Professor of Accounting Education, Middlesex University Business School, London NW4 4BT UK

Transcription

1 Luca Pacioli, a Work in Progress Alan Sangster Professor of Accounting Education, Middlesex University Business School, London NW4 4BT UK a.j.a.sangster@btinternet.com I am delighted to have been invited here today to present a resume of my work and that of myself, Greg Stoner and Pat McCarthy on Luca Pacioli. I would like to add my sincere thanks to you all for your patience as I read this speech in English; and to Professor Esteban Hernández Esteve for not only inviting me but also for translating my speech into Spanish. This, the 19th of June, is an auspicious date: the date upon which, in 1517, one of the greatest men of the Italian Renaissance died, Fra' Luca di Bartholomeo de' Pacioli. Accountants and accounting scholars revere Luca Pacioli for being the first known author of a printed text on an accounting topic: a 27 page treatise on how to do double entry bookkeeping and business practices, which was published within the 315 pages of Summa de Arithmetica, Geometria, Proportioni et Proportionalita (Summa) in Venice in Yet there is so much more to the man and to Summa than many of us realise. Luca Pacioli was a Franciscan friar, author of at least ten books, a school teacher, a university teacher, a mathematician, a magician, a designer of alphabetic characters, a linguist, advisor to Dukes, generals, and Popes, close friend and tutor of Leonardo da Vinci, a chess expert, an opportunist, a humanist, and a visionary. Orphaned at an early age in a small town in north east Italy, by the age of 18 (possibly 16), he managed to find his way 300km north to Venice and a job as a merchant's assistant and tutor/guardian of the three sons of that merchant. From that point onwards, he never stopped. His network of contacts reads like a "who's who" of his day and his access to all levels of society would have been matched by few of his contemporaries. We accountants and accounting scholars tend to forget (or are unaware) that Pacioli was so much more than a friar who happened to also be the author of a printed compendium of mathematics containing a short treatise on accounting related topics. Other disciplines recognise Pacioli for his other achievements. Calligraphers and printers have acclaimed his alphabet for the past 500 years; mathematicians see him as one of the pivotal figures of the development of algebra and, in particular, the divine proportion; architects revere his memory to such an extent that conferences are named after him; authorities on the development of business education identify him as the author of the greatest business school text of the Renaissance; modern day chess grand masters view him as a chess 1

2 player of exceptional ability. Yet, it is only when all these perspectives are viewed together that a true picture of Luca Pacioli, Renaissance Man begins to appear. The information we have concerning Pacioli and his life comes largely from the man himself. In true humanist style, he included many pieces of autobiographical information in his books. However, there is also information gathered from other sources, such as the notebooks of Leonardo da Vinci, the diaries of notable figures of his day, and the municipal records of cities such as Perugia and Florence. Italians have known of and revered Pacioli as a stepping stone in the development of accounting. There is no evidence to suggest he was ever forgotten in Italy or in Germany. However, the English speaking world only re awoke to Pacioli's contribution to accounting in the 19th century. For about 350 years, we were blissfully unaware of who it was that first described a double entry accounting method to the world, as opposed to an apprentice, a son, or a small group of students. Over the past 150 years, many have made a contribution to our knowledge of Pacioli and his works. Not least, Professor Esteban Hernández Esteve with his analytical work on the nature and content of Pacioli's bookkeeping treatise, Professor Basil Yamey, and the late Professor Carlo Antinori. Some attempts have been made at biographies, most notably by Taylor (1942), Jayawardene (1971), and Rankin (1992). These English language works were preceded by two notable contributions in Italian: Boncompagni in 1879 and Pacioli's first biographer, Baldi in 1589; and were superseded, in part, by the more recent works in Italian of Ciocci (2003, 2009). Baldi s 1589 work is considered less reliable than it may have been because it was written 72 years after Pacioli s death and Baldi could not have known Pacioli as Baldi was not born until However, Baldi was born in Urbino, where Pacioli spent some time researching and writing at least some of Summa and to the Duke of which Summa is dedicated. The biography nevertheless contains errors, as would be expected when much of its content would have been relayed to him second or even third hand by those who knew Pacioli or knew people who knew Pacioli: his list of Pacioli s publications, for example, omits at least three of Pacioli s works. We cannot, therefore, rely on Baldi s biography as a definitive source on Pacioli. Nor can we rely on Pacioli himself, for he makes errors in Summa concerning dates of events that we know to be incorrect. When you start with such uncertainty, it is difficult to be confident that a modern day biography of Pacioli will be correct. However, so many have tried to describe various aspects of Pacioli s life that we are almost certainly close to a point where we can be confident that much of what we write is correct. We do so through a combination of careful researching and careful writing. Certainty is only expressed when we are literally certain. For example, we know the 2

