Marchisotto E.A., Smith J.T. — Legacy of Mario Pieri in Geometry and Arithmetic :: Электронная библиотека попечительского совета мехмата МГУ

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Marchisotto E.A., Smith J.T. — Legacy of Mario Pieri in Geometry and Arithmetic

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Название: Legacy of Mario Pieri in Geometry and Arithmetic

Авторы: Marchisotto E.A., Smith J.T.

Аннотация:

Mario Pieri (1860-1913) left a strong impact on many areas of 20th century mathematics. A prominent disciple of two Italian schools at the University of Turin, namely that of Segre (algebraic geometry) and Peano (logic), Pieri's own research influenced many 20th mathematicians in such fields as algebraic and differential geometry, inversive geometry, number theory, and logic.

The Legacy of Mario Pieri in Arithmetic and Geometry is the first of two volumes that together will provide a broad picture of Pieri's work. In this volume, English translations are given for two of Pieri's most important results: his postulates for arithmetic, which Peano judged superior to his own, and his foundation of elementary geometry on the basis of point and sphere, which Alfred Tarski used as a basis for his own system. Additionally, his papers are examined in relation to the research of others, notably Peano and Tarski.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2007

Количество страниц: 420

Добавлена в каталог: 14.05.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

Skew lines      246
Skof, Fulvia (1932–)      71 399 450
Skolem, Thoralf Albert (1887–1963)      452
Smaller-than      See larger-than
Smid, Lucas Johannes (????–????)      143 455
Smith, David Eugene (1860–1944)      89 450
Smith, Helen Marie Patteson (1940–)      x
Smith, James Thomas (1939– )      iv x 357 450
Solid      349
Somigliana, Carlo (1860–1955)      10 79 110 403 417 450
Sommer, Julius (1871–1943)      380 440 451
Soncini, A.(18??–19??)      397 443
Sottile, Frank (1963–)      x 52 422 450
Speranza, Francesco (1932–1998)      x
Spezia, Giorgio (1842–1911)      332
Speziali, Pierre (1913–1995)      78 81 108 450
Sphere      160 349
Sphere as tool      154 157 283
Sphere in inversive geometry      137 140—142
Sphere in Point and Motion      146 272
Sphere in Point and Sphere      58 157 165 281
Sphere, concentric      349
Sphere, fundamental, of anti-inversion      238
Sphere, polar      194 272
Sphere, tangent      167. See also under Riemann; symbol
Spoglianti, Maria (19??–)      129 428
Springer — Verlag      460
SSS triangle-congruence      See under theorem
Staeckel, Paul (1862–1919)      451 455
Stahl, Wilhelm (1846–1894)      432 449 455
Stamm, Edward (????–1940)      345 450
Statics      See graphical statics
Staudt, Georg Karl Christian von (1798–1867)      54 110—111 136 408 429 431 444
Staudt, Georg Karl Christian von (1798–1867) 1847 Geometrie der Lage      vii 57 95 99 129 160—161 269 450
Staudt, Georg Karl Christian von (1798–1867) collineation or homography      207 380
Staudt, Georg Karl Christian von (1798–1867) complex projective geometry      56 134—136
Staudt, Georg Karl Christian von (1798–1867) Pieri's 1889a translation of Staudt 1847      20 107—108 123 335 338 379 393 437.
Steele, Donald A.(19??–????)      405
Stefanini, Annibale (18??–????)      398
Steiner, Jakob (1796–1863)      83 101 105 139 450
Steinhardt, Fritz (1922–1993)      426
Steinitz, Ernst (1871–1928)      404 431 448 454
Stephanos, Cyparissos (1857–1918)      398
Stereographic projection      138
Stolz, Otto (1842–1905)      291 408 425 450
Strambach, Karl (1939–)      424 444
Straneo, Paulo (1874–1968)      108 450
Straordinario      See under professore
Study, Eduard (1862–1930)      41 105 111—112 133 405 408 415 436 451
Stueckrad, Juergen (1948–)      52 450
Sturm, Rudolf (1841–1919)      445
Sturm, Rudolf (1841–1919), sequence      351
Sturmfels, Berndt (1962–)      52 422
Style, Hilbert      148—151 276 283 354
Style, Pieri      58 126 141 147 150—151 156 158 162 171 272—273 278 283—286 323 340 350 356 368 370
Style, Tarski      350 354 356
Successor      58 299 308 315—316 321—322
Successor, Frege's definition      298
