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

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Ќазвание: Legacy of Mario Pieri in Geometry and Arithmetic

јвторы: Marchisotto E.A., Smith J.T.

јннотаци€:

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.


язык: en

–убрика: ћатематика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 2007

 оличество страниц: 420

ƒобавлена в каталог: 14.05.2008

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ѕредметный указатель
$LRM^3D^2$      405
$\mathbb{Z}_n$      See integer modulo n
1848 revolutions      66 75 82Ч83 85 101
Abscissa      257 285
Absolute geometry      See under geometry
Abstraction, definition by      see under definition. See also under symbol
Academia pro Interlingua      See under journals; Giuseppe Peano
Ackerman, Michael (19??Ц)      426
Acknowledgments      x 459
Acoli, Graziadio Isaia (1829Ц1907)      97
Adamson, Iain T.(19??Ц)      421
Addition      See sum
Affinity, circular      See under transformation
Afghanistan      5
Agazzi, Evandro (1934Ц)      365 402 406
Air power      6 119
Algebraic curve      See under curve
Algebraic geometry      See under geometry
Algebraic number theory      76 84
Algebraic surface      See under surface
Alighieri, Dante (1265Ц1321)      395
Almagia, Virginia      See Virginia Volterra
Amaldi, Ugo (1875Ц1957)      65 98 402
Amaldi, Ugo (1875Ц1957), work with Enriques      368 415Ч416
Amato, Vincenzo (1881Ц1963)      72 402
Amaturo, Enrico (1863Ц19??)      42
American Mathematical Society      43 388
Amodeo, Federico (1859Ц1946)      20 62 107
Amodeo, Federico (1859Ц1946), correspondence      383 432 438
Amodeo, Federico (1859Ц1946), rivalry with Pieri      22Ч23 29 32 36
Analysis, arithmetization      291Ч292
Analysis, functional      see functional analysis
Analysis, Peano's work      301 334 337 365
Analysis, use of set theory      296 298
Anastasio, Angiolina      See Angiolina PIERI
Anastasio, Paolo (18??Ц19??)      37 see
Anastasio, Virginia Pieri (1867Ц1929?)      5 17 20 36 37 459
Anastasio, Virginia Pieri (1867Ц1929?), marriage      5 27 454
Andreini, Angelo (18??Ц19??)      10 62
Anellis, Irving H.(19??Ц )      302 402
Angelelli, Ignacio (19??Ц)      417
angle      146 149 272
Angle of triangle      205. See also under symbol
Angle, bisector      220
Angle, concave, convex, or right      204
Annuario scientifico ed industriale      See under journals
Anti-inversion      See under transformation
Antichi, Petronilla (18??Ц????)      4
Anticongruence      See under transformation
Anticongruent figures      150
Antihomography      See under transformation
Antinomies, Burali Ч Forti's      69
Antinomies, Burali Ч Forti's, responses to      302 304.
Antipolar plane      238
Antirotation      See reflection: rotary
Antitranslation      See reflection: glide
Applied mathematics      87 365
Appolonius of Perga (225Ц190 B.C.)      121 139
Aprile, Giorgio Antonio (1884Ц1943)      40 42 63 92 398 402 410
ARC      252
Archimedes (287Ц212 B.C.)      41 121 403 421
Archimedes (287Ц212 B.C.), principle      see under postulate
Archival institutions      ix 40 459
Archive      See Mario Pieri: Nachlass
Area      263
Aristotle (384Ц322 B.C.)      266 305 347
Arithmetic, cardinal      296Ч297
Arithmetic, complex      125 299
Arithmetic, integer, modulo n      320
Arithmetic, ordinal      297Ч298 387
Arithmetic, rational      77 289 292 294 299 334 392
Arithmetic, signed-integer      77 299 334.
Armano, Tiziana (19??Ц)      vi 446
Arrighi, Gino (1906Ц2001)      vi ix 6Ч7 36 42Ч44 63 382 388 398Ч399 403 443 460.
Arzela, Cesare (1847Ц1912)      10 63 98 109 398 426
