Abacus Tradition’ for the Economic and Social Development of the Society: Evidence from Tuscany (Italy) Between XIII and XVI Century

The role of the ‘abacus tradition’ for the economic and social development of the society: evidence from Tuscany (Italy) between XIII and XVI century

Maria Pia Maraghini University of Siena, Italy

Abstract This paper focuses on the “origins” of the book-keeping art which aims to record economic behaviour. In particular, this research investigates the early specific “places” arranged and organized to teach the accounting knowledge and the primitive “means” of study with which it could be handed over: the abacus schools and books. They prevalently spread in Italy between XIII and XVI century with the aim of transferring the knowledge generally defined as “practical maths”, such as the techniques to do arithmetic operations and practical rules to solve commercial and financial questions. The objective of this research is to further investigate the study of abacus schools and books, in order to recover and highlight the role held by the abacus phenomenon in the origins of the “accounting art” and, in general, the role of the “abacus tradition” for the economic and social development of the society during the medieval and renaissance period. To achieve this goal, the study relies upon some evidences from Tuscany (Italy) between XIII and XVI century. By combining theoretical and empirical insights, the analysis points out the contribution the abacus tradition has given to the better development of public life in the city-republic during the medieval and renaissance period, that is to say to the best and most effective exercise of duty and civic right. This contribution has been the basis to the growing interest shown towards the abacus culture by the then city-republic authorities.

Keywords: abacus schools; abacus books; medieval and renaissance period; origins of the “accounting art”; economic and social development of the society.

Corresponding author: Dr. Maria Pia Maraghini Department of Business Administration and Social Studies Faculty of Economics, University of Siena Piazza S. Francesco n° 8, 53100 Siena – Italy Phone: (0039)0577/235046, Fax: (0039) 0577/232641, [email protected] The role of the ‘abacus tradition’ for the economic and social development of the society: evidence from Tuscany (Italy) between XIII and XVI century

Table of contents:

1. Introduction ...... p. 2 2. The abacus schools and books...... p. 3 3. The abacus phenomenon in the historic studies upon mathematic and economic orientation ...... p. 7 4. The role of abacus schools and books in the “genesis” of accounting for companies...... p. 9 5. The study of abacus essential to people concerned with the carrying out of public “offices”...... p. 12 5.1. The abacus phenomenon in Arezzo between XIII and XVI century...... p. 14 6. Final considerations ...... p. 17

References...... p. 19

1. Introduction This research investigates the “origins” of the book-keeping art which aims to record economic behaviour. The historians of accountancy agree that it was generated and spread as a consequence of the great importance and significance of the changes in socio-economic conditions which took place between XIII and XVI century, although knowledge in this field was not unknown in antiquity (F. Besta, 1932; F. Melis, 1950; V. Masi, 1963).

Nevertheless, the same development of book-keeping records relevant to economic facts, has strongly contributed to producing these changes: in particular, as underlined by G. Catturi (1989), the accounting datum, being able to transfer information, gathers importance as a cultural means of transmission between different communities, since behavioural models, beliefs, values, laws and preconditions which set up the foundations of any culture, frequently find their translation in book-keeping data.

Within this perspective of investigation, much research into the history of book-keeping focuses on study of records of a period taken into consideration, with various references to merchants, public administration and/or home-property companies, proving the contribution offered to the development of company accounts, as well as underlining the part they took in the cultural change of the communities in question (see, among others, R. De Roover, 1974).

Actually, at the very beginning the “science of accounts” was established and spread in daily practice: accountancy knowledge could only be learnt on the field, by the reiterated use of those techniques (methods) or simply assisting the merchant or any other person in charge of “keeping the books” (A. Riparbelli, 1952; S. Pezzoli, 1977). But soon the need of wider diffusion of accounting knowledge and competences, due to the cultural changes previously referred to, began to be strongly felt. Arranging and organizing specific “places” where it could be taught and “means” of study with which it could be handed over were required.

The birth of abacus schools and books, prevalently spread in our country between XIII and XVI century with the aim of transferring the knowledge generally defined as “practical maths”, such as the techniques to do arithmetic operations and practical rules to solve commercial and financial questions, seemed to offer an answer to such requirements. It was in these “places” that the first principles of accountancy were laid, even before the codification of Brother Luca Pacioli gave it a self-sufficient theoretical dignity and laid the basis of its European diffusion (E. Hernandez Esteve, 2001; G. Catturi, 1997).

The abacus schools and books generally were given less attention within the studies of the History of Renaissance pre-academic school education, mostly interested in intensifying the grammatical education and the diffusion of linguistic and humanistic knowledge (E. Garin, 1957; P.F. Grendler, 1989). Such schools and books are mainly examined within the studies of History of Mathematics (see, among others, L. Franci 2003; E. Ulivi, 2004). Anyway, as highlighted by W. Van Egmond (1980, p. 12) particularly referring to the abacus treaties, “their value is not restricted merely to the specific field of the history of mathematics. Even the historians interested in many other aspects of the Italian renaissance period can take remarkable advantage of that”. Consequently, the

Author underlines the need to deepen and widen the study to further fields of investigation.

Within the economic-corporate field, some scholars examined the indirect influence wielded by the abacus books on the idea of renaissance economy and development of the accounting culture (U. Tucci, 1994; C. Antinori, 2002; M. Morelli, M. Tangheroni, 1994). However, a wider and closer examination upon the treaties of “practical mathematics” seems to be lacking and, in addition , the schools or “workshops” in which the knowledge relevant to it were taught.

