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Marchisotto E.A., Smith J.T. — Legacy of Mario Pieri in Geometry and Arithmetic
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Íàçâàíèå: Legacy of Mario Pieri in Geometry and ArithmeticÀâòîðû: Marchisotto E.A., Smith J.T. Àííîòàöèÿ: 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.
ßçûê: Ðóáðèêà: Ìàòåìàòèêà /Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö ed2k: ed2k stats Ãîä èçäàíèÿ: 2007Êîëè÷åñòâî ñòðàíèö: 420Äîáàâëåíà â êàòàëîã: 14.05.2008Îïåðàöèè: Ïîëîæèòü íà ïîëêó |
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Pluecker, Julius (1801–1868) 53 86 134 139 444 Poetry 5 6 8 97 101 337 Poggendorff, Johann Christian (1796–1877) 399 444 Pogoda, Zdzis aw (????– ) 350 411 Poincare, Jules Henri (1854–1912) 38 84 86 116 133 421 445. Point (defined) 349 Point and Motion See under Mario Pieri Point and Sphere See under Mario Pieri Point reflection See under reflection Poland under Russia 347 367 Polar plane for sphere 238 Polar plane for two points 188 Polar system, elliptic 278 Pole-placement problem 52 Poles of a sphere 194 Polyhedra 17 Poncelet, Jean-Victor (1788–1867) 104 Ponzi, L.(18??–19??) 397 443 Positivism See logical positivism Postulate 54 95 162 266—268 Postulate, American theorists 116 Postulate, Archimedes 117 137 141 213 273 276 278 284—285 287 336 355 Postulate, circle 355 358 361—362 Postulate, completeness 149 151 276 350 Postulate, congruence 146 149 274 Postulate, continuity 141 146—147 149 151 155 263—264 273 277—278 285 287 353 355 362 Postulate, Euclid see parallel postulate: Bolyai Postulate, incidence 11 95 146 149 274 Postulate, order 95 149 274 Postulate, parallel see parallel postulate Postulate, Pasch 95 196 198 274 283 353 356 451 Postulate, Sas congruence 149 150 274. Postulates, choice of 126 267 282 286 394 Postulates, Peano See under natural-number arithmetic Potts, Donald (1921–2001) x Preceding 251—252 Predicate 298—299 Prefix See under quantifier Presburger, Mojzesz (1904–1943?) 445 351 Press, Volker (1939–1993) 420 436 Prihonsky, Frantisek (1788–1859) 405 Primitive notions v vii 54 126—127 147 149 266—268 320—321 350 358 360—363 394 Primitive notions, binary relations as 360—363 Princeton, Institute for Advanced Study 116 Princeton, university 116 461 Pristem 403 445 460 Privatdozent 11 Product of cardinals 297 Product of natural numbers 299—300 314 318—319 344 Product of ordinals 297 Product of scalars 354 Product of transformations 270 273 (see Professore (all ranks) 11 16 Progression, ascending or descending 254—255 Projective geometry vii 8 11 20 22 51 56 71—73 99 116 121 125 143 277—278 283 379 393 397 Projective geometry, analytic 60 93 140 Projective geometry, complex vii 52 56 111 134—135 145 370 380 Projective geometry, consistency 59—60 Projective geometry, finite 116 Projective geometry, foundations vii 1 53—54 62 78 80 95 106 111 116 120 128—133 284 338 371 379—380 Projective geometry, multidimensional vii 51—54 57 65 80 107 117 128—129 135 145 338 374 376 379 396 Protothetic 348 350 Provinces xvii. See also Emilia–Romagna; Piedmont; Tuscany; Sicily Provinces sentence See under sentence Puccini, Giacomo (1858–1924) 4 Pythagoras (569? B.C.