Fra Luca Bartolomeo de
Pacioli (sometimes Paciolo) (1446/7–1517) was an
Italian mathematician and
Franciscan friar, collaborator with
Leonardo da Vinci, and seminal
contributor to the field now known as accounting. He was also called
Luca di Borgo after his birthplace, Borgo Santo Sepolcro, Tuscany.
Life
Luca
Pacioli was born in 1445 in Borgo San Sepolcro, a small Tuscan town and belonged, being the son of
Bartholomeus Pacioli, to a middle class family. His first
teacher was no less a person than the painter
Piero della Francesca, who, typically
for ItalianHumanism, masterfully connected mathematics, science and
art. In 1464 Luca Pacioli became employed as a private teacher by a
rich Venetian merchant by the name of Ailtonio de Rompiasi.
Together with Rompiasi's sons he attended the lectures of the
mathematician Domenico Bragadino in the Scuolo di Rialto, a school
of great importance for the history of
Aristotelianism. Most probably he also
worked as Rompiasi's bookkeeper.
In 1470 Pacioli stayed in Rome at the house
of the famous architect, philosopher and mathematician Leon Battista Alberti. This
move to Rome was advised by his teacher Piero, who had worked
together with Alberti in the church of Sail Francesco in Rimini
during the fifties. In 1473 Pacioli became a
Franciscan Minor under the name Frater Lucas de
Borgo San Sepulcro.
In 1475, he started teaching in Perugia and wrote a comprehensive
textbook in the vernacular for his students during 1477 and 1478.
It is thought that he then started teaching university mathematics
and he did so in a number of Italian universities, including
Perugia, holding the first chair in mathematics in two of them. He
also continued to work as a private tutor of
mathematics and was, in fact, instructed to stop
teaching at this level in Sansepolcro in 1491. In 1494, his first
book to be printed,
Summa de arithmetica, geometria,
proportioni et proportionalita, was published in Venice.
In 1497,
he accepted an invitation from Lodovico
Sforza ("Il Moro") to work in Milan.
There he met, collaborated with, lived with, and taught mathematics
to
Leonardo da Vinci. In 1499,
Pacioli and Leonardo were forced to flee Milan when
Louis XII of France seized the city and
drove their patron out. Their paths appear to have finally
separated around 1506. Pacioli died aged 70 in 1517, most likely in
Sansepolcro where it is thought he had spent much of his final
years.
Mathematics
Pacioli published several works on
mathematics, including:
- 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
the first published description of the method of bookkeeping that
Venetian merchants used during the Italian Renaissance, known as
the double-entry
accounting system. Although Pacioli codified rather than
invented this system, he is widely regarded as the "Father of
Accounting". 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 and income statement, respectively. He
demonstrated year-end closing entries and proposed that a trial balance be used to prove a balanced
ledger. Also, his treatise touches on a wide range of related
topics from accounting ethics to
cost accounting.
- 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, and 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, seen only by a small number of scholars since 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.[2721]
- Geometry (1509), a Latin translation of Euclid's Elements.
- 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 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 Pacioli's Summa.
Chess
Pacioli also wrote an unpublished treatise on
chess,
De ludo
scacchorum (
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 problems.
Notes
- 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, p.290)[1]
- The Met Store (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".
- Times Online: Renaissance chess master and the Da
Vinci decode mystery
- International Herald Tribune: Experts link Leonardo
da Vinci to chess puzzles in long-lost Renaissance
treatise
- Winnipeg Free Press: Chess
- Experts link Leonardo da Vinci to chess
puzzles
References
- Pacioli, Luca. De divina proportione (English: On
the Divine Proportion), Luca Paganinem de Paganinus de Brescia
(Antonio Capella) 1509, Venice
- Taylor, Emmet, R. No Royal Road: Luca Pacioli and his
Times (1942)
- Luca Pacioli: The Father of Accounting
- Full Biography of Pacioli (St.Andrews)
- Lucas Pacioli - Catholic Encyclopedia article
- Libellus de quinque corporibus regularibus, corredato
della versione volgare di Luca Pacioli [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
External links