3 dates when the printing of the core text of the two volumes of Summa terminated and when printing of the first 16 pages of Summa was completed. But, we do not know the date when the printing of each of the two volumes of Summa started. Nor do we know how many copies of Summa were printed. The paper I wrote on this topic focused on the process of printing in 1494 and revealed findings that suggested our previous perception concerning the number of copies printed was incorrect. It also drove me down a research path that led me to conclude that our views concerning the intended market for Summa were incorrect. For many years, English language accounting researchers assumed Summa was a compendium of mathematics and that its target market was mathematicians and other learned individuals. Italian writers on Pacioli wrote about the true market for the book in the late 19 th and early 20 th century. However, for whatever reason, their compatriots who followed them tended to ignore the purpose of the book when writing accounting history articles on Pacioli. Failure to recognise the nature of Summa meant that assumptions made by accounting researchers (concerning the viability of the bookkeeping treatise within it as a device from which to learn bookkeeping) may have been invalid. Pacioli s writing style in the treatise on bookkeeping has been widely criticised for the past 450 years. However, my colleagues and I found that it was written in true humanist style: in a manner that ensured it could be read and understood by as many people as possible; and that its style was instructional and didactic. It is undoubtedly the case that any other form of writing would have restricted the readership and minimised the possibility that its contents be widely disseminated. I would go so far as to suggest that had it been written entirely in Latin (whether scholastic Latin or High Latin) or entirely in correct (i.e. Tuscan/Florentine dialect) Italian, we would not today be recognising Pacioli as the father of accounting. More likely, one of those that leant heavily on his work to develop their own possibly Manzoni (1540) whose first edition was published in 1534, possibly Ympyn (1543) would be seen instead as the person whose printed work led to the development of modern accounting. It should also not be forgotten that printing using moveable type characters was 50 years old in By then, up to 35,000 titles had been printed at an average of copies of each title, and many of these titles have not survived, even in single copies. Pacioli may not have been the first person to have a text printed describing the double entry bookkeeping method. It is possible that someone else printed a book on bookkeeping similar to Pacioli s at some earlier date and that no copies of it have survived and that no copies of it were ever written about. As a case in point, there is a 200 year old reported sighting of a book on bookkeeping published in Pacioli s name in 1504 but the book so described was never written about by 3

4 anyone else who had seen it and has never been subsequently found see Yamey (1974). Do we believe that book existed? Some do. Some do not. Do we believe that a book or even a manuscript on bookkeeping existed that pre dates Pacioli s Summa but which no one ever mentioned? Many do not. Some do and, a century ago, one Italian academic sent his students into the Venetian archives in search of it, without success. Yet, there must have been manuscripts on bookkeeping before 1494 that covered at least some of the topics in Pacioli s treatise. Bookkeeping teachers must have made notes from which they lectured. In some cases, those notes would have been as comprehensive as Pacioli s treatise. There are clues in Pacioli s treatise very strong ones if you believe that Pacioli based his treatise on one manuscript that suggest it was originally written to teach bookkeeping somewhere outside Venice. If so, Pacioli s life would point to the most likely original source being bookkeeping tutor in Urbino, or in Sansepolcro (or somewhere else in Tuscany), or in Perugia, not one located in Venice. Alternatively, it may have been that the author of the original source document was the person who taught Pacioli bookkeeping in Venice in the 1460s and that the author wrote it while outside Venice, possibly in Tuscany. Alternatively, that teacher or Pacioli himself may have written the text of Chapters 1 35 so that someone outside Venice would understand why it was written from a Venetian perspective. We do not know and we will never know unless someone finds the manuscript(s) upon which the treatise is based. That Pacioli s bookkeeping treatise was based on [a] source document(s) and was not written especially for Summa is clear from the shift in style and language towards the end of the treatise. 1 Five hundred years is a long time to hope that evidence of what occurred will have survived. So it is with most of the research on Pacioli. We must take clues in his text and elsewhere and try to piece them together. If we miss one of the clues or the clue (or information) is lost, we may draw what appear to be sensible conclusions for example, that Summa was a book for mathematicians. When we find a clue we have missed or lost, we must redraw our conclusions. This is, essentially, what the research I have been conducting has been doing. As mentioned previously, I stated looking at the printing of Summa, then looked at the market for the book, then at the writing style adopted, then at why it may have been written in the manner selected. During these activities I have identified other issues worthy of investigation. For some of these, I have preliminary findings which I will recount later. 1 For a fuller description of the academic debate on this issue see Yamey (1967). 4

5 The research I have conducted was only possible following the expansion of world wide web since the early 1990s. This enabled me to locate articles and books I would never otherwise have found; articles in other disciplines I would never have thought to search; and to locate the most up to date data and information from all over the world and in a wide range of languages; all to an extent that simply was not possible as recently as 10 years ago, never mind 15 or 20. Those heroic individuals from Rui Fogo (1905) to Fenny Rankin (1992) and all those others including Federigo Melis, Carlo Antinori, and Basil Yamey who researched in this field up until the middle of this decade, who did their research the old fashioned way, were not wrong in what they concluded, they simply had no means available to them to discover our past in the way we now have. Printed Papers The Printing of Luca Pacioli s Summa Arithmetica in 1494 (Sangster 2007) The only previous researcher to look into this topic was Antinori (1980). He concluded that 300 copies had been printed. However, that would suggest that Summa was of limited interest and unlikely to have been either widely read or influential, which is inconsistent with how it was received. It is also inconsistent with survival rates (10 20 per cent of the print run of serious books published at that time) and the number of extant copies (30 60 copies would have been expected to have survived had the print run been 300, not c. 120 as found when conducting this research). In addition, it is also inconsistent with the market for the book, to which I will refer later. Reprints of some (but not all) of the pages took place after 1502 and after Extant copies in 1862/3 (Boncompagni, 1862/3) suggest these smaller print runs may have been for 25 per cent of the original print run and then around 10 per cent. As they were only reprints of a few pages of the book, they did not add to the number of copies originally printed. What they demonstrate is that there was a consistent but reducing demand for the book after it was printed, that perhaps 75 per cent were sold in the first 8 years and 90 per cent by the end of the first 15 years after publication. The average print run in the first 50 years of moveable type printing was copies. The average print run at the time Summa was printed was 1,000 1,500 copies. The printer of Summa (Paganino de Paganini) was renowned for high quality printing, which is also inconsistent with a print run of 300. All the evidence points to a larger print run that than the 300 Antinori estimated. From the dates provided by the typesetter in the text, we know that the time taken to print the last 5