–475? B.C.) 41 263 Pythagorean See under field Quadric See under surface. Quadrilateral See complete quadrilateral Quantifier 271 348 Quantifier elimination 351 361 Quantifier over sets 315 Quantifier prefix 271 Quasi-interpretable See under theory Queen's University 460 Rabin, Michael Oser (1931–) 352 417 Ranuccio I See Ranuccio I of Farnese Raschi, Leonida (1831–1917) 46 99 Rational number 392. See also under arithmetic Rausenberger, Otto (1852–19??) 263 445 Ray See half-line Razzaboni, Amilcare (1855–1920) 26 Real enumerative See under geometry Real-closed See under field Real-number arithmetic 257—258 263—264 276 278 285 288 289—292 Real-number arithmetic, Cantor 293 Real-number arithmetic, Dedekind 76 293—294 299 Real-number arithmetic, Pasch 293 Real-number arithmetic, Peano 293 334 Real-number arithmetic, Russell 293 Real-number arithmetic, Weierstrass 292 305 Realschule 7 Reciprocal radii see transformation: inversion. See also function: bijection Recursive definition See under definition Recursive function theory 315 Recursive proof See induction Reed College 369—370 Reflection 154 Reflection glide 245 248 Reflection hyperplane 140 Reflection line 139 147 155 164 176 Reflection plane 140 145 147 155 178 186—187 248 Reflection point 145 155 164 174—175 280 Reflection rotary 243 248. Reflexive See under relation Region See under Italy Regular open set 349 Reid, Constance (1917–) 85 100 445 460 Reinhardt, Curt (1855–1938?) 430 Relation 249 269 Relation, Pieri's see equidistance: ternary Relation, reflexive 165 Relation, symmetric 165 Relation, transitive 165 Relation, univocal 268 (see also function). See also betweenness; cyclic order; equality; equidistance; equilaterality; larger-than; order Renschuch, Bodo (19??–) 105 408 Representation 266. See also transformation Resta, Emilia Levi (1921–) 90—91 460 Reviews, sources of 402 Revista de mathematica See under journals Revolutions See 1848. Revue de metaphysique et de morale See under journals Revue des mathematiques See under journals Reye, Carl Theodor Reye (1838–1919) 57 71 72 99—100 106 136 137 139 418 445 448 453 Reyes Y Prosper, Ventura (1863–1922) 398 Ribaltamento See under transformation Ricco, Annibale (1844–1919) 17 32 37 398 445 Richard, Jules (1862–1956) 326 Riemann, Georg Friedrich Bernhard (1826–1866) 66 76 86 98—99 125 Riemann, Georg Friedrich Bernhard (1826–1866), sphere 140. See also under theorem Righi, Augusto (1850–1920) 8 9 25 100 397 409 445 451 461 Right angle see under angle Rindi, Scipione (1859–1952) 3 4 6—8 20 22 34 36 47 49 61 101 123—124 375 398—399 408 438 446 Rinow, Willi (1907–1979) 425 Rivista di matematica See under journals Rivista populare di politica, lettere e scienze sociali See under journals Rizzi, Fortunato (1880–1965) 99 446 Robertson, Edmund Frederick (1943–) 87 431 Robinson, Raphael Mitchel (1911–1995) 361—362 446 Rodriguez-Consuegra, Francisco A.(1951–) x 294 307 328 341 386 429 446 Roero, Clara Silvia (1952–) vi 11 18 32 69 74 95 341 418 428 446 Roero, Clara Silvia (1952–), Peano Cds vi 336 345 347 377—379 393—394 446 Rogers, Reginald Arthur Percy (1874–19??) 447 Rohn, Karl (1855–1921) 451 Rolland, Romain (1866–1944) 88—89 446 Romagnoli, Raffaello (19??–) x Roman Catholic Church xvii 4 Rome xvii xviii 11 Rome archives 459 Rome university 16 22—23 75 Rosario, university 91 Rosenthal, Arthur (1887–1959) 451 Ross, Robert Hemphill (1949–) 403 Rossi, Luigi (18??–????) 