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LUCA PACIOLI La Vita E Le Opere

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LUCA PACIOLI La Vita E Le Opere Biblioteca del Centro Studi “Mario Pancrazi” Quaderni 14 Argante Ciocci LUCA PACIOLI La Vita e le Opere Versione in lingua inglese a cura di Karen Pennau Fronduti Biblioteca del Centro Studi “Mario Pancrazi” In collaborazione e con il contributo di Quaderno n.14 della Serie “R&D” – Ricerca e Didattica – pubblicata dal Centro Studi “Mario Pancrazi” di Sansepolcro e diretta da Francesca Giovagnoli. Autorizzazione n. 6/10 del Tribunale di Arezzo Biblioteca Centro Studi “Mario Pancrazi” www.centrostudimariopancrazi.it facebook /centrostudimariopancrazi In redazione Matteo Martelli, Gabriella Rossi ISBN 978-88-97646-31-0 2017 © University Book di Digital Editor srl Finito di stampare nel mese di giugno 2017 dalla Digital Editor srl, Umbertide Progetto grafico Eva Giacchè - Digital Editor srl, Umbertide In copertina Luca Pacioli (busto) nell’interpretazione di Filippo Lombezzi (Istituto Tecnico Economico, Via Piero della Francesca, 43, Sansepolcro). In quarta di copertina: Dal Compendium de divina proportione, 1498, il Rombicubottaedro (Leonardo da Vinci). Dal De Divina Proprtione, 1509, le Lettere Capitali (Luca Pacioli). La versione inglese è stata curata da Karen Pennau Fronduti Per le riproduzioni fotografiche, grafiche e citazioni giornalistiche appartenenti alla proprietà di terzi, inserite in quest’opera, l’editore è a disposizione degli aventi diritti non potuti reperire. É vietata la riproduzione, anche parziale e ad uso interno didattico, con qualsiasi mezzo, non autorizzato. «Luca Pacioli – nonostante non abbia mai disdegnato l’insegnamento dell’aritmetica commerciale – è stato tra le menti più illuminate e feconde se non la più illuminata e feconda – dell’alta matematica tra la fine del XV e l’inizio del XVI secolo» (Esteban Hernández-Esteve) L’Autore/The Author Argante Ciocci, dopo aver conseguito la Laurea in Filosofia a Perugia (1993) e una seconda Laurea in Lettere (1995), è diventato dottore di ri- cerca in Storia della Scienza con una tesi su Luca Pacioli. I suoi interessi scientifici, testimoniati dalle precedenti pubblicazioni su riviste specialisti- che, vertono sul Rinascimento e la Rivoluzione scientifica del XVII secolo. Il suo lavoro di ricerca è incentrato sulla matematica del Rinascimento e, in particolare, sulle figure di Luca Pacioli, Piero della Francesca e Leonardo da Vinci. A queste tematiche sono dedicati i volumi su Pacioli (Luca Pacioli e la matematizzazione del sapere nel Rinascimento, Bari, Cacucci 2003; Luca Pacio- li tra Piero della Francesca e Leonardo, Sansepolcro, Aboca, 2009; Luca Pacioli. Letture e interpretazioni, Biblioteca del Centro Studi “Mario Pancrazi”, Selci- Lama, L’Artistica, 2012) e gli articoli sulla diffusione dell’Archimede latino di Iacopo da San Cassiano (L’Archimede latino di Iacopo da San Cassiano, Fran- cesco dal Borgo e Piero della Francesca, in “1492. Rivista della Fondazione Piero della Francesca”, Anno IV (2011) nn. 1-2- Anno V (2012), nn. 1-2, pp. 43-64; Luca Pacioli e l’Archimede latino, in “Bollettino di Storia delle scienze matematiche” Vol- XXXV- 2015, fasc. 2, pp. 165-184). Argante Ciocci, after having received a Degree in Philosophy from the University of Perugia (1993) and another in Literature in the year 1995, earned his PhD in Hi- story of Science with a thesis on Luca Pacioli. His scientific interests, as illustrated by previous publications in specialized periodicals, are concentrated mainly on the Re- naissance and the scientific revolution of the XVII century. His current research is focused on mathematics in the Renaissance and particularly on the figures of Luca Pacioli, Piero della Francesca and Leonardo da Vinci. Dedicated to these themes are his books regarding Pacioli (Luca Pacioli e la matematizzazione del sapere nel Rinascimento, Bari, Cacucci 2003; Luca Pacioli tra Piero della Francesca e Leonardo, Sansepolcro, Aboca, 2009; Luca Pacioli. Letture e interpretazioni, Biblioteca del Centro Studi “Mario Pancrazi”, Selci-Lama, L’Artistica, 2012) and his articles concerning the diffusion of Iacopo da San Cassiano’s Latin translation of Archimedes (L’Archimede latino di Iacopo da San Cassiano, Francesco dal Borgo e Piero della Francesca, in “1492” – Periodical of the Fondazione Piero della Francesca, Anno IV (2011), nos. 1-2 – Anno V (2012), nos. 1-2, pp. 43-64; Luca Pacioli e l’Archimede latino, in “Bollettino di Storia delle scienze matematiche”, Vol XXXV – 2015, fasc. 2, pp. 165-184). INDICE Premessa/Foreword di Matteo Martelli 11 PROLOGO/PROLOGUE Ritratto di un poliedrico intellettuale del Rinascimento 15 Portrait of a Polyhedric Renaissance Intellectual PARTE PRIMA/PART ONE LA VITA /THE LIFE Peregrinando per diversi paesi Wandering through Many Different Lands 1. La formazione