Based on the conditions mentioned above, the objective of this research is to further investigate the study of abacus schools and books, in order to recover and highlight the role held by the abacus phenomenon in the origins of the “accounting art”. In doing so, the analysis points out the contribution it has given to the better development of public life in the city-republic during the medieval and renaissance period, that is to say to the best and most effective exercise of duty and civic right. This contribution has been the basis to the growing interest shown towards the abacus culture by the then city-republic authorities.

2. The abacus schools and books The term “abacus schools” is used as appellation of those “circles” organized for the generally defined “practical mathematics” learning between the XIII and XVI century. In these circles the abacus masters (magistri abaci) instructed their students in arithmetic, geometry, elementary commercial studies and, should the need arise, surveying. In this sense, the abacus school had the main aim of preparing for the practice of merchant, commercial and artistic activities. As underlined by E. Ulivi (2002), it “was thus attended also by boys of noble family and by those who wanted to further their studies to then undertake a profession”.

The rise of the abacus school is connected to the unbelievable economic development which took place in the period between XIII and XVI century, whose importance justified the use of the term Commercial Revolution to point out the complex series of innovation in the ways of conducting business. Means of transport, roads, speed and road safety were improved, resulting in an intensification of merchant trade, that is an increase in the amount of goods exchanged and the widening of commercial links. To this we should add the development of the company (that is the partnership among several merchants) and the insurance which limited the risk of goods transport, evolution of banks, even international, the creation of financial instruments to promote payments even without the use of money, for example credit letters and bills of exchange and, last but not least, the increasing government protection upon contracts and property. Such development also created effects in the social ground, determining the gradual changeover from a rural population to an urban one, characterized by the contrast between “the new rich” and “the old landowners”. In addition to the status of the merchant, even the typology of the activities he performed changed: he was less and less involved in transport and the exchange of goods, but had to manage different people who attended to various single tasks including financial, administrative and accounting.

It is within this scenario that corporate bookkeeping, considered as the “art of keeping the books”, developed and is determined exactly by the necessity to ascertain and demonstrate to oneself and others (herein the expression “to account for something”), the amount of goods brought, produced, consumed, exchanged or given up and, most of all, the existence of debts and credits between two subjects, as a consequence of mutual remittance of goods or money (G. Catturi, 1989). Actually, the first form of records relevant to the recording of economic facts were disconnected, fragmented and not systematic: it was just a confused and strictly personal recording whose aim was only that of keeping the records of the business in progress, and therefore the accounting records undertook the function of a real “chronicle”, and then was often defined as a “remembrance”, “diary” or “report”. Afterwards, the development of business traffic and its no longer local extent, required the adoption of more elaborate “equipment” and accounting techniques, as well as more organic and safer accounting methods.

Upon the previous considerations it is easy to understand how the merchant of the newly- constituted urban society began to feel the need to gain knowledge of writing and to acquire major knowledge of calculus, in particular the one applied to business, as well as to pass this knowledge on to the relevant sons, who, mainly in the medieval period were called to follow in their fathers’ footsteps (U. Tucci, 2005).

As recalled by A. Sapori (1997: p. 139), who quotes the results pointed out by the Belgian scholar H. Pirenne (1929), the research of the above mentioned competences was first of all focused on the “monastery, among the men of church, who in the period of extreme mortification had kept part of the inherited knowledge; while the contrast upon the teaching program was even more defined, between the practical needs of the merchant and the spiritual concerns of the ecclesiastics, from home teaching, at least by the richest merchants, carried on by salaried clergymen (thus with no didactic autonomy), and then gradually by laymen. Eventually, when the merchant class gained more political power and handled public affairs, they arranged the constitution of public schools, with a professional profile.”

Thus starting from the XIII century the majority of Italian and European towns were equipped with that fundamental instrument of progress which is school (private and public).

Towards the end of the medieval period and during the renaissance, school was organized in three main education levels. The first one aimed to give pupils a primary education, that is to teach them to read and write in Italian and in local dialect. This was followed by a second scholastic cycle in which the education was “... when we would have liked to use modern expressions, not only elementary, but also, partly, that of an actual lower secondary school, enough to give a reasonable education, and most of all suitable for further advancement towards specialization” (A. Sapori, 1997: p. 150). Two different kinds of schools belonged to this course of studies: grammar and abacus schools. Whilst the grammar school was dedicated to closer examination of the Latin language and literature and study of the Classics, rhetoric and logic, the abacus school was dedicated to learning mathematics. Eventually, for the oldest, most skilled and clever pupils the doors of the higher education were opened.

Since their first appearance, the abacus and grammar schools were generally considered an intermediate level of education (R. Black, 1996). Students attended these schools for about two years at the age of 10 or 11 (A. Verde, 1973; P.F. Grendler, 1989, A. Sapori, 1997; E. Ulivi, 2002).

As to the attendance at the single schools, it varied from period to period and also according to the geographic area. Even within the same town, as carefully described and witnessed by E. Ulivi (2002), “the number of students could fluctuate to a large extent from one school to another. Several elements could influence this phenomenon: decisive factors obviously were the capacity of the workshop and therefore the number of its masters, the prestige of the school and of its holders, perhaps the location of the school”.

The abacus schools were essentially public: the local officers, interested in opening a school, hired one master or more and the community held, in all or in part and in different ways, the charges necessary to maintain him and the school. Anyway, in the most important commercial towns, such as Venice and Florence, the abacus schools were, mainly or completely, private: the education was carried out in houses or workshops owned or hired by the masters, hence the definition of “abacus workshop”.

