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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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Montanari, Enrica See Enrica Pieri Montesano, Domenico (1863–1930) 36 40 42 94 430 448 Montesano, Domenico (1863–1930) and Pieri's chair quest 22 25—27 29 398 Montgomery, Deane (1909–1992) 116 430 Moore, Eliakim Hastings (1862–1932) 116 342 Moore, Gregory H.(1944–) 59 351 420 430 Moore, Robert Lee (1882–1974) 116 342 351 431 Moraw, Peter (1935–) 420 436 Morrice, George Gavin (1859–1936) 425 Morrison, David Robert (1955–) 426 450 Mossotti, Ottaviano Fabrizio (1791–1863) 66 78 Mostowski, Andrzej (1913–1975) See hierarchy Motion 139 161 248 271 394 Motion, direct 57 145—147 150 152 271 278 280—281 338 340 Motion, indirect 145—146 271 Mueller, Felix (1843–1928) 416 423 455 Multidimensional See under differential and integral calculus; geometry; projective geometry Multiplication See product Multiplicity See under intersection MUSIC 4 7 70 76 83 88 92—93 101 103 Mussolini, Benito (1883–1945) 119 366 Nachlass See under Mario Pieri Nagel, Ernest (1901–1985) 128 418 431 Nannei, Enrico (1864–1961) 398 Naples xvii xviii 41 Naples university 5 16 22 25 Napoleon See Bonaparte Napoleonic wars, xvii 4 11 18 41 Napolitani, Pier Daniele (1951–) x Nardi Dei, Angiolo (1833–1913) 12 74 94 Nardini, Rodolfo (18??–19??) 385 Nastasi, Pietro (1941–) 63 65 73 88 101 119 414 420 431 460 Natorp, Paul Gerhard (1854–1924) 328 423 431 Natural-number arithmetic 291 294 Natural-number arithmetic, Cantor's theories 297 Natural-number arithmetic, consistency 60 85 290 306 see Natural-number arithmetic, Dedekind's theory see under Julius Dedekind Natural-number arithmetic, foundation 290 302 313 Natural-number arithmetic, Frege's theory 298 305 Natural-number arithmetic, Grassmann's work 84 294 Natural-number arithmetic, Padoa's reduction 321 322 325 Natural-number arithmetic, Peano's system 84 301 307 316—322 370 405 409 449 Natural-number arithmetic, Pieri's axioms see under Mario Pieri Natural-number definition 290 298 306—307 Negation See under symbol Nervo, Natalia (19??–) vi 446 Neugebauer, Otto (1899–1990) 426 Neumann, Hanna von Caemmerer (1914–1971) 455 Newson, Mary Francis Winston (1869–1959) 421 Newton, Sir Isaac (1643–1727) 316 Nidditch, Peter Harold (1928–1983) 299 302 431 434 Nielsen, Niels (1865–1931) 448 Nieri, Idelfonso (1853–1920) 101 Noble, Charles Albert (1867–1962) 425 Noether, Emmy (1882–1935) 414 Noether, Max (1844–1921) 65 111 122 431 Non-archimedean See under geometry Non-Euclidean See under geometry Normal school 7 Normal to a variety 374—375. See also orthogonality North, John David (1934–) 146 431 Notation in Point and Sphere 158 162—164 270 Notation Pieri's usage in general ix 59 87 126 306 323 340 366—367 383. Number theory 313 O'Connor, John J.(1945–) 87 431 Obituaries See under Mario Pieri Oettingen, Arthur Joachim von (1836–1920) 444 Ohm, Martin (1792–1872) 291—292 300 404 431 Ohrtmann, Carl (18??–????) 