abachistica e il primo soggiorno veneziano 55 2. Il soggiorno a Roma (1470-1471) e l’abito di San Francesco 63 3. Frate Luca Magister theologiae: Perugia e Firenze 69 4. La stesura della Summa e il secondo soggiorno romano (1489) 77 5. Luca Pacioli a Napoli 81 6. Dal Borgo ad Urbino 83 7. Luca Pacioli e Piero della Francesca 91 8. La stampa della Summa (1494) 109 9. Nella Milano di Ludovico il Moro: Luca Pacioli e Leonardo da Vinci 111 10. A Mantova, a Firenze, a Bologna 141 11. Pacioli e Dürer 149 12. La stampa della Divina proportione 169 13. Tra Perugia, Sansepolcro e Roma 171 Indicazioni bibliografiche 179 Argante Ciocci - luca Pacioli 10 PARTE SECONDA/PART TWO LE OPERE/THE WORKS Dalla contabilità alla filosofia della natura From Accounting to Natural Philosophy 1. Il Tractatus mathematicus ad discipulos Perusinos (1478) 183 2. La Summa de arithmetica, geometria, proportioni et proportionalita. Matematica dotta e matematica dei “pratici volgari”: la sintesi di Luca Pacioli 187 3. Le fonti della Summa 201 4. Luca Pacioli: il padre della Ragioneria 211 5. Il trattato sulla partita doppia e la codificazione teorica della ragioneria 213 6. Il Compendium de divina proportione (1498) 227 7. L’edizione a stampa della Divina proportione: Il Tractato de l’architectura, il Libellus di Piero e l’Alfabeto dignissimo (1509) 237 8. Il trattato De viribus quantitatis e i giochi matematici 269 9. De ludo scachorum: Pacioli scacchista e matematico 275 10. L’edizione latina degli Elementi di Euclide del 1509 291 11. Pacioli e la rivoluzione della stampa 303 12. Luca Pacioli: una nuova immagine della matematica 317 13. Le proporzioni e la matematizzazione delle scienze e delle tecniche 319 14. Un’antica-nuova immagine della natura 347 indicazioni bibliograFiche/ bibliograPhical notes 359 indice delle illustrazioni/ illustrations 365 indice dei nomi/names index 371 Matteo Martelli* Premessa/Foreword Il Centro Studi “Mario Pancrazi” The latest addition to the Biblioteca pubblica nella sua Biblioteca la mo- of the Centro Studi “Mario Pancrazi” nografia, organica e puntuale, che Ar- is the systematic and precise essay that gante Ciocci ha dedicato al frate del Argante Ciocci dedicates to Luca Pacioli Borgo in occasione delle celebrazioni as part of the celebrations in memory of del Cinquecentenario della morte di the Quincentenary of his death (1517- Luca Pacioli (1517-2017). 2017). Il Centro, fin dalla sua costitu- The Centro, ever since its establishment, zione, ha scelto di perseguire – sulla has chosen to pursue the objective – in the scia del Prof. Pancrazi – l’obiettivo di spirit of Prof. Pancrazi – of promoting promuovere la cultura delle matema- the cultivation of mathematics and, in con- tiche, e di conseguenza delle scienze, sequence, of the sciences, arts and letters, delle arti e delle lettere, sull’esempio del Pacioli, convinto assertore del taking as example Pacioli who was a con- “ruolo fondamentale dell’aritmetica vinced upholder of the “fundamental role of e della geometria nelle arti meccani- arithmetic and geometry in the mechanical che, nel commercio e nei mestieri” arts, commerce and the trades” (A. Ciocci), (A. Ciocci), conseguente sostenito- consequently proponent of the idea that ma- re dell’idea che le matematiche ga- thematics guarantees “cognitive precision” in rantiscono “esattezza conoscitiva” the practise of the liberal arts, the trivium nell’esercizio delle arti liberali, del and the quadrivium, and in the constitution trivio e del quadrivio, e nella costi- of all the disciplines followed in the univer- tuzione di tutte le discipline univer- sities of the time (jurisprudence, medicine, sitarie dell’epoca (giurisprudenza, philosophy, theology), being that the world medicina, filosofia, teologia), perché was created “through numbers, geometric il mondo è stato creato «per mezzo figures and proportion”. dei numeri, delle figure geometriche Ciocci’s lively and knowledgeable text e delle proporzioni». recounts the life of the friar from Sanse- La monografia di Ciocci, agile e polcro, examines his writings with balance informata, racconta la vita del frate del Borgo, esamina con equilibrio e and competence, paints the profile of a competenza gli scritti del Maestro noteworthy Renaissance intellectual well- di Sansepolcro, disegna il profilo di known the world over as father of modern Argante Ciocci - luca Pacioli 12 un grande intellettuale del Rinasci- accounting practices, one of the most illu- mento, notissimo in tutto il mondo strious mathematicians of his time, natu- come padre della ragioneria moder- ral philosopher. na, matematico tra i più insigni del This volume is addressed to scho- tempo, filosofo della natura. lars and researchers, as well as to the Il volume è destinato sia agli schools and to all those impassioned of studiosi, sia alle scuole, sia
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