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| Whitehead A.N. — A Treatise on Universal Algebra with Applications, Vol. 1 |
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| Предметный указатель |
Geometry, Parabolic, as a limiting Form 367
Geometry, spherical 355
Gerard 369
Gibbs 573
Graphic Statics 520.
Grassmann, H. 13 19 28 31 32 115 122 131 132 146 168 171 172 201 210 219 229 233 235 246 248 249 262 278 370 522
Grassmann, H.(The Younger) 317
Grassmann, H., Note upon 573 sqq.;
Grassmann, R. 575.
Gravelius, H. 281
Green's theorem 562
Groups of Systems 284 sqq.;
Groups of Systems, Common Null Lines of 286
Groups of Systems, Director Forces of 286
Groups of Systems, Dual and Congruences 288
Groups of Systems, Dual and Quadruple 287 sqq.
Groups of Systems, Dual, Central Systems of 402 455
Groups of Systems, Dual, Centres of 402
Groups of Systems, Dual, Diametral Plane of 532
Groups of Systems, Dual, Elliptic and Hyperbolic, defined 292
Groups of Systems, Dual, Parabolic 289 296
Groups, Dual, in Elliptic Space 402 sqq.;
Groups, Dual, in Euclidean Space 531 sqq.;
Groups, Dual, in Hyperbolic Space 455;
Groups, Dual, Principal and Secondary Axes of 532;
Groups, Dual, Self-Supplementary 292 296
Groups, Invariants of see Invariants
Groups, Quintuple 286 sqq.
Groups, Reciprocal 285 sqq.;
Groups, Semi-latent and Latent, defined 322;
Groups, Semi-latent and Latent, Types of 326 sqq.
Groups, Triple 295 sqq.;
Groups, Triple, Associated Quadric of 295 314 535;
Groups, Triple, Conjugate Sets of Systems in 298 306
Groups, Triple, in Euclidean Space 533 sqq.
Halsted 369.
Hamilton's Differential Operator 554.
Hamilton, W.R. 32 115 131 552 573.
Hamiltonian, defined 554.
hankel 32.
Harmonic Invariant see Invariant.
Heaviside, Oliver 550 573.
Helmholts 168 369 575.
Hill, M.J.M. 569 570.
Homography of Ranges, defined 133.
Houel 369.
Hyde, E.W. 575.
Hydrodynamics 562 sqq.
Hyperbolic Definition of Distance 352;
Hyperbolic Dual Group see Group;
Hyperbolic Geometry, Formulae for 362 sqq.;
Hyperbolic Geometry, investigated 414 sqq.
Hyperbolic Spatial Manifold, defined 355.
Ideal space 414.
Identical Equation of a Matrix 256 261
Incident Regions in Algebra of Symbolic Logic 42;
Incident Regions in Positional Manifolds 125
Independence of Elements in Positional Manifolds, denned 122
Inference and a Calculus 10
Infinity, plane at 497;
Infinity, points at 506.
Inner multiplication 207 sqq. 528
Integrals, Volume, Surface, and Line 562
Intensity 119 sqq. 162
Intensity and Secondary Properties 15
Intensity in Hyperbolic Geometry, of Points and Planes 415 sqq.;
Intensity in Non-Euclidean Geometry 364 366
Intensity in Parabolic Geometry 368 498;
Intensity Locus of Zero, defined 163;
Intensity of Forces in Non-Euclidean Geometry 399 452;
Intensity, Complex 120;
Intensity, Negative 120;
Intensity, Normal, defined 200;
Intensity, Opposite, defined 166
Intensively Imaginary, or Real, Elements 166
intercept 167 sqq. 358
Intercept, Antipodal, defined 168;
Intercept, Length of, defined 359 363;
Intercept, Polar, defined 358;
Intercept, The, defined 358
Interpretation, Prepositional, in Symbolic Logic 107.
Intersection of Manifolds, defined 15
Invariant Equations of Condition 172
Invariants of Groups of Systems 300 sqq. 531
Invariants, Conjugate, of Triple Groups 310 sqq.
Invariants, Harmonic, of Dual Groups 301 533
Invariants, Null, of Dual Groups 300
Invariants, of Groups in Euclidean Space 531 sqq
Invariants, Pole and Polar, of Triple Groups 305 534;
Involution, Lines in 280;
Involution, of Systems of Forces 291;
Involution, of Systems, Foci of 291.
Jevons 38 39 115
Johnson, W.E. 28 44 183
Junghans 574.
Kcenigs 278
Killing 370.
