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Fubini Guido:     more books (17)

Introduzione Alla Teoria Dei Gruppi Discontinui E Delle Funzioni, Automorfe (Italian Edition) by Guido Fubini, 2010-04-20 Il Parallelismo Di Clifford Negli Spazii Ellittici (1900) (Italian Edition) by Guido Fubini, 2010-09-10 Lezioni Di Analisi Matematica (1920) (Italian Edition) by Guido Fubini, 2008-06-02 La Matematica Dell'Ingegnere E Le Sue Applicazioni. Volume Primo by Guido Fubini & Giuseppe Albenga, 1949-01-01 Lezioni Di Analisi Matematica (1920) (Italian Edition) by Guido Fubini, 2010-09-10 Lezioni Di Analisi Matematica (1920) (Italian Edition) by Guido Fubini, 2010-09-10 Introduzione Alla Teoria Dei Gruppi Discontinui E Delle Funzioni Automorfe (1908) (Italian Edition) by Guido Fubini, 2009-03-20 Introduzione alla Teoria dei Gruppi Discontinui (Italian Edition) by Guido Fubini, 2009-11-25 Lezioni Di Analisi Matematica (Italian Edition) by Fubini Guido 1879-1943, 2010-09-29 Il Parallelismo Di Clifford Negli Spazii Ellittici (1900) (Italian Edition) by Guido Fubini, 2010-09-10 Introduzione Alla Teoria Dei Gruppi Discontinui E Delle Funzioni Automorfe (1908) (Italian Edition) by Guido Fubini, 2010-09-10 Introduzione Alla Teoria Dei Gruppi Discontinui E Delle Funzioni Automorfe (1908) by Guido Fubini, 2010-09-10 L'ultimo treno per Cuneo: Pagine autobiografiche (1943-1945) (Memoria) (Italian Edition) by Guido Fubini, 1991 Lungo viaggio attraverso il pregiudizio (Italian Edition) by Guido Fubini, 1996

lists with details

1. Fubini
   Guido Fubini. Born 19 Jan 1879 in Venice, Italy Died 6 June 1943 in New York, USA.Click the picture above to see two larger pictures Show birthplace location.  
   http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Fubini.html
   
   Extractions: Guido Fubini 's father Lazzaro Fubini was a mathematics teacher at the Scuola Macchinisti in Venice so he came from a mathematical background and was influenced by his father towards mathematics when he was young. Guido attended secondary school in Venice where he showed that he was brilliant at mathematics and it was clear from this stage that he would follow career in the subject. In 1896 Fubini entered the Scuola Normale Superiore di Pisa. There he was taught by Dini and Bianchi who quickly influenced Fubini to undertake research in geometry. He presented his doctoral thesis Clifford's parallelism in elliptic spaces in 1900. Most young doctoral students take a few years to make themselves well known in their area. However, Fubini was lucky for his teacher Bianchi was about to publish an important work on differential geometry and he discussed the results of Fubini's thesis in his treatise which appeared in 1902.

2. Guido Fubini
   Guido Fubini. Guido Fubini (January 19, 1879 June 6, 1943) wasan Italian mathematician, best-known for Fubini s theorem. Born  
   http://www.fact-index.com/g/gu/guido_fubini.html
   
   Extractions: Main Page See live article Alphabetical index Guido Fubini January 19 June 6 ) was an Italian mathematician , best-known for Fubini's theorem Born in Venice , he was steered towards mathematics at an early age by his teachers and his father, who was himself a teacher of mathematics. In he entered the Scuola Normale Superiore di Pisa, where he studied under the notable mathematicians Ulisse Dini and Luigi Bianchi. He gained some early fame when his doctoral thesis, entitled Clifford's parallelism in elliptic spaces , was discussed in a widely-read work on differential geometry published by Bianchi in After earning his doctorate, he took up a series of professorships. In he began teaching at the University of Catania in Sicily ; shortly afterwards he moved to the University of Genoa; and in he moved to the Politecnico in Turin and then the University of Turin, where he would stay for some decades. During this time his research areas focused primarily on topics in mathematical analysis , especially differential equations functional analysis , and complex analysis ; but he also studied the calculus of variations group theory non-Euclidean geometry , and projective geometry , among other topics. With the outbreak of

