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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.
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405 See integer modulo n 1848 revolutions 66 75 82—83 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??–) 426 Acknowledgments x 459 Acoli, Graziadio Isaia (1829–1907) 97 Adamson, Iain T.(19??–) 421 Addition See sum Affinity, circular See under transformation Afghanistan 5 Agazzi, Evandro (1934–) 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 (1265–1321) 395 Almagia, Virginia See Virginia Volterra Amaldi, Ugo (1875–1957) 65 98 402 Amaldi, Ugo (1875–1957), work with Enriques 368 415—416 Amato, Vincenzo (1881–1963) 72 402 Amaturo, Enrico (1863–19??) 42 American Mathematical Society 43 388 Amodeo, Federico (1859–1946) 20 62 107 Amodeo, Federico (1859–1946), correspondence 383 432 438 Amodeo, Federico (1859–1946), rivalry with Pieri 22—23 29 32 36 Analysis, arithmetization 291—292 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??–19??) 37 see Anastasio, Virginia Pieri (1867–1929?) 5 17 20 36 37 459 Anastasio, Virginia Pieri (1867–1929?), marriage 5 27 454 Andreini, Angelo (18??–19??) 10 62 Anellis, Irving H.(19??– ) 302 402 Angelelli, Ignacio (19??–) 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??–????) 4 Anticongruence See under transformation Anticongruent figures 150 Antihomography See under transformation Antinomies, Burali — Forti's 69 Antinomies, Burali — Forti's, responses to 302 304. Antipolar plane 238 Antirotation See reflection: rotary Antitranslation See reflection: glide Applied mathematics 87 365 Appolonius of Perga (225–190 B.C.) 121 139 Aprile, Giorgio Antonio (1884–1943) 40 42 63 92 398 402 410 ARC 252 Archimedes (287–212 B.C.) 41 121 403 421 Archimedes (287–212 B.C.), principle see under postulate Archival institutions ix 40 459 Archive See Mario Pieri: Nachlass Area 263 Aristotle (384–322 B.C.) 266 305 347 Arithmetic, cardinal 296—297 Arithmetic, complex 125 299 Arithmetic, integer, modulo n 320 Arithmetic, ordinal 297—298 387 Arithmetic, rational 77 289 292 294 299 334 392 Arithmetic, signed-integer 77 299 334. Armano, Tiziana (19??–) vi 446 Arrighi, Gino (1906–2001) vi ix 6—7 36 42—44 63 382 388 398—399 403 443 460. Arzela, Cesare (1847–1912) 10 63 98 109 398 426 Arzela, Cesare (1847–1912), Bologna affair 25—29 Asburgo See Habsburg Ascending See progression Aschieri, Ferdinando (1844–1907) 22—23 25 29 Askey, Richard Allen (1933–) 415 Aspray, William (1952–) 116 403 Associativity 270 294 395 August, Friedrich Wilhelm Oscar (18??–????) 374 Ausdehnungslehre 83—84 334 Aussant-Cara, P. (18??–19??) 426 Austin, John Langshaw (1911–1960) 417 Austria xvii—xix Automorphism 358 360 Avellone, Maurizio (19??–) 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 300—301 334—335 Axiomatic method in Pieri 54 124—127. Axis of rotation 183 Axis of symmetry 176 Baccarini, Pasquale (1858–1919) 32 Baccelli, Guido (1832–1916) 26—27 29 63—64 456 Bachi, Albina See Albina LEVI. Bachmann, Friedrich (1909–1982) 284 403 427 Balbo, Italo (1896–1940) 6 Baldwin, James Mark (1861–1934) 124 343 403 Baltzer, Richard (1818–1887) 93 403 430 Balzac, Honore de (1799–1850) 97 Bar-Hillel, Yehoshua (1915–1975) 403 Barbagli, Marzio (1938–) 7 15—17 403 Barbarin, Paul (1855–1931) 41 64 403 407 Barberis, Bruno (1953?–) 109 110 403 Baridon, Paolo (18??–19??) 408 Barker, William A.(????–????) 120 404 Barsocchini, Domenico (1777–1862) 4 96 443 Bartorelli, Antonio (18??–19??) 46 64 Barycentric calculus See under calculus Basso, Giuseppe (1842–1895) 20 64 332 416 Bastian, Beppina See Beppina PIERI. Battaglini, Giuseppe (1826–1894) 78—79 398 Battaglini, Giuseppe (1826–1894), Giornale di see journals: Giornale di matematiche Bauer-Mengelrerg, Stefan (1927–1996) 417 456 Beaufront, Louis de (1855–1935) 74 404 Beck, Hans (1876–1942) 381 443 454 Begriffsschrift See under Frege Bekemeier, Bernd (19??