In these cases, often two or more abacus masters entered into a partnership for a certain period, sharing the workshop. It is within a document relevant to the setting up of such a partnership – more specifically the one where Giuliano della Valle joined Francesco Galigai in a workshop near Borgo Pinti in Florence in 1519 for a period of three years – that we can find one of the few indications about the subjects taught at the abacus schools (R.A. Goldthwaite, 1972: pp.: 422-423).

Because of the difficulty in finding the teaching programmes – and thus the impossibility to proceed in a thorough analysis– the definition of the possible contents of the teaching technology carried out in the referred schools can generally be deduced by examining all the syllabus used by the different masters: the abacus books. We owe to this, the most part of the information relevant to the contents and methods used in abacus schools.

The first abacus book recognized as such is the Liber abaci (1202) of Leonardo Pisano, known as Fibonacci (son of Fibonaccio), who, for this reason, is acknowledged as the founder and the landmark of the whole abacus tradition. In it Fibonacci collects all the mathematic knowledge he could have learnt from the Arabian world. But the book was written in Latin, it was really massive and therefore too difficult to be the basis of a merchants’ education. Towards the end of the thirteenth century, some abridged versions began to appear, written in the common language, where the topics of theoretical nature had completely disappeared (V. Montebelli, 2008). This is the beginning of the abacus book tradition. We currently know of about three hundred copies, different in size and contents, all written in the common language of different regions, mainly in the Tuscan and Florentine of that time (W. Van Egmond, 1980).

These texts, then, were inspired by Fibonacci’s Liber abaci and were filled in upon his guidelines, but after revising the subjects in a clearer and more summarized way, even with the inclusion sometimes of innovative elements. With relation to the subject matters, they were approximately as follows (W. Van Egmond, 1980; V. Montebelli, 2008):

1. arithmetic: - elementary operations; - calculations with fractions; - proportion; - radical calculation; - algebra (problems solved with equations); 2. practical geometry problems: - calculating areas and volumes; - measuring heights and distances; 3. arithmetic applied to trade: - sales, costs, profits, payroll, and rent problems; - currency exchange, conversion of unit of measurement; - problems relevant to bartering; - financial mathematical problems: interest, discount, depreciation; - “company” problems, that is relevant to the composition of the company capital; - alloys and mixtures; - other problems which could happen daily in business deals; 4. in the end, they could also include, in various degrees, entertaining problems and parlour games, that is algebraic questions and recreational maths, sometimes speculative arithmetics, proportion theory and numbers theory.

The authors of the abacus treaties, sometimes maths lovers, but also merchant or actual artists (such as Piero della Francesca), were mostly abacus masters who wrote them in order to be used by their students or generally by anyone who would like to have a manual to examine anytime he needed to solve a problem in his business (E. Ulivi, 2002).

The abacus books are not indeed school books in the modern sense, but just reminders, a sort of storehouse where you can find the rules in a rather disorderly fashion (that of the “three”, the one of the false position simple and double, etc..) and a rich survey where they can be applied (“the occurred cases”) with the relevant solutions. In this sense, the abacus culture has a merely prescriptive and not explicative nature: the education is performed through problems (“the reasons”), the learning is catechetical, based on formulas to be kept in mind and behaviour to be imitated (“Do it this way” without any other explanation) (V. Montebelli, 2008).

Following this, the learning process took place by imitation of the solved cases, as seen in the workshops. The ability and cleverness of the reader was not in the capacity of creating logical links such as recognizing, comparing with the prefabricated model, verifying and approximating.

3. The abacus phenomenon in the historic studies upon mathematic and economic orientation Historically, the abacus phenomenon was substantially underestimated and, until the twentieth century, had very seldomly been studied and suitably placed under observation.

Starting from the second half of the last century, it began to gain attention, especially in the wider current of research tending to overcome the traditional medieval vision of the origins of modern science. A vision that implies a deep devaluation of the contribution given by the Renaissance, which was considered a mere “parenthesis” or, at most, a period of fundamental “preparation” (P.D. Napolitani, 2008).

More specifically, the history of mathematic studies were mostly taking this direction: a lot of research in this scope was addressed to investigating schools, workshops, masters and abacus books in order to analyze, understand and better evaluate the status and evolution of the science of mathematics during the Renaissance period. Thanks to such investigations, the mathematics of the abacus culture is no longer considered as a second class maths with reference to the so called “scholarly” mathematics, that is the one of the Euclidean and Platonic-Pythagorean tradition which, during the Renaissance period, was mostly spread at the courts and universities (E. Gamba, V. Montebelli, 1987; E. Gamba, 2006). On the contrary, even more often, if we want to understand the phenomenon of the birth of modern mathematic sciences and their links with the society that cause their affirmation, we should investigate upon a sort of “co-evolution” among the abacus schools and the courts, whether they are humanistic or not (P.D. Napolitani, 2008).

Unlike the mathematical disciplines in the accounting history studies, the contribution given by the Renaissance period to the development of the “book-keeping science” has always been recognized as strongly decisive and often underlined.

Several historic researches were addressed to investigate the state and evolution of the Low Middle Ages and Renaissance book-keeping. Only in isolated occasions, however, the main object of these researches had been the abacus schools and/or books. In particular, and in a simplified manner, compared to the abacus studies, the so called trading manuals had always been preferred to the abacus books.

Actually, as highlighted also by B. Dini (1980: p. 6): “In case the school could give a solid cultural base, the core of the professional training necessary to carry out the business was, with no doubt, the company”. The young stepped in at about 12 to 14 years of age, and found all the necessary instruments aimed to enrich and strengthen their preparation and, most of all, a direct contact with the complex economic reality in which the company operated.

