Fra Luca Bartolomeo de Pacioli (sometimes Paccioli or Paciolo; c.
1447–1517) was an Italian mathematician,
collaborator with Leonardo da Vinci, and a seminal contributor to the
field now known as accounting. He is referred to as "The Father of
Accounting and Bookkeeping" in Europe and he was the first person to
publish a work on the double-entry system of book-keeping in that
continent. He was also called Luca di Borgo after his birthplace,
Borgo Sansepolcro, Tuscany.
2.1 Translation of Piero della Francesca's work
3 Impact on
Accounting and Business
5 See also
8 External links
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
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
Franciscan friar. Thus,
Luca Pacioli could be referred to
In 1475, he started teaching in Perugia, first as a private teacher,
from 1477 holding the first chair in mathematics. 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 in 1517, most likely in
Sansepolcro where it is thought
that he had spent much of his final years.
The first printed illustration of a rhombicuboctahedron, by Leonardo
da Vinci, published in De divina proportione, 1509
De divina proportione
De divina proportione illustrating the proportions of the
human face. Note that the lines or rectangles drawn do not correspond
to the golden ratio; this is from the second part of the book,
covering the Vitruvian system.
Mathematics and art
Pacioli published several works on mathematics, including:
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. One part of 25 pages is missing
from the chapter on algebra. A modern transcription has been published
by Calzoni and Cavazzoni (1996) along with a partial translation of
the chapter on partitioning problems (Heeffer, 2010).
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 equaled 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 and income statement, respectively. He demonstrated year-end
closing entries and proposed that a trial balance be used to prove a
balanced ledger. He is widely considered the "Father of Accounting".
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.
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.
Geometry (1509), a Latin translation of Euclid's Elements.
De divina proportione
De divina proportione (written in
Milan in 1496–98, 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. Leonardo da
Vinci drew the illustrations of the regular solids in De divina
proportione while he lived with and took mathematics lessons from
Pacioli. Leonardo's drawings are probably the first illustrations of
skeletonic 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. As
a side note, the "M" logo used by the
Metropolitan Museum of Art
Metropolitan Museum of Art in
New York City is taken from De divina proportione.
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 De
divina proportione was an Italian translation of Piero della
Francesca's Latin writings On [the] Five Regular Solids. 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 De divina proportione, and that it may just have
been appended to his work. However, no such defence can be presented
concerning the inclusion of Piero della Francesca's material in
Accounting and Business
Friar Luca dramatically affected the world of accounting, thereby
revolutionizing the manner that business managers could oversee
internal operations, enabling improved efficiency and profitability.
The Summa's section on accounting was used internationally as the
world's premier accounting textbook up to the mid-16th century. The
essentials of double-entry accounting have for the most part remain
unchanged for over 500 years. These essentials facilitated the
progress of business, which includes the formation of capital market
systems and modern economies, which in turn contributed to the
ever-rising standards of living in nations around the globe.
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.”
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 22,000-volume library of
Count Guglielmo Coronini. 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 De 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
List of Roman Catholic scientist-clerics
Della mercatura e del mercante perfetto
^ "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). 80. Treccani. Retrieved 30
^ Diwan, Jaswith.
Accounting Concepts & Theories. London: Morre.
pp. 001–002. id# 94452.
^ "Pacioli biography". www-groups.dcs.st-and.ac.uk. Retrieved
^ St-and.ac.uk A Napierian logarithm before Napier, John J O'Connor
and Edmund F Robertson
^ McDonald, Lucy (10 April 2007). "And that's renaissance magic ..."
The Guardian. Retrieved 30 January 2015.
^ The Met Store (
Metropolitan Museum of Art
Metropolitan Museum of Art shopping catalog),
"Renaissance 'M' Bookmark" The Museum claims this origin in its
descriptions of many souvenir items decorated with this logo, which it
calls the "Renaissance M".
^ Smith, Murphy (2018). "Luca Pacioli: The Father of Accounting".
^ Times Online: Renaissance chess master and the Da Vinci decode
^ International Herald Tribune: Experts link
Leonardo da Vinci
Leonardo da Vinci to
chess puzzles in long-lost Renaissance treatise
^ Winnipeg Free Press: Chess
^ Experts link
Leonardo da Vinci
Leonardo da Vinci to chess puzzles
Bambach, Carmen (2003). "Leonardo, Left-Handed Draftsman and Writer".
New York: Metropolitan Museum of Art. Retrieved 2006-09-02.
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.
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.
De divina proportione
De divina proportione (English: On the Divine
Proportion), (Antonio Capella) Venice:
Paganino Paganini (1509).
Smith, Murphy, Luca Pacioli: The Father of
Available at SSRN: https://ssrn.com/abstract=2320658 or
Taylor, Emmet, R. No Royal Road: Luca Paccioli and his Times (1942)
Full Biography of Pacioli (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., XLIV-213, XXII-223 pp.).
Varisco, Alessio, Borgo Sansepolcro. Città di cavalieri e pellegrini
Pessano con Bornago, Mimep-Docete (2012).
Wikiquote has quotations related to: Luca Pacioli
Wikimedia Commons has media related to Luca Pacioli.
Works by or about
Luca Pacioli at Internet Archive
Luca Pacioli at the
Mathematics Genealogy Project
Palladio's Literary Predecessors
The Enigma of Luca Paccioli's Portrait
Outline of Paccioli's Treatise - Particularis de Computis et
Full text of De divina proportione
Luca Paccioli's economic research programme
Pacioli Institute for a true and fair view of the knowledge-based
Online Galleries, History of Science Collections, University of
Oklahoma Libraries High resolution images of works by and/or portraits
Luca Pacioli in .jpg and .tiff format.
Diuina proportione, Venice, 1509, digitized at Biblioteca Digital
Hispánica, Biblioteca Nacional de España
Lauwers, Luc & Willekens, Marleen: Five Hundred Years of
Portrait of Luca Pacioli
Portrait of Luca Pacioli (Tijdschrift voor Economie en
Management, Katholieke Universiteit Leuven, 1994, vol. XXXIX
issue 3 p. 289–304) pdf
ISNI: 0000 0001 2135 5781
BNF: cb11918350c (data)