Kinematics in Euclidean Geometry 536 sqq. 551
Kinematics in Non-Euclidean Geometry 456 sqq
Klein 127 135 278 351 353 354 369 381 456 500 501
Kraft, F. 575.
Lachlan 138.
Ladd, Miss Christine 98
Lasker, E. 575.
Latent and Semi-Latent Regions, Types of, in Three Dimensions 317 sqq.;
Latent Group, defined 322;
Latent Groups and Systems, Types of 326sqq.
Latent Point, defined and discussed 254 sqq.
Latent Regions, corresponding to roots conjointly 316
Latent Regions, defined and discussed 248 258
Latent Regions, Root 254;
Latent Regions, Root, Repeated 257;
Latent Regions, System, defined and discussed 322 sqq
Law of absorption 37
Law of Simplicity 39
Law of Simplicity, Partial Suspension of 88
Law of Unity 38;
Law of Unity, Partial Suspension of 88
Law, Associative, and Combinatorial Multiplication 174;
Law, Associative, and Matrices 251
Law, Associative, and Symbolic Logic 37
Law, Associative, and Universal Algebra 25 27
Law, Commutative, and Congruent Transformations 464;
Law, Commutative, and Symbolic Logic 37
Law, Commutative, and Universal Algebra 27
Law, Distributive, and Combinatorial Multiplication 174;
Law, Distributive, and Existential Expressions 84
Law, Distributive, and Symbolic Logic 37;
Law, Distributive, and Universal Algebra 26
Laws of Thought 110.
Leibnitz's theorem 273
Letters, Greek, Roman, and Capital, Conventions concerning 86 119 177 550;
Letters, Regional 87;
Letters, Umbral 86.
Lie 369
Limit Line 495;
Limit Line, Surface 447 sqq. 486 494
Limited Field, defined 61
Limiting Equation, defined 59
Lindemann 281 369
Line-Geometry 278
Linear complexes 278;
Linear Complexes and Quintuple Groups 286
Linear Complexes, Theorems concerning 292;
Linear Element, compared to Mechanical Force 273
Linear Element, defined 177;
Lines, Null 278 286;
Lines, Parallel, in Elliptic Space 404 sqq.
Lines, Parallel, in Hyperbolic Space 436 sqq.;
Lines, Secant and Non-Secant 436;
| Lines, Spatial and Anti-Spatial 418;
Lines, Straight, defined 130
Lobatschewsky 369 436 438 487
Locus, Containing, defined 131;
Locus, Curvilinear, defined 130;
Locus, defined 128;
Locus, Flat, defined 129;
Locus, of Zero Intensity, defined 163;
Locus, Surface and Curve, defined 130
Logic, Application of Algebra to 99
Logic, Generalization of Formal 105
Logic, Symbolic, Algebra of, mentioned 22 29
Logic, Symbolic, Formal Laws of Algebra of 35 sqq.
Logic, Symbolic, Interpretations of Algebra of 38 99 107
Lotze 6 116
Love 560.
Magnitude, Extensive, denned 176 sqq
Manifolds 13 sqq.;
Manifolds, Algebraic 22 26
Manifolds, Algebraic, Orders of 27 171 175
Manifolds, Algebraic, Self-Multiplicative 27
Manifolds, Complete Algebraic System of 27
Manifolds, Derived 175
Manifolds, Extensive, and Elliptic Geometry 399 sqq.
Manifolds, Extensive, and Hyperbolic Geometry 452 sqq.;
Manifolds, Extensive, mentioned 31;
Manifolds, Extensive, of Three Dimensions 273 sqq.;
Manifolds, Positional, investigated 117 sqq.
Manifolds, Positional, mentioned 30;
Manifolds, Spatial, defined 349 355;
Manifolds, Special, defined 16 sqq
Matrices 248 sqq. 316 456 500
Matrices and Forces 316 sqq.;
Matrices, congruent 457 sqq. 500 536
Matrices, Denominators and Numerators of 249;
Matrices, Null Spaces of 252;
Matrices, Nullity of 253;
Matrices, Skew 248 267;
Matrices, Skew, symbolized 280;
Matrices, Spaces (or Regions) preserved by 253
Matrices, Sums and Products of 250;
Matrices, Symmetrical 248 262;
Matrices, Vacuity of 261;
Matrices, Vacuous Regions of 262
Maxwell 573
Metageometry 369
Metrics, Theory of 273 347
Meunier's Theorem, in Euclidean Space 547;
Meunier's Theorem, in Non-Euclidean Space 493
Middle Factor, Extended Rule of the 188;
Middle Factor, Rule of the 185;
Middle Factor, Rule of the, for Inner Multiplication 208
Mitchell, Dr 116
Mixed Product, defined 184
Mobile Differential Operator, defined 554
Mode of a Property 8 13
Moebius 131.