6 16 pages was 9 working days. The likely rate of printing on folio sized paper would have been 2,000 copies of two pages on one side of paper per day. It would have taken four days to print those 1,000 copies of the 16 pages if 1,000 copies of two single sides (i.e. 4 pages) were printed each day. Paganino de Paganini would have employed high quality workers (or his reputation for quality work would not have emerged or survived). There is no reason to believe that they would not have been capable of these rates of printing. As double this time was taken to print these 16 pages, this suggests that the print run was actually 2,000 copies and that 2 pages were printed each day. Two thousand, or a multiple of that number based on using more printing presses is the most likely figure for the original print run. Given the intended market for the book (a school textbook, for which the expected survival rate would be virtually zero), the print run could have been a number of times 2,000 had the printer the capacity to do so. Unfortunately, we have no information concerning the resources at the disposal of the printer so can do no more than suggest that the print run was possibly higher than 2,000 copies. Survival rates support a print run on copies which were sold for reference of between 600 and 1,200 leaving 800 1,400 as the number of copies sold as textbooks: 2,000 may well have been the size of the print run. Whether it was larger than that figure or not, it was many times higher than the previous estimate of 300. The market for Luca Pacioli s Summa Arithmetica (Sangster et al. 2008) Many accounting researchers have held the view that Summa was published for mathematicians and other learned individuals. 2 However, the target market for Summa was neither mathematicians nor learned individuals nor even university students of mathematics, it was merchants and the sons of merchants. Summa is the most comprehensive of all the more than 500 abbaco textbooks that have survived (Jayawardene 1971; Rowland 1995). It covered all the mathematics and business related curriculum of the abbaco schools. 3 Some dispute the evidence but most who have looked at the abbaco curriculum and at Summa are agreed that this is what the book was: a school textbook and reference manual for merchants. Lessons from the classroom from Luca Pacioli (Sangster et al. 2007) This paper took an entirely different slant on Pacioli s work. Rather than investigating issues relating to Pacioli s life and his 15 th century world it sought to demonstrate that that there are lessons to be learned today in both textbook writing and in classroom instruction from Pacioli s 2 See, for example, Yamey (2004). 3 See Van Egmond (1981, pp ) for the abbaco school curriculum. 6

7 treatise on bookkeeping. The paper sought to discover whether Pacioli s treatise on bookkeeping was a document we could all treat as an exemplar of good pedagogic practice. A modern 7 stage framework for the development of learning materials was consulted (Rowntree 1994). The paper found that Pacioli followed a similar model in developing his treatise on bookkeeping and the rest of Summa: 1. Specify the kind of materials your learners need 2. Track down materials that may be suitable 3. Evaluate collected materials using appropriate criteria 4. Customize materials that are not quite suitable as they stand 5. Write new materials suited to the needs of your learners 6. Edit materials and prepare them for the production process 7. Evaluate and improve your materials It also looked at the pedagogical devices in the treatise. It found that the treatise is replete with many devices doing similar things to those done in modern texts, such as marginal annotations, use of signposting, forwards and backwards referencing, summaries of what is coming next, appendices, contents lists, use of an index, instructions in how to use the indices to find relevant text, frequent contextualisation. It also includes advice on how to teach. In conclusion, it found (p. 455) that, The frequent references within the treatise to other ideas and concepts along with the broad contextualization of the processes of bookkeeping to legal, social, ethical, and moral codes, as well as to business practice, meant that readers of the treatise learned double entry bookkeeping in context, rather than by learning how to apply a formulaic approach in isolation from the reality of business. As a result, readers could link what they learned to their own knowledge and experience, see its relevance, and thus gain understanding something most faculty would aspire to with their students but, as research shows, they do not always achieve One clear lesson from the bookkeeping treatise is that we should resist teaching accounting as a technical subject devoid of context. Context is essential, as is paying heed to the other relevant advice in the treatise. For 500 years, accountants ignored the advice the bookkeeping treatise contained concerning ethics, morals, and auditing, and paid the price with massive corporate failures over the last 300 years, culminating in the collapse of Enron which, in turn, resulted in the failure of one of the world s largest accounting firms. These lessons in the risks inherent in practicing accounting in a contextual vacuum can also be applied to the teaching of accounting, and to the manner in which we teach it in the classroom. There are lessons for us all in Pacioli s bookkeeping treatise, lessons from the pedagogic Pacioli. 7

8 Pacioli and Humanism: pitching the text in Summa Arithmetica (McCarthy et al. 2008) There is a style to Pacioli s writing that is clearly planned it is not simply the jotting down of isolated or even related points. Rather, it is a planned web of interwoven words and phrases that, at times, appears strange and alien to the modern eye. 4 It was also alien to the cultured eye of mid 16 th century Italy. What was the reason for Pacioli adopting the style he used in Summa? Pacioli was not interested in the future, he was interested in the present. He would have been well aware that the vernacular (i.e. spoken language) with which he chose to write Summa would be looked upon with some disdain by future generations. He knew it was the language of the masses rather than the language of the (Latin school educated) upper and upper middle class; and he knew that future scholars, who would be from those classes, would not naturally be drawn to it. But his view was for the present, not for future generations. He knew that his peers who were educated in the Latin schools would not like the language, but he knew that if he was to follow the spirit of the humanist movement and take his work to the widest possible audience, this was how to do it; and he knew that the humanist educationalists of his day would understand why he had done so and agree with his choice. Thus, at the root of Pacioli s choice of language and style was the humanist movement of the Italian Renaissance and its goal of reaching as wide an audience as possible and to engage and persuade it, even though this meant using the vernacular rather than Latin for instruction. Mathematics was not taught in Latin Schools. At that level it was taught in the abbaco schools. Other than in Florence, school pupils in Northern Italy, attended only one of those schools. 5 As a result, school pupils in most of Northern Italy either received a Latin education or an abbaco education. They either learnt how to do mathematics and apply it to business, or they did not. If they did, they were taught in the vernacular, not in Latin. In addition, abbaco pupils were only taught elementary (scholastic) Latin. They could understand it up to a point. Their ability to speak it was very limited. Following the humanist desire for wide dissemination was not Pacioli s only motivation. He was also an experienced abbaco teacher who was used to teaching this material in the vernacular. He knew his market and he knew how much Latin and how much references to the classics of Rome and Greece and later writer s on those topics would be understandable to a merchant and abbaco school audience. His selection of middle ages scholastic (i.e. bad ) Latin 4 See, for example, Yamey (1994). 5 In Florence, they typically received two years of abbaco as part of their normal schooling. 8