Successor, Pieri's definition      290 307
Successor, Zermelo's construction      300. See also under symbol
Sum in mereology      349
Sum of angles      220 228 395
Sum of cardinals      297
Sum of natural numbers      299—300 311 314—315 318—319 324
Sum of ordinals      297
Sum of scalars      354
Sum of segments      210 220 226 272 392
Sundial      52 376
Superposition      218
Superposition argument      150 338
Suppes, Patrick (1922– )      297 421 431 451
Surface, algebraic      vii 12 15 20—21 51 72 75 375—376 383
Surface, birationally equivalent      79
Surface, helicoidal      51 374
Surface, quadric      51 57 140 375
Surface, ruled      vii 51—52
Surface, system      378
Sweden, mathematics in      68 153—154
Symbol, abstraction      316
Symbol, angle notation, $\hat{A}.BC, \breve{A}.BC$       163 204
Symbol, arc O(AB)      252
Symbol, between, q-p-r, Bqpr      272 351
Symbol, collinear, Cabc      357
Symbol, congruent, $F \cong= F'$       162—163 216 218 274
Symbol, conjunction, $\Phi & \Psi$       162—163
Symbol, difference of sets, A – B      162
Symbol, disjunction, $\Phi \vee \Psi$       162 164
Symbol, empty set      316
Symbol, equality by definition, $r \equiv AB$       163 265
Symbol, equality, A = B      162—163 165 316
Symbol, equidistance, quaternary, Dpqrs      357
Symbol, equidistance, ternary, Ipqr, Ppqr      280 357
Symbol, equivalence, logical, $\Phi \Leftrightarrow \Psi$       162—163
Symbol, existential quantifier string, $\Sigma$       271
Symbol, existential quantifier, $\existsx \Phi$       271
Symbol, following, $\sigma_{A,B}C, \sigma_{O, A, B}C$       163 249 253
Symbol, half-line, $\mid AB$       163 200
Symbol, half-plane, $\mid rP$       202
Symbol, homothety $\{ O^{A'}_A\}$       233
Symbol, image by transformation, $\mathscr{R}A$       269
Symbol, implication, $\Phi \Rightarrow \Psi$       162—163 316
Symbol, inclusion, $\phi \subseteq \psi$       162—163 165
Symbol, inequality, $A \neq B$       162—163
Symbol, intersection, $\phi \cap \psi$       162—163 165
Symbol, line joining 2 points, AB      162 167
Symbol, line reflection, /r      176
Symbol, membership, $Y \in r$       162—163 316
Symbol, midpoint $A \mid B, Mabc$       162 174 357
Symbol, negation, $\neg \Phi$       162—163
Symbol, nonmembership, $Y \not< r$       162—163
Symbol, orthogonality $r \perp s$       163 179 357
Symbol, plane joining 3 points, ABC      162 170
Symbol, plane reflection, $/\pi$       186
Symbol, point reflection, /A      162 174—175
Symbol, product of transformations, $\mathscr{L}\mathscr{P}, \mathscr{L} \cdot \mathscr{P}$       270
Symbol, quantification (Peano's)      316
Symbol, ray      see symbol: half-line
Symbol, right angle, Rabc      357
Symbol, segment, $\mid AB \mid$       163 195
Symbol, semicircle, O(AB)      252
Symbol, singleton, {X}      162
Symbol, sphere, , Sph(A,B)      160 162 165 194
Symbol, substitution of variables, $\begin{pmatrix}D, & C, & A, \\ A, & B, & C \end{pmatrix}$ P7§2      163 316
Symbol, successor, suc x, x+1      311 316 319 321
Symbol, sum, $\alpha + \beta$       226 228 318
Symbol, translation {A', A}      237
Symbol, triangle, $\mid A.BC \mid, \mid ABC\mid$       163 205
Symbol, union, $\phi \cup \psi$       162 164—165
Symbol, universal quantifier string, $\Pi$       271. See also notation; Giuseppe Peano: symbolic notation
Symbol, universal quantifier, $\forall x \Phi$       271
symmetric      See under relation
Symmetry      160
Symmetry over a line      176
Symmetry over a plane      187
Symmetry over a point      174—175
system      See simply infinite system
Szczerba, Les aw W odzimierz (1938–)      271 347—348 350—351 354 356 369 426 451
Szeg , Gabor (1895–1985)      451
Szmielew, Wanda Montlak (1918–1976)      350 354—357 360—362 368 406 448
Tabarroni, Giorgio (1921–2001)      100 451
Tactile-physical space      160
Tajtelbaum, Alfred      See Alfred Tarski
Tajtelbaum, Ignacy (1869–1942)      347
Tajtelbaum, Rosa Prussak (1879–1942)      347
Tajtelbaum, Wacl aw      See Wac aw Tarski
Tangent to a variety      374—375 383
Tangent, line and sphere      181 200
Tangent, spheres      167
Tangent, triple      see Mario Pieri: 1889b
Tannery, Jules (1848–1910)      74 325 448

