The Mathematics Textbook That Inspired Da Vinci at Auction

Luca Pacioli's Summa is considered the most important treatise on arithmetic, geometry and proportions of the Renaissance age. A superb first edition of the Summa, preserved in its original binding, will be auctioned by Finarte in Rome on June 20th.

The Mathematics Textbook That Inspired Da Vinci at Auction

The famed Leonardo da Vinci is synonymous with Renaissance genius, but one of his friends and collaborators, Luca Pacioli, was also one of the era's brilliant minds and is considered the father of modern accounting. Pacioli's book Summa de arithmetica, geometria, proportioni et proportionalita, that was published in 1494, is the most important treatise of arithmetics, geometry and proportions of the Renaissance age and was entirely written in Italian, a complete novelty for the time. Leonardo da Vinci purchased the Summa in 1495, as evidenced by his notebook the Codex Atlanticus, and some time later, he befriended the author in Milan where Pacioli lived in 1496 following the success of the book. The book was always on Leonardo's work table and Pacioli's study of proportions helped him in the creation of his masterpiece The Last Supper. 

Luca Pacioli, Summa de Arithmetica Geometry Proportioni & Proportionalita, 1494 Venice, Paganino de Paganini, November 10 - 20, 1494. Photo © Finarte
Luca Pacioli, Summa de Arithmetica Geometry Proportioni & Proportionalita, 1494 Venice, Paganino de Paganini, November 10 - 20, 1494. Photo © Finarte

Considered the father of modern accounting because the Summa de Arithmetica introduces the double-entry accounting concept, Luca Pacioli was born in 1445 in Borgo Sansepolcro, Tuscany, and took his vows in 1470, entering the Franciscan Order. Pacioli summarizes in his book all the mathematical knowledge of the time and wrote it in the vernacular, Italian, which is notable because it was probably intended as a reference textbook for math and business students in the merchant middle class.

Portrait of Luca Pacioli (1495), attributed to Jacopo de 'Barbari, National Museum of Capodimonte
Portrait of Luca Pacioli (1495), attributed to Jacopo de 'Barbari, National Museum of Capodimonte

The Summa de arithmetica, geometry, proportioni et proportionalita was also the result of Pacioli's decades of meetings, studies and cultural exchanges with the most important Renaissance personalities, such as Leon Battista Alberti, who took the young Pacioli under his wing and taught him how important mathematics was in understanding art and science. Thanks to the humanist, Luca Pacioli arrived in Venice in the 1490s, the era's main center of commerce, where he became tutor to a rich family of merchants, the Rompiasis, synthesizing his years of studying mathematics and accounting with the business world of trade.

Luca Pacioli, Summa de Arithmetica Geometry Proportioni & Proportionalita, 1494. Venice, Paganino de Paganini, November 10 - 20 1494. Photo © Finarte
Luca Pacioli, Summa de Arithmetica Geometry Proportioni & Proportionalita, 1494. Venice, Paganino de Paganini, November 10 - 20 1494. Photo © Finarte

In Venice he also rediscovered treatises of other scholars, in particular those of Fibonacci, an Italian mathematician who had introduced the Arabic numerical system into Europe in the 13th century. The first part of the Summa, dedicated to algebra, owes a great deal to Fibonacci's Liber Abaci, while for the rest of the work is influenced by the theories of Boezio, Sacrobosco, Tolomeo, Euclid and Archimedes, in addition to humanist and mathematician Piero della Francesca. The Summa collected and ordered the knowledge of the past in a single work, thus becoming the most complete mathematical text ever published until then. The first edition was published in Venice in 1494 and was dedicated to Guidobaldo da Montefeltro, the Duke of Urbino, Pacioli's patron.

The book has a contemporary binding in cypress and leather boards with dry-embossed geometric patterns. Photo © Finarte
The book has a contemporary binding in cypress and leather boards with dry-embossed geometric patterns. Photo © Finarte

The work is divided into ten chapters, covering arithmetic, algebra, book-keeping, billing, investment, accounting and more. While Pacioli did not originate all of these ideas, he did aggregate them into one text. However, the accounting chapter is in fact the first modern treatise on economics: Pacioli defines and illustrates all the activities related to the market, analyzes the concept of goods, productive activity, profits and losses, and how to resolve problems and accounting operations algebraically. For the first time, the double-entry method of accounting was disseminated through the press. The Italian word ragioniere (meaning accountant in English) was introduced by Pacioli to identify the key figures capable of making the calculations readable and clear.

Luca Pacioli, Summa de Arithmetica Geometry Proportioni & Proportionalita, 1494 Venice, Paganino de Paganini, November 10 - 20, 1494. Photo © Finarte
Luca Pacioli, Summa de Arithmetica Geometry Proportioni & Proportionalita, 1494 Venice, Paganino de Paganini, November 10 - 20, 1494. Photo © Finarte

Between 1496-98, Pacioli and da Vinci collaborated on the book Divina Proportione that focused on proportions and mathematics, such as the golden ratio, in relation to a range of topics, including art, architecture and faith. The Proportione delves into the concept that man has the desire to detach himself from earthly things to discover the metaphysical principle that allows him to understand God. Pacioli wrote the text and da Vinci illustrated. However, just a year later both Pacioli and da Vinci had to leave Milan because King Louis XII of France conquered the city. Therefore, the book wasn't published until a decade after in 1509 in Venice.

The Divine Proportion (De divina proportione), Luca Pacioli, drawing by Leonardo Da Vinci. Photo © Veneranda Biblioteca Ambrosiana
The Divine Proportion (De divina proportione), Luca Pacioli, drawing by Leonardo Da Vinci. Photo © Veneranda Biblioteca Ambrosiana

Now, collectors can own one of the most important works of Renaissance mathematics history: the first edition of the first issue of the Summa, dating from November 10-20, 1494, which will be auctioned by Finarte auction house in Rome on June 20. This is especially unique at market, distinguishable from the two subsequent editions due to the presence of some internal changes recorded by DA Clarke. The estimate is upon request.

The auction will be held on June 20 at Palazzo Odescalchi in Rome. In the meantime, you can also discover all the other lots for sale directly on Barnebys or browse the catalog dedicated to the Summa.

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