Luca Pacioli, also called Luca di Borgo or Brother Luca di Borgo (1445-1517), was born in Borgo San Sepolcro in Tuscany. After the first studies in his native town, he moved to Venice where he became student of Domenico Bragadino, a public lecturer of mathematics in the Serenissima. The following years he undertook various trips on behalf of the Venetian merchant Antonio Rompiasi. This allowed him to improve his knowledge of mathematics and algebra, but also to come into contact with important persons of his time. He entered the Franciscan Order approximately in 1470. In 1476, he was in Perugia, where he wrote a treatise on algebra; some time later he was asked by Pope Leo X to teach mathematics and algebra in Rome, at the University La Sapienza, and in the years 1501-1502 he is lecturer of mathematics at the Studio of Bologna. In 1497 he was invited by Lodovico Maria Sforza, “il Moro”, to Milan, where he worked with Leonardo da Vinci, author of the engravings used by Pacioli for his De Divina Proportione, printed in 1497. For Isabella d’Este and the court of Ferrara, Pacioli wrote De ludo scachorum, an enjoyable treaty about the chess game. The only manuscript copy we know about was found only some years ago. Besides the already mentioned Leonardo, Pacioli certainly met Leon Battista Alberti, Piero della Francesca and the architects and painters Melozzo da Forlì and Marco Palmezzano.

In December of 1494, Pacioli entrusted the famous Venetian typographer Paganino de’ Paganini with the printing of his first work (the author was almost fifty at that time), the Somma di arithmetica, geometria, proporzioni e proporzionalità. Thanks to this book, which contains and integrates also his unpublished previous works, the author gained the scientific and mathematical fame which has lasted until present times. The book divided into two parts, is the first work about general arithmetic, practical arithmetic for commercial purposes, with references to coins, weights and measures, and algebra, in which also previous theories by scientists such as Euclid, Boethius, Giovanni Sacrobosco and Leonardo Fibonacci are applied. The Somma should be seen in the cultural context of the Italian Renaissance: its aim is not to be a mathematical treatise in the strict sense of the term, but to transmit the mathematical science by combining arithmetic, geometry, astrology, music, perspective, architecture and cosmography. It is an encyclopaedic summa of knowledge and references linked one to the others.

The Somma contains numerous woodcut illustrations and diagrams, partially at full page, and at the margins of almost all leaves. It also displays a large initial woodcut that shows the author with an open book and a compass in his hand, repeated several times within the text. The chapter De computis et scripturis - also part of the book - may be considered to be the first printed treatise about the double-entry book-keeping system, which represents the first example of a Naperian logarithm, calculated before Napier. His fundamental role for modern commercial science is obvious. Pacioli uses in the Somma the Italian language, even if the text actually contains a mixture of Latin, Greek and Italian terms (L. Ricci, Il lessico matematico della “Summa” di Luca Pacioli, in: Studi di Lessicografia Italiana, 1994, pages 5-71). The use of the Italian language was an absolute innovation at that time, but the book was intended not only for theoretical studies, but also for a practical use by mathematicians, architects, painters, sculptors, engravers and merchants. The success of the book was immediate: we know about three different states of the first edition, and of a second edition printed in 1523 (cfr. D. A. Clarke, The first edition of Pacioli’s ‚Summa de Arithmetica’ (Venice, Paganinus de Paganinis, 1494), in: Gutenberg Jahrbuch 1974, pages 90-92).

Very common during his publishing time, the Somma di arithmetica may be considered a rare book today. As far as we know, it has been auctioned only four times in the last forty years and just one copy was sold in Italy as long as fourteen years ago. Therefore the auction house bolaffi is particularly proud to offer a full margin copy in original vellum binding of this extremely rare editio princeps in the sale of 16th December 2014. An important detail relates to the fact, that the four copies sold within the last forty years belong to the more common first printing with a worldwide higher registration of copies, while the volume in sale belongs to the rare first edition in second state (carrying a large historiated “L” on the recto of the ninth leaf), which never came to auction.

By Annette Popel Pozzo