3. WIEM: Fubini Guido
   fubini guido (18791943), matematyk woski. Profesor uniwersytetu w Turynie (1908-1938) - od 1939 w USA w Institute for Advanced Study Zamiast 89 z zapacisz 59 z. fubini guido ( 1879-1943), matematyk woski  
   http://www.encyklopedia.pl/wiem/00e165.html
   
   Extractions: Fubini Guido (1879-1943), matematyk w³oski. Profesor uniwersytetu w Turynie (1908-1938) - od 1939 w USA w Institute for Advanced Study w Princeton. Autor prac z zakresu analizy matematycznej i geometrii ró¿niczkowej. WIEM zosta³a opracowana na podstawie Popularnej Encyklopedii Powszechnej Wydawnictwa Fogra zobacz wszystkie serwisy do góry

4. Guido Fubini - Encyclopedia Article About Guido Fubini. Free Access, No Registra
   encyclopedia article about Guido Fubini. Guido Fubini in Free onlineEnglish dictionary, thesaurus and encyclopedia. Guido Fubini.  
   http://encyclopedia.thefreedictionary.com/Guido Fubini

5. Guido Fubini | Mathe Board Lexikon
   Translate this page A B C D E F G H I J K L M N O P Q R S T U V W X Y Z. Guido Fubini. Definition,Erklärung, Bedeutung. Verbessern Mitmachen. Guido Fubini. Guido Fubini (* 19.  
   http://www.matheboard.de/lexikon/index.php/Guido_Fubini
   
   Extractions: Startseite Mathe Board Lexikon Mathe Tools ... Partner Das Mathe Board: Kostenlose Nachhilfe in Mathematik von der Grundschule bis zur Hochschule. A B C D ... Z Definition, Erklärung, Bedeutung Verbessern Mitmachen Guido Fubini 19. Januar 6. Juni ) war ein italienischer Mathematiker Er arbeitete vorwiegend in Turin auf den Gebieten projektive Differentialgeometrie sowie Gruppentheorie und Funktionentheorie Er ist für den Satz von Fubini bekannt, nach dem Integrale in mehrdimensionalen Räumen schrittweise in den einzelnen Dimensionen ausgeführt werden können. en:Guido Fubini Hits Verweisseiten Verlinkte Seiten Vielen Dank an " Wikipedia " für die freundliche Unterstützung! Suchen auf matheboard.de: Suchen in ... Mathe Board Erklärung Definition, Erklärung, Bedeutung von Guido Fubini im Lexikon für Mathematik. Wenn Guido Fubini Deiner Meinung nach nicht richtig erklärt oder definiert wurde, schreib bitte

6. Guido Fubini - Wikipedia
   Translate this page Guido Fubini. aus Wikipedia, der freien Enzyklopädie. Guido Fubini (* 19.Januar 1879, † 6. Juni 1943) war ein italienischer Mathematiker.  
   http://de.wikipedia.org/wiki/Guido_Fubini
   
   Extractions: Guido Fubini 19. Januar 6. Juni ) war ein italienischer Mathematiker Er arbeitete vorwiegend in Turin auf den Gebieten projektive Differentialgeometrie sowie Gruppentheorie und Funktionentheorie Er ist für den Satz von Fubini bekannt, nach dem Integrale in mehrdimensionalen Räumen schrittweise in den einzelnen Dimensionen ausgeführt werden können.

7. Matematica - Rubriche - Lo Sapevate Che...
   Translate this page fubini guido, professore nel Politecnico e nella Università di Torino. FubiniGuido, professore nel Politecnico e nella Università di Torino.  
   http://matematica.uni-bocconi.it/fubini/fubini.htm
   