9 to highlight key points was appropriately pitched for his audience. In case he overestimated their understanding, he usually gave a translation of the Latin in the text that followed it or, in the absence of a translation, he made the meaning of the Latin clear in the surrounding text. His selection of the vernacular of the northern Italian markets 6 was entirely appropriate. This was the language of the merchants and was how they communicated with many of their customers. It was a language that would have been well understood in Venice where Summa was published and where all its original sales took place. It was also well understood throughout Northern Italy at that time. If it were not, why did Leonardo da Vinci (a barely educated native of the small village of Anchiano, 2km from the small town of Vinci which lies between Pisa and Florence) not only buy the book but (probably) arrange for Pacioli to move to Milan and work for the Duke while tutoring him on powers and roots and helping him with his calculations? Also, why was there a second full printing of Summa in 1523 funded by the printer if it was not written in a vernacular and style that its market would understand? The manner in which Pacioli used words is similar to that in which humanist designers and artists used the images in their paintings to instruct. An example of this is to be found in the money changers guild in Perugia the place where merchants met to arrange loans and settle debts. The frescos in the meeting place were commissioned in They are replete with Latin referents and sayings. Their message is also conveyed by the subjects of the paintings. In Pacioli s Summa, Latin is used in the same way and the message is also conveyed in the vernacular text. Pacioli uses Latin in order to engage and persuade the intended audience, as a tool of emphasis. This is the same as its use in the frescos in the money changers guild. Pacioli s use of humanist symbolism references to the Cardinal Virtues, Theological Virtues, to Dante and to Cato also bears similarity to its use in the frescos of the money changers guild. Pacioli s choice of language and use of classical referents and sayings to convey ideas, concepts, advice, images and moral values appears to have been deliberate. It was calculated and was consistent with the humanist age in which he wrote his text. Analysis of the frescos in the money changers guild and of the text of Summa suggests that what the artist did with his palette, Pacioli did with his pen. By the time the style and use of language in Summa came to be criticised in the mid 16 th century, the Tuscan dialect (i.e. that of Florence, the heart of the Renaissance) had been the offical Italian language for at least 20 years (since 1525). However, this would have made the language and style of writing in Summa no less appropriate. (Markets continued and the language in them was unlikely to have been affected; and modern day evidence is that local dialects have been retained far more in Italy than in, for example, the UK where language 6 See Marinoni

10 unification came even later.) Nevertheless, it could be suggested that the selection of Tuscan as the basis for an Italian language could have made humanists more aware of the heritage of their language and more critical of non Tuscan vernacular. Also, the passage of a further 50 years of humanist influence on school education since 1494 would have cemented the qualities of High Latin in the minds of humanists and would likely have also made them less willing to recognise scholastic Latin as a suitable form of the old language. This could explain why Pacioli s selection of language and style were viewed in such a bad light in the mid 16 th century and would explain why his writing and the style he adopted were praised when Summa was published (Taylor 1942, p. 196) but criticised 50 years later. With respect to his treatise on bookkeeping, Pacioli wrote for one audience. By the 1530s other authors were establishing themselves as authors of treatises on bookkeeping. His treatise had done its job and needed to be replaced by something better. It was. However, in terms of fitness for purpose and instruction in context, few that succeeded Pacioli came close to achieving what he achieved in terms of encouraging engagement with the material. The actual accounting material may be better and more detailed in the likes of Manzoni (1540) but the contextualisation in a business setting is not. It is only with Zappa s 1926 Italian manifesto which declared that accounting was not a separate discipline but, rather, that it was at the core of the discipline of business 7 that we saw a return to the contextualisation of accounting in Italy. It would be in the spirit of Pacioli for the rest of the world to do likewise. Work in Progress Why are the final three pages of the treatise on bookkeeping in conflict with the rest? A Historical Note (paper submitted to the Accounting, Business and Financial History conference, Cardiff, September 2009) This is one of the aspects of the treatise that has most puzzled accounting researchers. The research focus has always started with Pacioli s statement that he used other people s material as the basis for everything in Summa. The consensus view is that there were at least two sources for the treatise: the one that formed the basis of Chapters 1 35 and another that provided the text for the rest of the treatise. This is not necessarily the case: it has been found that the language and style in the treatise is generally consistent with the rest of Summa. 8 For this to be so, Pacioli must have rewritten large tracts of the text of the rest of Summa as well as most of the treatise on bookkeeping. He certainly did, for the treatise contains not just forward 7 See, for example, Costa and Torrecchia (2008). 8 See Antinori (1994). Antinori owned copies of both editions of Summa and devoted much time to studying the text. He was considered one of the few people who was able to read the text without difficulty. 10

