Luca Pacioli  

Born  c. 1447^{[2]} 
Died  19 June 1517 Sansepolcro, Republic of Florence  (aged 69–70)
Citizenship  Florentine 
Occupation(s)  Friar, mathematician, writer 
Known for  Summa de arithmetica, Divina proportione, doubleentry bookkeeping 
Fra. Luca Bartolomeo de Pacioli (sometimes Paccioli or Paciolo; c. 1447 – 19 June 1517)^{[3]} was an Italian mathematician, Franciscan friar, collaborator with Leonardo da Vinci, and an early contributor to the field now known as accounting. He is referred to as the father of accounting and bookkeeping and he was the first person to publish a work on the doubleentry system of bookkeeping on the continent.^{[4]}^{[a]} He was also called Luca di Borgo after his birthplace, Borgo Sansepolcro, Tuscany.
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Luca Pacioli: Father of Accounting

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The History of DoubleEntry Bookkeeping
Transcription
Life
Luca Pacioli was born between 1446 and 1448 in the Tuscan town of Sansepolcro where he received an abbaco education. This was education in the vernacular (i.e., the local tongue) rather than Latin and focused on the knowledge required of merchants. His father was Bartolomeo Pacioli; however, Luca Pacioli was said to have lived with the Befolci family as a child in his birth town Sansepolcro.^{[7]} He moved to Venice around 1464, where he continued his own education while working as a tutor to the three sons of a merchant. It was during this period that he wrote his first book, a treatise on arithmetic for the boys he was tutoring. Between 1472 and 1475, he became a Franciscan friar.^{[7]} Thus, he could be referred to as Fra ('Friar') Luca.
In 1475, he started teaching in Perugia as a private teacher before becoming first chair in mathematics in 1477. During this time, he wrote a comprehensive textbook in the vernacular for his students. He continued to work as a private tutor of mathematics and was instructed to stop teaching at this level in Sansepolcro in 1491. In 1494, his first book, Summa de arithmetica, geometria, Proportioni et proportionalita, was published in Venice. In 1497, he accepted an invitation from Duke Ludovico Sforza to work in Milan. There he met, taught mathematics to, collaborated, and lived with Leonardo da Vinci. In 1499, Pacioli and Leonardo were forced to flee Milan when Louis XII of France seized the city and drove out their patron. Their paths appear to have finally separated around 1506. Pacioli died at about the age of 70 on 19 June 1517, most likely in Sansepolcro, where it is thought that he had spent much of his final years.^{[7]}
Mathematics
Pacioli published several works on mathematics, including:
 Tractatus mathematicus ad discipulos perusinos (Ms. Vatican Library, Lat. 3129), a nearly 600page textbook dedicated to his students at the University of Perugia where Pacioli taught from 1477 to 1480. The manuscript was written between December 1477 and 29 April 1478. It contains 16 sections on merchant arithmetic, such as barter, exchange, profit, mixing metals, and algebra, though 25 pages from the chapter on algebra are missing. A modern transcription was published by Calzoni and Cavazzoni (1996) along with a partial translation of the chapter on partitioning problems.^{[8]}
 Summa de arithmetica, geometria. Proportioni et proportionalita (Venice 1494), a textbook for use in the schools of Northern Italy. It was a synthesis of the mathematical knowledge of his time and contained the first printed work on algebra written in the vernacular (i.e., the spoken language of the day). It is also notable for including one of the first published descriptions of the bookkeeping method that Venetian merchants used during the Italian Renaissance, known as the doubleentry accounting system. The system he published included most of the accounting cycle as we know it today. He described the use of journals and ledgers and warned that a person should not go to sleep at night until the debits equalled the credits.^{[9]} His ledger had accounts for assets (including receivables and inventories), liabilities, capital, income, and expenses – the account categories that are reported on an organization's balance sheet and income statement, respectively. He demonstrated yearend closing entries and proposed that a trial balance be used to prove a balanced ledger. Additionally, his treatise touches on a wide range of related topics from accounting ethics to cost accounting. He introduced the Rule of 72, using an approximation of 100*ln 2 more than 100 years before Napier and Briggs.^{[10]} Its exercises were largely copied without credit from Piero della Francesca's earlier book, Trattato d'abaco.^{[11]}
 De viribus quantitatis (Ms. Università degli Studi di Bologna, 1496–1508), a treatise on mathematics and magic. Written between 1496 and 1508, it contains the first reference to card tricks as well as guidance on how to juggle, eat fire, and make coins dance. It is the first work to note that Leonardo was lefthanded. De viribus quantitatis is divided into three sections: Mathematical problems, puzzles, and tricks, along with a collection of proverbs and verses. The book has been described as the "Foundation of modern magic and numerical puzzles," but it was never published and sat in the archives of the University of Bologna, where it was seen by only a small number of scholars during the Middle Ages. The book was rediscovered after David Singmaster, a mathematician, came across a reference to it in a 19thcentury manuscript. An English translation was published for the first time in 2007.^{[12]}
 Geometry (1509), a Latin translation of Euclid's Elements.