   Extractions: " Nel trovarci qui riuniti al III Congresso dell'Unione Matematica Italiana -diceva Alessandro Terracini nel 1948 pare impossibile non rivedere tra noi la figura di FUBINI, come la vedevamo, sempre in moto; non riudire la sua voce e potente, espressiva piena di accenti e di inflessioni. Eppure è proprio così e se. aderendo all'Unione Matematica Italiana, mi accingo a rievocare l'opera di FUBINI nei suoi rapporti con la geometria proiettiva differenziale, forse a ciò non è estraneo il desiderio di illudermi quasi che Egli sia qua, in questa Pisa dove si è formato, che non ha dimenticato mai" Dedichiamo questo inserto alla figura di Guido Fubini, di qui quest'anno ricorre il cinquantenario della morie e pubblichiamo, tra l'altro, alcuni materiali inediti che ci sembra bene contribuiscano ad illustrare la figura Ci sarebbe in realtà piaciuto riprodurre anche il testo di una conferenza ("Il teorema di riduzione per gli integrali doppi“ apparsa postuma sui Rend. Sem. Mat. Torino, 1949) in cui Fubini aveva ricostruito motivazioni e idee che lo avevano portato, all'inizio del secolo, a dare uno dei più noti, risultati nella teoria dell'integrazione, ma questioni di spazio ci hanno costretto a rinunciare. Guido Fubini era nato a Venezia il 19 gennaio 1879. Nel 1896 entrò alla Scuola Normale ,Superiore di Pisa,a dove ebbe come maestri Ulisse Dini, Eugenio Bertini e soprattutto Luigi Bianchi sempre citato come il grande ispiratore della sua attività di matematico. Una conferenza tenuta a Pisa, alla Normale, sui Fondamenti della geometria proiettiva differenziale, ad esempio, era anche l'occasione per esprimere la soddisfazione di “parlare in quest'aula ove ancora si muove lo spirito del mio grande Maestro Prof. Luigi BIANCHI, dove tanti e tanti studiosi, ed io tra essi, abbiamo appreso l'amore della ricerca geometrica”.

8. Matematici Italiani
   Translate this page Frisone Rosetta, 1888-1912, Frola Eugenio, 1906-1962, R. Frullani Giuliano, 1795-1834,R. fubini guido, 1879-1943, R. Fuortes Tarquinio, 1848-1927, Fusinieri Ambrogio,  
   http://www.dm.unito.it/sism/m_italiani/elmatematici.html
   
   Extractions: Abetti Antonio Abbati Marescotti Pietro Abetti Giorgio Abrahm Max Agnesi Maria Gaetana R Agostinelli Cataldo R Agostini Amedeo Aimonetti Cesare Alagna Rosario Alasia Cristoforo Albanese Giacomo Albanese Maria Albeggiani Giuseppe Albeggiani Michele Luigi Ales Maria Alessio Alberto Almansi Emilio Amaldi Italo Amaldi Ugo Amanzio Domenico ... Amato Vincenzo Amaturo Enrico Amerio Luigi Amici Giovanni Battista Amici Nicola Amodeo Federico Amoroso Luigi Andreoli Giulio Andreotti Aldo R Angelitti Filippo Antonelli Giovanni Antoniazzi Anton Maria Aprile Antonio Giorgio Araldi Giambattista Araldi Michele Aresti Giuseppe Ariani Agostino Armellini Giuseppe Armenante Angelo Arrighi Gino Arrigo Michelangelo Artom Emilio R Aschieri Ferdinando Ascoli Giulio Ascoli Guido R Audisio Fausta Avondo Bodino Giuseppe Azzarelli Mattia Bagnera Giuseppe Bajada Emilio ... Barilari Pacifico Barilli Giuseppe (pseud. Quirico Filopanti) Baroni Ettore Baraco Vito Rodolfo Barsotti Giovanni Barsotti Iacopo Bartolozzi Giuseppe Bassani Anselmo ... Bassi Achille Bassi Laura Basso Giuseppe Battaglini Giuseppe R Beccaria Giambatista R Bedarida Albero Maria Belardinelli Giuseppe Bellacchi Giacomo Bellavitis Giusto R Belli Giuseppe Belli Serafino Bellino Rosina Antonio Belluzzi Odone Beloch Piazzolla Margherita Beltrami Eugenio R Bemporad Azeglio Bemporad Giulio Benedetti Piero Benevento Rodolfo Bernstein Vladimiro Bersano carlo Bertelli Timoteo Bertini Eugenio R Bertini P. M.