398 Rota, Gian-Carlo (1932–1999) 148 446 Rotary reflection See under reflection Rotation See under transformation Rothe, Rudolf Ernst (1873–1942) 378 443 Rowe, Charles Henry (1893–1943) 447 Rowe, David E.(1950–) x 56 446 Royden, Halsey Lawrence (1928–1993) 361 447 Ruffini, Ferdinando Paolo (1823–1908) 8 28 101 444 Ruffini, Paolo (1765–1822) 101 Ruled See under surface Russ, Steven (19??–) 405 Russell's antinomy 102 302 304—305 447 Russell's antinomy, Frege's response 302 304 417 Russell, Bertrand Arthur William (1872–1970) viii x 47 74 102—103 120 125 300 304—305 327 339 341—342 392 402 406 417 419—420 428 446—448 456 Russell, Bertrand Arthur William (1872–1970) on real numbers 289—290 293—294 Russell, Bertrand Arthur William (1872–1970), 1900 Paris epiphany 74 102 302 341 Russell, Bertrand Arthur William (1872–1970), 1903 Principles of Mathematics 38 102 129 249 290 294 302 304 328 338 386 392 Russell, Bertrand Arthur William (1872–1970), Archives 416 459 Russell, Bertrand Arthur William (1872–1970), letter from Pieri 307—308 386 398 441 459 Russell, Bertrand Arthur William (1872–1970), regard for Pieri v 2 38 129 328 338 343 Russell, Bertrand Arthur William (1872–1970), view of logic 386 307 327 386 Russell, Bertrand Arthur William (1872–1970), view of mathematics 307. See also under real-number arithmetic; Russell's antinomy; A.N.Whitehead Russo, Achille (1866–1955) 37 Ruziewicz, Stanis aw (1888–1941) 450 Saint-Saens, Camille (1835–1921) 88 Salesians of Don Bosco 460 Salkowski, Erich (1881–1943) 405 412 431—432 448 456 Salmon, George (1819–1904) 52 103 117—118 419 429 447 Saluta, Andrea (18??–19??) 40 104 410 447 Saluzzo, Giuseppe Angelo, Count of Monesiglio (1734–1810) 18 Sannia, Achille (1823–1892) 79 85 93 Sant'Andrea di Compito 6 44 47 49 459 Santagata, Domenico (1812–1901) 8 10 Sardinia kingdom xvii 18 Sardinia region xvii xix 16 SAS See under postulate Savi, Paolo (1798–1871) 70 Savoia, Savoja See Savoy Savoy dynasty xvii 18 Savoy, Carlo Emanuele Ii of (1634–1675) 18 Savoy, Umberto I of (1844–1900) 70 Savoy, Vittorio Amedeo III of (1725–1796) 18 Savoy, Vittorio Emmanuele II of (1820–1878) xvii 18 Savoy, Vittorio Emmanuele III of (1869–1947) 423 Scaccianoce, Rosario (1880–19??) 40 43 104 389 410 447 Scale determined by two points 155 212 354 Scandinavian Congress of Mathematicians, 1911 153 448 Scanlan, Michael (1957?–) 116 278 360 448 Schappacher, Norbert (19??–) 421 Schayer, W.(????–????) 348 452 Scheibner, Wilhelm (1826–1908) 430 Schepp, Adolf (1837–????) 418 Schiff, Hugo Josef (1834–1915) 332 Schilling, Friedrich Georg (1868–1950) 425 Schlegel, Viktor (1843–1905) 380 408—409 433—434 440 448 Schlesinger, Ludwig (1864–1933) 41 Schmid, Anne-Fran?oise (1949– ) 305 448 Schneewind, Jerome Borges (1930–) 428 Schoeneberg, Bruno (1906–1995) 87 408 Schoenflies, Arthur Moritz (1853–1928) 377 398 438—439 Scholz, Heinrich (1884–1956) 454 456 School, Hilbert vii ix 84—85 143 284 School, Peano vii 1 2 22 27 32 40 54 58—59 66 69 71—74 80 84 95 102 108 110 114 80 123 126—127 131 153 300—301 305 308 320 326 331 335—338 341—342 346 363—366 369 405 School, Segre vii ix 1 22 32 51 72 107 123 131 333 337—338 346 School, system see under Italy School, Tarski viii 58 113 352—353 356 361 367—368 370 School, Volterra 123. See also logical positivism; middle school; normal school; postulate: American theorists; technical school; Vienna Circle Schraubenbewegung See transformation: screw Schroeder, Friedrich Wilhelm Karl Ernst (1841–1902) 104 316 334 341 Schroeter, Heinrich Eduard (1829–1892) 95 105 Schubert, Hermann Caesar Hannibal (1848–1911) vii 52 104—105 112 325 396 398 408 417 424 448 453 456 Schubert, Hermann Caesar Hannibal (1848–1911), calculus 52 104 112 Schubring, Gert (19??