11 and backwards references within itself but also references back to pages in earlier parts of Summa. Pacioli may simply have run out of time to complete his rewriting of the final chapter of the treatise. It may all have originated in one manuscript and Pacioli may have been rewriting that single manuscript to produce his treatise. There are some possible reasons why Pacioli may have run out of time. It is almost certain that the treatise was a late addition to Summa the dedication to the Duke of Urbino implies as much: it is the Duke who wanted it included, not Pacioli. It is possible that Pacioli s work on preparing the treatise for publication was interrupted before it was completed and that he was unable to finish it in the timeframe required by the printing schedule. There is also some additional information that may help explain why there is a difference between the style and language of the first 35 chapters and the rest. The bookkeeping treatise ends at the foot of the reverse side of the last sheet in a bundle for binding of 20 pages. This would not have occurred by accident. The final bundle in Volume 1 of Summa follows the end of the treatise on bookkeeping. It is a treatise on tariffs and is 28 pages long. The appropriate bundling of these 48 pages would have been three bundles of 16 pages, the length of all other bundles in Volume 1, suggesting that this stage of the printing was unusual. There are a number of possible explanations why these 48 pages were bound in two bundles rather than three. The two most plausible may be that: (i) the treatise on tariffs was not available when the bookkeeping treatise was being printed (in which case printing would have continued on the basis that the treatise on tariffs might never appear); or, (ii) the treatise on tariffs was printed in one bundle of 28 pages so as to enable the pages to be sold or used separately. The most likely of these two explanations is the second. The first page of the treatise on tariffs is a contents list showing the location in the treatise of product exchange values for each city/town cross referenced to other cities/towns. This is continued briefly at the top of the second page. All merchants in Venice (and in the other places mentioned in it) would have been interested in having a copy of this treatise. It may even have been used as promotional material for Summa. When I wrote the paper about the printing of Summa (Sangster 2007), I speculated that the treatise on tariffs was included at the last minute. However, without the treatise on bookkeeping and by careful typesetting, the tariffs material and the first volume would have ended at the bottom of a 20 page bundle, as is the case for the bookkeeping treatise. When combined with the fact that the Duke of Urbino asked for a treatise on bookkeeping to be included in Summa, this suggests that the treatise on tariffs was always intended to be included 11

12 in Summa and that the treatise on bookkeeping was a late addition. Consequently, I now feel that it is more likely it was originally intended to start printing the treatise on tariffs where the bookkeeping treatise starts and that it was the treatise on bookkeeping that was added late. It is also possible that, around the time that it was decided to insert a treatise on bookkeeping, a decision was made that the treatise on tariffs should be bundled separately; and that this was done so as to enable the treatise on tariffs to be used separately: either to be sold on its own or, to be distributed as publicity for Summa. This led me down a line of research which I have not yet published: Chapters 3, 12, 15, and 16 of the treatise on bookkeeping mention the date of November 8 th It is the only date used in any chapter before Chapter 35. In Chapter 35, the date of 17 th April 1494 is used. These were possibly the dates when Pacioli started working on these chapters. There was no reason why Pacioli should have invented dates. He was not writing a case study or even extracts from entries for the same business where the date an entry was made would affect his description of the event. It was simpler just to use today s date. If this was the case, his rewriting of the original material was done over a long period of time but Pacioli probably finished Chapter 35 on or soon after April 17 th Once the first and last pages of a bundle were printed (simultaneously on the same sheet of paper) it was too late to change the contents of that bundle. Based on a print run of 2,000 copies, after handing over the text for the first bundle, Pacioli would have had approximately eight working days in which to amend the text of the material in that final bundle of the treatise, which runs from the middle of Chapter 9 to the end of the treatise. However, the use of an April date in Chapter 35 suggests that Pacioli had finished all the revision of that material to that point long before the bundle was needed for printing. (It is unlikely that it would have taken over 5 months to print the 151 pages of Volume 2 which was completed on November 10 th 1494.) In April 1494, the printer would have known how many pages he was going to print to complete the treatise subject to any rewrite of Chapter 36 and the material that follows it: 20 pages. The printer s preference would have been to print all but the last four pages of the treatise as a bundle of 16 pages and then print the last four pages at the start of the first bundle in which the treatise on tariffs was to be printed. The printer would only have decided to print a 20 page bundle to complete the bookkeeping treatise if (a) the material on tariffs was unavailable or (b) if it was to be printed separately. Either of these situations would also explain why the bookkeeping treatise appears before the treatise on tariffs in Summa. Comparing Chapter 36 with the earlier chapters, Pacioli was probably lengthening the text as he amended it. It is bereft of proverbs and contains no Latin and it appears more terse. 12

13 This could explain why he failed to rewrite the material towards the end of the treatise: the printer did not want to add more sheets of paper and just a few lines more would have required the addition of another sheet which would then have needed to be filled with four pages of text. Adding to the uncertainty, the text in Chapter 36, although flagged as being in the treatise in the contents list printed two bundles earlier, is significantly inconsistent with the text in Chapters 1 35, and far more so than mentioned above. 9 There are more full stops. A different currency is used: Grossi and Picioli are replaced by Denari; and Grossi does not appear in the list of currencies given in the second additional section of text despite its being used consistently throughout Chapters Tuscan terms are used rather than the Venetian terms used previously. The ten examples of ledger entries at the end are in the Tuscan (not the Venetian) style and use Tuscan rather than Venetian names. Pacioli certainly had not rewritten this material to make it consistent with the material in the first 35 chapters. If he had been given time, Pacioli could have rewritten Chapter 36 and brought it and the examples into line with the rest of the treatise. However, it would not have been easy for him to have rewritten these final few pages without adding to the length. In addition, he would have needed to refer back to how the topics and items were treated earlier, and the printer needed those manuscript pages to create formes for the next days printing. Time cost money and no one wanted to spend time waiting for a manuscript when one was already available. This was an argument Pacioli is unlikely to have won. If the material on tariffs was unavailable and material on bookkeeping was available, Pacioli s time would simply have runout. Alternatively, time may have been available if the treatise on tariffs was to be printed separately, which suggests that Pacioli was not in Venice when the treatise on bookkeeping was being printed. He would, therefore, probably have been unaware that time had expired for amendments to the treatise. This is a feasible explanation for the difference between the style of the material after Chapter 35 and the first 35 chapters, but there are others for example, Pacioli could have been ill. Printing would have continued, regardless. In fact, given that Pacioli was a highly vocationally motivated educator, it is inconceivable that he would have willingly allowed this material beyond Chapter 35 to be included without rewriting it to make it consistent with the rest of the treatise. Pacioli was, therefore, probably not present when this final bundle of the treatise was printed. In fact, he may not have been there when any of the treatise on bookkeeping was 9 See Hernández Esteve (1994). 13