 Divina proportione (written in Milan in 1496–1498, published in Venice in 1509). Two versions of the original manuscript are extant, one in the Biblioteca Ambrosiana in Milan, the other in the Bibliothèque Publique et Universitaire in Geneva. The subject was mathematical and artistic proportion, especially the mathematics of the golden ratio and its application in architecture. It incorporates without credit a translation of the entire book De quinque corporibus regularibus by Piero della Francesca.^{[11]} Leonardo da Vinci drew the illustrations of the regular solids in Divina proportione while he lived with and took mathematics lessons from Pacioli. Leonardo's drawings are probably the first illustrations of skeletal solids, which allowed an easy distinction between front and back. The work also discusses the use of perspective by painters such as Piero della Francesca, Melozzo da Forlì, and Marco Palmezzano.^{[b]}
Translation of Piero della Francesca's work
The majority of the second volume of Summa de arithmetica, geometria. Proportioni et proportionalita was a slightly rewritten version of one of Piero della Francesca's works. The third volume of Pacioli's Divina proportione was an Italian translation of Piero della Francesca's Latin book De quinque corporibus regularibus. In neither case did Pacioli include an attribution to Piero. He was severely criticized for this and accused of plagiarism by sixteenthcentury art historian and biographer Giorgio Vasari. R. Emmett Taylor (1889–1956) said that Pacioli may have had nothing to do with the translated volume Divina proportione, and that it may just have been appended to his work. However, no such defense can be presented concerning the inclusion of Piero della Francesca's material in Pacioli's Summa.
Impact on accounting and business
Pacioli dramatically affected the practice of accounting by describing the doubleentry accounting method used in parts of Italy. This revolutionized how businesses oversaw their operations, enabling improved efficiency and profitability. The Summa's section on accounting was used internationally as an accounting textbook up to the mid16th century. The essentials of doubleentry accounting have for the most part remained unchanged for over 500 years. "Accounting practitioners in public accounting, industry, and notforprofit organizations, as well as investors, lending institutions, business firms, and all other users for financial information are indebted to Luca Pacioli for his monumental role in the development of accounting."^{[13]}
The ICAEW Library's rare book collection at Chartered Accountants' Hall holds the complete published works of Luca Pacioli. Sections of two of Pacioli's books, 'Summa de arithmetica' and 'Divina proportione' can be viewed online using Turning the Pages, an interactive tool developed by the British Library.^{[14]}
Chess
Luca Pacioli also wrote an unpublished treatise on chess, De ludo scachorum (On the Game of Chess). Long thought to have been lost, a surviving manuscript was rediscovered in 2006, in the 22,000volume library of Count Guglielmo CoroniniCronberg in Gorizia. A facsimile edition of the book was published in Pacioli's home town of Sansepolcro in 2008. Based on Leonardo da Vinci's long association with the author and his having illustrated Divina proportione, some scholars speculate that Leonardo either drew the chess problems that appear in the manuscript or at least designed the chess pieces used in the problems.^{[15]}^{[16]}^{[17]}^{[18]}
See also
References
Footnotes
 ^ Benedetto Cotrugli predates him with the idea of a doubleentry system with his manuscript Della Mercatura e del mercante perfetto which was written in 1458, but officially published in the 16th century.^{[5]}
 ^ The Metropolitan Museum of Art in New York City claims that the "M" logo it uses to decorate souvenir items (which the museum calls "the Renaissance M") is from an illustration originally in the Divina proportione. See "Renaissance 'M' bookmark". The Met Store (Metropolitan Museum of Art shopping catalog)..
Citations
 ^ "The Enigma of Luca Pacioli's Portrait". RitrattoPacioli. Retrieved 30 January 2015.
 ^ Di Teodoro, Francesco Paolo (2014). "Pacioli, Luca". Dizionario Biografico degli Italiani (in Italian). Vol. 80. Treccani. Retrieved 30 January 2015.
 ^ Tarquini, Luca (23 December 2016). il Falco e il Topo Manualetto di Gestione Aziendale. Lulu.com. ISBN 9781326893934 – via Google Books.
 ^ Diwan, Jaswith. Accounting Concepts & Theories. London: Morre. pp. 001–002. id# 94452.
