Luca Pacioli and The Summa
Luca Pacioli was a true Renaissance man, with knowledge of literature, art, mathematics, business and
the sciences, at a time when few could even read. Born about 1445 at Borgo San Sepulcro in Tuscany,
Frater Luca Bartolomes Pacioli acquired an amazing knowledge of diverse technical subjects – religion,
business, military science, mathematics, medicine, art, music, law and language. He accepted the
popular belief in the inter-relatedness of these widely varying disciplines and in the special importance
of those, such as mathematics and accounting, which exhibit harmony and balance.
His friend Leonardo da Vinci helped prepare the drawings for Pacioli's 1497 work, Divina Proportione; In
turn, Pacioli is reputed to have calculated for da Vinci the quantity of bronze needed for the artist's huge
statue of Duke Lidovico Sforza of Milan.
Around 1482, after completing his third treatise on mathematics, Pacioli, who like many of his time
sought preferment as a teacher, became a Franciscan friar. He traveled throughout Italy lecturing on
mathematics, and, in 1486, completed his university education with the equivalent of a doctorate
Pacioli never claimed to have invented double entry bookkeeping. Thirty-six years before his
monumental treatise on the subject, Benedetto Cotrugli wrote Delia Mercatura et del Mercante Perfetto
(Of Trading and the Perfect Trader), which included a brief chapter describing many of the features of
double entry. Although this work had not been published for more than a century, Pacioli was familiar
with the manuscript and credited Cotrugli with originating the double entry method.
Pacioli was about 50 years old in 1494 – just two years after Columbus discovered America – when he
returned to Venice for the publication of his fifth book, Summa de Arithmetica, Geometria, Proportioni
et Proportionalita (Everything About Arithmetic, Geometry and Proportion). It was written as a digest
and guide to existing mathematical knowledge, and bookkeeping was only one of five topics covered.
The Summa's 36 short chapters on bookkeeping, entitled "De Computis et Scripturis" ("Of Reckonings
and Writings"), were added, "in order that the subjects of the most gracious Duke of Urbino may have
complete instructions in the conduct of business," and to, "give the trader without delay information as
to his assets and liabilities." (All quotes from the translation by J.B. Geijsbeek, "Ancient Double Entry
Bookkeeping: Lucas Pacioli's Treatise," 1914).
Perhaps the best proof that Pacioli's work was considered potentially significant, even at the time of
publication, was the very fact that it was printed on November 10, 1494. Gutenberg had, just a quarter
century earlier, invented metal type, and it was still an extremely expensive proposition to print a book.