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| Colonel L., Hime H.W.L. — The outlines of quaternions |
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| Предметный указатель |
Angle of a Q., Definition of the 31
Angle-Bisectob, Expression for 20
Anharmonic Q., Function, Definition of 149
Anharmonic Ratio, Definition of 13
Apollonius of Perga, Cyclic Cone of 109
Apollonius of Perga, Theorem by 73
Arc, V., Definition of 86
Area, V. of spherical triangle 143
Area, V., Definition of 51
Axis of a Q. 46
Central Conic, General Equation of 158
Centre, Circum-, of plane triangle 21
Centre, Ex-, of plane triangle 21
Centre, In- of plane triangle 20
Centre, Mid- of plane triangle 21
Centre, Ortho- of plane triangle 21
Circle, Circum-, of spherical triangle 136
Circle, Equations of 106 153
Circle, In-, of spherical triangle 134
Circular Harmonic Groups 152
Cissoid, the 169
Condition of Equality of two Qs. 63
Condition of Equality of two V. Arcs 86
Condition of Equality of two Versors 63
Condition of Equality of two Vs. 2
Condition that four planes meet in a point 177
Condition that four points may be coplanar 176
Condition that four vectors may terminate in a plane 28 176
Condition that three vectors may be coplanar 99
Cone Cyclic, Equation of 109 185
Cone, Right, Equation of 184
Conic, General Equation of a 156
Conical Rotation 90
Conjugate Functions, Definition of 127
Conjugate of a Q. 68
Conjugate of a V. 69
Conjugate of Scalar 69
Conjugates, isogonal 22
Conjugates, isotomic 22
Curvature, Radius of, Expression for the 171
Cyclic normals of a Cone 186
Cyclic planes of a Cone 186
Cycloid, The 170
Differential of a Q. 117
Differential of a V. 115
Differential, General Definition of a 112
Euler, Theorem by 82
Function, Anharmonic Q. 149
Functions, Conjugate 127
Functions, Self-conjugate 127
Gauss, Theorem by 146
Harmonic Group, Circular 152
Harmonic Mean, Definition of the 151
Helicoid, The 175
Helix, The 173
i,j, k, Properties of 37
Index of a right Q. 51
Isogonal conjugates 22
Isotomic conjugates 22
KEOGH, Theorem by 144
| Logarithmic Spiral, The 171
MacCULLAGH, Theorem by 187
Mean Harmonic, Definition of 151
Mean point of triangle 19
Moivre's Theorem 55
n-GON inscribed in circle 153
n-GON inscribed in sphere 181
Normal Plane of a Curve, Definition of 174
Normal, Cyclic, of a cone 186
Normal, Cyclic, of Ellipse 159
Normal, Cyclic, of Hyperbola 159
Normal, Cyclic, of Parabola 165
Plane, Equations of 104
Plane, Radical of two spheres 183
Points, Inverse, with respect to circle 72
Polyhedra, Sum of V.-areas of faces of, is zero 179
Quadrilateral, Spherical, A property of 146
Quaternion, Amplitude of a 56
Quaternion, Angle of a 31
Quaternion, Definition of a 30
Quaternions, Collinear 66
Quaternions, conjugate 68
Quaternions, Coplanar 31
Quaternions, Diplanar 31
Quaternions, Opposite 67
Quaternions, Reciprocal 66
Quaternions, Right 37
Quaternions, Right ternions, Condition of equality of two 63
Radical plane of two spheres 183
Radius of curvature of the cycloid 171
Radius of curvature, general expression for 171
Radius Vector, Distinction between a, and a Vector 2
Reciprocal of a Q. 66
Reciprocal of a V. 41
Rotation, Conical 90
Rotation, Positive and Negative, Definition of 34
Scalar, Definition of a 8
Section, Anharmonic and Harmonic, of Vs. 13
Sections, Antiparallel (or Subcontrary) of cone 109 185
Segments, Six, of triangle 15
Signs of geometric figures 15
Sphere, Diameter of, circumscribing a tetrahedron 182
Sphere, Equations of 107 181
Spiral, logarithmic 171
Tensor, Definition of a 8
Theorem by Apollonius of Perga 73
Theorem by C. Keogh 144
Theorem by Euler 82
Theorem by Gauss 146
Theorem by MacCullagh 187
Theorem by Moivre 55
Triangle, Chordal, of a spherical triangle 145
Unit V., Definition of a. 8
Vector Reciprocal of a, Definition of the 30
Vector, Definition of a null 2
Vector, Definition of a real and actual 2
Vector-arcs, Circular 86
Vector-arcs, Condition of equality of two 86
Vector-area, Definition of a 51
Versor Right, Definition of a 37
Versor, Definition of a 34
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