Editing Luca Pacioli

{{Short description|15th c. Franciscan Friar, mathematician and publisher of accounting treatise}}
{{distinguish|Luca Pacioni}}
{{Use dmy dates|date=September 2020}}
{{Infobox person
 |name        = Luca Pacioli, [[Order of Friars Minor|O.F.M.]]
 |image       = Pacioli.jpg
 |image_size  = 
 |alt         = Portrait of Friar Luca Pacioli
 |caption     = ''[[Portrait of Luca Pacioli]]'', traditionally attributed to [[Jacopo de' Barbari]], 1495<ref>{{Cite web|title=The Enigma of Luca Pacioli's Portrait|url=http://www.ritrattopacioli.it/texting.htm|website=RitrattoPacioli|access-date=30 January 2015}}</ref>
 |birth_date  = {{circa}} 1447<ref name="Treccani">{{Cite encyclopedia|title=Pacioli, Luca|encyclopedia=Dizionario Biografico degli Italiani|language=it|volume=80|year=2014|last=Di Teodoro|first=Francesco Paolo|publisher=Treccani|url=http://www.treccani.it/enciclopedia/luca-pacioli_%28Dizionario-Biografico%29/|access-date=30 January 2015}}</ref>
 |birth_place = [[Sansepolcro]], [[Republic of Florence]]
 |death_date  = {{Death date and age|df=yes|1517|6|19|1447}}
 |death_place = Sansepolcro, Republic of Florence
 |citizenship = Florentine
 |occupation  = Friar, mathematician, writer
 |known_for   = ''[[Summa de arithmetica]]'',<br/>''[[Divina proportione]]'',<br/>[[Double-entry bookkeeping system|double-entry bookkeeping]]
}}

'''Luca Bartolomeo de Pacioli, [[Order of Friars Minor|O.F.M.]]''' (sometimes ''Paccioli'' or ''Paciolo''; {{circa}} 1447 – 19 June 1517)<ref>{{Cite book|url=https://books.google.com/books?id=Sj6RDgAAQBAJ&pg=PA40|title=il Falco e il Topo Manualetto di Gestione Aziendale|first=Luca|last=Tarquini|date=23 December 2016 |publisher=Lulu.com|isbn=9781326893934 |via=Google Books}}</ref> was an Italian [[mathematician]], [[Order of Friars Minor|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 [[Double-entry bookkeeping system|double-entry system of book-keeping]] on the continent. He was also called '''Luca di Borgo''' after his birthplace, [[Sansepolcro|Borgo Sansepolcro]], [[Tuscany]].

==Life==
[[File:Luca Pacioli in the Summa.jpg|thumb|A woodcut of Pacioli which appears throughout the ''[[Summa de arithmetica]]''<ref>{{cite journal |doi=10.2307/3619717 |title=The Portrait of Fra Luca Pacioli |journal=[[The Mathematical Gazette]] |volume=77 |issue=479 |pages=132, 160 |year=1993 |last1=MacKinnon |first1=Nick|jstor=3619717 |s2cid=195006163 }}</ref>]]
Luca Pacioli was born between 1446 and 1448 in the Tuscan town of [[Sansepolcro]] where he received an [[Abacus school|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.<ref name=bio>{{Cite web|url=http://www-groups.dcs.st-and.ac.uk/history/Biographies/Pacioli.html|title=Pacioli biography|website=www-groups.dcs.st-and.ac.uk|access-date=24 March 2016}}</ref> 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.<ref name=bio/> 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, {{lang|la|[[Summa de arithmetica|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.<ref name=bio/>

==Mathematics==
[[Image:De divina proportione - Vigintisex Basium Planum Vacuum.jpg|thumb|The first printed illustration of a [[rhombicuboctahedron]], by [[Leonardo da Vinci]], published in ''[[Divina proportione]]'']]
[[Image:Pacioli De Divina Proportione Head Equilateral Triangle 1509.jpg|thumb|Woodcut illustrating the proportions of the human face from the second part of ''Divina proportione'', which covers the Vitruvian system]]
{{further|Mathematics and art}}

