Luca Bartolomeo de Pacioli,
O.F.M. (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, mathematical structure, structure, space, Mathematica ...
,
Franciscan friar, collaborator with
Leonardo da Vinci
Leonardo di ser Piero da Vinci (15 April 1452 - 2 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 o ...
, and an early contributor to the field now known as
accounting
Accounting, also known as accountancy, is the process of recording and processing information about economic entity, economic entities, such as businesses and corporations. Accounting measures the results of an organization's economic activit ...
. 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
Tuscany ( ; ) is a Regions of Italy, region in central Italy with an area of about and a population of 3,660,834 inhabitants as of 2025. The capital city is Florence.
Tuscany is known for its landscapes, history, artistic legacy, and its in ...
.
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.
He moved to
Venice
Venice ( ; ; , formerly ) is a city in northeastern Italy and the capital of the Veneto Regions of Italy, region. It is built on a group of 118 islands that are separated by expanses of open water and by canals; portions of the city are li ...
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
The Franciscans are a group of related organizations in the Catholic Church, founded or inspired by the Italian saint Francis of Assisi. They include three independent Religious institute, religious orders for men (the Order of Friars Minor bei ...
friar.
[ Thus, he could be referred to as Fra ('Friar') Luca.
In 1475, he started teaching in ]Perugia
Perugia ( , ; ; ) is the capital city of Umbria in central Italy, crossed by the River Tiber. The city is located about north of Rome and southeast of Florence. It covers a high hilltop and part of the valleys around the area. It has 162,467 ...
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 a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...
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
Ludovico Maria Sforza (; 27 July 1452 – 27 May 1508), also known as Ludovico il Moro (; 'the Moor'), and called the "arbiter of Italy" by historian Francesco Guicciardini, to work in Milan
Milan ( , , ; ) is a city in northern Italy, regional capital of Lombardy, the largest city in Italy by urban area and the List of cities in Italy, second-most-populous city proper in Italy after Rome. The city proper has a population of nea ...
. There he met, taught mathematics to, collaborated, and lived with Leonardo da Vinci
Leonardo di ser Piero da Vinci (15 April 1452 - 2 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 o ...
. 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.[
]
Mathematics
Pacioli published several works on mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...
, 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.
* (Venice
Venice ( ; ; , formerly ) is a city in northeastern Italy and the capital of the Veneto Regions of Italy, region. It is built on a group of 118 islands that are separated by expanses of open water and by canals; portions of the city are li ...
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, 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
Accounting ethics is primarily a field of applied ethics and is part of business ethics and human ethics, the study of moral values and judgments as they apply to accountancy. It is an example of professional ethics. Accounting was introduced b ...
to cost accounting. 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](_blank)
A Napierian logarithm before Napier, John J O'Connor and Edmund F Robertson Its exercises were largely copied without credit from Piero della Francesca'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 (; ; 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 geometry that largely domina ...
'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 summation, sum to the larger of the two quantities. Expressed algebraically, for quantities and with , is in a golden ratio to if
\fr ...
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 construction, constructi ...
. It incorporates without credit a translation of the entire book '' De quinque corporibus regularibus'' by Piero della Francesca.[ ]Leonardo da Vinci
Leonardo di ser Piero da Vinci (15 April 1452 - 2 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 o ...
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.[The ]Metropolitan Museum of Art
The Metropolitan Museum of Art, colloquially referred to as the Met, is an Encyclopedic museum, encyclopedic art museum in New York City. By floor area, it is the List of largest museums, third-largest museum in the world and the List of larg ...
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'' .
Translation of Piero della Francesca's work
The majority of the second volume of 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
Giorgio Vasari (30 July 1511 – 27 June 1574) was an Italian Renaissance painter, architect, art historian, and biographer who is best known for his work ''Lives of the Most Excellent Painters, Sculptors, and Architects'', considered the ideol ...
. 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
Around 1500, Pacioli wrote an unpublished treatise on chess
Chess is a board game for two players. It is an abstract strategy game that involves Perfect information, no hidden information and no elements of game of chance, chance. It is played on a square chessboard, board consisting of 64 squares arran ...
, '' 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 typewritten, as opposed to mechanically printed or reproduced in some indirect or automated way. More recently, the term has ...
was rediscovered in 2006, in the 22,000-volume library of Count Guglielmo Coronini-Cronberg in Gorizia
Gorizia (; ; , ; ; ) is a town and (municipality) in northeastern Italy, in the autonomous region of Friuli-Venezia Giulia. It is located at the foot of the Julian Alps, bordering Slovenia. It is the capital of the Province of Gorizia, Region ...
. 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.
See also
* List of Roman Catholic scientist-clerics
* Della mercatura e del mercante perfetto
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).
* Taylor, Emmet, R. ''No Royal Road: Luca Paccioli and his Times'' (1942)
*
Lucas Paccioli
- Catholic Encyclopedia 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 (Katholieke Universiteit Leuven) is a Catholic research university in the city of Leuven, Belgium. Founded in 1425, it is the oldest university in Belgium and the oldest university in the Low Countries.
In addition to its main camp ...
, 1994, vol. XXXIX issue 3 pp. 289–304
pdf
{{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 Italian male writers