14 printed. Given that there are so many examples of bad typesetting in the treatise (for example, when the journal entries are presented) and, for example, / characters are represented by blanks, this makes sense. If so, he may have had to leave Venice before he had completed rewriting the text of the treatise and left a copy of the original manuscript with the printer in case he did not provide the final rewritten pages in time for them to be included in the printing. If all this is correct, it still leaves unanswered the questions: 1. Why was Pacioli not in Venice at that time? 2. Why did Pacioli not manage to get rewritten text to the printer in time? 3. It would only have taken less than two weeks to print the final 20 pages of the treatise; if the printer had allowed Pacioli 20 pages in which to present his rewritten text for Chapter 36 and the material that follows it, why were these pages not reprinted when Pacioli supplied the printer with the rewritten text? The additional cost would not have been significant in the context of printing a book of 615 pages. Perhaps these questions are what researchers should be focusing upon. If it can be shown that Pacioli was elsewhere during the printing of Summa between (say) mid April and mid July 1494 (which is as late as it could have been before the printing of Volume 2 started), this could provide the answers to the first two questions. The third may simply have been a matter of cost. The sponsor of the printing was not a merchant or a bookkeeper. He may have been unwilling to pay for the pages to be reprinted. Summarising, a possible explanation for the inconsistency between Chapters 1 35 and the rest of the treatise is that Pacioli rewrote the material in Chapters 1 35 but did not rewrite the rest of the treatise. Pacioli told the printer there would be 36 chapters in the treatise. The printer committed Pacioli to providing a summary of the treatise in the form of a 36 th chapter when the contents list of the treatise was printed. The printer needed to complete the final sheet of four pages and used the original manuscript for Chapter 36 and the other material at the end of the treatise in order to fill what would otherwise have been virtually three blank pages. In addition, the length of the treatise on bookkeeping meant that there was an extra four pages of text beyond the end of a second printing bundle of 16 pages. Either, the treatise on tariffs was unavailable when printing of the second bundle of pages for the bookkeeping treatise began or, a decision had been taken to print the treatise on tariffs in one bundle so as to enable it to either be sold separately or used for publicity purposes. As a result, the final sheet of four pages from the treatise on bookkeeping was added to the second bundle containing material from that treatise rather than to the first bundle containing material from the treatise on tariffs. 14

15 Luca Pacioli s Education Despite the assertions of many researchers that Pacioli had a humanist (Latin) school education, Luca Pacioli s handwriting reveals that his education was not in a Latin school but in an abbaco school, the school system developed for the sons of merchants and other craftsmen. He uses merchant script, which was taught in the abbaco schools (hence its name) and was not taught in the Latin (or Grammar ) schools. We do not know who Pacioli s teacher was in Sansepolcro but, given that he was the author of abbaco texts, his teacher may well have been the artist and mathematician and fellow citizen of Sansepolcro, Piero della Francesca ( ). Piero was well connected and may well have been the person who opened the first doors to Pacioli s career. If Pacioli was his star pupil (as seems likely), he may have taken Pacioli with him to Urbino and he may have been instrumental in Pacioli obtaining his first position with the merchant Rompiasi in Venice. Piero may be the reason why a humble merchant s apprentice (Pacioli) was travelling around Italy in 1470 in the company of one of the most renowned men of his times, Leon Battista Alberti ( ) the definitive Renaissance Man. It would further justify Pacioli s virtually unaltered use of Francesco s geometry text as the second volume of Summa. [ The only difference appears to be the deletion of his [Piero s] personal asides (Albrecht Heefer 2007).] Some researchers have gone so far as to suggest that Pacioli helped Piero write his text (for which there is no evidence) and so had no compunction in using it in Summa. However, a better justification for simply dropping it into his text without attribution could be that, as a former school pupil of Piero, when Piero wrote down the text at the behest of the Duke of Urbino, Pacioli could have viewed the text as being a transcription of what he had heard in class and his to use as he saw fit, which was a normal view at that time. The fact that he attributed many of his sources, including Piero, for the contents of Summa but not Piero specifically for the volume on geometry supports the argument that he may have helped Piero write it. It may also mean that Pacioli knew the source of Piero s manuscript and that the source was not Piero (there are very few original thinkers among the writers of academic textbooks), and that he only believed in granting attribution for original work. Whatever the answer to that particular riddle, Pacioli received an abbaco education and it does seem likely that at least part of Pacioli s abbaco education was delivered by Piero della Francesca. 15