Pacioli published several works on [[mathematics]], including:
*{{lang|la|Tractatus mathematicus ad discipulos perusinos}} (Ms. Vatican Library, Lat. 3129), a nearly 600-page 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.<ref>Heeffer, 2010</ref>
*{{lang|la|[[Summa de arithmetica|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 [[double-entry 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.<ref>{{Cite book |url=https://books.google.com/books?id=3ydxTif500YC&q=%22Luca%20Pacioli%22%20bed%20night |title=Fundamental Accounting Principles: Student Learning Tools |first1=Barbara |last1=Chiappetta |first2=Kermit D. |last2=Larson |publisher=[[McGraw-Hill Higher Education]] |isbn=9780256207484 |page=209 |date=1995-11-15 |access-date=2023-11-10 |via=Google Books}}</ref> 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 year-end 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 [[John Napier|Napier]] and [[Henry Briggs (mathematician)|Briggs]].<ref name="paccioliLog">[http://www-history.mcs.st-andrews.ac.uk/Extras/Pacioli_logarithm.html St-and.ac.uk] A Napierian logarithm before Napier, John J O'Connor and Edmund F Robertson</ref> Its exercises were largely copied without credit from [[Piero della Francesca]]'s earlier book, ''Trattato d'abaco''.<ref name=davis>{{cite book
 | last = Davis | first = Margaret Daly
 | language = en,it
 | page = 64
 | publisher = Longo Editore
 | title = Piero Della Francesca's Mathematical Treatises: The Trattato D'abaco and Libellus de Quinque Corporibus Regularibus
 | year = 1977}}</ref>
* {{lang|la|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 left-handed. ''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 19th-century manuscript. An English translation was published for the first time in 2007.<ref>{{cite news |title=And that's renaissance magic ... |last=McDonald |first=Lucy |date=10 April 2007 |newspaper=[[The Guardian]] |url=https://www.theguardian.com/italy/story/0,,2053433,00.html |access-date=30 January 2015}}</ref>
* ''Geometry'' (1509), a Latin translation of [[Euclid]]'s [[Euclid's Elements|''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]].<ref name=davis/> [[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]].<ref group=lower-alpha>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'' {{cite web |url=http://store.metmuseum.org/magnets+bookmarks/renaissance-m-bookmark/invt/10086668 |website=The Met Store (Metropolitan Museum of Art shopping catalog) |title=Renaissance 'M' bookmark}}.</ref>

===Translation of Piero della Francesca's work===
The majority of the second volume of {{lang|la|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 sixteenth-century 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 double-entry 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 mid-16th century. The essentials of double-entry accounting have for the most part remained unchanged for over 500 years. "Accounting practitioners in public accounting, industry, and not-for-profit 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."<ref>{{Cite SSRN|last=Smith|first=L. Murphy|date=2018|title=Luca Pacioli: The Father of Accounting|ssrn=2320658}}</ref>

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.<ref>{{cite web |title=Turning the Pages: ICAEW's collection of rare books |url=https://www.icaew.com/library/library-collection/historical-accounting-literature/turning-the-pages |website=ICAEW.com |publisher=ICAEW |access-date=22 June 2020}}</ref>

==Chess==
Around 1500, Pacioli 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 22,000-volume library of Count Guglielmo Coronini-Cronberg 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 problem]]s that appear in the manuscript or at least designed the chess pieces used in the problems.<ref>[https://web.archive.org/web/20080509143211/http://www.timesonline.co.uk/tol/life_and_style/court_and_social/article3523718.ece Times Online: Renaissance chess master and the Da Vinci decode mystery]</ref><ref>{{Cite web|url=http://www.iht.com/articles/ap/2008/03/14/europe/EU-GEN-Italy-Da-Vinci-Chess-Code.php|title=International Herald Tribune: Experts link Leonardo da Vinci to chess puzzles in long-lost Renaissance treatise}}</ref><ref>{{Cite web|url=http://www.winnipegfreepress.com/life/story/4150848p-4739893c.html|title=Winnipeg Free Press: Chess}}</ref><ref>{{Cite web|url=https://usatoday30.usatoday.com/tech/science/discoveries/2008-03-14-leondardo-chess-puzzles_N.htm|title=Experts link Leonardo da Vinci to chess puzzles - USATODAY.com|website=usatoday30.usatoday.com}}</ref>

