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| Whitehead A.N. — A Treatise on Universal Algebra with Applications, Vol. 1 |
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| Предметный указатель |
Point and Vector Factors 514;
Point Inside a Triangle, denned 375 ;
Point, Latent 254 257 317
Points, Normal 199 sqq.;
Points, Normal or quadrantal, in Non-Euclidean Geometry 383 414 426
Polar Form of Elliptic Geometry, defined 355;
Polar Form of Elliptic Geometry, Intercept, defined 358;
Polar Invariant see Invariant;
Polar Invariant Regions, Absolute 367 384 420;
Polar Invariant Self-, denned 145
Polar Invariant, Reciprocally, defined 145;
Pole and Polar 145;
Pole and Polar in Hyperbolic Geometry 420
Pole Invariant see Invariant.
Positional Manifolds, defined 30;
Positional Manifolds, investigated 117 sqq
Positive System of Generators 207
Premises, Over-Strong 104
Primitive Predication and Negation 112 sqq
Principal Systems of a Dual Group, denned 532;
Principal Triangles 373 sqq. 380
Principal Vector of a System of Forces 518
Products, Order of, defined 175;
Products, Pure and mixed 184
Progressive Multiplication 181
Projection 224 sqq
Propositional Interpretation of Symbolic Logic 107 sqq.
Propositions, Equivalence of, defined 108;
Propositions, Nugatory Forms of 100;
Propositions, Reciprocal 38;
Propositions, Self-condemned, defined 111;
Propositions, Simple 107;
Propositions, Symbolic Forms of 99 sqq. 111
Pure Products, defined 184.
Quadrantal Points 383
Quadrics 144 sqq.;
Quadrics and Inner Multiplication 210;
Quadrics, Absolute 355;
Quadrics, Associated with Triple Groups see Group
Quadrics, Closed 153 355 376;
Quadrics, Conical, defined 150;
Quadrics, Conical, investigated 155;
Quadrics, Line-Equation of, generalized 213
Quadrics, Oval, defined 376
Quadrics, Self-normal, defined 199;
Quadrics, Self-normal, Extended Definition of 201
Quadrics, Transformation of, Direct and Skew 338 sqq.
Quaternions, mentioned 32 115 131 554 573
Quotient, name for Matrix 249.
Ratio, Anharmonic, defined 132;
Ratio, Anharmonic, of Systems of Forces 291
Reciprocal Groups 285
Reciprocal Propositions 38
Reciprocal Systems of Forces 281 303
Reciprocal Systems of Forces and Work 469 477 538
Reciprocity between Addition and Multiplication in Symbolic Logic 37.
Rectangular Normal Systems in Euclidean Space 524;
Rectangular Rectilinear Figures in HyperbolicSpace 433.
Reference Figures 138
Regional Element, in Calculus of Extension 177;
Regional Letters, in Symbolic Logic 87
Regions and Symbolic Logic 38
Regions and Symbolic Logic, Co-ordinate 126;
Regions and Symbolic Logic, Complete, defined 123
Regions and Symbolic Logic, Containing 126
Regions and Symbolic Logic, Generating 147;
Regions and Symbolic Logic, Generating, and Non-Euclidean Geometry 397 451;
Regions and Symbolic Logic, Incident 42
Regions and Symbolic Logic, Latent and Semi-Latent 248 256
Regions and Symbolic Logic, Latent and Semi-Latent, corresponding to Roots conjointly 316
Regions and Symbolic Logic, Latent and Semi-Latent, Types of, in Three Dimensions 317 sqq.;
Regions and Symbolic Logic, Mutually Normal 203
Regions and Symbolic Logic, Non- vertical 159
Regions and Symbolic Logic, Null, of Matrices 252
Regions and Symbolic Logic, Parallel 397 451
Regions and Symbolic Logic, Preserved by Matrices 253
Regions and Symbolic Logic, Semi-Latent see Regions Latent
Regions and Symbolic Logic, Supplementary 126
Regions and Symbolic Logic, Symbolism for, in Calculus of Extension 177;
Regions and Symbolic Logic, Vacuous, of Matrices 262
Regressive Multiplication 181 sqq
Relation, General Definition of 8
Resultants of Subsumption 3 59
Resultants, defined 51 sqq.
