The Principles of Mathematics: Volume 1 (Cambridge Library Collection - Mathematics) - Softcover

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Book may have numerous typos, missing text, images, or index. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. 1903. Excerpt: ... INDEX The references are to pages. References in black type are to passages where a technical term is defined or explained. Absolute, 226, 448 Abstraction, principle of, ix, 166, 219, 242, 285, 305, 314, 497, 519 Acceleration, 474, 483; absolute, 490, 491 Achilles and the tortoise, 350, 358 Action and Reaction, 483 Activity, 450 Addition, arithmetical, 118, 307; of indi- viduals, 71, 133-135; logical, 17, 21, 116; ordinal, 318; of quantities, 179, 180; relational, 182, 254; of relations, 321; relative, 26, 387 n.; of vectors, 477 Adjectives, 20 n., 42 Aggregates, 67, 139, 442; and classes as one, 141; infinite, 143 Algebra, universal, 376 Aliorelative, 203 n., 320n. All, 72, 105, 113, 305 Analysis, how far falsification, 141, 466; conceptual and real, 466 And, 67, 69, 71, 130 Angles, 205, 414; axioms of, 415, 416 Anharmonic ratio, 390, 391, 420 Antinomies, of infinity, 188, 190-193; Kant's, 259, 458-461 Any, 45, 46, 57, 105, 263, 305, 351; and kindred words, 55, 56, 59, 89, 91 Archimedes, axiom of, 181, 252, 254, 288, 332, 333, 337, 408 Area, 333, 417 Arithmetic, has no indemonstrables, 127; and progressions, 240; relation-, 321 Arrow, Zeno's argument of, 350 Assertion, 34-35, 48, 100, 502 ff. Assertions, 39, 44, 82, 83, 98, 106, 505 Associative law, 307 Assumptions, 503 Axioms, iu Geometry, 373, 441 Being, 43, 49, 71, 446, 449 Bernouilli, 329 n. Bernstein, 306 n., 367 n. Bettazzi, 181 n., 185 Between, 200, 201, 205, 207, 214; three theories of, 208; is a relation between its terms? 210; and difference of sense, 211; indefinable? 213; in projective Geometry, 391, 393, 426; in descriptive Geometry, 393 Bolyai, 373 Bolzano, 70, 201 n., 307, 357 n. Boole, 10, 24, 376 Borel, 306 n., 367 re. Bradley, 41, 43 n., 47, 90, 99, 161 n., 221, 224, 448, 471 Burali-Forti, 112 n., 323, 364 n. Cal...