–) 406 448 Schumann, Richard (1864–1945) 456 Schur, Friedrich (1856–1932) 41 86 99—100 105—106 124 148 263 398 448 453 Schur, Issai (1875–1941) 148 Schwabhaeuser, Wolfram (1931–1985) 350 354—357 360—362 448 Schwartze, Heinz (1924–2006) 84 448 Scorza, Bernardino Gaetano (1876–1939) 46—47 94 106 448 Scott, Charlotte Angas (1858–1931) 343 422 449 Screw See under transformation Scriba, Cristoph J.(1929–) 84 406 408 413 Scuola Reale Normale Superiore See under Pisa Secant space 377 395—396 Segment 128 146 195 272 335 394 Segment, open 277 Segment, projective 54 128 130 131 134—135 338. Segre, Beniamino (1903–1977) 98 449 Segre, Corrado (1863–1924) 20 36 42 55 69 107—108 118 383 393 398—399 410 428 440 449—450 460 Segre, Corrado (1863–1924) and Pieri's chair quest 23 26 28—29 Segre, Corrado (1863–1924), algebraic geometry v vii ix 51 53 72 78—79 87 89 91 105 123—124 133 333 405 414 418 449 Segre, Corrado (1863–1924), projective geometry 53 80 123 335 393 Segre, Corrado (1863–1924), rift with Peano 108 114 337—338 346 428 434 449 Segre, Corrado (1863–1924), supporting Pieri 56—58 131 135 145—146 157 160 376 380—381 436—437 441—442. Segre, Michael (1950–) 291—292 301 320 332 335—337 342 346 449 Seidenberg, Abraham (1916–1988) 96 449 Semicircle 252 Sempronio 268 Senate See under Italy Sense 247 251—252. Sentence, 271 373 Sentence, classification by quantifier prefix 271 276—277 282—283 Sentence, existential 271 Sentence, universal 271 Separation See cyclic order Sequence, fundamental See fundamental sequence Sequent of natural number 311 324 Series, fundamental See fundamental sequence Sernesi, Edoardo (19??–) See under Brigaglia Serret, Joseph Alfred (1819–1885) 78 Set theory in Dedekind 77 293 299 305 314—315 Set theory in Point and Sphere 157 294 305 350 352 360 Set theory, antinomies 69 304 Set theory, axiomatic 290 300 304 Set theory, Cantor's development 296—297 299 305 Set theory, general usage 313 316 324 360 Set theory, Pieri's natural-number model 61 290 Set theory, Tarski's work 113 348. Seton-Watson, Christopher (1918–) 43—44 449 Severi, Francesco (1879–1961) 42 77 104 114 290 398 450 Severini, Carlo (1872–1951) 34 98 108 450 Sforza, Giuseppe (18??–1927) 306 398 Shadow of line 202 Shadow of plane 204 Shadow of point 200 Siacci, Francesco (1839–1907) 20 27 91 109 332 403 Sibirani, Filippo (1880–1957) 46 63 98 109 454 Sicilies, Kingdom of Two xvii 41 Sicily xvii xix 16 41 Side of line in plane 203 Side of plane 204 Side of point on line 202 Signed integer See under arithmetic Signorini, Antonio (1888–1963) 110 450 Silla, Lucio (1872–1959) 88 450 Similar figures 207 160 Similarity 57 139 154 161 206—207 281 Similarity classification 278 284 Similarity in hyperbolic geometry 361 Simply infinite system 300 314 Simply infinite system, existence 300 307 314 Sinaceur, Hourya (1940–) 351 450 Singleton See under symbol Singular point vii 12 50—51 375 Sinigallia, Luigi (1864–1944) 46 110 Sinsheimer, Thomas (1943–) x
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