Resultants, Existential 90 sqq.
Riemann 13 17 368 369
Rigid Body, Motion of, in Non-Euclidean Geometry 487
Rotation in Euclidean Geometry 502;
Rotation in Non-Euclidean Geometry 460 471
Russell, B.A.W. 369 370.
Salmon 151
scalar 552.
Schemes, Algebraic 22 26 35
Schlegel, V. 575.
Schroder 37 42 51 62 66 67 74 82 115 116
Scott, R.F. 180
Secant lines 436
Secondary Properties of Elements 14 120
Secondary Triangles 373.
Self-condemned Propositions, defined 111
Self-Conjugate Tetrahedrons and Conjagate Sets of Systems 308
Self-normal Elements 199 204;
Self-normal Elements, Quadric 199 201 204
Self-normal Elements, Sphere 524
Semi-Latent see Latent.
shadows 87 sqq.;
Shadows, Weak Forms of 84
Sign, Standard 363 416
Signs and Symbolism 3 sqq
Simple Extensive Magnitude, defined 177
Simplicity, Law of 39;
Simplicity, Partial Suspension of 88
Skew Transformation of a Quadric 336 342
Space and Symbolic Logic 30 sqq. 38
Space, Constant 363;
Space, defined 354;
Space, Descriptive Properties of 119 sqq.;
Space, Division of 355 379;
Space, Elliptic, Hyperbolic, and Parabolic 355 sqq.;
Space, Euclidean 505 sqq.;
Space, Flatness of 451;
Space, ideal 414;
Space, Non-Euclidean, Formulse for 356 sqq. 362
Space, Null, of a Matrix 252;
Space, Preserved by a Matrix 253;
Space, Vacuous, of a Matrix 262.
Spaces as Spherical Loci 450 sqq
Spatial Elements 414 sqq.;
Spatial Interpretation of Universal Algebra 31;
Spatial Manifolds, defined 354 sqq
Species of algebras 27
Sphere, defined 376;
Sphere, investigated 391 sqq. 441
Sphere, Self-normal 524
| Spherical geometry 355
Staeckel 369 370
Standard Form of Planes 415;
Standard Sign see Sign.
Stationary Differential Operator 553
Staudt, von 215 317.
Staudtian, Formulas for 374.
steps 25 507.
Stereometriesl Triangles 382 425.
Stokes' theorem 562.
Stout 3 4.
Sturm, Dr Rudolf 278.
Subgroup, Parabolic, of Triple Group 296 311.
Submanifold, defined 15.
Subplane, denned 130.
Subregions, defined and investigated 123 125;
Subregions, Distances of 365;
Subregions, Parallel 397 451
Substitutive 8 sqq. 14
Substitutive Schemes 8;
Substitutive Signs 3 sqq.
Subsumptions, defined and investigated 42 sqq. 59.
Subtraction and Symbolic Logic 80 ;
Subtraction and Universal Algebra 22 sqq. 28
Supplementary Terms, interpreted 39 110
Supplements and Reciprocal Polars 201;
Supplements in Euclidean Space 523 sqq.;
Supplements in Symbolic Logic 36 sqq.;
Supplements, defined 181 sqq.;
Supplements, Different kinds of 202 ;
Supplements, Extended Definition of 201;
Supplements, investigated 199 sqq
Surface Locus, defined 130
Surfaces in Euclidean Space 539 sqq.;
Surfaces in Non-Euclidean Space 488 sqq.;
Surfaces of Equal Distance from Planes 391 442;
Surfaces of Equal Distance from Subregions 397 451
Syllogism 101;
Syllogism, Generalization of 105;
Syllogism, Symbolic Equivalents of 103
Sylvester 154 253 254.