409 450 One 258 Operation on points See transformation Opposite See diametrically opposite and under order Order in elliptic geometry 356 360—361 Order on a circle 252 Order on a line 251 Order, opposite 252 254. Ordinal number 297 313 323. Ordinario see professore Ore, Oystein (1899–1968) 414 Orientation 145 247 271 Origin 257 Origin of half-plane 202 Origin of ray 200 Orthogonality 154—155 280 Orthogonality of line and plane 147 183 188 272 Orthogonality of lines 147 155 179 272 280 362 Orthogonality of planes 192. See also under symbol Ostrowski, Alexander Markowich (1873–1986) 374 410 438 457 Otte, Michael (1938–) 404 Pacifism 74 102 Padoa, Alessandro (1868–1937) vi 94—95 167 281 316 318 320—327 337 341—342 392 398 419 424 431 446 Padoa, Alessandro (1868–1937), 1902 Theory of Natural Numbers 308 310 314 321—323 Padoa, Alessandro (1868–1937), method 321 360—362 Padoa, Alessandro (1868–1937), [1900] 1901 Essay on an Algebraic Theory of Integers 320—322 360 Padoa, Alessandro (1868–1937), [1900] 1902 New System of Definitions for Geometry 148 161 278 281 341—342 Padua xviii Padua university 16 Pagli, Paolo (19??–) 424 Pagliero, Giuliano (18??–19??) 398 Palladino, Franco (1945– ) x 20 22 27 34 62 73 147 156 383 432 438. Pambuccian, Victor (1959– ) 362 432 Panetti, Modesto (1875–1957) 85 432 Pannelli, Marino (1855–1934) 36 Pannwitz, Erika (1904–1975) 409 Papal States xvii 11 Pappus (290–350) See under theorem Parallel postulate, Bolyai's form 155 206 209 278 285 Parallel postulate, independence 125 287 Parallel postulate, Playfair's form 149 155 274 277 Parallelism 229 Parallelism of line and plane 232 Parallelism of lines 155 229 Parallelism of planes 231 Parducci, Amos (1877–1949) 5 79 97 432 Parma xvii xviii 11 41 44 Parma university 16 41 44 90 460 Parsons, Charles Dacre (1933– ) 300 305 432 Pascal, Blaise (1623–1662) 117. See also under theorem Pascal, Ernesto (1865–1940) 110 398 Pasch, Moritz (1843–1930) 54 95—96 132 161 197 398 415 418 424 432—433 436 449 460 Pasch, Moritz (1843–1930) on real numbers 289—290 293—294 305. Pasch, Moritz (1843–1930), 1882b Lectures on Geometry 58 126—128 146—148 338 351 394 Pascoli, Giovanni (1855–1912) 96 Peano, Bartolomeo (????–1888) 332 333 Peano, Bartolomeo (????–????) 332 333 Peano, Carola Crosio (????–1940) 333 Peano, Francesco (????–????) 332 333 Peano, Giuseppe (1858–1932) v—ix 20 53—54 59—60 69 71 73—74 82 84 87 95 96 102 107—108 114—115 127 129 156 167 294 299—305 303 315—322 327—328 331—347 339 363—368 380 392 395—396 398 409 412 417 419 424 428 431—436 446 450 453 460 Peano, Giuseppe (1858–1932), 1889 Principles of Geometry Presented Logically 128 334—335 338 340 433 Peano, Giuseppe (1858–1932), 1891d Concept of Number 317—318 320—321 336—337 434 Peano, Giuseppe (1858–1932), 1894 Fundamentals of Geometry 127 147 338 340 351 434 Peano, Giuseppe (1858–1932), 1895–1908 Mathematical Formulary 66 69 71 269 301 306 317—318 321 336—337 342—343 344 345 364 409 436 Peano, Giuseppe (1858–1932), 1903 Geometry Based on Ideas of Point and Distance 161 280 341 351 394 434 Peano, Giuseppe (1858–1932), Academia pro Interlingua 42 49 345 Peano, Giuseppe (1858–1932), birth 332 Peano, Giuseppe (1858–1932), calculus text 82 333 336 418 Peano, Giuseppe (1858–1932), death 346 Peano, Giuseppe (1858–1932), differential equations research 334 Peano, Giuseppe (1858–1932), early career 333 Peano, Giuseppe (1858–1932), family 332—333 Peano, Giuseppe (1858–1932), Lingua see Latin: Uninflected Peano, Giuseppe (1858–1932), linguistics research 345 364—365 Peano, Giuseppe (1858–1932), logic, view of 59 301 305—306 308 315 318—319 327 340 342 386 Peano, Giuseppe (1858–1932), Pieri, relationship with see under Mario Pieri Peano, Giuseppe (1858–1932), politics 333 346 365 Peano, Giuseppe (1858–1932), postulates see under natural-number arithmetic Peano, Giuseppe (1858–1932), praising or supporting Pieri viii 27 38 43 56 124 131 135 153 325 329 378 399 414—415 439—441 443 Peano, Giuseppe (1858–1932), professorship at Turin 335 346 Peano, Giuseppe (1858–1932), schooling 332 Peano, Giuseppe (1858–1932), Segre polemic 108 337 449 Peano, Giuseppe (1858–1932), space-filling curve see under curve Peano, Giuseppe (1858–1932), students 71 80 89 94 365 396 Peano, Giuseppe (1858–1932), symbolic notation ix 59 87 126 301 306 316 319 325 334 336 338 340 342—345 364—367 383 395—396 Peano, Giuseppe (1858–1932), teaching 108 333 345—346 364 395 Peano, Giuseppe (1858–1932), university studies 332 Peano, Giuseppe (1858–1932), Veronese polemic 117. See also school: Peano and under real-number arithmetic Peano, Giuseppe (1858–1932), [1888] 2000 Geometric Calculus viii 53 84 334 433 Peano, Giuseppe (1858–1932), [1889] 1973 Principles of Arithmetic 58 294 301 303 308 313—314 316 324 334—335 343 433 Peano, Michele (????–????) 332—333 Peano, Rosa (????–????) 332 Peano, Rosa Cavallo (????–1910) 332 Pearson, Patricia M.Cowan (1928?–) x 145 151 369—370 436 Pedagogy, mathematical 40 98 108 327 336 346 351 365 367 Pedagogy, mathematical, for arithmetic 322—323 326 395—396 Pedagogy, mathematical, for geometry 29 117 127 147—148 150 153—154 157 160 162 266 286—288 348 393—394. Pedrazzi, Maino (19??–) 156 436 Peirce, Charles Sanders (1839–1914) 296 316 334 413 436 Pejlare, Johanna (19??–) 68 153—154 407 436 Pellegrini, Aldo (????–1940) 6 Pellegrini, Geminiano (18??–????) 5—6 Pellegrini, Paolina Livia Pieri (1865–1959?) 5—6 Pennacchietti, Giovanni (1850–1916) 32 34 37 96 413 Pensa, Angelo (18??–19??) 286 436 Pentaspherical See under coordinates Periphery See boundary Permutable transformations 270 Perpendicularity See orthogonality Petersen, Julius Peter Christian (1839–1910) 120—122 Petkantschin, Boyan Lazarov (Ïåòêàí÷èíú, Áîÿí Ëàçàðîâ, 1907—1987) 143 436 Petri, Cesare (18??–????) 398 Pfaff, Johann Friedrich (1765–1825) 93 Pfanner, Pietro (1864–1935) 48—49 Phillips, Esther Rodlitz (1933–) 430 436 Philosophy of mathematics and science 80 125—128 147 160 162 266—267 286 341 343 381—382 394 Physics, mathematical 123 394 Picard, Charles Emile (1856–1941) 64 74 Pickert, Guenter (1917–) 96 436 460 Piedmont xvii xix 11 16 18 Pieri, Alfonso (nephew, 1890–1890) 5 Pieri, Angiolina Anastasio Janelli (wife, 18??–19??) 5—6 36 45 385 391 459 Pieri, Beppina Bastian (sister-in-law, ????–????) 5 Pieri, Enrica Montanari (sister-in-law, 18??–????) 5 27 97 Pieri, Erminia Luporini (mother, 1826–1914) 4—5 39 Pieri, Felice Ettore Pacifico Giovanni (brother, 1866–1920?) 5—6 Pieri, Ferruccio Fabio (brother, 1864—1933?) 5—6 39 390 436 Pieri, Gemma (niece) See Gemma Meriano Pieri, Gemma (sister) See Gemma Campetti Pieri, Maria Dal Poggetto (sister-in-law, 18??–19??) 