 ^ Sangster, Alan; Rossi, Franco (December 2018). "Benedetto cotrugli on double entry Bookkeeping". De Computis, Revista Española de Historia de la Contabilidad. 15 (2): 22–38. doi:10.26784/issn.18861881.v15i2.332.
 ^ MacKinnon, Nick (1993). "The Portrait of Fra Luca Pacioli". The Mathematical Gazette. 77 (479): 132, 160. doi:10.2307/3619717. JSTOR 3619717. S2CID 195006163.
 ^ ^{a} ^{b} ^{c} "Pacioli biography". wwwgroups.dcs.stand.ac.uk. Retrieved 24 March 2016.
 ^ Heeffer, 2010
 ^ Chiappetta, Barbara; Larson, Kermit D. (15 November 1995). Fundamental Accounting Principles: Student Learning Tools. McGrawHill Higher Education. p. 209. ISBN 9780256207484. Retrieved 10 November 2023 – via Google Books.
 ^ Stand.ac.uk A Napierian logarithm before Napier, John J O'Connor and Edmund F Robertson
 ^ ^{a} ^{b} Davis, Margaret Daly (1977). Piero Della Francesca's Mathematical Treatises: The Trattato D'abaco and Libellus de Quinque Corporibus Regularibus (in English and Italian). Longo Editore. p. 64.
 ^ McDonald, Lucy (10 April 2007). "And that's renaissance magic ..." The Guardian. Retrieved 30 January 2015.
 ^ Smith, L. Murphy (2018). "Luca Pacioli: The Father of Accounting". SSRN 2320658.
 ^ "Turning the Pages: ICAEW's collection of rare books". ICAEW.com. ICAEW. Retrieved 22 June 2020.
 ^ Times Online: Renaissance chess master and the Da Vinci decode mystery
 ^ "International Herald Tribune: Experts link Leonardo da Vinci to chess puzzles in longlost Renaissance treatise".
 ^ "Winnipeg Free Press: Chess".
 ^ "Experts link Leonardo da Vinci to chess puzzles  USATODAY.com". usatoday30.usatoday.com.
Sources
 Bambach, Carmen (2003). "Leonardo, LeftHanded Draftsman and Writer". New York: Metropolitan Museum of Art. Retrieved 2 September 2006.
 Calzoni, Giuseppe and Gianfranco Cavazzoni (eds.) (1996) Tractatus Mathematicus ad Discipulos Perusinos, Città di Castello, Perugia.
 Galassi, Giuseppe. "Pacioli, Luca (c. 1445c.1517)." In History of Accounting: an International Encyclopedia, edited by Michael Chatfield and Richard Vangermeersch. New York: Garland Publishing, 1996. pp. 445–447.
 GleesonWhite, Jane, "Double Entry: How the Merchants of Venice Created Modern Finance," New York: Norton, 2012.
 Heeffer, Albrecht, "Algebraic partitioning problems from Luca Paccioli's Perugia manuscript (Vat. Lat. 3129)" in Sources and Commentaries in Exact Sciences, (2010), 11, pp. 3–52.
 Pacioli, Luca. De divina proportione (English: On the Divine Proportion), (Antonio Capella) Venice: Paganino Paganini (1509).
 Taylor, Emmet, R. No Royal Road: Luca Paccioli and his Times (1942)
 O'Connor, John J.; Robertson, Edmund F., "Luca Pacioli", MacTutor History of Mathematics Archive, University of St Andrews
 Lucas Paccioli  Catholic Encyclopedia article
 Libellus de quinque corporibus regularibus, corredato della versione volgare di Luca Paccioli [facsimile del Codice Vat. Urb. Lat. 632]; eds. Cecil Grayson,... Marisa Dalai Emiliani, Carlo Maccagni. Firenze, Giunti, 1995. 3 vol. (68 ff., XLIV213, XXII223 pp.). ISBN 8809010205
 Varisco, Alessio, Borgo Sansepolcro. Città di cavalieri e pellegrini Pessano con Bornago, MimepDocete (2012).
External links
 Works by or about Luca Pacioli at Internet Archive
 Luca Pacioli at the Mathematics Genealogy Project
 The Enigma of Luca Paccioli's Portrait
 Full text of De divina proportione
 Luca Paccioli's economic research programme
 Diuina proportione, Venice, 1509, digitized at Biblioteca Digital Hispánica , Biblioteca Nacional de España
 Lauwers, Luc & Willekens, Marleen: Five Hundred Years of Bookkeeping: A Portrait of Luca Pacioli (Tijdschrift voor Economie en Management, Katholieke Universiteit Leuven, 1994, vol. XXXIX issue 3 pp. 289–304) pdf