Symbolic Logic, Formal Laws of Algebra of 35 sqq.;
Symbolic Logic, interpreted 38 99 107
Symbolic Logic, mentioned 22 29.
Synthesis, General Definition of 8
Systems and Quadrics 294 sqq. 298 338 535
Systems in Euclidean Space 518 sqq.
Systems in Non-Euclidean Space 401 sqq. 454
Systems in Notation of Pure Vector Formulae 551;
Systems of Forces 273 sqq.;
Systems, associated with Congruent Transformation 466 473 476 536
Systems, Axes of 401 454
Systems, Groups of see Groups
Systems, Latent, defined 322
Systems, Non-Axal 404 455
Systems, Parameters of 401 454
Systems, Reciprocal 281;
Systems, Reciprocal, and Work 469 477 538
Systems, Vector 406 sqq. 454;
Systems, Vector, and Vector Transformations 473
Systems, Vector, Unit 407.
Tait 554 573
Taylor, H.M. 215
Terms and Points, distinguished 360;
Terms, Congruence of, defined 122
Terms, Constituent, denned 47
Terms, defined 20;
Terms, defining Triangle 372;
Terms, Equivalence of, interpreted 38 ;
Terms, Null 24;
Terms, Supplementary, interpreted 39
Thought, Laws of 110
Tortuosity, Order of 131
Transformation of a Quadric, Direct and Skew 338 456
Transformation, Congruent 456 500 537
Transformation, Congruent, and Characteristic Lines 470;
Transformation, Congruent, and Work 469 477 537
Transformation, Congruent, Associated Systems of Forces of 466 473 476 536;
Transformation, Congruent, Axes of 458 471
Transformation, Congruent, Parameters of 460 471
Transformation, Elliptic, Hyperbolic, Parabolic 134
Transformation, linear 133 227 248 316
Transformation, Vector 472 sqq
Translation in Euclidean Space 502 ;
Translation in Non-Euclidean Space 460 471
Triangles 371 sqq. 378 422
Triangles, defined by Terms 372
Triangles, Principal 373 380;
Triangles, Principal, Set of 373
Triangles, Secondary 373;
Triangles, Spatial and Semi-Spatial 423
Triangles, Stereo metrical 425 482.
Trigonometry, spherical 375 383 426
Umbral Letters 86 sqq.
Uninterpretable Expressions in a Calculus 10
Units, Independent, defined 122
Unity, Law of 38
Unity, Partial Suspension of 88
Universal algebra 11 18
Universal Algebra, Propositions and Equations 105.
Universe and Primitive Predication 113;
Universe and Primitive Predication of Discourse 100
Universe and Primitive Predication, defined 36;
Universe and Primitive Predication, interpreted 39 109;
Universe and Primitive Predication, Properties of 37;
Unlimiting Equations 59 sqq.
Vacuity of a Matrix 261
Vacuous Region of a Matrix 262
Vector analysis 573;
Vector in Elliptic Space viz.
Vector in Euclidean Space viz.
Vector System of Forces 406 sqq. 454 473
Vector System, Associated with Motion 473
Vector System, Right and Left 406 sqq.
Vector System, Unit, denned 407;
Vector Transformations 472
Vector, Areas 509 sqq.;
Vector, Differentiation 560;
Vector, Factor 514;
Vector, Flow of a 572;
Vector, Formulae, Pure 548 sqq.;
Vector, Moment 518 551;
Vector, Operation of Taking the 516 sqq.
Vector, potential 565;
Vector, Principal, of System of Forces 518 ;
Vector, Volumes 513 sqq.
Velocity in Non-Euclidean Space 482
Venn 115 116.
Veronese 139 147 152 161 370
Vortex Motion 562.
Weak forms of Shadow Letters 84
Weakened conclusion 104
Webb 560
Work in Euclidean Space 537
Work in Non-Euclidean Space 468
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