Luca Pacioli Biography

Fra Luca Bartolomeo de Pacioli was born in 1447 in Sansepolcro, a commercial town in the Tiber valley in Tuscany, Italy. His father’s name was Bartolomeo Pacioli. However, he was apparently raised by the Befolci family in Sansepolcro. He completed his initial studies in the local language and not in Latin. He received at least part of his early education at the studio/atelier of Piero Della Francesca in Sansepolcro.

During his late teens (1464), Luca Pacioli went to Venice, where he began working for a merchant named Antonio Rompiansi/Rompiasi of the Giudecca district. While staying in the merchant’s house, he tutored his three sons. Simultaneously, he continued his higher studies in mathematics under Domenico Bragadino in Venice.

Apart from being involved in mathematical studies, Pacioli also gained knowledge of business while helping Rompiansi. This resulted in his first arithmetic book in 1470, which he dedicated to his first students, the three sons of Rompiansi. The merchant probably died by 1470.

Luca Pacioli moved to Rome, where he lived for several months in the home of mathematician/architect Leone Battista Alberti. Through Alberti, Pacioli came in contact with the papal chancery and began studying theology. Between 1472 and 1475, he was ordained as a Franciscan friar.

Following this, Pacioli continued moving from one place to another, teaching mathematics, particularly arithmetic. Between 1477 and 1480, he taught at the ‘University of Perugia,’ where he became the first chair in mathematics (1477). Between December 1477 and April 1478, he wrote his second book on arithmetic (for his students at the university), titled ‘Tractatus Mathematicus ad discipulos perusinos.’ It consisted of 16 sections that discussed merchant arithmetic.

After this, Luca Pacioli went to Zara, which was then under the Venetian Empire (now Zadar in Croatia). There, he wrote yet another arithmetic book, in 1481. These first three arithmetic books were not published, and except the book written in Perugia, the others were lost. Subsequently, Pacioli once again taught at the ‘University of Perugia,’ followed by the universities of Naples and Rome.

Federico da Montefeltro was made the duke of Urbino in 1474. Apparently, Pacioli was a teacher of Federico’s son, Guidobaldo, who became the duke of Urbino in 1482. From 1487 to 1489, Pacioli taught at the ‘University of Rome,’ after which he returned to teach in Sansepolcro. However, following a complaint in 1491, he was banned from teaching the young men of the town. Yet, in 1493, he was invited to give Lenten/Lent sermons. He had been granted minor privileges by the pope, which probably stirred jealousy in his religious order, resulting in his teaching getting banned.

In Sansepolcro, Pacioli wrote his most well-recognized work, ‘Summa de arithmetica, geometria, proportioni et proportionalita.’ In 1494, he went to Venice to publish this book, dedicating it to Guidobaldo, Duke of Urbino.

In 1494, Ludovico Sforza became the duke of Milan. His court was well-known among the European states for its artists and scholars. In 1496, Pacioli was invited by Duke Sforza to teach mathematics at the court of Milan. There, he met Leonardo da Vinci, who was part of the court, as a painter and engineer. The two became good friends. Between 1496 to 1498, Pacioli worked on his other famous book, ‘Divina Proportione.’

In 1499, when Louis XII of France invaded Milan, both Pacioli and Leonardo fled to Mantuaa and stayed for a while as guests of Marchioness Isabella d’Este. They went to Venice in March 1500 and to Florence later, where they shared the same house.

Luca Pacioli was invited to teach Euclid’s ‘Elements’ at the ‘University of Pisa,’ Florence. Between 1501 and 1502, he taught at the ‘University of Bologna,’ while Leonardo worked for Cesare Borgia for 10 months. Barring these periods, they both stayed in Florence till 1506. Pacioli was chosen as the superior of his order in Romagna, and in 1506, he was made a member of the monastery of Santa Croce, Florence.

Apparently, after 1506, Pacioli and Leonardo da Vinci went their separate ways. Following an appeal to the doge of Venice, it was decided that Pacioli, and no one else, would have the privilege of publishing his work in the republic for the next 15 years. Later, he was again called to teach in Perugia (1510) and Rome (1514). However, he spent most of his final years in Sansepolcro.

Luca Pacioli was chosen as the commissioner of his convent in Sansepolcro. Later, he gave up the privileges given to him earlier. In 1517, the town’s population made an appeal that he be appointed as the minister of the order for the province of Assisi. However, Pacioli died on June 19, 1517, in Sansepolcro.

His book ‘Summa de arithmetica, geometria, proportioni et proportionalita’ was about the combined studies of algebra, geometry, arithmetic, and trigonometry. It was the first printed book on algebra in Italian. Though it did not present any original ideas, it covered general dissertations on academic and applied arithmetic, elements of algebra, tables containing weights, measures of contemporary Italian states, a treatise on double-entry bookkeeping, and Euclid’s geometry.

In the book, Pacioli had incorporated the right methods of using ledger books. He had also mentioned a note of caution that nobody should end their working day unless they made their debit and credit columns agree. The book also contained the ethics of accounting, the method of determining economic returns (‘Rule of 72’), and the methods of cost-accounting. The bookkeeping system of the Venetian merchants, better known as the “double-entry accounting,” was described for the first time in the book.

Paoli probably wrote ‘De viribus quantitatis’ between 1496 and 1508. The 309 folios of this book were divided into three parts. The first part was a collection of mathematical, recreational puzzles and problems. The second consisted of games and geometrical problems, and the third part contained proverbs and verses. The book also contained card tricks and guidelines for juggling and fire eating. However, the book was not published back then. It was discovered much later, and an English translation of the book was published in 2007. Pacioli’s original manuscript showed drawings and figures by Leonardo da Vinci, and the same were found in Leonardo’s notes. This indicates that he, too, had worked with Pacioli on this book.

The figures and illustrations in ‘Divina proportione’ (sketched on solids) were created by Leonardo da Vinci. Pacioli wrote three books in this series. The first one was ‘Compendio de divina proportione,’ written in 1497 and dedicated to Sforza, which dealt with the “golden ratio” or the “divine proportion.” It elaborated on Euclid’s theorems related to this ratio and regular and semi-regular polygons. The second book, ‘Tractato de l’architectura’ was a treatise on architecture. It was dedicated to his students in Sansepolcro. The third volume of ‘Divina Proportione’ was an Italian translation of Piero della Francesca’s work.

In 1509, Luca Pacioli translated Euclid’s ‘Elements’ in Latin. His unpublished treatise on chess, ‘De ludo scachorum,’ was discovered in 2006 and was published in 2008.

Francesca’s biographer Giorgio Vasari accused Pacioli of plagiarizing Piero della Francesca’s work. In Pacioli’s defense, Pittarelli, in 1908, clarified that Pacioli had acknowledged Francesca’s work in both ‘Summa’ and ‘Divina.’