Arzela, Cesare (1847Ц1912), Bologna affair      25Ч29
Asburgo      See Habsburg
Ascending      See progression
Aschieri, Ferdinando (1844Ц1907)      22Ч23 25 29
Askey, Richard Allen (1933Ц)      415
Aspray, William (1952Ц)      116 403
Associativity      270 294 395
August, Friedrich Wilhelm Oscar (18??Ц????)      374
Ausdehnungslehre      83Ч84 334
Aussant-Cara, P. (18??Ц19??)      426
Austin, John Langshaw (1911Ц1960)      417
Austria      xviiЧxix
Automorphism      358 360
Avellone, Maurizio (19??Ц)      127 129 403
Axiom      54 (see also postulate)
Axiom of Choice      315 360
Axiom of determinacy      360
Axiom of foundation      323
Axiom of infinity      300 307
Axiomatic method in general      v vii 87 95 291 350 370
Axiomatic method in Hilbert      84 277
Axiomatic method in Peano      300Ч301 334Ч335
Axiomatic method in Pieri      54 124Ч127.
Axis of rotation      183
Axis of symmetry      176
Baccarini, Pasquale (1858Ц1919)      32
Baccelli, Guido (1832Ц1916)      26Ч27 29 63Ч64 456
Bachi, Albina      See Albina LEVI.
Bachmann, Friedrich (1909Ц1982)      284 403 427
Balbo, Italo (1896Ц1940)      6
Baldwin, James Mark (1861Ц1934)      124 343 403
Baltzer, Richard (1818Ц1887)      93 403 430
Balzac, Honore de (1799Ц1850)      97
Bar-Hillel, Yehoshua (1915Ц1975)      403
Barbagli, Marzio (1938Ц)      7 15Ч17 403
Barbarin, Paul (1855Ц1931)      41 64 403 407
Barberis, Bruno (1953?Ц)      109 110 403
Baridon, Paolo (18??Ц19??)      408
Barker, William A.(????Ц????)      120 404
Barsocchini, Domenico (1777Ц1862)      4 96 443
Bartorelli, Antonio (18??Ц19??)      46 64
Barycentric calculus      See under calculus
Basso, Giuseppe (1842Ц1895)      20 64 332 416
Bastian, Beppina      See Beppina PIERI.
Battaglini, Giuseppe (1826Ц1894)      78Ч79 398
Battaglini, Giuseppe (1826Ц1894), Giornale di      see journals: Giornale di matematiche
Bauer-Mengelrerg, Stefan (1927Ц1996)      417 456
Beaufront, Louis de (1855Ц1935)      74 404
Beck, Hans (1876Ц1942)      381 443 454
Begriffsschrift      See under Frege
Bekemeier, Bernd (19??Ц )      292 404
Bellavitis, Giusta (1803Ц1880)      117 139 404
Beltrami, Eugenio (1835Ц1900)      65 97
Beman, Wooster Woodruff (1850Ц1922)      413
Benz, Walter (1931Ц)      143
Berkeley      See University of California
Berlin, Imperial Library      2
Bernays, Paul Isaac (1888Ц1977)      421Ч422
Bernstein, Felix (1878Ц1956)      See under theorem
Bertini, Eugenio (1846Ц1933)      30 65 78 398 404
Bertini, Eugenio (1846Ц1933) as referee      22Ч23 26 28Ч29 31 42 404
Bertrand, Joseph Louis Franiois (1822Ц1900)      78
Berzolari, Luigi (1863Ц1949)      22 65Ч66 107 398 405
Berzolari, Luigi (1863Ц1949) at Pavia      31Ч32 36 94
Berzolari, Luigi (1863Ц1949) at Turin      20 23 26 89
Berzolari, Luigi (1863Ц1949), Encyclopedia      69 71 81 95 327 404
Beth, Evert Willem (1909Ц1964)      300 304Ч305 314Ч315 319 404
Bettazzi, Rodolfo (1861Ц1941)      10 12 18 20 66 337 404
Betti, Enrico (1823Ц1892)      12 13 66 406 409 437
Betti, Enrico (1823Ц1892), works by      167 374 398Ч399 404 416
Betweenness      146 334Ч335 354 358 360Ч362
Betweenness on arc      252
Betweenness undefined      149 274 277 288 351 353.
Betweenness, Pieri's definition      152 195 272 357
Bezout, Etienne (1739Ц1783)      53 404.
Biagini, Roderigo (18??Ц19??)      398
Bianchi, Francesco Saverio (1827Ц1908)      67
Bianchi, Luigi (1856Ц1928)      13 34 67 398 409 461
Bianchi, Luigi (1856Ц1928), Pieri's teacher      v 12 50 374Ч375 437
Bibliographic citations      ix 4 373 401Ч403
Bibliographic citations in chapter 3      62 157 167 416
Bieberbach, Ludwig Georg Elias Moses (1886Ц1982)      412