– ) 292 404 Bellavitis, Giusta (1803–1880) 117 139 404 Beltrami, Eugenio (1835–1900) 65 97 Beman, Wooster Woodruff (1850–1922) 413 Benz, Walter (1931–) 143 Berkeley See University of California Berlin, Imperial Library 2 Bernays, Paul Isaac (1888–1977) 421—422 Bernstein, Felix (1878–1956) See under theorem Bertini, Eugenio (1846–1933) 30 65 78 398 404 Bertini, Eugenio (1846–1933) as referee 22—23 26 28—29 31 42 404 Bertrand, Joseph Louis Franiois (1822–1900) 78 Berzolari, Luigi (1863–1949) 22 65—66 107 398 405 Berzolari, Luigi (1863–1949) at Pavia 31—32 36 94 Berzolari, Luigi (1863–1949) at Turin 20 23 26 89 Berzolari, Luigi (1863–1949), Encyclopedia 69 71 81 95 327 404 Beth, Evert Willem (1909–1964) 300 304—305 314—315 319 404 Bettazzi, Rodolfo (1861–1941) 10 12 18 20 66 337 404 Betti, Enrico (1823–1892) 12 13 66 406 409 437 Betti, Enrico (1823–1892), works by 167 374 398—399 404 416 Betweenness 146 334—335 354 358 360—362 Betweenness on arc 252 Betweenness undefined 149 274 277 288 351 353. Betweenness, Pieri's definition 152 195 272 357 Bezout, Etienne (1739–1783) 53 404. Biagini, Roderigo (18??–19??) 398 Bianchi, Francesco Saverio (1827–1908) 67 Bianchi, Luigi (1856–1928) 13 34 67 398 409 461 Bianchi, Luigi (1856–1928), Pieri's teacher v 12 50 374—375 437 Bibliographic citations ix 4 373 401—403 Bibliographic citations in chapter 3 62 157 167 416 Bieberbach, Ludwig Georg Elias Moses (1886–1982) 412 Biermann, Kurt-Reinhold (1919–2002) 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 (1909–1988) 404 432 Blaiklock, Mary (18??–19??) 446 Blair, David E.(1940–) 138—141 404 Blanc, Charles (19??–) 416 Blanchet, Marie Parfait Alphonse (1813–????) 426 Blaschke, Wilhelm Johann Eugen (1885–1962) 425 Blumberg, Albert Emanuel (????–19??) 127 405 Blumenthal, Otto (1876–1944) 60 405 Boccherini, Luigi (1743–1805) 4 Bodewig, Ewald (1902–????) 112 405 Boggio -LERA, Enrico (1862–1956) 10 67—68 Boggio, Tomasso (1877–1963) 31 34 398 Bohlmann, Georg (1869–1928) 418 Boi, Luciano (1957–) 129 133—134 405 Bollati Boringhieri Editore 460 Bollettino di bibliografia e storia della scienza See under journals Bologna xvii xviii 7—8 11 Bologna affair 25—28 Bologna, Royal Technical Institute 7—8 459. university Bologna, university of 10—11 16 459 Bologna, university of, faculty renaissance 8 63 70 75 98 Bologna, university of, Pieri's chair quest 25—28 Bolondi, Giorgio (19??–) 17 405 Bolyai, Farkas Wolfgang (1775–1856) 209 405. Bolyai, Janos (1802–1860) 125 155 405 Bolzano, Bernard Placidus Johann Nepomuk (1781–1848) 291—292 300 405 450 Bompiani, Enrico (1889–1975) 66 405 Bonaccorso, G.(18??–19??) 33 Bonaparte, Napoleon (1769–1821) xvii 11 18 41 Bonfante, Giuliano (1904–1983) 4 5 8 20 49 97 405 444 Bonola, Roberto (1874–1911) 327 Boole, George (1815–1864) 316 334 Boolos, George Stephen (1940–1996) 299 318 405 Borbon, Borbone See Bourbon Bordiga, Giovanni (1854–1933) 42 Bordoni, Antonio (1789–1860) 75 Borel, Felix Edouard Justin Emile Borel (1871–1956) See under theorem Borga, Marco (????– ) x 60 147 156 403 405—406 Borga, Marco (????– ), Borga & Palladino 1992 54 58 153 301 316 326 335 406 Borkowski, Ludwik Stefan (1914–1993) 428 Borodin, Alexandr Ivanovich (Áîðîäèí, Àëåêñàíäð Èâàíîâè÷, 19??–) 41 406 Borsuk, Karol (1905–1982) 361 406 Boschi, Pietro (1833–1918) 8 10 68 Bosio (cav. uff., 18??–19??) 48 Bottazzini, Umberto (1947–) 92 131 406 Bottazzini, Umberto (1947–), Enriques & Castelnuovo 70 72—73 80 Bottazzini, Umberto (1947–), Enriques & Castelnuovo, Bologna affair 23 25—28 31—32 Bottazzini, Umberto (1947–), 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 (1799–1883) xvii 41 Bourbon, Ferdinando II of (1810–1859) 41 Bourbon, Maria Luisa of (1782–1824) xvii 41 Boutroux, Emile (1845–1921) 381 406 423 440 Brancoli, Giuseppe (18??