance, Riemann's formula in space of constant curvature 199
Double points of an involution 3 158
Duality in regard to a conic 21 22
Duality in regard to a conic, dual of Pascal's theorem 25
Eleven-point conic 41
Elliptic integral, from two conies 211
Elliptic, hyperbolic and parabolic plane 186
Envelope of a line cutting two conies in harmonic conjugates 44 125
Envelope of a line cutting two conies in harmonic conjugates, of line joining points of two circles bisected by radical axis 132
Envelope of a line cutting two conies in harmonic conjugates, of line meeting two conies in points conjugate in regard to a third conic 127
Envelope of a line cutting two conies in harmonic conjugates, of polar lines of a point in regard to confocal conies 90 120
Envelope of a line cutting two conies in harmonic conjugates, the same generalised 134
Equation of a line 98
Equation of a line, of a circle 107 108
Equation of a line, of a conic 101
Equation of a line, of a conic referred to self-polar triad 107
Equation of a line, of a plane 190 191
Equation of a line, of a point 100
Equation of a line, of coaxial circles 109
Equation of a line, of confocal conies 119
Equation of a line, of conic referred to centre and axes 118
Equation of a line, of tangent, and polar 104
Equidistant curve 183
Euclid's distance, and triangle 184 185
Exponential function 157
Extent, between two lines, in elliptic plane, equal to twice their angular interval 188
Extent, of a circle 189
Extent, of a plane 188 201
Extent, of a triangle 188 203
Exterior and interior points of a real conic 159 164
Feuerbach's theorem 59 75 89 113 122
Figure determined by (n + 2) points, or hyperplanes, in n dimensions 218
Focal distances for a conic, in general form 200 211
Focal lines of a cone 209
Foci and axes of a conic 77
Foci and axes of a conic, of a parabola 81
Fontene 75
Four lines in four dimensions, figure derived from 225
Gaskin's theorem, for conies through two points outpolar to another conic 48
Gauss 154 237
Grossmann 235
Hamilton's extension of 59 117
Hamilton's modification of Feuer-bach's theorem 59 117
Harmonic, condition for two pairs of points to be 111
| Harmonic, harmonic images 37
Hatton 62
Helmholte 237
Hesse's theorem 31
Hessian line of three points of a conic 30 124
Hessian line of three points of a conic, Hessian point of three tangents 30
Hessian line of three points of a conic, of a circle 148
Hessian line of three points of a conic, of a parabola 149
Horocvcle, another view of 203
Horocvcle, construction of 183
Hyperbolic, parabolic and elliptic plane 186 see
Imaginary points 9 158 161
Imaginary points, imaginary and real symbols 154
Imaginary points, imaginary conic 163
Inpolar conic 33—36
Inpolar conic, algebraic condition for 142
Inpolar conic, expressed by sum of four squares 144 218
Interior and exterior points of a real conic 159 164
Intersections of two conies, number assumed 9
Interval of two points, or two lines, after Laguerre 166 167
Interval of two points, or two lines, interval for circumference of circle 189
Interval of two points, or two lines, interval in regard to an Absolute conic 168
Invariants of two conies 141
Invariants of two conies, their geometrical significance 142
Inversion in regard to a circle 67
Inversion in regard to a circle, circle and two inverse points invert into similar figure inverse of centre of circle 69
Inversion in regard to a circle, circles at right angles invert into circles at right angles 69
Inversion in regard to a circle, Feuerbach's theorem by inversion 74
Inversion in regard to a circle, inverse of a circle is a circle or line 68
Involution 2
Involution, apolar triads as particular case 147
Involution, common pairs of two involutions 3 158
Involution, composition of a projectivity from two involutions 6 50
Involution, determined by conies through four points 138
Involution, determined by two sets 136
Involution, dual of this 4 25
Involution, general involution 135
Involution, on a conic 14
Involution, on a line by conies through four points 4 12
Involution, reality of double points 158
Involution, symbolic representation of 111
Kirkman 227 235
Klug 236
Laguerre interval 167
Laguerre interval, angle interpreted on a quadric 192 196
Lambert's quadrilateral 181
Length, and movement 169
Limiting points of coaxial circles 66
Lobatschewsky — Bolyaigeometry, angle of parallelism 182
Lobatschewsky — Bolyaigeometry, circle 182
Lobatschewsky — Bolyaigeometry, equidistant curve 183
Lobatschewsky — Bolyaigeometry, horocycle 183
Lobatschewsky — Bolyaigeometry, interpretation with minimal lines as circles 203
Locus of point from which tangents to two conies form a harmonic pencil 125
Locus of point from which tangents to two conies form a harmonic pencil, of intersection of tangents at right angles of two confocals 133
Locus of point from which tangents to two conies form a harmonic pencil, of poles of line in regard to conies through four points 4
Logarithmic function 157
Maclaurin's definition of a conic 13
Magnitude, order of, for real symbols 156
Measurement in regard to two points 166
Measurement in regard to two points, comparison of the several methods 186 187