9. Rivisteweb Gli Autori Degli Articoli
   D. Ftaiti J. fubini guido; Fuccillo Antonio; Fuchs Dieter; Fullin  
   http://www.mulino.it/rivisteweb/riviste_list.php?letter=F&type=autori

10. Guido Fubini
    Guido Fubini. Born 19 Jan 1879 in Venice , Italy Died 6 June 1943in New York , USA. Guido Fubini s father Lazzaro Fubini was a  
    http://umm.kou.edu.tr/math/Guido Fubini .htm
    
    Extractions: Died: 6 June 1943 in New York USA Guido Fubini 's father Lazzaro Fubini was a mathematics teacher at the Scuola Macchinisti in Venice so he came from a mathematical background and was influenced by his father towards mathematics when he was young. Guido attended secondary school in Venice where he showed that he was brilliant at mathematics and it was clear from this stage that he would follow career in the subject. In 1896 Fubini entered the Scuola Normale Superiore di Pisa. There he was taught by Dini and Bianchi who quickly influenced Fubini to undertake research in geometry. He presented his doctoral thesis Clifford's parallelism in elliptic spaces in 1900. Most young doctoral students take a few years to make themselves well known in their area. However, Fubini was lucky for his teacher Bianchi was about to publish an important work on differential geometry and he discussed the results of Fubini's thesis in his treatise which appeared in 1902. Fubini remained at Pisa to qualify as a university teacher. Most mathematicians at this stage in their careers extend the work they have begun in their doctoral thesis. Not so Fubini. He attacked a completely new topic to the one he had studied for his doctoral thesis studying the theory of

11. Fubini
    Guido Fubini. Born 19 Jan 1879 in Venice, Italy Died6 June 1943 in New York, USA. Show birthplace location.  
    http://intranet.woodvillehs.sa.edu.au/pages/resources/maths/History/Fbn.htm
    
    Extractions: Previous (Alphabetically) Next Welcome page Guido Fubini 's father Lazzaro Fubini was a mathematics teacher at the Scuola Macchinisti in Venice so he came from a mathematical background and was influenced by his father towards mathematics when he was young. Guido attended secondary school in Venice where he showed that he was brilliant at mathematics and it was clear from this stage that he would follow career in the subject. In 1896 Fubini entered the Scuola Normale Superiore di Pisa. There he was taught by Dini and Bianchi who quickly influenced Fubini to undertake research in geometry. He presented his doctoral thesis Clifford's parallelism in elliptic spaces in 1900. Most young doctoral students take a few years to make themselves well known in their area. However, Fubini was lucky for his teacher Bianchi was about to publish an important work on differential geometry and he discussed the results of Fubini's thesis in his treatise which appeared in 1902. Fubini remained at Pisa to qualify as a university teacher. Most mathematicians at this stage in their careers extend the work they have begun in their doctoral thesis. Not so Fubini. He attacked a completely new topic to the one he had studied for his doctoral thesis studying the theory of harmonic functions in spaces of constant curvature.

12. Accademia Nazionale Dei Lincei - Premi E Borse Di Studio - Premi Reali Conferiti
    Translate this page Fisica GARBASSO ANTONIO. Memorie varie. 1919. Matematica fubini guido. Memorievarie. 1920 Astronomia ARMELLINII GIUSEPPE. Teoria del V satellite di Giove.  
    http://www.lincei.it/premi/assegnati_reali.php

13. Guido Fubini - Information
    An online Encyclopedia with information and facts Guido Fubini Information, anda wide range of other subjects. Guido Fubini - Information. deGuido Fubini.  
    http://www.book-spot.co.uk/index.php/Guido_Fubini
    
    Extractions: de:Guido Fubini Guido Fubini January 19 June 6 ) was an Italian mathematician , best-known for Fubini's theorem Born in Venice , he was steered towards mathematics at an early age by his teachers and his father, who was himself a teacher of mathematics. In he entered the Scuola Normale Superiore di Pisa , where he studied under the notable mathematicians Ulisse Dini and Luigi Bianchi . He gained some early fame when his doctoral thesis, entitled Clifford's parallelism in elliptic spaces , was discussed in a widely-read work on differential geometry published by Bianchi in After earning his doctorate, he took up a series of professorships. In he began teaching at the University of Catania in Sicily ; shortly afterwards he moved to the University of Genoa ; and in he moved to the Politecnico in Turin and then the University of Turin , where he would stay for some decades. During this time his research areas focused primarily on topics in mathematical analysis , especially differential equations functional analysis , and complex analysis ; but he also studied the calculus of variations group theory non-Euclidean geometry , and projective geometry , among other topics. With the outbreak of

