Fra Luca Bartolomeo de Pacioli (sometimes ''Paccioli'' or ''Paciolo''; 1447 – 19 June 1517) was an Italian

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History ...

Franciscan , image = FrancescoCoA PioM.svg , image_size = 200px , caption = A cross, Christ's arm and Saint Francis's arm, a universal symbol of the Franciscans , abbreviation = OFM , predecessor = , ...

friar A friar is a member of one of the mendicant orders founded in the twelfth or thirteenth century; the term distinguishes the mendicants' itinerant apostolic character, exercised broadly under the jurisdiction of a superior general, from the ...

, collaborator with

Leonardo da Vinci Leonardo di ser Piero da Vinci (15 April 14522 May 1519) was an Italian polymath of the High Renaissance who was active as a painter, draughtsman, engineer, scientist, theorist, sculptor, and architect. While his fame initially rested on h ...

, and an early contributor to the field now known as

accounting Accounting, also known as accountancy, is the measurement, processing, and communication of financial and non financial information about economic entities such as businesses and corporations. Accounting, which has been called the "languag ...

. 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 system of book-keeping on the continent. He was also called Luca di Borgo after his birthplace, Borgo Sansepolcro,

Tuscany it, Toscano (man) it, Toscana (woman) , population_note = , population_blank1_title = , population_blank1 = , demographics_type1 = Citizenship , demographics1_footnotes = , demographics1_title1 = Italian , demogra ...

. Several of his works were plagiarised from

Piero della Francesca Piero della Francesca (, also , ; – 12 October 1492), originally named Piero di Benedetto, was an Italian painter of the Early Renaissance. To contemporaries he was also known as a mathematician and geometer. Nowadays Piero della Francesca ...

, in what has been called "probably the first full-blown case of plagiarism in the history of mathematics".

Life

Luca Pacioli was born between 1446 and 1448 in the Tuscan town of

Sansepolcro Sansepolcro, formerly Borgo Santo Sepolcro, is a town and '' comune'' founded in the 11th century, located in the Italian Province of Arezzo in the eastern part of the region of Tuscany. Situated on the upper reaches of the Tiber river, the town ...

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. He moved to

Venice Venice ( ; it, Venezia ; vec, Venesia or ) is a city in northeastern Italy and the capital of the Veneto region. It is built on a group of 118 small islands that are separated by canals and linked by over 400 bridges. The isla ...

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

friar. 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 Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

and was instructed to stop teaching at this level in Sansepolcro in 1491. In 1494, his first book, , was published in Venice. In 1497, he accepted an invitation from Duke Ludovico Sforza to work in

Milan Milan ( , , Lombard language, Lombard: ; it, Milano ) is a city in northern Italy, capital of Lombardy, and the List of cities in Italy, second-most populous city proper in Italy after Rome. The city proper has a population of about 1.4 ...

. There he met, taught mathematics to, collaborated, and lived with

. In 1499, Pacioli and Leonardo were forced to flee Milan when

Louis XII of France Louis XII (27 June 14621 January 1515), was List of French monarchs, King of France from 1498 to 1515 and King of Naples from 1501 to 1504. The son of Charles, Duke of Orléans, and Maria of Cleves, he succeeded his 2nd cousin once removed and b ...

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.

Mathematics

Pacioli published several works on

, including: * (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. * (

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. 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 In financial accounting, a balance sheet (also known as statement of financial position or statement of financial condition) is a summary of the financial balances of an individual or organization, whether it be a sole proprietorship, a business ...

and

income statement An income statement or profit and loss accountProfessional English in Use - Finance, Cambridge University Press, p. 10 (also referred to as a ''profit and loss statement'' (P&L), ''statement of profit or loss'', ''revenue statement'', ''stateme ...

, 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 Cost accounting is defined as "a systematic set of procedures for recording and reporting measurements of the cost of manufacturing goods and performing services in the aggregate and in detail. It includes methods for recognizing, classifying, al ...

. He introduced the Rule of 72, using an approximation of 100*ln 2 more than 100 years before Napier and Briggs.St-and.ac.uk
A Napierian logarithm before Napier, John J O'Connor and Edmund F Robertson Its exercises were largely copied without credit from

's earlier book, ''Trattato d'abaco''. * (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. * ''Geometry'' (1509), a Latin translation of

Euclid Euclid (; grc-gre, Εὐκλείδης; BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the '' Elements'' treatise, which established the foundations of ...