5—6 39 Pieri, Mario (1860–1913) I 19 24 130 Pieri, Mario (1860–1913) as referee 34 42 388—389 Pieri, Mario (1860–1913) on algebraic geometry viii 1 12 38 50—53 73 75 99 103 343 363—364 370 374—378 Pieri, Mario (1860–1913) on arithmetic and logic vii–viii 1 3 38 61 77 290 305—313 320 322—329 342 363 370 381—382 Pieri, Mario (1860–1913) on foundations of geometry vii ix—x 1 32 38 54—58 61 86 118 123—125 145—156 305—306 327—328 331 340—342 347—351 363 366—370 374 381 385 394—395 Pieri, Mario (1860–1913) on foundations of projective geometry vii 99 111 121 128—137 287 328 336 367 370 379—380 Pieri, Mario (1860–1913) on inversive geometry vii 46 137 139 141—142 145 363 370 381 443 Pieri, Mario (1860–1913) on vector analysis viii 1 46 53 343 364 378 Pieri, Mario (1860–1913), 1884b,c dissertations 12 14 15 50 374—375 459 Pieri, Mario (1860–1913), 1889a translation of Staudt 1847 20 107 111 123 137 335—336 338 393 Pieri, Mario (1860–1913), 1889b Triple Tangents 20 21 375 Pieri, Mario (1860–1913), 1895a, 1896a,b Principles Governing Geometry of Position 124 128 137 305—306 338 379 Pieri, Mario (1860–1913), 1896c Postulates for Projective Geometry of hyperspaces 128 379 Pieri, Mario (1860–1913), 1897c Primitive Entities of Projective Geometry 128—129 380 Pieri, Mario (1860–1913), 1898b New Method for Developing Projective Geometry 133 380 Pieri, Mario (1860–1913), 1898c Principles of Geometry of Position 38 57 59 102 120 129 131 134 137 306—307 327 338 340 343 367 371 380 Pieri, Mario (1860–1913), 1900a Point and Motion 57—58 84 124 126 134 145 148—157 271—274 276—278 280—282 285—287 327 340—343 367 369—371 381 Pieri, Mario (1860–1913), 1901b Principles of Line Geometry 124 134 380 Pieri, Mario (1860–1913), 1904a Staudt's Fundamental Theorem 137 306 336 343 380 Pieri, Mario (1860–1913), 1905c, 1906a Complex Projective Geometry 134—135 380 Pieri, Mario (1860–1913), 1906d New Logico-Mathematical Direction 289 304 307 343 382 Pieri, Mario (1860–1913), 1906e Definition of the Irrationals 289 328 343 382 Pieri, Mario (1860–1913), 1906f Staudtian Homography Definition 137 380 Pieri, Mario (1860–1913), 1906g Consistency of Arithmetic 60 74 289—290 306—308 326—327 340 343 363 382 Pieri, Mario (1860–1913), 1907a Axioms of Arithmetic viii 3 58 289 300—301 308—313 321—328 343 370 382 Pieri, Mario (1860–1913), 1908a Point and Sphere viii 3 58 84 90 145 153—271 278 280—287 340 349—351 355—358 361 366—368 371 381 Pieri, Mario (1860–1913), 1911d, 1912c Geometry of Inversions 137 141 145 381 Pieri, Mario (1860–1913), archive see Mario Pieri: Nachlass Pieri, Mario (1860–1913), birth 4 Pieri, Mario (1860–1913), burial 48—50 90 459 Pieri, Mario (1860–1913), chair quest 22– 32 384 Pieri, Mario (1860–1913), character 2 23 42—43 47 50 124 131 363 383 390—392 Pieri, Mario (1860–1913), death 2 6 47 Pieri, Mario (1860–1913), early career 5 17 20 22 27 31 383 Pieri, Mario (1860–1913), editing De Paolis 1892 78 123—124 393 414 Pieri, Mario (1860–1913), election to academies 34 Pieri, Mario (1860–1913), family 3—8 9 17 27 36 37 39 42—44 45 46—49 96 382—383 385 388 390—391 459 Pieri, Mario (1860–1913), finances 8 34 43—44 382 388 390 Pieri, Mario (1860–1913), formulas ix 1 52 Pieri, Mario (1860–1913), health 8 43 46—47 117 388—389 391—392 Pieri, Mario (1860–1913), interest in pedagogy 20 49 147 154 160 162 265—267 286—287 322 326—327 368 392—396 Pieri, Mario (1860–1913), knighthood 2 42 389 Pieri, Mario (1860–1913), lecture notes taken by 12 392 397—399 