14. Catalogo Articoli
    fubini guido Ritornarealla Costitutzione Il Ponte (Firenze), 56(7), 2000, pp. 15 - 18;  
    http://serials.cib.unibo.it/cgi-ser/start/it/spogli/ds-s.tcl?data_ins=Tutti&fasc

15. Record Trovati 1; In Questa Pagina Dal No. 1 Al No. 1
    fubini guido Lungo viaggioattraverso il pregiudizio - ROSENBERG E SELLIER, - Fr. 24,50, 2000, pp.  
    http://www.casagrande-online.ch/libreriavirtuale/risultati.phtml?tipo=AUTORE&val

16. Un Elenco Di Matematici
    Translate this page Frisiani Paolo, 1797-1880, Frola Eugenio, 1906-1962, Frullani Giuliano, 1795-1834,fubini guido, 1879-1943, Fuortes Tarquinio, 1848-1927, Gabba Luigi, 1872-1948,  
    http://www.math.unifi.it/matematicaitaliana/matematici.html
    
    Extractions: Matematici italiani del primo secolo dello stato unitario pubblicata nel 1962 da G. F. Tricomi nelle Memorie dell'Accademia delle Scienze di Torino. Classe di Scienze fisiche matematiche e naturali , serie IV tomo I; qui sono raccolte 371 brevi biografie di matematici italiani morti tra il 1 gennaio 1861 e il 31 dicembre 1960. Si ringraziano L'Accademia delle Scienze di Torino e Lettera Pristem per il permesso di utilizzare il materiale da loro pubblicato. A B C D ... Amoroso Luigi Andreoli Giulio Andreotti Aldo Angelitti Filippo Antonelli Giovanni Antoniazzi Anton Maria ... Barilari Pacifico Barilli Giuseppe (pseud. Quirico Filopanti)

17. Storia E Memoria
    Translate this page 1980, 18,00. Frescobaldi Dino, Jugoslavia, Ponte alle Grazie, 5,00.fubini guido, Lungo viaggio ecc, Rosemberg, 10,00. Galbraith John, Lenuove  
    http://www.ilponte.it/libreria/st.html
    
    Extractions: www.ilponte.it STORIA e POLITICA - AUTORI A-L vai a autori M-Z AUTORE TITOLO EDITORE ANNO EURO AA. VV,. Dissenso sul mondo Terra nuova AA.VV La rivoluzione ungherese Mondadori AA.VV Storia del partito comunista bolscevico dell'URSS edizione stampata in URSS Mosca AA.VV. Le giornate della liberazione Milano: dal 28 marzo al 6 maggio 1945 AA. VV. Il sapere delle lotte Spray AA.VV. Marzo 1943 ore dieci AA.VV Democrazia e diritto 5-6 Ed. riuniti AA.VV Studi storici Ist. Gramsci AA.VV Democrazia e diritto 2-3 Ed. Riuniti AA.VV Le ragioni della sinistra Micromega AA.VV Un nuovo europeismo Ed. Riuniti AA.VV Le scissioni sindacali BFS AA.VV Cina e Terzo Mondo 1° e 2° vol. Mazzotta AA.VV I rapporti culturali con l'Urss Italia-Urss AA.VV Il sindacato e le trasformazioni… Ediesse AA.VV Il sindacato in Italia 1960-70 Rass. Sindacale AA.VV L'Internazionale socialista l'Unità AA.VV Se vince Gorbaciov l'Unità AA.VV Testimonianze AA.VV Dal Galeazzi al San Raffaele Ediesse AA.VV La donna e le scelte… AA.VV new Politics vol. 1 n. 3

18. Citta' Di Torino - Regolamenti - N. 257 - C. O. S. A. P. Canone Di Occupazione S
    Translate this page 23463, FROSINONE (VIA), 05. 23485, FROSSASCO (VIA), 03. 23504, FRUGAROLO (VIA),03. 66871, fubini guido (VIA), 05. 52342, FUNICOLARE DI SOPERGA (STRADA COMUNALEALLA), 03.  
    http://www.comune.torino.it/regolamenti/257/Alleg_2D.htm
    