–????) 5 Brancoli, Teresa Pieri (1853–1942?) 5—6 390—391 Braunmuehl, Anton, Edler von (1853–1908) 375 438 446 Brazil 6 17 36 44 Bredow, Ilse (????–????) 448 Bresadola, Marco (1969–) 100 406 Breveglieri, Bruno (1942–) 406 Brigaglia, Aldo (1945–) 53 129 403 406 460 Brigaglia, Aldo (1945–), Brigaglia & Ciliberto 1995 52 80 406 Brigaglia, Aldo (1945–), Brigaglia & Masotto 1982 1 42 131 406 Brigaglia, Aldo (1945–), Brigaglia, Ciliberto, & Sernesi 2005 74 92 106 406 Brill, Alexander Wilhelm von (1842–1935) 65 Brioschi, Francesco (1824–1897) 66 75 167 416 Broadbent, Thomas Arthur Alan (1903–1973) 103 406 Broden, Torsten (1857–1931) 68 124 153—154 407 436 Browder, Felix Earl (1928–) 407 424 Brown, Harold Chapman (1879–1943) 290 382 407 442 Bruno, Giuseppe (1828–1893) 20 22—23 68—69 107 332 375 398 438 446 Bucca, Lorenzo (18??–19??) 32 37 Buek, Otto (1873–1966) 47 398 Buetzberger, Friedrich (18??–19??) 139 408 Buhl, Adolphe (1878–1949) 64 407 Bulletin des sciences mathematiques See under journals Burali-Forti, Cesare (1861–1931) vi 55 460 Burali-Forti, Cesare (1861–1931), geometry 52 58 156 Burali-Forti, Cesare (1861–1931), life 12 20 69 398 429 Burali-Forti, Cesare (1861–1931), logic 301 306—307 316 321 326—328 Burali-Forti, Cesare (1861–1931), Peano school 22 337 341—342 Burali-Forti, Cesare (1861–1931), vector analysis 46—47 53 378 392 428. Burau, Werner (1906–1994) 84 87 105 111 112 408 448 Burkhardt, Heinrich (1861–1914) 430 Burstall, Rod M.(1934–) 313 408 Bussey, William Henry (1879–19??) 116 Caemmerer, Hanna von See Hanna NEUMANN Caio 268 Cajori, Florian (1859–1930) 313 315 408 Calapso, Renato (1901–1976) 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 (1865–19??) 34 40 69—70 Caldarera, Grazia Macrina (1880–19??) 40 70 408 410 California State University x California, University of See University of California Cambria, Maria (1923–) 114 Camivi, Mario (18??–19??) 397 442 Campedelli, Luigi (1903–1978) 12 74 101 408 Campetti family 6 36 39 44 459 Campetti, Annarosa (1920–2004) 6 Campetti, Beatrice Giusfredi (1894–1995) 6 Campetti, Francesco (1969–) x 5 6 17 36 43 97 408 412 444 454 Campetti, Gaetano Enrico (1890–1980) 6 39 42 44 48 390 442 Campetti, Gemma Pieri (1863–1955?) 5—6 36 39 44 47 390 408 411 459 Campetti, Ghigo See Ottorino Campetti Campetti, Marco (1924–) x 6 47 390—391 397 436—437 442—443 459 Campetti, Ottorino (1888–1947) 6 36 39 42—44 46 48 63 390—391 443 Campetti, Pellegrino (1892–1974) 6 36 39 43 Campetti, Umberto (1863–1929) 5—6 17 36 44 Campetti, Vittorio (1930–) x 4 6 411 459 Cancer See throat cancer Candido, Giacomo (1871–1941) 147 408 Cantor, Georg Ferdinand Ludwig Philipp (1845–1918) 408—409 413 420 Cantor, Georg Ferdinand Ludwig Philipp (1845–1918), infinite sets 69 117 296—298 300 305—306 Cantor, Georg Ferdinand Ludwig Philipp (1845–1918), logic 299 302 306 313 Cantor, Georg Ferdinand Ludwig Philipp (1845–1918), real numbers 254 263 289 290 292—294. Cantor, Moritz Benedikt (1829–1920) 281 409 Capellini, Giovanni (1833–1922) 8 29 70 414 454 Caratheodory, Constantin (1873–1950) 140 404 409 Cardani, Pietro (1858–1925) 100 391 409 cardinal number 296 315. Carducci, Giosue (1835–1907) 96—97 Carlo Emabuele II See Carlo Emanuele II of Savoy Carlo Lodovico See Carlo Lodovico of Bourbon Carruccio, Ettore (1908–1980) 67 92 409 Cartesian geometry See under geometry Casati, Gabrio (1798–1873) See under laws Casorati, Felice (1835–1890) 65—66 91 97 Cassina, Ugo (1897–1964) 71 139 319 409 436 450 Cassina, Ugo (1897–1964) on Peano 337 345—346 365 Cassina, Ugo (1897–1964) on Pieri 2—3 22 31 34 42 284—285 307 326 399 Castellano, Filiberto (1860–1919) 20 71 79 334 337 410
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