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PACIOLI, LUCA (b. Sansepolcro, Italy, ca. 1445;
d. Sansepolcro, 1517), mathematics, bookkeeping.
Luca Pacioli (Lucas de Burgo), son of Bartolomeo
Pacioli, belonged to a modest family of Sansepolcro,
a small commercial town in the Tiber valley about
forty miles north of Perugia. All we know of his early
life is that he was brought up by the Befolci family of
Sansepolcro. It has been suggested that he may have
received part of his early education in the atelier of his
older compatriot Piero della Francesca (1410-1492).
As a young man he entered the service of Antonio
Rompiansi, a Venetian merchant who lived in
the fashionable Giudecca district. Pacioli lived in
Rompiansi's house and helped to educate his three
sons. While doing so he studied mathematics under
Domenico Bragadino, who held classes in Venice,
probably at the school that the republic had established
near the Church of San Giovanni di Rialto for those
who did not want to go to Padua. The experience
Pacioli gained in Rompiansi's business and the knowledge
he gathered at Bragadino's school prompted him
to write his works on arithmetic, the first of which he
dedicated to the Rompiansi brothers in 1470. Their
father was dead by then and Pacioli's employment
probably had ended. He then stayed for several months
in Rome as the guest of the architect Leone Battista
Alberti.
Sometime between 1470 and 1477 Pacioli was
ordained as a friar in the Franciscan order in fulfillment
of a vow. After completing his theological studies
he began a life of peregrination, teaching mathematics
in various cities of Italy. From 1477 to 1480 he gave
lessons in arithmetic at the University of Perugia and
wrote a treatise on arithmetic for the benefit of his
students (1478). In 1481 he was in Zara (now Zadar,
Yugoslavia), then under Venetian rule, where he wrote
another work on arithmetic. After teaching mathematics
successively at the universities of Perugia,
Naples, and Rome in 1487-1489, Pacioli returned to
Sansepolcro. In 1494 his major work, Summa de
arithmetica, geometria, proportioni et proportionalita,
was ready for the publisher and he went to Venice to
supervise the printing. He dedicated the book to the
young duke of Urbino, Guidobaldo da Montefeltro
(1472-1508), who, it is believed, was his pupil. The
dedicatory letter suggests that Pacioli had been closely
associated with the court of Urbino. This is confirmed
by the altarpiece painted by Piero della Francesca for
the Church of San Bernardino in Urbino (now in
Milan), in which the figure of St. Peter the Martyr is
portrayed by Pacioli. The painting shows Duke
Federigo (Guidobaldo's father) praying before the
Virgin and Child surrounded by angels and saints. A
painting by Jacopo de' Barbari in the Naples Museum
shows Pacioli demonstrating a lesson in geometry to
Guidobaldo.
In 1497 Pacioli was invited to the court of Ludovico
Sforza, duke of Milan, to teach mathematics. Here he
met Leonardo da Vinci, who was already in Sforza's
employment. That Leonardo consulted Pacioli on
matters relating to mathematics is evident from entries
in Leonardo's notebooks. The first part of Pacioli's
Divina proportione was composed at Milan during
1496-1497, and it was Leonardo who drew the figures
of the solid bodies for it. Their stay in Milan ended in
1499 with the entry of the French army and the
consequent capture of Sforza. Journeying through
Mantua and Venice, they arrived in Florence, where
they shared quarters. Leonardo's stay in Florence,
which lasted until the middle of 1506, was interrupted
by a short period in the service of Cesare Borgia.