    Extractions: SERVIZIO CENTRALE CONSIGLIO COMUNALE RACCOLTA DEI REGOLAMENTI MUNICIPALI REGOLAMENTO C. O. S. A. P. Canone di Occupazione Spazi ed Aree Pubbliche Allegato 'B' - Elenco delle strade e degli altri sedimi della Citta' con la classificazione A B C D ... Z Cod.via Denominazione della via Cat. DALLA CHIESA GEN. CARLO ALBERTO (PIAZZA) DALMAZIA (VIA) DAMIANO LUIGI (VIA) DANDOLO ENRICO (VIA) DANEO EDOARDO (VIA) DANTE (CORSO) DAUN (VIA) DAVANZATI CHIARO (VIA) DE AMICIS EDMONDO (PIAZZA) DE BERNARDI LAMBERTO (VIA) DE CANAL BERNARDO (VIA) DE CRISTOFORIS TOMMASO (VIA) DE GASPERI ALCIDE (CORSO) DE GENEYS GIORGIO (VIA) DE GUBERNATIS ANGELO (VIA) DE MAISTRE FRATELLI (VIA) DE MARCHI EMILIO (VIA) DE NICOLA ENRICO (CORSO) DE ROLANDIS GIOVANNI BATTISTA (VIA) DE SANCTIS FRANCESCO (VIA) DE SONNAZ ETTORE (VIA) DEGO (VIA) DEI COLLI - PINO SOPERGA (VIA) DEL CARRETTO LUISA (VIA) DEL PRETE CARLO (VIA) DEL SARTO ANDREA (VIA) DELEDDA GRAZIA (VIA) DELLA PORTA CARLO (VIA) DELLA ROBBIA LUCA (LARGO) DELLA ROBBIA LUCA (VIA) DELLALA FRANCESCO (VIA) DELLEANI LORENZO (VIA) DEMARGHERITA FRANCESCO (VIA) DEMONTE (VIA) DENINA CARLO (VIA) DENZA PADRE FRANCESCO (VIA) DEPANIS GIUSEPPE (VIA) DERNA (PIAZZA) DES AMBROIS LUIGI (VIA) DESANA (VIA) DESTEFANIS GIOVANNI (VIA) DI NANNI DANTE (VIA) DI VITTORIO GIUSEPPE (PARCO PUBBLICO) DIAZ ARMANDO (LUNGO PO) DICIOTTO DICEMBRE (PIAZZA) DIGIONE (VIA) DINA GIACOMO (VIA) DIOCLEZIANO (CORSO) DOGALI (VIALE) DOGLIANI (VIA) DOGLIOTTI ACHILLE MARIO (CORSO) DOMODOSSOLA (VIA) DONATELLO (AIUOLA) DONATI VITALIANO (VIA) DONATORE DI SANGUE (PIAZZA DEL)

19. Guido Fubini
    Guido Fubini. Guido Fubini (January 19, 1879 June 6, 1943) wasan Italian mathematician, best-known for Fubini s theorem. Born  
    http://www.sciencedaily.com/encyclopedia/guido_fubini
    
    Extractions: Front Page Today's Digest Week in Review Email Updates ... Outdoor Living Main Page See live article Guido Fubini January 19 June 6 ) was an Italian mathematician , best-known for Fubini's theorem . Born in Venice , he was steered towards mathematics at an early age by his teachers and his father, who was himself a teacher of mathematics. In he entered the Scuola Normale Superiore di Pisa, where he studied under the notable mathematicians Ulisse Dini and Luigi Bianchi. He gained some early fame when his doctoral thesis, entitled Clifford's parallelism in elliptic spaces , was discussed in a widely-read work on differential geometry published by Bianchi in . After earning his doctorate, he took up a series of professorships. In

20. CheatHouse.com - Guido Fubini- This Essay Is About A Famous Mathematician.
    guido fubini, A famous mathematician, was born January 19th 1987 in Venice, Italy. His father, Lazzaro fubini, was a mathematics teacher so he came from a mathematical background. in 1902 who quickly influenced guido to undertake research in geometry guido fubini Semitism  
    http://www.cheathouse.com/eview/2254-guido-fubini-this-essay-is-about-a-famou.ht
    
    Extractions: Guido Fubini, A famous mathematician, was born January 19th 1987 in Venice, Italy. His father, Lazzaro Fubini, was a mathematics teacher so he came from a mathematical background. Guido was influenced by his father towards mathematics when he was young. He attended secondary school in Venice where Note! The sentences in this essay are shuffled, making this essay unusable

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