'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 In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Expressed algebraically, for quantities a and b with a > b > 0, where the Greek letter phi ( ...

and its application in

architecture Architecture is the art and technique of designing and building, as distinguished from the skills associated with construction. It is both the process and the product of sketching, conceiving, planning, designing, and constructing building ...

. It incorporates without credit a translation of the entire book '' De quinque corporibus regularibus'' by

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

, Melozzo da Forlì, and Marco Palmezzano.The

Metropolitan Museum of Art The Metropolitan Museum of Art of New York City, colloquially "the Met", is the largest art museum in the Americas. Its permanent collection contains over two million works, divided among 17 curatorial departments. The main building at 1000 ...

New York City New York, often called New York City or NYC, is the most populous city in the United States. With a 2020 population of 8,804,190 distributed over , New York City is also the most densely populated major city in the Un ...

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'' .

Translation of Piero della Francesca's work

The majority of the second volume of was a slightly rewritten version of one of

's works. The third volume of Pacioli's ''Divina proportione'' was an Italian translation of

'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 Giorgio Vasari (, also , ; 30 July 1511 – 27 June 1574) was an Italian Renaissance Master, who worked as a painter, architect, engineer, writer, and historian, who is best known for his work '' The Lives of the Most Excellent Painters, Sculp ...

. 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 ''Summas 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." 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.

Chess

Luca Pacioli also wrote an unpublished treatise on

chess Chess is a board game for two players, called White and Black, each controlling an army of chess pieces in their color, with the objective to checkmate the opponent's king. It is sometimes called international chess or Western chess to dis ...

, '' De ludo scachorum'' (''On the Game of Chess''). Long thought to have been lost, a surviving

manuscript A manuscript (abbreviated MS for singular and MSS for plural) was, traditionally, any document written by hand – or, once practical typewriters became available, typewritten – as opposed to mechanically printed or reproduced in ...

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 A chess problem, also called a chess composition, is a puzzle set by the composer using chess pieces on a chess board, which presents the solver with a particular task. For instance, a position may be given with the instruction that White is to ...

s that appear in the manuscript or at least designed the chess pieces used in the problems.

References

Footnotes Citations

Sources

* * Calzoni, Giuseppe and Gianfranco Cavazzoni (eds.) (1996) ''Tractatus Mathematicus ad Discipulos Perusinos'', Città di Castello, Perugia. *Galassi, Giuseppe
"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. 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. 3–52. * Pacioli, Luca. ''De divina proportione'' (English: ''On the Divine Proportion''), (Antonio Capella) Venice: Paganino Paganini (1509). * Smith, Murphy, Luca Pacioli: The Father of Accounting (2018). Available at SSRN: https://ssrn.com/abstract=2320658 or https://dx.doi.org/10.2139/ssrn.2320658. * Taylor, Emmet, R. ''No Royal Road: Luca Paccioli and his Times'' (1942)
Full Biography of Pacioli (St.Andrews)

-

Catholic Encyclopedia The ''Catholic Encyclopedia: An International Work of Reference on the Constitution, Doctrine, Discipline, and History of the Catholic Church'' (also referred to as the ''Old Catholic Encyclopedia'' and the ''Original Catholic Encyclopedia'') i ...

article * ''Libellus de quinque corporibus regularibus'', corredato della versione volgare di Luca Paccioli acsimile 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.). * Varisco, Alessio, ''Borgo Sansepolcro. Città di cavalieri e pellegrini'' Pessano con Bornago, Mimep-Docete (2012).

External links

* *
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 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 KU Leuven (or Katholieke Universiteit Leuven) is a Catholic research university in the city of Leuven, Belgium. It conducts teaching, research, and services in computer science, engineering, natural sciences, theology, humanities, medicine, ...

, 1994, vol. XXXIX issue 3 pp. 289–304
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{{DEFAULTSORT:Pacioli, Luca 1440s births 1517 deaths People from Sansepolcro 15th-century Italian mathematicians 16th-century Italian mathematicians Leonardo da Vinci Italian accountants Magic squares Italian Franciscans Catholic clergy scientists Number theorists History of accounting 15th-century Italian writers 16th-century Italian writers 16th-century male writers