Tarski, Alfred (1901–1983)      v viii x 113 116 156 278 288 305 331 347 359 412 416 419 421 427 431 448 451—452 460
Tarski, Alfred (1901–1983) and Pieri      349—350 353—354 356—357 367—370
Tarski, Alfred (1901–1983), birth      347
Tarski, Alfred (1901–1983), career at Berkeley      113
Tarski, Alfred (1901–1983), change of surname      348
Tarski, Alfred (1901–1983), death      113
Tarski, Alfred (1901–1983), definability research      357—358 360—361
Tarski, Alfred (1901–1983), doctorate      348
Tarski, Alfred (1901–1983), early employment      348 351—352
Tarski, Alfred (1901–1983), emigration to the United States      113 352
Tarski, Alfred (1901–1983), family      113 347 352
Tarski, Alfred (1901–1983), marriage      351—352
Tarski, Alfred (1901–1983), politics      347
Tarski, Alfred (1901–1983), schooling      347. See also under elementary geometry; school; style
Tarski, Alfred (1901–1983), [1927] 1983 Foundations of geometry of solids      349—350 368 451
Tarski, Alfred (1901–1983), [1957] 1959 What is elementary geometry      ix 288 352—357 368 452
Tarski, Janusz (1934– ), x      113 352
Tarski, Krystina      See Krystina Tarski Ehrenfeucht
Tarski, Maria Witkowska (????–1990)      113 351
Tarski, Wac aw (1903–1944)      347—348
Tartufari, Luigi (1864–1931)      47 453
Taurinorum, Augusta      18
Tautologous point      See fixed point
Tazzioli, Rossana (1962–)      34 40 73 81 88 92 94 108 453
Technical institute and school      7
Teitelbaum      See Tajtelbaum)
Teixeira, Francisco Gomes (1851–1933)      375 438
Terracini, Alessandro (1889–1968)      79 347 453
Tetracyclic      See under coordinates
Theorem      126 267
Theorem, Bezout      52—53
Theorem, Cantor — Bernstein      435
Theorem, Desargues      232 276
Theorem, Heine — Borel      277
Theorem, intermediate value      291
Theorem, Miquel      143
Theorem, Pappus — Pascal      143 276 388
Theorem, Pythagoras      263
Theorem, Riemann mapping      141
Theorem, SSS triangle-congruence      281
Theorem, Staudt      see fundamental theorem of projective geometry
Theorem, three perpendiculars      185
Theory, axiomatic      see hypothetical-deductive system
Theory, categorical      151 317
Theory, complete      351
Theory, consistent      54 59—61 290 306 382
Theory, decidable      351
Theory, quasi-interpretable      278 360
Thiel, Christian (1936–)      399 453
Thomae, Johannes Karl (1840–1921)      393 439 453
Thomson, William, Lord Kelvin (1824–1907)      139 453
Thorup, Anders (1943–)      424
Throat cancer      2 5—6 46—47 97 391
Timerding, Heinrich Carl Franz Emil (1873–1945)      100 453
Tizio      268
Toepell, Michael-Markus (19??–)      x 148 453
Toeplitz, Otto (1881–1940)      376 439
Tonelli, Leonida (1885–1956)      98 453
Topology, general      349—350 352
Toponymy      444
Totalitarianism      ix 366
Transactions of the American Mathematical Society      See under journals
Transformation      71 154 161 249 269 394
Transformation as a tool      157 278 283—284.
Transformation by reciprocal radii      see transformation: inversion
Transformation, affinity, circular      see transformation: Moebius
Transformation, anti-inversion      238
Transformation, anticongruence      247—248 (see also motion: indirect)
Transformation, antihomography      247
Transformation, antiprojectivity      135
Transformation, antirotation      see reflection: rotary
Transformation, antitranslation      see reflection: glide
Transformation, birational      51 65 72 75 80 374 377—378
Transformation, circular      57 139—142
Transformation, collineation      207 394
Transformation, conformal      139—141 236
