None
Limit Line, 495 ; Surface, 447 sqq,, 486, 494. Limited Field, defined, 61. Limiting Equation, defined, 59. Lindemann, 281, 369. Line-Geometry, 278. Lines, NuU, 278, 286; Parallel, in Elliptic Space, 404 sqq. ; in Hyperbolic Space, 436 sqq.; Secant and Non-Secant, 436 ; Spatial and Anti-Spatial, 418 ; Straight, defined, 130. Linear Complexes, 278 ; and Quintuple Groups, 286 ; Theorems concerning, 292 ; Element, defined, 177 ; compared to Mechanical Force, 273. Lobatschewsky, 369, 486, 438, 487. Locus, Containing, defined, 181 ; Curvilinear, defined, 130 ; defined, 128; Flat, defined, 129 ; of Zero Intensity, defined, 163 ; Locus, Surface and Curve, defined, 13Q. Logic, Application of Algebra to, 99 ; Generalization of Formal, 106 ; Symbolic, Algebra of , meniioDed, Formal Laws of Algebra of, S3 Interpretations of Algebra of, 99, 107. Lotze, 6, 116. Love, 560. MeCoU, 112, 116. Magnitude, Extensive, defined, 176 tqq. Bianifolds, 13 sqq. ; Algebraic, 22, 26 sqq, ; Orders of, 27, 171, 175 ; Self-MultipUcative, 27 ; Complete Algebraic System of, 27 ; Derived, 175 ; Extensive, and Elliptic Geometry, 399 tqq,; and Hyperbolic Geometry, 452 sqq,; mentioned, 31 ; of Three Dimensions, 273 8qq. ; Positional, investigated, 117 sqq. ; mentioned, 30 ; Spatial, defined, 349, 355 ; Special, defined, 16 sqq. Matrices, 248 sqq,, 816 sqq., 456 sqq., 500 sqq. ; and Forces, 816 sqq, ; Congruent, 457 sqq., 500, 536 ; Denondnators and Numerators of, 249 ; Null Spaces of, 252 ; Nullity of, 253 ; Skew, 248, 267 ; symbolized, 280 ; Spaces (or Regions) preserved by, 253 ; Sums and Products of, 250 ; Symmetrical, 248, 262 ; Vacuity of, 261 ; Vacuous Regions of, 262. Maxwell, 573. Metageometry, 369. Metrics, Theory oi; 273, 347 sqq, Meunier's Theorem, in Euclidean Space, 547; in Non-Euclidean Space, 493. Middle Factor, Extended Rule of the, 188 ; Rule of the, 185; for Inner Multiplication, 208. MitcheU, Dr, 116. Mixed Product, defined, 184. Mobile Differential Operator, defined, 554. Mdbius, 131. Mode of a Property, 8, 13. Moment of a System of Forces, 278. •» m 9 INDEX. 683 Monge» 479, 641. Motion, AsBodated System with, 487. MtlUer, 192. Maltiplieation, Combinatorial, investigated, 171 sqqr, FormulflB for, in Three Di- mensions, 274 ; Flux, 628; in Symbolic Logic, interpreted, 88, 108; Inner and Outer, 207 ; in Eaolidean Space, 628 sqq.; mentioned, 18; Principles of, defined and difloossed, 26 sqq,; Progressive and Regressive, 181 sqq, Mcdtiplicative Combination, defined, 175. Napier's Analogies and Non-Enolidean Geo- metiy, 875, 425. Negation, Primitive, 113. Negative Intensity, 120 ; System of Generators, 207. Newcomb, 870. Non-Eadidean Geometry, Historical Note upon, 869 sgg.; investigated, 347 <99- Non-secant lines, 436. Normal Intensity, defined, 200; Points, defined, 199 sqq. ; Regions, defined, 203 ; and Points in Endidean (Geometry, 523 s^g.; in Non-Endidean Geometry, 383 <9g., 426 <99.; Systems of Points, defined, 200 ; Rectangular, 524. Nagatory Forms of Propodtions, 100. Null Element and Sdf-Condemned Propodtions, in Symbolic Logic, 35, 37 sqq.; inteipxeted, 38, 109 ; in Universal Algebra, 24 sqq,, 28; Invariants of a Dual Group, 800 ; Lines, Planes, and Points, 278; Points, Latency of, 823 sqq. ; Space of Matrix, 253 ; Term, 24. Nullity of