Moment of a System of Forces 278.
Monge 479 541.
Motion, Associated System with 487
Muller 192.
Multiplication in Symbolic Logic, interpreted 38 108
Multiplication, Combinatorial, Formulae for, in Three Dimensions 274
Multiplication, Combinatorial, investigated 171 sqq.
Multiplication, Flux 528;
Multiplication, Inner and Outer 207;
Multiplication, Inner and Outer, in Euclidean Space 523 sqq.
Multiplication, mentioned 18
Multiplication, Principles of, defined and discussed 25 sqq.
Multiplication, Progressive and Regressive 181 sqq
Multiplicative Combination, defined 175.
Napier's Analogies and Non-Euclidean Geometry 375 425
Negation, Primitive 113
Negative Intensity 120
Negative Intensity, System of Generators 207
Newcomb 370.
Non-Euclidean Geometry, Historical Note upon 369 sqq.;
Non-Euclidean Geometry, investigated 347 sqq
Non-secant Lines 436
Normal Intensity, defined 200
Normal Points, defined 199 sqq.
Normal Regions, and Points in Euclidean Geometry 523 sqq.;
Normal Regions, and Points in Non-Euclidean Geometry 383 sqq. 426
Normal Regions, defined 203;
Normal Systems of Points, defined 200;
Normal Systems of Points, Rectangular 524.
Nugatory Forms of Propositions 100
Null Element and Self-Condemned Propositions 111
Null Element in Symbolic Logic 35 37
Null Element in Symbolic Logic, interpreted 38 109
Null Element in Universal Algebra 24 sqq. 28
Null Invariants of a Dual Group 300
Null Lines, Planes, and Points 278
Null Points, Latency of 323 sqq.
Null Space of Matrix 253
Null Term 24.
Null, and Propositional Interpretation 109 111;
Null, in Universal Algebra 24 sqq. 28
Nullity of Matrix, defined 253
Numbers, Alternate 180.
One-sided Planes 379
Operation of Taking the Flux 522 527;
Operation of Taking the Flux, Vector 516 522.
Operation, General Definition of 7 sqq.
Order and the Operation of Addition 19 sqq.;
Order and the Operation of Manifolds 27 171 175;
Order and the Operation of Tortuosity 131.
Origin with Pure Vector Formulae 550
Origin, defined, for Euclidean Geometry 524;
Origin, defined, for Hyperbolic Geometry 414;
Outer Multiplication 207
Oval Quadrics, defined 376;
Oval Quadrics, Spheres, intersection of 396
Over-Strong Premises 104.
Parabolic Definition of Distance 353 sqq.
Parabolic geometry 355 496
Parabolic Geometry as a Limiting Form 367
Parabolic Group 289 296;
Parabolic Group, Semi-Latent, and Latent 322 sqq.
Parabolic Linear Transformation 135
Parabolic Self-Supplementary Group, General Type of 296;
Parabolic Subgroup of Triple Group 296 311
Parallel Lines in Elliptic Geometry 404 sqq.;
Parallel Lines in Hyperbolic Geometry 436 sqq.
Parallel Planes in Hyperbolic Geometry 439
Parallel Regions in Elliptic Geometry 397 sqq
Parallelism, Angle of 438
Parallelism, Bight and Left 405
Parallelogram in Elliptic Space 410.
Parallelogram of forces 273
Parameters of a Congruent Transformation 460 471;
Parameters of a System of Forces 401 454
Partition of a manifold 15
Pascal's theorem 231 237
Peano, G. 575
Peirce, B. 172;
Peirce, B.C.S. 3 10 37 42 115
Perpendiculars in Non-Euclidean Geometry 383 sqq. 426
Perspective 139 sqq.
Pfaff's Equation 573.
Planar Elements, defined 177;
Planar Elements, Intensities of, in Non-Euclidean Geometry 366 415.
Planes, Angles between, in Non-Euclidean Geometry 365 382 417
Planes, Central, of Spheres 442;
Planes, Defined 130;
Planes, Diametral, of Groups 532;
Planes, One-sided 379 sqq
Planes, Parallel, in Hyperbolic Space 439;
Pluecker 213 278
Poincare 369
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