Transformation, congruence      247—248 (see also motion: direct)
Transformation, continuous      139
Transformation, Cremona      see transformation: birational
Transformation, group      56 57 81 86 133 146
Transformation, holomorphism      see under function homography
Transformation, homography      56 133 247 340 377—378 380
Transformation, homothety      233
Transformation, identity      183 237 269
Transformation, inverse      269 273
Transformation, inversion      57 137—140 142 238
Transformation, involution      137 176 270
Transformation, Kreisverwandtschaft      see transformation: circular
Transformation, Moebius      see transformation: circular
Transformation, projectivity      137
Transformation, ribaltamento      176
Transformation, rotation      145 183
Transformation, screw      246—247
Transformational geometry      See under geometry
Transitive      See under relation
Translation (geometric)      145 237 247
Translation (geometric), normal, parallel, or oblique      242
Translation strategy      ix 157—158 162—164
Treutlein, Peter (1845–1912)      409 425 444 449
triangle      205. See also under symbol
Tricomi, Francesco Giacomo (1897–1978)      81 113—115 453
Tricomi, Francesco Giacomo (1897–1978), citations      12 18 20 26 34 40 62 67 110 346
Tricomi, Francesco Giacomo (1897–1978), effect on Peano's and Pieri's reputations      346 363—365 453
Tricomi, Francesco Giacomo (1897–1978), unreliability      42 115 364
Trigonometric series      292 294
Turin      xvii—xviii 5 17—18 27
Turin, Royal Academy of Sciences      18 20—21 27 148 335 346 460
Turin, Royal Military Academy      18 19 333 459 460. university
Turin, university of      16 18 20 23 31 123 332
Turin, university of, rift between Peano, Segre schools      32 108 110 114 337 346
Tuscany      xvii xix 4 11 16 44
Type theory      102 304
Ullrich, Peter (19??–)      455
Ultrasymmetric point      212
Umberto I      See Umberto I of Savoy
Undefined concepts      See primitive notions
Unger, Leo (????–????)      421—422
Unification      See under Italy
union      165 314.
Unit of measure      258
Unit point      257
Universal sentence      See under sentence
Universities, Italian      See Italian universities
University of California at Berkeley      x 113
Usiglio (18??–19??)      33
Ustica      xviii 5 6 27 454
Vacca, Giovanni (1872–1953)      313 337 341 343 454
Vai, Gian Battista (19??–)      70 454
Vailati, Giovanni (1863–1909)      34 153 333 337 341 398 454
Variations      See calculus: of variations
Variety, algebraic      51 377
Variety, Jacobian      12 50 375
Varignon, Pierre (1654–1722)      418
Varoli, Giuseppe (????–????)      109 454
Vassilief, Alexander (1853–1929)      398
Veblen, Andrew Anderson (1818–1906)      115
Veblen, Oswald (1880–1960)      43 115—116 120 279 351 357 369 388 403 428 430 441 454 461
Veblen, Oswald (1880–1960) on Pieri      131 133 370
Veblen, Oswald (1880–1960), 1904 System of Axioms for Geometry      161 271 277—278 279 283 285 340 360 366—367 448
Veblen, Oswald (1880–1960), complex projective geometry      135 137
Veblen, Thorstein (1857–1929)      115
Vector analysis      viii 1 46—47 53 69 71 83—84 334 378
Vector space      334
Vellano      4
Venice, Istituto di Scienze, Lettere, ed Arti      460
Vergerio, Attilio (1877–1937)      44 46—47 117
Veronese, Giuseppe (1852–1917)      117—118 132 447 449 490
Veronese, Giuseppe (1852–1917) as referee      22—23 29 36 42
Veronese, Giuseppe (1852–1917) on foundations of geometry      131 133 146 148 161 263 280 342 394 405 454—455
Veronese, Giuseppe (1852–1917), difference with Peano      129 338 428 434

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