Matrix, defined, 253. Numbers, Alternate, 180. One-dded Planes, 379. Operation, General Definition of, 7 sqq.; of Taking the Flux, 522, 527 ; Vector, 516, 522. Order and the Operation of Addition, 19 sqq.; of Manifolds, 27, 171, 175 ; of Tortuodty, 131. Origin, defined, for Euclidean Geometry, 524; for Hyperbolic Geometry, 414; with Pure Vector Formul», 550. Outer Multiplication, 207. Oval Qnadrics, defined, 376; Spheres, intersection of, 396. Over-Strong Premises, 104. Parabolic Definition of Distance, 353 sqq. ; (Geometry, 355, 496 sqq. ; as a Limiting Form, 367; Group, 289, 296 ; Semi-Latent, and Latent, 322 sqq. ; Linear Transformation, 135 ; Self-Supplementary Group, General Type of, 296 ; Subgroup of Triple Group, 296, 311 sqq. Pamllel Lines in Elliptic Geometiy, 404 sqq.; in Hyperbolic Geometry, 436 sqq.; Planes in Hyperbolic Geometiy, 439; Regions in Elliptic Geometry, 397 sqq. Parallelism, Angle of, 438 ; Right and Ldt, 405. Parallelogram of Forces, 273 ; in ElUptio Space, 410. Parameters of a Congruent Transformation, 460, 471 ; of a System of Forces, 401, 454. Partition of a Manifold, 15. Pascal^s Theorem, 231, 237. Peano, G., 575. Peirce, B., 172 ; 0. S., 3, 10, 37, 42, 115. Perpendiculars in Non-Eudidean Geometry, 383 sqq.j 426 sqq. Perspective, 139 sqq, Pfafl's Equation, 573. Planar Elements, defined, 177 ; Intendties of; in Non-Eudidean Geo- metry, 366, 415. Planes, Angles between, in Non-Eudidean Geometry, 365, 382, 417 sqq. ; Central, of Spheres, 442 ; Defined, 130; Diametral, of Groups, 532 ; Paralld, in Hyperbolic Space, 439 ; One-sided, 379 sqq, Pliicker, 213, 278. Polar Form of Elliptic Geometry, defined, 355; Intercept, defined, 858 ; 584 INDEX. Polar Invamnt, $ee Invariant ; Bedprooally, defined, 145 ; Regions, Absolute, 367, 384, 420 ; Self-, defined, 145. Pole Inyariant, 8ee Invariant. Pole and Polar, 145 ; in Hyperbolic Geometry, 420. Poincar6, 369. Point and Vector Factors, 614 ; Inside a Triangle, defined, 375 ; Latent, 254, 257, 317. Points, Normal, 199 8qq. ; Normal or qoadrantal, in Non-Enclidean Geometry, 883, 414, 426. Positional Manifolds, defined, 30; investigated, 117 sqq. Positive System of Generators, 207. Premises, Over-Strong, 104. Primitive Predication and Negation, 112 sqq. Principal Systems of a Daal Ghronp, defined, 532; Triangles, 373 8qq.,d80 sqq.; Vector of a System of Forces, 518. Products, Order of, defined, 175 ; Pore and mixed, 184. Progressive Multiplication, 181. Projection, 224 sqq, Propositional Interpretation of Symbolic Logic, 107 sqq. Propositions, Equivalence of, defined, 108 ; Nugatory Forms of, 100 ; Bedprooal, 38 ; Self-condemned, defined. 111 ; Simple, 107 ; Symbolic Forms of, 99 aqq.^ Ill sqq. Pure Products, defined, 184. Qnadrantal Points, 383. Quadrics, 144 sqq. ; Absolute, 355 ; and Inner Multiplication, 210 ; Associated with Triple Groups, see Group; Conical, defined, 150 ; investigated, 155 ; Closed, 153, 355, 376 ; Line-Equation of, generalized, 213 ; Oval, defined, 376; Self-normal, defined, 199 ; Extended Definition of, 201 ; Transformation of. Direct and Skew, 338 sqq. Quaternions, mentioned, 32, 115, 131, 554, 573. Quotient, name for Matrix, 249. Batio, Anhannonio, defined, 132 ; of Systems of f*oroes, 291. Beciprocal Groups, 285 ; Propositions, 38 ; Systems