Biermann, Kurt-Reinhold (1919Ц2002)      77 404
Bijection      See under function
Binary relations      See under primitive notions
Biographical sketches, x      3 4 62
Birational, equivalence      see under surface. See also under geometry; transformation
bisector      See under angle
Black, Max (1909Ц1988)      404 432
Blaiklock, Mary (18??Ц19??)      446
Blair, David E.(1940Ц)      138Ч141 404
Blanc, Charles (19??Ц)      416
Blanchet, Marie Parfait Alphonse (1813Ц????)      426
Blaschke, Wilhelm Johann Eugen (1885Ц1962)      425
Blumberg, Albert Emanuel (????Ц19??)      127 405
Blumenthal, Otto (1876Ц1944)      60 405
Boccherini, Luigi (1743Ц1805)      4
Bodewig, Ewald (1902Ц????)      112 405
Boggio -LERA, Enrico (1862Ц1956)      10 67Ч68
Boggio, Tomasso (1877Ц1963)      31 34 398
Bohlmann, Georg (1869Ц1928)      418
Boi, Luciano (1957Ц)      129 133Ч134 405
Bollati Boringhieri Editore      460
Bollettino di bibliografia e storia della scienza      See under journals
Bologna      xvii xviii 7Ч8 11
Bologna affair      25Ч28
Bologna, Royal Technical Institute      7Ч8 459. university
Bologna, university of      10Ч11 16 459
Bologna, university of, faculty renaissance      8 63 70 75 98
Bologna, university of, Pieri's chair quest      25Ч28
Bolondi, Giorgio (19??Ц)      17 405
Bolyai, Farkas Wolfgang (1775Ц1856)      209 405.
Bolyai, Janos (1802Ц1860)      125 155 405
Bolzano, Bernard Placidus Johann Nepomuk (1781Ц1848)      291Ч292 300 405 450
Bompiani, Enrico (1889Ц1975)      66 405
Bonaccorso, G.(18??Ц19??)      33
Bonaparte, Napoleon (1769Ц1821)      xvii 11 18 41
Bonfante, Giuliano (1904Ц1983)      4 5 8 20 49 97 405 444
Bonola, Roberto (1874Ц1911)      327
Boole, George (1815Ц1864)      316 334
Boolos, George Stephen (1940Ц1996)      299 318 405
Borbon, Borbone      See Bourbon
Bordiga, Giovanni (1854Ц1933)      42
Bordoni, Antonio (1789Ц1860)      75
Borel, Felix Edouard Justin Emile Borel (1871Ц1956)      See under theorem
Borga, Marco (????Ц )      x 60 147 156 403 405Ч406
Borga, Marco (????Ц ), Borga & Palladino 1992      54 58 153 301 316 326 335 406
Borkowski, Ludwik Stefan (1914Ц1993)      428
Borodin, Alexandr Ivanovich (Ѕородин, јлександр »ванович, 19??Ц)      41 406
Borsuk, Karol (1905Ц1982)      361 406
Boschi, Pietro (1833Ц1918)      8 10 68
Bosio (cav. uff., 18??Ц19??)      48
Bottazzini, Umberto (1947Ц)      92 131 406
Bottazzini, Umberto (1947Ц), Enriques & Castelnuovo      70 72Ч73 80
Bottazzini, Umberto (1947Ц), Enriques & Castelnuovo, Bologna affair      23 25Ч28 31Ч32
Bottazzini, Umberto (1947Ц), Enriques & Castelnuovo, otherwise involving Pieri      8 22 36 38 42
Boundary of triangle      205
Bourbaki, Nicolas (pseudonym)      115 294 406
Bourbon dynasty      xvii 41
Bourbon, Carlo Lodovico of (1799Ц1883)      xvii 41
Bourbon, Ferdinando II of (1810Ц1859)      41
Bourbon, Maria Luisa of (1782Ц1824)      xvii 41
Boutroux, Emile (1845Ц1921)      381 406 423 440
Brancoli, Giuseppe (18??Ц????)      5
Brancoli, Teresa Pieri (1853Ц1942?)      5Ч6 390Ч391
Braunmuehl, Anton, Edler von (1853Ц1908)      375 438 446
Brazil      6 17 36 44
Bredow, Ilse (????Ц????)      448
Bresadola, Marco (1969Ц)      100 406
Breveglieri, Bruno (1942Ц)      406
Brigaglia, Aldo (1945Ц)      53 129 403 406 460
Brigaglia, Aldo (1945Ц), Brigaglia & Ciliberto 1995      52 80 406
Brigaglia, Aldo (1945Ц), Brigaglia & Masotto 1982      1 42 131 406
Brigaglia, Aldo (1945Ц), Brigaglia, Ciliberto, & Sernesi 2005      74 92 106 406
Brill, Alexander Wilhelm von (1842Ц1935)      65
Brioschi, Francesco (1824Ц1897)      66 75 167 416
Broadbent, Thomas Arthur Alan (1903Ц1973)      103 406
