Incunabula and the Keio University Library Collection


Lucas de Burgo S. Sepulchri [Luca Pacioli], Somma di aritmetica, geometrica, proporzioni e proporzionalità (Venice: Paganinus de Paganinis, 10-20 Nov. 14[9]4)

Somma di arithmetica, geometria, proporzioni e proporzionalita. Prelim: Fa. Pompilius: Epigramma ad lectorem. Giorgio Sommariva: Epigramma ad auctorem (I, II).

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This is one of the most famous works by the Italian mathematician Luca Pacioli (sometimes Paccioli). His Latin name, Lucas de Burgo S. Sepulchri, comes from the Latin name of his birthplace, Borgo Santo Sepolcro (now Sansepolcro), in the south-east of Tuscany. Pacioli studied mathematics related to commerce and accounting from an early age, and there is some conjecture that he gained at least a part of his education at the studio of della Francesca, the Renaissance artist and mathematician. When he was around nineteen years old, Pacioli served as a private tutor at the house of a great Venetian merchant, Antonio de Rompiasi, where he studied practical mathematics under Domenico Bragadino. In 1470, at the age of twenty-five, Pacioli went to Rome, and some time afterwards he entered the Franciscan order. From around 1475 he taught mathematics and geometry at several universities, including those of Perugia, Rome and Naples.

When he returned to Venice in 1494, Pacioli supervised the preparation for publication of his Somma di aritmetica, geometrica, proporzioni e proporzionalità, and published it from Paganinus de Paganinis's printing house. This was the first mathematical treatise to cover the mathematical and geometrical knowledge of several authors who were popular in contemporary Italy, such as Euclid (IKUL 025), Boethius (IKUL 028), and Leonardo Pisano. It is also notable for containing the first published description of the double-entry accounting system, and thus Pacioli is praised as the 'father of modern accounting'.

Around 1496 Ludovico Sforza, Duke of Milan, invited Pacioli to come to Milan, possibly at the request of Leonardo da Vinci, who had a keen interest in mathematics. Pacioli and Leonardo became very firm friends.

Numerous woodcut diagrams and mathematical formulae are used throughout this book; this required the direction of Pacioli himself, since the printer Paganinus de Paganinis was not experienced enough to handle such a large number of woodcuts at that time. In 1498, from the same printing house, Pacioli published De divina proportione, which describes Euclid's theory of the golden ratio and contains studies of regular and semi-regular polygons.

There are three variants of this edition, which the union catalogue of incunabula in Italian libraries distinguishes as 7132 (the first issue), 7133 and 7134. The Keio copy is an example of the 7132 variant. The ownership mark, 'Accademica della Valle Tiberina Toscana', is stamped on sig. n1r.

  片岡泰彦 編『我国パチョーリ簿記論の軌跡』上下巻 (東京: 雄松堂書店, 1998)
  『パチョリ簿記論』本田耕一 訳 (東京: 現代書館, 1975)



Lucas de Burgo S. Sepulchri [Luca Pacioli]
Place of Publication
Paganinus de Paganinis de Paganinis


Date of Publication

16th-century wooden boards, modern calf on the spine, clasps missing, catches intact.

Bibliographical Notes

308 leaves; a number of woodcut initials and diagrams, a woodcut historiated initial capital and woodcut border decoration on a1r.

Goff L315, HC (+ADD)4105, BMC V 457, IJL 201, IJL2 252, PP 100
Acquisition Year

Accademia della Valle Tiberina Toscana (stamp; π1r).