Based on these considerations, the research on economic and book-keeping history, tended to give priority to the study of life in the workshops, as pleasantly figured by A. Sapori (1997: pp. 154-155): “...other than elapsing under the nightmare of silence and mystery, it unrolled through the animation of movement and conversation”, conscious that: “It was just in the midst of such loud, picturesque but neat bustle, that the merchant sharpened his mind, learned to stiffen his nerves, felt the bold stimulus, sensed the need for prudence, shaped in one word, what he looks like, and what he was, inspiring our admiration and helping to understand the greatness of the age he belonged to”.

In particular, the same author (pp.146 e 152) highlighted, as the learning achieved in workshops certainly took place, to give that character of uniformity that leaps out at anyone who has in his hands more than one merchant-like record, even though they didn’t belong to one city or a single region, from the way to manage a business, the way to keep the books, to the same calligraphy, different from that of writers of public documents and notaries, which is not always easy and sometimes not even possible, to recognize one from another: this fact lets us realize logically, that it comes from a single source, and that a single school had been attended.

Life – and we could say, school – of the workshop has been thus variously studied through the detailed analysis of so many texts produced in coincidence with the company business (generic and specialized letters – such as bills of exchange and consignment notes – account books) (F. Melis, 1964).

Taking into consideration the other set of original sources of economic history, that is the large order of texts which in the same surroundings have been used both for consultation and for staff qualification (texts that in some cases were not issued by a company, but a school), we can take note of the fact that the abacus books received in the years considerably less attention from the economic historiographers, who generally preferred the analysis of the so called trading knowledge. This is because, as affirmed by F. Melis (1964), the trading knowledge “(...) ranges over wider grounds and around multiple aspects”.

Specifically, such files, available and used by companies of some importance at the time, generally included a wide, organic and methodical representation of information about the varied commercial habits and the tax system, varying from country to country, all these essential to the current tradesman to profitably run his business. Furthermore, those files, especially the old ones, contained tables and handbooks which allowed the accountants to easily calculate what was required. That is why, in alluding to these “handbooks”, A. Sapori (1997: p. 163) described them as “abacus in the matter, because they summarized, for whatever was needed in a commercial company, Leonardo’s work, while they were lacking both a question and answer system, but this was only a matter of form, preparation and execution of several operations, which we could find in the Pisano, and even more in the unpretentious school treaties since they were essentially a didactic system”.

However, the fact remains that the commercial handbooks were primarily intended to spread information and techniques of business nature rather than accounting information. They are therefore more significant for the analysis of life and economic history of the middle ages, rather than to trace the origins of book-keeping. Moreover, even with reference to the first one of the two studies, as astutely highlighted by Melis (1964): “Its importance (of the commercial practice, editor’s note), as a primary source of the economic history (...) has been at times exaggerated: (...) too many factors sow doubts among the data, not to mistrust its application”.

4. The role of abacus schools and books in the “genesis” of accounting for companies The considerations expressed in the paragraph above, lead us to study in detail the research of economic history, and, more precisely, the history of book-keeping, the study of schools and abacus books. The aim is to regain and to enhance the role of schools and books of that kind in the “genesis” of the book-keeping art. This role, as we have already said, has always been considered inferior to practical experience, prevalent in workshops and merchants’ stores during the medieval and renaissance period, even if it was spreading throughout different and new surroundings. As a matter of fact, the social and economic background of the Late Middle Ages, and, moreover, of the Renaissance, was more and more enlivened by different and new figures, corporations and economic organizations, both public and private, which all had to manage even huge properties at some time: businesses, banks, family businesses , public bodies, welfare services, parishes, convents, Episcopal bodies, companies which were divided and undivided both by typology or territorial location of the businesses practised, individual companies, family companies, firms and so on… (G. Catturi, 2008).

Actually, it is possible to outline a kind of “co-evolution” between the book-keeping culture which was taught in abacus schools, let alone displayed in the related books, and the culture that was developed in workshops and merchants’ stores, as well as in many other “places” of practice of the book-keeping activity, which were spreading (Figure 1).

Figure 1. – Correlations between abacus schools and books and corporate accounting culture

Accounting d schools and handbooks from XVI sec. Public or Private Corporations Propagation in Italy and Abacus schools and books c abroad of the double entry XIII-XVI sec. The abacus culture (that is the knowledge of maths applied to a business) is learned and spread about

Public or Private Corporations Place of application of instruments Corporate book-keeping and methods of memorization of the Strict definition of an accounting economic facts and self development method which jointly coordinates of innovative book-keeping methods the corporate activity

Specifically, schools and abacus books, while spreading a new book-keeping culture that goes through almost all social classes, also generate interest and expectations towards the same “keeping accounts system” and its applications. In other words, young people who completed this kind of school and who had studied applied mathematics books; the first principles of book-keeping art aiming to memorize economic behaviour, were not only “able”, but, in a certain way, “anxious” to carry out the acquired knowledge (arrow a).

The abacus phenomenon has allowed the coagulation of important practises in public and private companies of that time. These experiences have allowed improvement and reinforcement of existing book-keeping knowledge and ability, consequently, to form schools of thought and an actual “accounting” tradition as well (arrow b).

Actually, the book-keeping knowledge which was taught in abacus schools and diffused by relevant books, focused on learning single operations of management by heart. For this reason, this knowledge, even if essential for business management, was prevalently of a disjointed kind. Anyway, in the range of companies, in order to better rule the complex development of managerial dynamics, we perceive the need to organize all of those particular notes aiming to express in quantitative terms all the events concerning economic life.