==See also==
*[[List of Catholic churchmen-scientists|List of Roman Catholic scientist-clerics]]
*[[Della mercatura e del mercante perfetto]]

==References==
'''Footnotes'''
{{notelist}}

'''Citations'''
{{reflist}}

===Sources===
*{{cite web| url = http://www.metmuseum.org/special/Leonardo_Master_Draftsman/draftsman_left_essay.asp| title = Leonardo, Left-Handed Draftsman and Writer| access-date = 2 September 2006| last = Bambach| first = Carmen| year = 2003| publisher = New York: Metropolitan Museum of Art}}
* Calzoni, Giuseppe and Gianfranco Cavazzoni (eds.) (1996) ''Tractatus Mathematicus ad Discipulos Perusinos'', Città di Castello, Perugia.
*Galassi, Giuseppe. [https://archive.today/20121211103236/http://clio.lib.olemiss.edu/u?/aah,525 "Pacioli, Luca (c. 1445-c.1517)."] In ''History of Accounting: an International Encyclopedia,'' edited by [[Michael Chatfield]] and [[Richard Vangermeersch]]. New York: Garland Publishing, 1996. pp.&nbsp;445–447.
* Gleeson-White, 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.&nbsp;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)
* {{MacTutor|id=Pacioli}}
* [http://www.newadvent.org/cathen/11383b.htm 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., XLIV-213, XXII-223 pp.).  {{isbn|88-09-01020-5}}
* Varisco, Alessio, ''Borgo Sansepolcro. Città di cavalieri e pellegrini'' Pessano con Bornago, Mimep-Docete (2012).

==External links==
{{wikiquote}}
{{commons category}}
* {{Internet Archive author |sname=Luca Pacioli}}
* {{MathGenealogy|id=126888}}
* [http://www.ritrattopacioli.it/texting.htm The Enigma of Luca Paccioli's Portrait]
* [https://issuu.com/s.c.williams-library/docs/de_divina_proportione Full text of ''De divina proportione'']
* [https://web.archive.org/web/20120120141459/http://www.pacioli-institute.org/ Luca Paccioli's economic research programme]
* [http://bdh.bne.es/bnesearch/detalle/1811636 ''Diuina proportione''], Venice, 1509, digitized at {{ill|Biblioteca Digital Hispánica|es}}, [[Biblioteca Nacional de España]]
* Lauwers, Luc & Willekens, Marleen: ''Five Hundred Years of Bookkeeping: A Portrait of Luca Pacioli'' (Tijdschrift voor Economie en Management, [[w:Katholieke Universiteit Leuven|Katholieke Universiteit Leuven]], 1994, vol.&nbsp;XXXIX issue&nbsp;3 pp.&nbsp;289–304) [https://lirias.kuleuven.be/bitstream/123456789/119065/1/TEM1994-3_289-304p.pdf pdf]

{{Mathematics and art}}
{{Authority control}}

{{DEFAULTSORT:Pacioli, Luca}}
[[Category:1440s births]]
[[Category:1517 deaths]]
[[Category:People from Sansepolcro]]
[[Category:15th-century Italian mathematicians]]
[[Category:16th-century Italian mathematicians]]
[[Category:Leonardo da Vinci]]
[[Category:Italian accountants]]
[[Category:Magic squares]]
[[Category:Italian Franciscans]]
[[Category:Catholic clergy scientists]]
[[Category:Number theorists]]
[[Category:History of accounting]]
[[Category:15th-century Italian writers]]
[[Category:16th-century Italian writers]]
[[Category:16th-century Italian male writers]]