Con regole ferme
e canoni perfectissimi

The Summa of Luca Pacioli, Venezia 1494
In auction on 20 June at Finarte


The Summa offers itself as a text open to the future, due to the fact its variegated and multifaceted lesson has transmitted the thought of Pacioli beyond time and space: an economic civilization was formed on the XI treatise of the double entry and on the many reflections of corporate law, management and economic analysis, of business administration, that Luca was able to admirably condense and explain in these papers.

Translated into all the languages of the world, studied and reputed as one of the fathers of the modern economy, Pacioli would have liked to remember him as a diligent master who offers his book open to learners who came to listen to him ... and this is the image of himself that he leaves us, the iconography of the friar with the book open before him in the act of explaining and unfolding his thought. And his voice still seems to be heard in the university lecture halls, in the courts of Italy as well as among the bricks of Venetian merchants, to give and take lessons all day.

the first modern treatise
on business economics

The importance of Pacioli’s work exceeds indeed the innovative aspects linked to the accounting language and extends to the birth of the concept of modern business as it became morally permissible to seek and obtain adequate remuneration from the capital invested in the enterprise, as a result of the risks faced by the enterprise itself.

Massimo Ciambotti, Luca Pacioli e le innovazioni del linguaggio contabile...,
in Cultura Giuridica e diritto vivente, 2016, p.15


Pacioli’s Summa de arithmetica, geometria, proportions et proportionalita (Summary of arithmetic, geometry, proportions and proportionality) is the most important treatise on arithmetic, geometry and commerce of the Renaissance age. It is entirely written in vernacular Italian - an absolute novelty for the time - and intended for architects, painters, sculptors, engravers, mathematicians and musicians.

It includes the first treatise on the DOUBLE-ENTRY BOOKKEEPING SYSTEM (De computis et scripturis), the foundation of modern accounting.The general mathematics, from Euclid to Fibonacci, is here adequately represented: it is one of the capital works of Renaissance’s mathematics (Burckhardt, demonstrating the superiority of Italy in mathematics and natural sciences, cited only three people: Paolo Toscanelli, Luca Pacioli and Leonardo da Vinci). Doctor of theology of the Order of the Franciscans, itinerant professor within the courts of Italy, Pacioli included in the Summa all the mathematical knowledge and cultural references of his era.

Et per questo Summa de Arithmetica Geometria Proporioni er Proportionalità me par sia suo condecente Titolo



Luca Pacioli was neither a scientist, nor a mathematician, nor a physicist, nor an architect, nor an astrologer, nor a philosopher, nor a merchant, nor a theologian, nor a lawyer; he was all of them combined and much more. His Summa had the clear and declared intention to codify/"dar norma" the knowledge of the time, through defined rules and perfect canons/“con regole ferme e canoni perfectissimi.” Pacioli, following the lesson of his master, Leon Battista Alberti, considered Arithmetic as the foundation of every knowledge.

The Summa is written in "materna e vernacula lingua" (Italian vernacular) to allow everyone to practice and exercise, thus widening the audience of readers. The Summa addressed everyone and covered all areas and disciplines known at the time, as numbers and measurements inform all human activities:

Leva el numero e la mesura con la proportione in tutte e cose, tutto peresci.
E chi non sa per ragion de numeri debitamente computare: dagli altri bruti non è differente.

Pacioli and Leonardo:
great minds, good friends

The encounter with Pacioli [Milan, 1496] marks a turning point in Leonardo's life as regards the study of mathematics. Guided by his master and friend, he started a systematic study of theoretical mathematics..." Sylvie Duvernoy, Leonardo and Theoretical Mathematics, p.40.,

Sylvie Duvernoy, Leonardo and Theoretical Mathematics, p.40.

The Summa was undoubtedly the most important scientific text for the entire Renaissance, a real prelude to the Copernican, Newtonian and Galilean revolutions. We do not know if these scientists had a copy of the book in their libraries, but we certainly know that Leonardo bought a copy of the Summa for 119 soldi in 1495, as recorded in the Codex Atlanticus at c.288r. This book partially changed the destiny of Leonardo's thinking and career.

The last supper

The Last Supper was strongly affected by Pacioli’s lesson on proportion and geometry, as visible in the structural layout of the fresco. Moreover, several notes in Leonardo's codexes refer to passages from the Summa. Pacioli was a teacher, a disseminator of knowledge, a reformer able to reorganize and codify all of Renaissance mathematics and to show its enormous potential. The Summa is a collection of knowledge that Pacioli was able to adapt and reformulate in a modern key.


In tutte cose se ha aritrovare la proportione... perche el condimento de ogni faculta..

The Proportione is the centre of Pacioli’s reasoning, and it is that golden rule that in a few years became the subject of his masterpiece: the De Divina Proportione, a splendid example of scientific rigour and formal perfection, whose illustrations are again by his friend Leonardo. From the Summa to the De Divina Proportione the step was short, as already in the second part of the treatise the geometric theme was thoroughly explored with figures of solids very similar to those later found in the 1509 work.

Both books appear in the famous and mysterious Capodimonte’s painting, where the Summa lays on a table, with the inscription Li [ber] R [egularum] Luc [ae] Bur [gensis], right below the elegant figure of the Duke Guidubaldo da Montefeltro, the dedicatee of the work.

A single path leads Pacioli from the tight argumentation of the Summa to the light and symbolic representations of De Divina Proportione: light like that polyhedron suspended in the air, an ethereal image able to mirror the surrounding environment. The lesson of the friar of San Sepolcro is all here, in the desire to break away from earthly things to recover - in mathematical form - the "most universal rule:" that divine proportion which is the metaphysical principle that allows men to understand the world and therefore - indirectly - God.

Lot 507

The first Edition and first Issue of the Summa by Pacioli, preserved in its original conditions

Venice, Paganinus de Paganinis, 10-20 November 1494.

Super-chancery folio (319 x 217 mm). 308 leaves. Collation: π8 a-z8 <et>8 <cum>8 <orum>10AA14 A-H8 I-K6 (p1r title and contents; p1v author’s address to Marco Sanuto, epigrams by Fa Pompilius and Giorgio Sommariva, quire register, colophon; p2r dedicatory letters to Guidobaldo da Montefeltro; p4v summaries of part one; p4v table of contents of part one; a1r preface, text of part one; AA14v second colophon; A1r text of part 2 (Geometria); K5r-6r table and register of Geometria; K6v blank. 56 lines and headline. Types: 9/12:130G, 10:92Ga, 8:84G, 13:68Gb, 16:87G. Dedication and incipit on a1r printed in red. Large woodcut historiated initial “L” depicting Pacioli and the Summa and some geometric instruments, all within a refined woodcut frame with a border decorated with white spirals; figures, calculations, and many woodcut diagrams, one full-page diagram printed in red and black, woodcut initials from several sets, four of which depict Pacioli. A few pages present traces of foxing, in particular the fascicles s-t-v-x and y, ink notes on the t6r title-page, small wormholes on some pages. Original binding in wooden boards, some defects and leaks. Note of possession to the front flyleaf in an early hand (Sixteenth Century); on the reverse, handwritten annotations, with some mathematical notes.

Estimate on request  

Lot 507
Offered in the Books, Autographs and Prints sale on 20 June at Finarte in Rome


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