Specifically, merchants, but, in general terms, all the economic operators of the time, while continuing to document “disjointed” accounting records, of which the technique they learned by attending the abacus schools or reading related books, had improved with daily practise and began to feel the need to develop a technique which allowed the unitary management of the patrimonies they managed.

In other words, we begin to feel the need of knowledge concerning the indissoluble coordination of those events, the valuation of the changes which the available patrimony has had and the determination of the result achieved of the economic activity (G. Catturi, 1989: p. 101). It is in this way that, in the actual book-keeping practise, new techniques and different methods of records set themselves up and spread. Among them we can remember the “single entry” method, the first to be used in order of time, and that of “double entry”, which proved to be the most rational and effective. The latter, actually, as G. Catturi (1989: p. 103) underlines, are indissolubly connected, in an organic whole, “ the facts concerning the management of any company, noting the events, that is to say the changes regarding its patrimony and allowing to determine the result achieved through the synthesis of those same changes”.

Such cultural enrichment inevitably permeates, even if at variable times, in “settings” (schools and books) of abacus culture, at first and in a minor way, and afterwards the one of book-keeping (arrow c).

This is, in particular, due to Luca Pacioli, who, in Tractatus XI of Summa da Arithmetica, Geometria, Proportioni et proportionalità (1494) which he wrote, dwells upon the description of the recording method in double entry of business events, then adding to theoretical arithmetic topics, of which he was a well-known professor, a “particular case” of applied notions to business.

The Tractatus XI, even if it derives from experiences and practises which were from some time used in European merchant cities, and most of all, in Italian ones, had the merit of

promoting the development of book-keeping as to its diffusion, counting on the use of the press (arrow d). In merit to this, the double entry mechanics penetrates the European cultural settings, which, with no exception, adopts it as an indispensable instrument for the rule of economic and financial events of business nature.

Therefore, the Summa offers a contribution to the development of book-keeping for companies, which we could define more “direct”. But the Summa, on the other hand, also marks the end of the abacus phenomenon: even if it goes on for all the sixteenth century, it is subject to a substantial transformation.

On the mathematical side, the abacus phenomenon, slowly enlarges its effect till it overruns the “learned” sphere, entering the university world. On the contrary, if we analyse the aspects which are more connected to business practise, we have to consider that from the second half of the fifteenth century the book-keeping technique and the merchant one, which were closely linked inside the abacus school, were getting more and more disassociated. More specifically, as A. Sapori makes clear (1946: p. 652): “The separation begins inside the biggest companies when, with the assignment of specific functions to various employees, accounting inevitably tends to assume an auxiliary value in comparison with business management. In this way, the book-keeping art obtains its independence, with it, the book-keeping job becomes more autonomous and the connected treatise writing, which in the sixteenth century continued to regard the merchant company, began to enlarge its application to the other classes of companies”. As a consequence, abacus schools and books were replaced by more specialized schools and more professional book-keeping manuals.

In short, while spreading the knowledge and the use of definite techniques, the abacus phenomenon has let the acquisition of experiences and, therefore, the acceptance of abilities that, when mastered by the various subjects who use them, change the levels and characteristics of the prevailing merchant culture and, in particular in favour of the present research, of the accounting one, therefore starting a circular process, or better still a spiral one.

One of the first merits of the existing correlations between abacus schools and books, social –economic changes and evolution of book-keeping culture for companies has been made by C. Antinori (2002: p. 610), who has pointed out how the diffusion of the Liber Abaci by Fibonacci has “contributed towards the best knowledge from merchants of different markets, has taught them how to make calculations of profit in a more certain and rapid way, has supported the mutual knowledge between merchants of different races and religions. All these elements have promoted the expansion of business companies, and the increase in number of operations carried out in one year, with the consequential need to perfect the entry techniques and to look for new probative means in case of controversy”.

This way, the contribution of abacus schools and books to the evolution of accounting for companies from the XIII to XVI century fundamentally introduces itself as a supply of “indirect” kind, even if it is always fundamental. Actually, if the above mentioned prevailing derivation of abacus schools and books from the merchant world and practise, where accounting art “reigns” and develops, it reveals a lot of occasions of explicit “contamination”, it is harder to prove the existence of clear influences practised towards

an opposite direction, that is the direct contributions offered by the abacus phenomenon to the improvement of accounting. Such supplies, on the contrary, prove to be generally “mediate” from the different practises developed in the administration of any patrimony, public or private, and, usually, as we will study in depth afterwards, with the daily civic duty and rights.

5. The study of abacus essential to people concerned with the carrying out of public “offices” Within the above paragraph, the correlations and interdependences existing between the abacus phenomenon and the progress of the accounting culture achieved in Europe, in Italy in particular, in the period between XIII and XVI century have been underlined and, as a consequence, the role played by abacus schools and books in early economic development.

For example, if we think about the fortune of the Italian merchant in the Middle Ages and the beginning of the Renaissance, precursor by at least two centuries from the European accounting civilization, on the one hand, it was simplified by the geographical position of his country, but on the other hand, as highlighted by A. Sapori (1997: p. 168), it was also closely linked to his great personal attributes. A scrupulous, sharp observer and elegant speaker, willing to learn, not only did he achieve a notably high education but, coordinating and linking his multiple knowledge, he gained a wide and solid, genial business culture”. The author then specifies (p. 48): “That Italian merchant, of the Middle Ages, seen as a constant and faithful annotator of the whole facts of his life and of the news of interest which came to his knowledge, had the strong will to be strictly accurate in his calculations, and clear in his book-keeping, deeply believing that accuracy and clarity were essential in the running of commercial business: he realized this would be supported by an adequate mathematical culture”.