16 Language The language used is the same throughout Summa. It is Italian of the northern Italian markets. That is, it is the language as used by merchants and their families and by those who bought from them. It is the Italian that merchants and their agents from other countries and other parts of Italy would have needed to use in the markets in Genoa, Turin, Milan, Venice, Padova, Ferrara, Perugia, Florence, and Pisa, and the rest of Northern Italy. As such, it would have been the form of Italian most understood by foreign merchants and their agents. This would explain why copies of Summa are to be found all over Europe and why Pacioli s treatise on bookkeeping was so widely disseminated across Europe. It also explains why the Venetian method it presents in Chapters 1 35 is the one that gained virtual universal acceptance across Europe within a 100 years or so of the publication of Summa. Perugia Pacioli spent a lot of time in Perugia. Each of the entries in the municipal records relating to his appointments in Perugia from refers to his teaching abbaco. However, abbaco is something that we believe was taught in merchant schools, not in universities. Yet, Pacioli is said to have worked at the university in Perugia, if not in the first few years of his teaching in the city ( ) at least in the years he was there between 1487 and 1510 (Grendler 2004, p. 67). This claim is also made by Italian scholars who are currently based at the University of Perugia. 10 This suggests that abbaco was, uniquely among the 13 Italian universities in the last quartile of the 15 th century, one of the topics taught in the University of Perugia. Perugia was the most mercantile of all the Italian cities of this period. It was run by the guilds for the guilds; and merchants were particularly powerful and influential among them. It is possible that the University of Perugia was a special case among the 13 Italian universities of the last quartile of the 15 th century and that it taught business subjects as well as those subjects taught in other universities at an advanced level: law, medicine, arts. [Without these three topics and the advanced teaching of them, the title of university would have been inappropriate as the institution would not have been awarded the papal bull or imperial charter which gave it the power to award doctorates (and masters degrees).] It is also possible that the vernacular was used for teaching abbaco in the university, while Latin was used in all the others subject areas, as was the case generally across all 13 of the Italian universities at that time. Intuitively, this makes sense. Yet, so far as I am aware, no one has investigated precisely what was being taught in the University of Perugia when Pacioli 10 See, for example, Cavazzoni (1992). 16

17 was working there. In the absence of such information, a more reasonable view would be that Pacioli only taught at the abbaco school level in Perugia, not at the university level. Was Pacioli a university graduate? To have taught at university, Pacioli must have held either a master s degree or a doctorate but the evidence we have other than by implication he certainly taught at that level is ambiguous, to say the least. The scribal abbreviations for magister (master) and maestro (teacher) can be the same (e.g. m or mr ). They can also be different (e.g. magr v mro ). Magister can also mean teacher and maestro can also mean master. Consequently, when he is given a title it is impossible to tell what Pacioli s qualifications were. Even when the name is spelt out as when, for example, da Vinci refers to Pacioli as maestro in his diaries it does not clarify the ambiguity as both words can have both meanings. However, this may be resolved by the municipal records of Perugia. From October 1477 up to and including March 1479, Pacioli is variously referred to as frater/fratris/fris, i.e. friar. There is no attribution of either magister or maestro. However, in January 1480, an entry is made that appears to draw special attention to Pacioli having been awarded a master of the arts in mathematics after having spent the requisite period teaching arithmetic and geometry. The text of this municipal record is in Latin and contains a great number of scribal abbreviations. This entry has been known to scholars since at least Boncompagni (1879). Yet, I have seen no attempt being made to translate it, possibly because of the excessive inclusion of abbreviations. Biographies of Pacioli have tended to skip around the issue of his academic credentials. None have suggested a specific year when Pacioli obtained a master s degree or a doctorate nor whether he did or did not have one or the other, other than to state that he must have. Yet, it was an important stage in his career. This may explain why he spent an extended period of time in one place (Perugia) from 1477 to He never did this again after It may also explain why many (but, by no means, all) of his subsequent appointments were at universities where none had been previously. I am working on the translation of this entry in the municipal records of Perugia and will publish my findings once this work has been completed, along with an English translation of Baldi s biography. The interpretation described above is preliminary and awaits confirmation. At the same time, it is compelling: if correct, it would complete one more missing piece in the jigsaw of Pacioli s life. 17

18 Pacioli s employer in Venice in the 1460s: Ser Antonio de Rompiasi We are told by Pacioli that Rompiasi was a merchant. However, Ser was an honorary title used by notaries (see White, p. 13). This may explain how Pacioli appears to have known so much about legal issues when he wrote his treatise on bookkeeping. The Summa Summarum From Pacioli s treatise, you can see how the accounting system based on double entry bookkeeping was still being developed; how the parts had not yet been distinguished despite at least 200 years having passed since it was first used. No more so is this the case than with the Summa Summarum. Pacioli talks about the need for both a summa summarum and a trial balance. However, only the latter is needed for the purpose of flagging clerical errors through the preparation of statements of this type and the former only offers one piece of information: is the total of all the debit entries equal to the total of all the credit entries? something that is automatically shown by comparing the totals of both sides of the trial balance. However, the summa summarum does do one thing the trial balance does not do: it is better at revealing errors in the original entries because it uses original data. Trial Balances by their nature use secondary data that is, data derived from something else. They can balance when the entries are incorrect as a result of the balances drawn on the individual accounts containing offsetting errors in calculation of the balances which result in a trial balance that balances when it should not. However, the summa summarum also cannot flag compensating errors of this type. The form of compensating error that arises when balances are calculated one where an error in the original entries of a transaction is matched by a compensating error in the account balances when account balances are prepared is probably so rare it is seldom (if at all) considered. It would be flagged by the summa summarum (as it would not balance) but not by a trial balance. It is hard to justify the use of a summa summarum simply on the off chance that there is an error in one or more of the entries to the ledger that was or were compensated for by a compensating error or errors when balances were calculated for the ledger accounts. Consequently, as this was the only additional benefit of preparing a summa summarum, once bookkeepers realised that the trial balance did virtually everything that a summa summarum did and did so a lot easier, the latter disappeared from use. 18