Broden, Torsten (1857Ц1931)      68 124 153Ч154 407 436
Browder, Felix Earl (1928Ц)      407 424
Brown, Harold Chapman (1879Ц1943)      290 382 407 442
Bruno, Giuseppe (1828Ц1893)      20 22Ч23 68Ч69 107 332 375 398 438 446
Bucca, Lorenzo (18??Ц19??)      32 37
Buek, Otto (1873Ц1966)      47 398
Buetzberger, Friedrich (18??Ц19??)      139 408
Buhl, Adolphe (1878Ц1949)      64 407
Bulletin des sciences mathematiques      See under journals
Burali-Forti, Cesare (1861Ц1931)      vi 55 460
Burali-Forti, Cesare (1861Ц1931), geometry      52 58 156
Burali-Forti, Cesare (1861Ц1931), life      12 20 69 398 429
Burali-Forti, Cesare (1861Ц1931), logic      301 306Ч307 316 321 326Ч328
Burali-Forti, Cesare (1861Ц1931), Peano school      22 337 341Ч342
Burali-Forti, Cesare (1861Ц1931), vector analysis      46Ч47 53 378 392 428.
Burau, Werner (1906Ц1994)      84 87 105 111 112 408 448
Burkhardt, Heinrich (1861Ц1914)      430
Burstall, Rod M.(1934Ц)      313 408
Bussey, William Henry (1879Ц19??)      116
Caemmerer, Hanna von      See Hanna NEUMANN
Caio      268
Cajori, Florian (1859Ц1930)      313 315 408
Calapso, Renato (1901Ц1976)      92 408
Calculus of variations      123. See also differential and integral calculus and under SCHUBERT
Calculus, barycentric      93
Calculus, geometric      see under Giuseppe Peano
Calculus, mathematics as uninterpreted      59
Caldarera, Gaetano (1865Ц19??)      34 40 69Ч70
Caldarera, Grazia Macrina (1880Ц19??)      40 70 408 410
California State University      x
California, University of      See University of California
Cambria, Maria (1923Ц)      114
Camivi, Mario (18??Ц19??)      397 442
Campedelli, Luigi (1903Ц1978)      12 74 101 408
Campetti family      6 36 39 44 459
Campetti, Annarosa (1920Ц2004)      6
Campetti, Beatrice Giusfredi (1894Ц1995)      6
Campetti, Francesco (1969Ц)      x 5 6 17 36 43 97 408 412 444 454
Campetti, Gaetano Enrico (1890Ц1980)      6 39 42 44 48 390 442
Campetti, Gemma Pieri (1863Ц1955?)      5Ч6 36 39 44 47 390 408 411 459
Campetti, Ghigo      See Ottorino Campetti
Campetti, Marco (1924Ц)      x 6 47 390Ч391 397 436Ч437 442Ч443 459
Campetti, Ottorino (1888Ц1947)      6 36 39 42Ч44 46 48 63 390Ч391 443
Campetti, Pellegrino (1892Ц1974)      6 36 39 43
Campetti, Umberto (1863Ц1929)      5Ч6 17 36 44
Campetti, Vittorio (1930Ц)      x 4 6 411 459
Cancer      See throat cancer
Candido, Giacomo (1871Ц1941)      147 408
Cantor, Georg Ferdinand Ludwig Philipp (1845Ц1918)      408Ч409 413 420
Cantor, Georg Ferdinand Ludwig Philipp (1845Ц1918), infinite sets      69 117 296Ч298 300 305Ч306
Cantor, Georg Ferdinand Ludwig Philipp (1845Ц1918), logic      299 302 306 313
Cantor, Georg Ferdinand Ludwig Philipp (1845Ц1918), real numbers      254 263 289 290 292Ч294.
Cantor, Moritz Benedikt (1829Ц1920)      281 409
Capellini, Giovanni (1833Ц1922)      8 29 70 414 454
Caratheodory, Constantin (1873Ц1950)      140 404 409
Cardani, Pietro (1858Ц1925)      100 391 409
cardinal number      296 315.
Carducci, Giosue (1835Ц1907)      96Ч97
Carlo Emabuele II      See Carlo Emanuele II of Savoy
Carlo Lodovico      See Carlo Lodovico of Bourbon
Carruccio, Ettore (1908Ц1980)      67 92 409
Cartesian geometry      See under geometry
Casati, Gabrio (1798Ц1873)      See under laws
Casorati, Felice (1835Ц1890)      65Ч66 91 97
Cassina, Ugo (1897Ц1964)      71 139 319 409 436 450
Cassina, Ugo (1897Ц1964) on Peano      337 345Ч346 365
Cassina, Ugo (1897Ц1964) on Pieri      2Ч3 22 31 34 42 284Ч285 307 326 399
Castellano, Filiberto (1860Ц1919)      20 71 79 334 337 410
1 2 3 4 5 6 7 8
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