If such a culture was a result of and developed by an active participation to commercial life, it’s also true that it had been generated within the abacus school and through consultation – and sometimes editing – of the relevant textbooks.

The necessity of abacus education and its importance for business development were early recognized also from contemporary society and, on more than one occasion, they were underlined by town magistrates’ resolutions which established, among others, to elect an abacus master who “teaches to pupils so that they would be more careful and keen in business” (P. Barsanti, 1905: pp. 54-57, 239).

Interest in such education, however, had to go further, considering and knowing that from an abacus education, not only the mercantile class, but the whole community could benefit. Actually, as effectively underlined by G. Catturi (2008: p. 8), values which come from groups of individuals within the social community “merged with those of society considered as a whole in an uninterrupted action of exchange, correlation and interference, which, whilst defining the anthropologic culture, synergically links the ethic values of single groups. (…) Therefore, it is interesting to underline the fact that the innovative elements which take part in the development process of a certain social

aggregation, with no doubt, affect and fertilize even the cultural development of other groups, even if part of the social community that includes all”.

Such a contamination, in particular, becomes more evident referring to the progress of the accounting culture during the Middle Ages and the first period of the Renaissance. In fact, consenting the effective realization of business and work in general, if on one hand it has undoubtedly been the fundamental assumption for the strong acceleration of the contemporary economic development and to the progress of the whole mercantile class and of the economic operators in general, on the other hand it has given a fundamental contribution to better performance of “city” life, that is to say, to a better daily civic duty and rights.

All this in consideration of the fact that, during the Middle Ages and the Renaissance, only citizens belonging to a certain corporation, working people or active in business, could enter the highest civil offices. In several centers of our country, as in London, the corporation representatives were called to take part in the local government (F. Valsecchi, 1931; L. Viviani, 2004). For example, starting from the 13th century, in Florence the nobles that intended to take part in politics were forced to join one of the existing corporations. Dante Alighieri himself was forced to join the Art of Physicians and Apothecary to enter the local government offices.

So, it was the city school, which had always been the object of interest to the local authorities, which prepared many for business life, enabling masses of people to exercise, with dignity and advantage, the sought-after citizen rights (as well as duties).

The role of scholastic education had to be even more valued starting from the 13th century, when, according to the constitution of the Italian City-Republics, the majority of the population, increasing year after year, took active part in public life.

In particular, the abacus education was useful in this sense: the effective performance of many public “offices” required an appropriate mathematical and accounting culture. For example, the figure of podestà, who was in charge of all city administration; of those who, acting as calculatores or rationerii, were part of the union as well as the retiring magistrates; of the charge of camarlingo, that is “he who collects or keeps in his custody the municipal money or, for extension, that of a brotherhood, of a monastery, or of any company”; to those who sit in the various and crowded committees of multiple economic organizations, in charge of checking the accounts of their respective chancellors and attorneys and to collaborate with them in the administration; etc..

With the aim to better investigate the actual recognized and assigned role given to the abachaistic education in the period between 13th and 16th century, in the following paragraph we analyze the evolutionary process that abacus study and schools in Arezzo underwent during the period in question. The choice of Arezzo territory is justified by the will to identify an area characterized by a supposedly lower interest in abacus education, so that to investigate the possible evolution, pursuing its causes. The sources under investigation make reference to documentation existing at the State Archives of Arezzo up until 1530, formerly selected and edited by R. Black (1996).

5.1. The abacus phenomenon in Arezzo between XIII and XVI century The history of Arezzo in the period between the XIII and XVI century has undergone various changes.

In 1200 the town was still at the height of communal freedom. In this period, which was not always fortunate, marked by the blusterous military events, Arezzo gained a grandeur and a prosperity never before and never more after enjoyed: besides the renewed political importance, we assisted a cultural flourishing and vivid economic development.

As to partially confirming the existence of a certain kind of economic zeal in the city there is the recent finding, at the State Archive of Florence, of the Articles of partnership of the Wares of Arezzo, dated 1341. As stated by A. Barlucchi (2008: p. XIV), in fact, “it’s fairly evident that an institution like the Wares couldn’t be established where merchants and pioneers are not, where the rhythm of productive life is mostly scanned by the agricultural seasons, as it had already been in Arezzo since the early fourteenth century according to an old historiographic tradition”.

While the power of Arezzo was increasingly growing, simultaneously ripened the ambition of the nearby cities to match its importance, and therefore it was rather unavoidable to come in collision with Siena and Florence, which, in the meantime, had been growing and developing flourishing handicrafts and several industries: it therefore aimed to widen its sphere of political influence and attain new markets for the sale of its products.

During the second half of the 13th century Arezzo fought for a long time against Florence and the other Guelph cities of Tuscany which, in 1288, formed a coalition against Arezzo and the other Ghibelline cities and in the famous Campaldino battle (1289), beat them violently. A period of decline started in 1384 which lead Arezzo to become part of the Florentine territory, losing its freedom. Upon the affirmation of the Medicean Rule, the inhabitants of Arezzo acknowledged to be part of the Dukedom of Tuscany (afterward Grand Duchy), which meant a long period of calm and peace for all the region.