Measurement in regard to two points, in regard to a conic 170 178 184
Metrical properties 63
Metrical properties, metrical geometry in a plane with two Absolute points deducible from geometry on quadric surface 189
Middle point of two points 63
Miquel's theorem, for a triad of points and three circles 70
Morley 114
Moulton 186
Movement 169
Nanson 61
Napier's analogies 206
Nine points circle see “Feuerback's theorem”
Nine points circle, is locus of middle point of orthocentre and point of circumcircle 89
Nine points circle, of self-polar triangle of parabola contains the focus 83
Nine points circle, point of contact with inscribed circle 114
Non-Archimedean (non-Eudoxian) symbols 155
Normal of a conic 91
Normal of a conic, condition three normals meet in a point 119
Normal of a conic, feet lie on a rectangular hyperbola 91
Normal of a conic, four can be drawn from an arbitrary point 91
Normal of a conic, normals to a parabola from a point, their feet lie on a circle through the vertex 94
Normal of a conic, three of the feet and the opposite of the other lie on a circle 93 119
Orthocentre of three points 64
Orthogonal circles, condition for 110
Orthogonal circles, invert into orthogonal circles 69
Orthogonal circles, line through centre of either cuts circles harmonically 66 126
Outpolar conies 33—36
Outpolar conies, algebraic condition for 142
Outpolar conies, and triangularly circumscribed conic 146
Pappus' theorem, complete figure 215
parabola 81
Parabola, obtained as envelope of polars of a point in regard to confocal conies 90
Parabolic, or Euclidean, plane 186
Parameter expression for a general conic 103
Parameter expression for a general conic, for conic referred to its centre and axes 118
Pascal's theorem 13
Pascal's theorem, and related ranges of points on a conic 15
Pascal's theorem, converse of 16
Pascal's theorem, dual of 25
Pascal's theorem, Pascal line, symbol for in general figure 223 227
Pascal's theorem, Pascal's figure derived from four dimensions 224
Pascal's theorem, Pascal's hexagrammum mysticum 219
Pedal line of three points of a conic 29
Pedal line of three points of a conic, of a circle 71
Pedal line of three points of a conic, of parabola is tangent at vertex 82
Pedal line of three points of a conic, pedal circle of a point for three lines 87
Pedal line of three points of a conic, pedal line for a triad in involution 139
Pedal line of three points of a conic, pedal of conic from focus is auxiliary circle 85
Pedal line of three points of a conic, when point moves on a line through circumcentre 88
Perpendicular lines 63
Plane, equation of 190 191
Pluecker 227 235
Poincare 197
Polar line and point, dual of this 42 90
Polar line and point, in regard to a conic 20
Polar line and point, polar lines of a point in regard to conies through four points meet in a point 37
Polar line and point, polar reciprocal of a certain parabola gives the rectangular hyperbola of Apollonius 91
Polar line and point, polar reciprocal of one conic in regard to another 47 91 140 147
Polar line and point, polars of a point in regard to conies through fives of six points touch a conic 61
Polar line and point, polars of three points give a triad in perspective with original 27 31 123
Polar line and point, poles of a line in regard to conies through four points lie on a conic 41
Polar line and point, self-polar triad 23
Polynomial, roots of 110 135 157
Poncelet's theorem, for porism of tangents of conies through four points 55 96
Positive and negative real symbols 155
Projectivity on a conic resoluble into succession of two involutions 50
Quadratic system of conies, inpolar to another conic 145
Quadric surface, elementary properties of 190
Quadrilateral with three right angles 181
Radical axis of two circles 66
Radical axis of two circles, radical axes of three circles meet in a point 70 112
Range of points on a conic 14 52
Range of points on a conic, on variable line, by conic and joins of three points of this 28
Real and imaginary points 9 160
Real and imaginary points, real and imaginary conic 163
Real and imaginary points, real and imaginary symbols 154
Reality of common harmonic conjugates with respect to two given pairs 158
Reality of common harmonic conjugates with respect to two given pairs, reality a relative term 160
Reality of common harmonic conjugates with respect to two given pairs, reality of common self-polar triad of two conies 164
Reciprocal polar of one conic in regard to another 47 140 147
Rectangular hyperbola, conjugate diameters of, examples of 84
Rectangular hyperbola, contains orthocentre of three of its points 84
Rectangular hyperbola, definition 83
Rectangular hyperbola, through three points, locus of centres 88
Related ranges on the same line 1
Related ranges on the same line, condition two ranges be related, abbreviated argument for 8
Related ranges on the same line, envelope of line joining corresponding points of two related ranges on a conic 52
Related ranges on the same line, relation of two ranges reduced to two involutions 6 50
Richmond 219 236
Riemann's space, as derived from projective space 199
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