Pieri, Mario (1860–1913), lecture notes, published ix 20 22 46 397—398 Pieri, Mario (1860–1913), legacy 2 61 115 363—371 Pieri, Mario (1860–1913), letters from ix 382—392 399 Pieri, Mario (1860–1913), letters to vi ix 382 398 403 Pieri, Mario (1860–1913), libera docenza 20 22 Pieri, Mario (1860–1913), licenza 12 Pieri, Mario (1860–1913), logic, view of 59 102 272—273 289—290 306—308 327 340 342—343 363 386 Pieri, Mario (1860–1913), marriage 5—6 36 385 Pieri, Mario (1860–1913), Mars drawing 8 9 397 459 Pieri, Mario (1860–1913), music 7 42 Pieri, Mario (1860–1913), Nachlass ix 6 398—399 Pieri, Mario (1860–1913), obituaries of 49 61 90 399 Pieri, Mario (1860–1913), on differential geometry viii 1 15 50—51 53 374 Pieri, Mario (1860–1913), Peano, relationship with ix 22 27 42 49 59 338 340 342—343 345 363 386 Pieri, Mario (1860–1913), philosophy of mathematics viii x 102 147 160—162 266—267 289 306—308 343 363 370 386 Pieri, Mario (1860–1913), physical stature 8 43 Pieri, Mario (1860–1913), Poincare dispute 58 74 290 326 343 Pieri, Mario (1860–1913), professorship at Catania 4 32 34 38 384—385 387 390 Pieri, Mario (1860–1913), professorship at Parma 4 44 46—47 390 Pieri, Mario (1860–1913), promotion 36 37 38 386 459 Pieri, Mario (1860–1913), relation see equidistance: ternary Pieri, Mario (1860–1913), reviews by ix 38 393—397 Pieri, Mario (1860–1913), schooling 5 7—8 100 382 397 Pieri, Mario (1860–1913), student records 8 10 12 382—383 459 Pieri, Mario (1860–1913), students 34 38 40 70 75 82 92 104 388—389 393 395—397 Pieri, Mario (1860–1913), university studies 5 8 10 12—15 382—383 397 Pieri, Mario (1860–1913), workload 33—34 44 384 387—390 Pieri, Mario (1860–1913), works (collected or listed) vi ix 3 50 329 373—374 379 392 398 401. Pieri, Mario (1860–1913), [1900] 1901 Geometry as a Purely Logical System 1 36 74 126—127 148 153 278 306 320—322 327 341—343 379 381 Pieri, Nisedi (mother of sister-in-law, 18??–????) 6 Pieri, Paolina (sister) See Paolina Pellegrini Pieri, Pellegrino (father, 1826–1882) 4 5 17 96 443 Pieri, Pellegrino [Rinuccio] (nephew, 18??–19??) 5 8 97 398 Pieri, Piero (nephew, 1893–1979) 5 97 Pieri, Rinuccio See Pellegrino [Rinuccio] Pieri Pieri, Romano (grandfather, ????–18??) 4 Pieri, Silvio Dante (brother, 1856–1936) 5 7—8 9 17 34 39 49 79 96—97 398 405 432 444 459 Pieri, Teresa (sister) See Teresa Brancoli Pieri, Teresa Ricci (grandmother, ????–18??) 4 Pieri, Virginia (sister) See Virginia Anastasio Pierpont, James (1866–1932) 342 444 Piesyk, Zbigniew (????– ) 355 420 Pincherle, Salvatore (1853–1936) 10 25—29 30 46 91 97—98 101 108 292 398 402 444 449 453 455 459 Pinl, Maximilian (1897–1981) 454 Pirondini, Geminiano (1857–1914) 10 98—99 426 Pisa xvii xviii 11 Pisa, Scuola Reale Normale Superiore 4 8 10—12 13 17 23 50 66—67 78 459 Pisa, university 10—12 15—16 50 459 461 Pittarelli, Giulio (1852–1934) 36 411 Plana, Giovanni (1781–1864) 82 Plane at infinity 277 Plane of symmetry 187 Plane, antipolar 238 Plane, defined 129 146 154 167 170 272 281 341 Plane, reflection see under reflection. See also under polar plane; symbol Plane, undefined 149 274 Plato (427?–347? B.C.) 436 Plaumann, Peter Klaus (19??–) 424 444 Playfair, John (1748–1819) See under parallel postulate
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