Under Florentine rule, Arezzo was a city in decay where the decreasing of population corresponded to an increase in poverty and a depressed economy, even if, as pointed out by B. Dini (1984: p. VI), the economic vitality that the city had expressed when it was autonomous and had never died out. As well as the pride of its inhabitants which has never been extinguished: frequently underlined and richly documented by R. Black (1996: p. 128 and next), there was a strong awareness that the inhabitants of Arezzo were people endowed with an outstanding intelligence and particular attitudes: they “were proud that their tradition boasted famous men of science and letters, and wanted to maintain this heritage for greater fame and glory of the city”. For this purpose, since the time of the autonomous state of the city and during the whole Renaissance period, the local authority made a great effort to institute and permanently keep the school education, grammar in particular.

The inhabitants of Arezzo gave priority to grammar education because doctrine, and in particular the Arts, were considered precious and just deserving value for themselves, where the knowledge of Latin was thought to be the foundation of the whole culture. Actually, as highlighted by the same author Black (1996: p. 128), “during the Renaissance grammar stood as the Queen of Science in Arezzo” and its education was usually

considered more important than the practical and technical education given by the abacus master.

In effect, arithmetic was considered a lower level subject, suitable for more ordinary and less gifted intelligence, as we can deduct from a document dated 1513, when an abacus master was appointed because there were “many young people in the city who, owing to low assets or intelligence, or to any other effect are not keen on letters and studies”. In addition, the ability in arithmetic wasn’t considered a characteristic of the Aretine but rather of the Florentine, being excellent in their business activities. Due to this, the majority of the abacus masters who taught in Arezzo were not native of this city.

The inhabitants of Arezzo at the time instead claimed a rich tradition and wide knowledge in law, medicine and literary studies, and it was only in these professions that they wanted to study. On the contrary, also considered not a particularly prosperous economy, they seldom aspired to join the business world, and were absolutely pessimistic as to the possibility to initiate their children in this profession, as we can deduce from findings of the Town Hall of Arezzo dated 1416, in which it is stated that: “the inhabitants of Arezzo are not rich enough to turn their children into merchants” (R. Black, 1996: p. 133).

This is the reason why, just in part, there was less attention given to the abacus school compared to the the grammar schools in the city: the abacus pupils were much rarer than the grammar students, as results from the abacus masters’ statements in 1471 and 1506, which noted that the number of their students were respectively 40 and 25. Furthermore, the abacus masters were paid far less than their grammar collegues: in Arezzo, as deduced by the archived documents collected and analyzed by R. Black (1996), an abacus master usually earned 25 florins per year, and the higher salaries registered were of 35 and 36 florins, whereas any other grammar master was never paid less than 40 florins and his average salary, at the beginning of 16th century, was around 100 florins per year. Eventually, the effort supported by the Town hall in Arezzo to guarantee the continuity of the abacus schools was less than that assured to the grammar ones.

Anyway, the situation changed gradually starting from the second half of the 15th century the inclination to give a greater consideration to arithmetic and abacus education was progressively spreading in Arezzo, so that, in 1494 the General Council declared that the abacus education was not less useful and fruitful than the grammar education (“considerato quello non essere di mancho fructo et utilità a imparare che la gramaticha”), a point of view that was repeated in 1497 (“considerato non manco essere necessario né de manco fructo et utile che se instruischa e figlioli vostri in tale scientia de arismetricha che in gramaticha”) and in 1501 (“considerate non manco essere necessaria che la gramaticha”).

It was told that Mathematics was one of the fundamental subjects and “God created everything in nature according to numbers, weight and measurements”. In addition, as affirmed in 1506, the progress in arithmetic and geometry was significant in higher education, such as philosophy and astronomy, because this represented the highest level of knowledge as a fact (“Inter ceteras necessarias virtutes que potissimum valent, non solum in agibili bus mundi et inter merchatores et artifices necessarie sunt, verum etiam multum convenit virtus arti geometrie seu arismetrice philosofie, astronomie et aliis scientiis. Est enim in primo gradu certitudinis”)

The abacus knowledge, anyhow, was approved not only because it gave honor to Arezzo, but because it was useful: in fact, whilst grammar education was necessary to be admitted to the professions, the abacus started off as an art, a trade, or at best, a business. In 1456 it was said that merchants and craftsmen “needed to know how to reckon, a practice vulgarly said abacus” (“Cum inter cives mercato rum consuedinem summe decet penes qua[s]cumque civitates dignas quod scientia rationis calculande – vulgariter dicitur l’abicho – summe exprimentatur”), while in 1523 mathematics was considered a knowledge “no one could run business without” (“negociari nemo potest”).

But, moreover, the abacus education was considered as a fundamental element of civil life, as we can partly deduce by findings of the Town Hall of Arezzo in 1451, where it’s written: “Given that the knowledge of arithmetic is very useful and necessary in any republic, as the experience of our great Florentine lords, who overcame all the others with this doctrine, and it’s a good and necessary thing that the youth in Arezzo study this science”, acknowledging that from the abacus education “could be of great use both to the individual and the community as a whole” (R. Black, 1996: pp. 93-94).

Again, in 1456 it was written: “a great use for individuals, not to mention for our municipality, can be derived from the abacus education” (“grande utile tam civibus particularibus quam etiam nostre comunitati posset resultare”), and similar statements were common.

In 1523, in particular, it was declared: “Più cose sono … quali mantengono, augumentono et extollono le ciptà, infra le quali una de le principali et più necessarie si è la merchantia, la quale, comme ci mostra la experentia, ha inalzato et continuamente inalza tucte le principali ciptà di Italia, e senza la quale le ciptà non proprio si poterino dimandare ciptà. Et conciosiacosachè non si possa in modo alchuno tal merchantia exercitare senza arismetricha overo abacho, comme ognuna de le prudenzie vostre da per se cognoschono, et ancho gliene dimostra quello, che li loro antecessori, questo medesimo considerando, hanno sempre usato di condurre uno maestro d’abacho”.