of Forces, 281, 303; and Work, 469, 477, 638. Reciprocity between Addition and Mnltiplieatiaa in Symbolic Logic, 37. Rectangular Normal Systems in EneUdeu Space, 524 ; Rectilinear Figures in H7peii»& Space, 433. Reference Figures, 138. Regional Element, in Calcolns of Bxteosiao, 177; Letters, in Symbolic Zjogic, 87. Regions and Symbolic Logic, 38 ; Incident, 42; Complete, defined, 123 ; Containing, 126; Co-ordinate, 12G; Generating, 147 ; and Non-Euclidean Oeometiy, 897, 451; Latent and Semi-Latent, 248, 256 sqqr, corresponding to BootB coujoinUj, 316; Types of, in Three DimensioD^ 317 sqq. ; Mutually Normal, 203 ; Non-vertical, 159; Null, of Matrices, 252 ; Parallel, 397, 451 ; Preserved by Matrices, 253 ; Semi-Latent, see Regions, Latent ; Supplementary, 126; Symbolism for, in Calcalns of Exten- sion, 177 ; Vacuous, of Matrices, 262. Regressive Multiplication, 181 sqq. Relation, General Definition of, 8. Resultants, defined, 51 sqq.\ Existential, 90 sqq. ; of Subenmptions, 59. Riemann, 13, 17, 368, 369. Rigid Body, Motion of, in Non-Eudidesn Geometry, 487. Rotation in Euclidean Geometry, 502 ; in Non-Euclidean Geometry, 460, 47t Russell, B. A. W., 369, 370. Salmon, 151. Scalar, 552. INDEX. 585 Sdhemea, Algebnio, 92, 36, 85 ; Subatitativd, 8 sqq.^ 14. Sohlegel, Y., 576. Sohrdder, 87, 42, 51, 62, 66, 67, 74, 82, 115, 116. Scott, B. F., 180. Secant Lines, 436. Secondary Properties of Elements, 14, 120 sqq.; Triangles, 878. Self-condemned Propositions, defined. 111. Self-Conjugate Tetrahedrons and Conjngate Sets of Systems, 808. Self-normal Elements, 199, 204 ; Qnadric, 199. 201, 204 ; Sphere, 524. Semi-Latent, see Latent. Shadows, 87 sqq, ; Weak Forms of, 84. Sign, Standard, 863, 416. Signs and Symbolism, 8 sqq. Simple Extensive Magnitude, defined, 177. Simplicity, Law of, 39 ; Partial Suspension of, 88. Skew Transformation of a Qnadric, 888, 842 sqq. Space and Symbolic Logic, 80 sgg., 88 sqq, ; Constant, 868; defined, 854 ; Descriptive Properties of, 119 sqq, ; Division of, 855, 879; Elliptic, Hyperbolic, and Parabolic, 855 sqq,; Enclidean, 505 sqq,; Flatness of, 451 ; Ideal, 414 ; Non-Euclidean, Formulaa for, 856 sqq,^ 862 sqq,; Null, of a Matrix, 252; Preserved by a Matrix, 258 ; Vacuous, of a Matrix, 262. Spaces as Spherical Loci, 450 sqq. Spatial Elements, 414 sqq.; Interpretation of Universal Algebra, 81 ; Manifolds, defined, 854 sqq. Species of Algebras, 27. Sphere, defined, 876 ; investigated, 891 sqq.^ 441 sqq. ; Self-normal, 524. Spherical Geometry, 855. Stiiokel, 869, 870. Standard Form of Planes, 415 ; Sign, see Sign. Stationary Differential Operator, 558. Staudt, von, 215, 817. Staudtian, Formnlie for, 874. W. Steps, 25, 507. Stereometrical Triangles, 882, 425. Stokes* Theorem, 562. Stout, 8, 4. Sturm, Dr Bndolf, 278. Subgroup, Parabolic, of Triple Qronp, 296, 811. Submanifold, defined, 15. Subplane, defined, 180. Subregions, defined and investigated, 128, 125 ; Distances of, 865 ; Parallel, 397, 451. Substitutive Schemes, 8 ; Signs, 8 sqq. Subsnmptions, defined and investigated, 42 sqq.f 59. Subtraction and Symbolic Logic, 80 ; and Universal Algebra, 22 sqq., 28. Supplementary Terms, interpreted, 89, 110. Supplements and Reciprocal Polars, 201 ; defined, 181 sqq.; Different kinds of, 202 ; Extended Definition of, 201 ; in EncUdean Space, 528 sqq.; in Symbolic Logic, 86 sqq.; investigated, 199 sqq. Surface Locus, defined, 180. Surfaces in Euclidean Space, 589 sqq. ; in Non-Endidean Space, 488 sqq.; of Equal Distance from Planes, 891, 442; from Subregions, 897, 451. SyllogiEon, 101 ; Qeneralization of, 105 ; Symbolic Equivalents of, 108. Sylvester, 154, 253, 254. Symbolic Logic, Formal Laws of Algebra of, 35 sqq. ; interpreted, 38, 99 sqq*^ 107 sqq. ; mentioned, 22, 29. Synthesis, General Definition of, 8. Systems of Forces, 278 sqq. ; and Quadrics, 294 sqq., 298, 888, 535; associated with Congruent Transform- ation, 466, 478, 476, 536; Axes of, 401, 454 ; Groups of, see Groups ; in Euclidean Space, 518 sqq.; in Non-EucUdean Space, 401 sqq., 454 in Notation of Pure Vector Formulie, 551; Latent, defined, 322 ; Non-Axal, 404, 455 ; Parameters of, 401, 454 ; Bedprocal, 281 ; 38 586 INDEX. Systems, Beoiprocal, and Work, 469, 477, 538; Vector, 406 «gg., 464; and Vector Transformations, 478 ; Unit, 407. Tait, 554, 573. Taylor, H. M., 215. Terms, defined, 20 ; and Points, distinguished, 360 ; Constituent, defined, 47 ; Congruence of, defined, 122 ; defining Triangle, 872 ; Equivalence of, interpreted, 38 ; NuU, 24 ; Supplementary, interpreted, 39. Thought, Laws of, 110. Tortuosity, Order of, 131. Transformation, Congruent, 456, 500, 537 ; and Characteristic Lines, 470; and Work, 469, 477, 687 ; Associated Systems of Forces of, 466, 473, 476, 536; Axes of, 458, 471 ; Parameters of, 460, 471 ; EUiptio, Hyperbolic, Parabolic, 134; Linear, 133, 227, 248, 316 ; of a Quadric, Direct and Skew, 338, 466 sqq. ; Vector, 472 sqq. Translation in Eudidean Space, 502 ; in Non-Euclidean Space, 460, 471. Triangles, 371 sqq., 378, 422 sqq.\ defined by Terma, 372; Principal, 373, 380 ; Set of, 373 ; Secondary, 373 ; Spatial and Semi-Spatial, 423 ; Stereometrical, 425, 482. Trigonometiy, Spherical, 375, 383, 426. Umbral Letters, 86 sqq. Uninterpretable ExpressioEis io a CsLetdoA, Vk Units, Independent, defined, 122. Unity, Law of, 38 ; Partial Suspension of, 88. Universal Algebra, 11, 18 ; Propositions and Equationa, 105. Universe and Primitive Predioation, 113 ; defined, 36 ; interpreted, 39, 109 ; Properties of, 37 ; of Discourse, 100. Unlimiting Equations, 59 sqq. Vacuity of a Matrix, 261. Vacuous Region of a Matrix, 262. Vector in EUiptic Space, viz. Vector System of Forces, 406 sqq., 454, 473 ; Associated with Molioii, 473 ; Right and Left, 406 gqq. ; Unit, defined, 407 ; Transformations, 472. Vector in Euclidean Space, viz. Vector Analysis, 573 ; Areas, 509 sqq. ; Differentiation, 560 ; Factor, 514 ; Flow of a, 572 ; Formuls, Pure, 548 sqq,; Moment, 518, 551 ; Operation of Taking the, 616 sqq., 532 ; Potential, 565 ; Principal, of System of Foroee, 518 ; Volumes, 513 sqq. Velocity in Non-Euclidean Spaoe, 482. Venn, 115, 116. Veronese, 139, 147, 152, 161, 370. Vortex Motion, 562. Weak forms of Shadow Letters, 84. Weakened Condnsion, 104. Webb, 560. Work in Eudidean Spaoe, 637 ; in Non-Euclidean Space, 468, 477. CAMBBIDOB: PBINTVD by J. and O. p. clay, at the UNITERSITY P1UC88. \J d 1 I ■i ''.i *»-■■ • A • .: •« I *fc ii'lii- iS^URftED ^ ^IS BOOK IS " ^ — '*aiiE LIBRARY ON X DATE STAMPED SEPTSTT ^ ta/' ■», ..r: ''tssat fcr I '1 1 - !• mmm v"\. ^■W ' 0 '1 -^^ ^ 4 w». 