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Pacioli

Name: Lucas de Burgo Pacioli

Nickname/Alias: Luca Pacioli

Achievements: Double-entry book-keeping

Born: c. 1445; Sansepolcro, Umbria, Italy

Died: 1517; Sansepolcro, Umbria, Italy (Aged about 72)

Field & Discipline: Mathematics

Language: Italian

Father: Bartolomeo Pacioli

Mother: Unknown

Siblings: 2 brothers

Spouse: None

Children: None

Education: Unknown

Major Work:

"Summa de arithmetica, geometria, proportioni et proportionalita"

"De Divina proportione"

Life & Times:

Pacioli may have briefly attended a Franciscan school, (he eventually became a friar), but at an early age was apprenticed to a merchant, Folco de Befolci.  He met artist [met] della Francesca*, also a native of Sansepolcro, through whom he got access to the library of [used library of] Federigo di Montefeltro*, Duke of Urbino. 

In his teens, Pacioli became tutor to the three sons of a rich Venetian merchant, Antonio de Rompiasi.  While tutoring, he continued his own education, studying mathematics under Domenico Bragadino, who operated a school in Venice.  At 25,  Pacioli wrote his first mathematical manual, dedicating it to Rompiasi's sons. 

He next went to Rome, where he lived for a time as guest of architect [house-guest of] Alberti*, and then joined the Franciscan order of monks.  His two brothers also joined the order.

Pacioli  then began to travel the Italian peninsula, giving lectures in mathematics.  At the University of Perugia, (1477 to 1480), he wrote a mathematical treatise dedicated to the "Youth of Perugia.”  He visited the Venetian province of Zara (now Zadar, in Yugoslavia) in 1481, where he wrote another mathematical work.  In 1489, he stayed with Giuliano della Rovere (later to become Pope [house-guest of] Julius II*) in his palace in Rome and taught in Rome and Naples before returning to Sansepolcro around 1490.

Pacioli wrote his most important work, "Summa de arithmetica, geometria, proportioni et proportionalita,” published in 1494, to correct what he considered the lamentable state of mathematical teaching in Italy.  His main source for the book was the thirteenth-century work of Leonardo Fibonacci of Pisa. 

Written in Italian, "Summa" included  the first accurate written description of [formalized] double-entry bookkeeping*, a system already used in European commerce, though Pacioli linked it with the classical theories of Greek mathematician Pythagoras.  "Summa" also included a discourse on theoretical and practical arithmetic, tables of various currencies, weights and measures used in various Italian states, a summary of [did summary of] Euclid*'s  geometry, and the elements of algebra.  Pacioli made the book more interesting by including military games and exercises that involved mathematics.

Pacioli's volume was a breakthrough in practical mathematics because other works prompted by the growth of commercialism were usually only relevant to one particular profession or trade. 

Widely read, "Summa" influenced the work of other mathematicians, including [influenced] Tartaglia*, and the practice of double-entry bookkeeping spread throughout Europe.  Pacioli dedicated "Summa" to Guidobaldo da Montelfeltro, the Duke of Urbino.  (It is clear Pacioli spent considerable time in Urbino: he is portrayed as St. Peter the Martyr in a painting by della Francesca  commissioned for Urbino's Church of San Bernadino; and a painting by Jacopo de' Barbari shows what is more than likely Pacioli teaching the young Guidobaldo.)

Duke Lodovico Sforza persuaded Pacioli to move to Milan and made him Professor of Mathematics at the University of Pavia and at the Academy in Milan.  During his stay, Pacioli met [a pal of] da Vinci*, and the two became close friends.  Da Vinci illustrated the first part of Pacioli's "De Divina proportione,” a volume he began at the Duke's court and was to complete some years later.

Renaissance artists, architects and designers constantly argued about "perfect proportion,” that is, the proportion of lines and shapes that would create a classical, esthetically satisfying whole. Pacioli defined perfect proportion -- known as the Golden Mean -- as the division of a line so that the shorter part is to the longer as the longer is to the whole: approximately 8:13.  His writings on proportion influenced da Vinci, [influenced] Durer*, and other painters.

Soon after the French captured Milan in 1499, Pacioli and da Vinci left Milan together, staying briefly in Mantua and Venice before settling together in Florence.  In 1500, Pacioli began teaching geometry according to Euclid's "Elements" at the University of Pisa, which was under Florentine control.  He had already begun both a Latin version and an Italian version of Euclid from the original Greek text. 

In 1501, he was appointed Lecturer at Bologna University, and also gave lectures in Perugia, Rome and Venice.  In 1508, his friend Pope Julius II  exempted Pacioli from the rules of the Franciscan Order that prohibited ownership of property.

Also in 1508, Pacioli gave an important lecture in Venice on "Proportion and Proportionality.”  Basing his lecture on the fifth book of Euclid, he discussed the relevance of proportion to religion, medicine, printing, sculpture, architecture, music, law and grammar. 

In 1509, "De Divina Proportione,” the book he began in Milan, was published.  It included the first Italian translation of Piero della Francesca's manual on perspective.  In his writing on Euclid, Pacioli included his discourse on the Golden Mean.  He used practical examples to illustrate his theory, such as fortress walls and battlements, stables, fountains, and even latrines. He also included designs for an alphabet constructed on geometrical principles.  The large, beautiful lettering is presumed to have been done by da Vinci.

In 1510, Pacioli was recalled to Sansepolcro to head the Franciscan Order there.  As far as is known, he remained there for the last seven years of his life, apart from a short visit in 1514 to Rome, where he was summoned by Pope Leo X to teach mathematics at the Rome Academy.

Extra Connections: Dedicated a book to [dedicated book to] Isabella D’Este*

Assessment: Best known for accurately describing double-entry bookkeeping, the practice of which spread throughout Europe.

Oneliner: Luca Pacioli, who introduced double-entry bookkeeping

Bibliography:

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