As a result, while in 1451 it was underlined, as already said, that Arezzo, unlike Florence, didn’t have a local tradition of abacus education, now in 1523, it was declared that “the ancient institutes and habits” of Arezzo included the abacus education and that the previous generations had always delegated a master for that (R. Black, 1996: p. 128).

Therefore, even if it’s impossible to trace a single and certain cause of such an altered interest towards abacus in Arezzo, by the joint interpretation of the previous proceedings we carry out that it was first of all caused by the recognition that the abacus knowledge was fundamental for a better exercise of civil life and the carrying out of the relevant offices, more than to allow the efficient performance of business life and jobs in general, which was simply considered as a useful prerequisite to the former.

Actually, as we have already mentioned, during the late Middle Ages and the Renaissance it was a common practise that only citizens belonging to a corporation or in any case businessmen or workmen could enter the highest civil and political offices. Even in Arezzo, the Rectors of Arts belonged to the General Council and it’s fairly possible that at the beginning of the 14th century the Guilds had reached a worrying hegemony in the city. It was evident that within little time they were cancelled twice as political subjects: in 1274, when there were 12 of them and in 1287 when they amounted to 15 (F. Paturzo,

2002). In 1337, moreover, the interdiction to constitute corporations was established and then abolished, with the concern that the revived arts would not have established cartels of monopoly or took political sides.

The excellence in business, thus, was a good viaticum to get to cover the most important civil and political offices in the city. And the knowledge of abacus proved to be even more fundamental to excel in business. That is why the renewed interest towards such an education, mostly starting from the second half of the 15th century, that is to say when the Florentine hegemony lowered in the taking over of “its own men” in the top civic positions, even more relying on the “local minds”( even if constantly faithful to Florence) for the local administration.

6. Final considerations The reflections conducted in the present research partly explain the reasons why less attention was dedicated until today to the abacus schools and books within the studies and researches in accountancy history.

On the other hand, book-keeping, aside from being taught at an elementary level, represented only a little part of didactic programs and contents in both abacus schools and books. Actually, as already discussed, during the Middle Ages and the first part of the Renaissance the development of book-keeping happened almost exclusively in practice and that is where its teaching occurred. School education from the accounting point of view, in fact, began to gain a substantial importance only in the middle of the 15th century, according to the influential opinion of F. Melis (1950: p. 609-611), who tends to consider scarce both the number and the contents of book-keeping handbooks up to the beginning of the 16th century.

On the other hand, the former considerations highlight how the abachaistic phenomenon could give a fundamental, even if often “intangible”, contribution to the book-keeping progress: in fact it concurred to create those attentions, expectations and knowledge inherent to the process of keeping records of economic nature, which represented the necessary substrate to the development of efficient and innovative practices and, therefore, to the development of the book-keeping tradition.

Then, in turn, the new book-keeping culture reflected and penetrated the abacus surroundings, setting up that “process of incessant contamination” hitherto described. Ultimately, the development of the abachaistic phenomenon and that of the book-keeping culture, during the whole 15th century, were implemented side by side,each influencing the self, culminating the first birth and diffusion of the accounting schools and handbooks, and the second in that extraordinary “book-keeping” advancement recorded, mainly in our country, since the 16th century.

By recovering and highlighting the function performed by the abacus school and books in the “genesis” of the book-keeping art, the research also traces the influences operated by the abachaistic phenomenon in the considerable transformations experienced in the Renaissance period in our country in every sphere of human action specifically economic.

In particular, the current analysis pauses on and underlines the specific contribution that the abacus schools and books had in giving shape to the cities and the citizens of that time. More so in detail, and referring to the specifics of Arezzo between 13th and 16th century, it reveals the existence and the progressive affirmation of an actual consciousness by public authorities in relation to the above mentioned contribution, which determines a growing attention towards the abacus education.

This interest– which could lead us to affirm–has partially concurred to “reconsign” Arezzo to its citizens, who, thanks to the knowledge acquired by attending the abacus school, have been able to assist and then, gradually, take over the positions held by sent by the Florentine authority in the different civic and political offices of the city. This research is included in a much wider study of which tends to investigate and confirm, in a longitudinal perspective, the existing correlation between the abacus schools and books and the socio-economical changes of the period between the late Middle Ages and the Renaissance, thus highlighting the “indirect” contribution to book-keeping.

The objectives of this investigation and the relevance of the specific purposes in this research underlie the necessity of trying to limit the field of investigation. In particular, it has been preferred to proceed to “only” consider the abacus schools and books released in Tuscany between the 13th and the 16th century. Actually, as affirmed by Black R. (1996: p. 167), the whole of Tuscany, throughout the Middle Ages and the Renaissance, “ has been a fertile ground for the growth of the cultural institutions and the emergence of school subjects”. It was, moreover, the homeland of the first abacus book recognized as such (the Liber Abaci of Fibonacci) and the effervescence of the business run by the hard working Tuscan merchant has been the fertile substrate which consented Pacioli to appreciate all the importance of the double entry method.

Even more specifically, the different socio-economical evolution occurred in Arezzo, Florence and Siena during the Renaissance were analyzed in a comparative perspective, placing them in relation to spreading of both the abacus schools and books in the same territories, with the aim to investigate their reciprocal relations.

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