19 This mid stage status for Pacioli s treatise is something that has been very underdeveloped in the literature and it is a long time since anyone wrote about it. It may be time for someone to show just how much of a contribution Pacioli made and how much work was still required in order to arrive at the accounting system employed today. Conclusion This has been a fertile furrow to plough. I recall asking Richard Macve three years ago at the annual Accounting, Business and Financial History conference in Cardiff if he felt it was worth my while continuing to conduct research on Pacioli (by which time I had finished the first drafts of the four Pacioli papers I have so far published in journals). Richard s response was a typical, probably. I can now report that it was definitely worthwhile and that I intend continue doing so for as long as I can. Thank you all very much! Bibliography Antinori, C. (1980), An Anomalous Edition of the Summa, 1494 by Luca Pacioli. Parma: Palatina Editrice. Antinori, C. (1995), Luca Pacioli e il trattato XI. In Convegno internazionale straordinario per celebrare Fra Luca Pacioli, Venezia, aprile Corsico (MI): Ipsoa Scuola D Impressa: Baldi, B. (1589), Fra Luca dal Borgo S. Sepolcro. Republished in Boncompagni, B. (ed.) (1879), Bulletino di bibliographia e di storia delle scienze matematiche e fisiche, Volume XII, pp Boncompagni, B. (1862/3), Intorno ad un Trattato d Aritmetica Stampato nel 1478, Atti dell Accademia Pontificia de Nuovi Lincei 16, Anno 16. Boncompagni, B. (1879), Intorno alle vite inedite di tre matematici (Giovanni Danck di Sassonia, Giovanni de Lineriis e Fra Luca Pacioli da Borgo San Sepolcro), Bulletino di bibliographia e di storia delle scienze matematiche e fisiche, Volume XII, pp Cavazzoni, G. (1992), Tractatus mathematicus ad discipulos perusinos: funzionalità e pedagogicità dell opera di Luca Pacioli, Revista Italiano di Ragioneria e di Economia Aziendale, No. 5 6, Maggio Giugno: Ciocci, A. (2003), Luca Pacioli e le matematizzazione del sapere nel Rinascimento. Bari: Caccuci. Ciocci, A. (2009), Luca Pacioli tra Piero della Francesca e Leonardo. Sansepolcro, AR, Italy: Aboca Museum Edizioni. Costa, M. and Torrechia, P. (2008), Value and accounting between history and theory: The Italian case. Paper presented at the 20 th Accounting, Business and Financial History Conference, Cardiff, 11 th 12 th September. (Available at on 13 th May 2009.) Fogo, J.R. (1905), History of Book Keeping, in Brown, R. (ed.) A History of Accounting and Accountants. New York: Cosimo Books, Inc., 2004 reprint:

20 Grendler, P.F. (2004), The Universities of the Italian Renaissance. Baltimore: The Johns Hopkins University Press. Heefer, A. (2007), Correspondence with the author relating to his comparison of Summa with the abbaco manuscript by Piero della Francesca on the subject of geometry. Jayawardene, S. A. (1971), Luca Pacioli. In Dictionary of Scientific Biography. New York, NY: Charles Scribners Sons: (available online on 12 May 2008 at Manzoni, D., (1540), Quaderno doppio col suo giornale second il costume di Venetia. Venice: Comin de Tridino de Monferrato. Marinoni, A., (1997) Introduction to Luca Pacioli s De Viribus Quantitatis. Milan: Ente Raccolta Vinciana. Melis, F. (1950), Storia della Ragioneria. Bologna: Dott. Cesare Zuffi Editore. Pacioli, L. (1494), Summa de Arithmetica, Geometria, Proportioni et Proportionalita. Venice: Paganino de Paganini. Rankin, F.K.C. (1992), The Arithmetic and Algebra of Luca Pacioli (c ), Ph.D. thesis. London: Warburg Institute, University of London. Rowland, I. D., (1995), Abacus and Humanism, Renaissance Quarterly, Vol.48(4): Rowntree, D. (1994). Preparing Materials for Open, Distance and Flexible Learning. London: Kogan Page. Sangster, A. (2007), The Printing of Luca Pacioli s Summa Arithmetica in 1494, Accounting Historians Journal, Vol. 34 (1): Sangster, A., Stoner, G. and McCarthy, P. (2008), Lessons for the classroom from Luca Pacioli Issues in Accounting Education, Vol. 22(3): Sangster, A., Stoner, G. and McCarthy, P. (2008),The market for Luca Pacioli s Summa Arithmetica, Accounting Historians Journal, Vol. 35(1): Taylor, R.E. (1942), No Royal Road. New York: Arno Press. Van Egmond, W. (1981), Practical Mathematics in the Italian Renaissance: A Catalog of Italian Abbacus Manuscripts and Printed Books to Firenze: Editrice Giunti Barbèra. White, M. (2001), Leonardo da Vinci: the first scientist. London: Abacus. Yamey, B.S. (1967), Fifteenth and sixteenth century manuscripts on the art of bookkeeping, Journal of Accounting Research, Vol. 5(1): Yamey, B.S. (1974), Luca Pacioli's "Scuola Perfetta": A bibliographical puzzle, Gutenberg Jahrbuch: Yamey, B.S. (1994), Preface in Gebsattel, A. and Yamey, B. S., Luca Pacioli: Exposition of double entry bookkeeping, Venice Venice: Albrizzi Editore. Yamey, B.S. (2004), Pacioli s De Scripturis in the Context of the Spread of Double Entry Bookkeeping, De Computis: Revista Española de Historia de la Contabilidad, No. 1: Ympyn, J. (1543), Nieuwe Instructie Ende Bewijs der Looffelijcker Consten des Rekenboeckse ende Reckinghe te houdene nae die Italiaensche maniere. Antwerp. 20