Ernest Stevelinck BRUSSELS, BELGIUM

GOODBYE TO MY FRIEND PACIOLI

I studied accountancy without ever hearing about him. I would have liked to have heard the lecturer, leaving off — for a time — the doctoral tone he employed for teaching debits and credits, to look into the life of this forerunner of accountants and to talk to him about his work. But it is a safe bet that he himself did not know of the existence of one who was later to be called the Father of Accounting.

The last World War (1940-1944 in Belgium) gave me some leisure, a physical infirmity in the right eye preventing me from serving my country by bearing arms. I took advantage of this situation to study accounting and history in depth, and finally, the history of accounting. It was then that I made acquaintance with this venerable ancestor of ours.

After hostilities were over, I met Robert Haulotte, who was also very interested in accounting history. We had numerous telephone conversations in the evening about a series of articles we were writing together (Galerie des grands auteurs comp-tables). Eventually, those conversations led to a commitment to publish a book on Luca Pacioli which compelled us to study closely his life and his work on accounting.

Later on, I became acquainted with a painter who had translated Pacioli’s Divina Proportione into French. This Frenchwoman — Mademoiselle Sarrade — was also fond, like us, of this genial precursor and we therefore exchanged many letters on this subject.

Now, both of my correspondents on Pacioli are gone. Mademoiselle Sarrade died January 8th, 1987 and Robert Haulotte on October 6th the same year. I alone remain of the three to

This paper is written in the memory of Mademoiselle Sarrade and Robert Haulotte. As usual, this paper has been corrected — gently and diligently — by Miss Anna Dunlop to who I am infinitely indebted. Nil novi sub sole: as Cardan said, speaking of Pacioli, “Without him, my own work would not be what it is”. I can say, speaking of Miss Dunlop, “Without her, my own work could not be what it is.”

celebrate the fifth century of the publication of Pacioli’s Summa de Arithmetica.

From the notes I have amassed, some coming directly from both of the above-mentioned friends, I should like to recall the man who was Luca Pacioli from Borgo San Sepolcro, a Franciscan monk of the second half of the 15th century.

Having familiarized myself with him for nearly 50 years via his works, he seems like a friend to me. Somehow, it seems to me that I have met him . .. with his enthusiasms and his intransigences, his assurance of being the apostle of a good cause, the care he took to detail before us his works and his labors, taking into account his corroborations in order to prove the veracity of his assertions. All of this from a simple detour taken in a mathematical demonstration, with a poignant inge-niousness.

His physical appearance is known to us by three good por-traits. The first two, owed to the brush of the great painter, Piero della Francesca born himself at Borgo San Sepolcro some thirty years before Luca, portray him at about age 30. The salient features are those of a young monk, serious and meditative, his inward glance that of one who pursues in himself his own reflections.

First, there is the painting, “Pale Urbinate,” now at the Pinacoteca di Brera in Milan, representing “La Madonna col Bambino Gesu” and the donor, Frederic di Montefeltro, kneeling before her. Ten other personages form a circle behind this group, and Luca Pacioli is the second from the right. In the second painting, “Virgin, Child and Saints,” Luca Pacioli is on the left with a book in his hands. Formerly at the Church of Sant’ Antonio in Perugia, this painting is now in that city’s art gallery.

The third portrait is still more striking. The artists of this remarkable work remains unknown — despite the flood of ink speculation it has caused and a signature difficult to interpret. Pacioli is around 50 years old and presents himself with the authority of a mathematical demonstration. Square face, firm chin, straight look, with a wave of the hand, he is the evocative expression of confidence. In fact, all we know from Luca’s own pen, on his life and work, introduce us to a man who cannot conceive of being in doubt.
He directed his life between two roads on which, in his mind, he travelled at the same speed. He is a monk, with the certitude conferred by faith. He subsequently said that he was a professor of sacred theology. He is also a mathematician, and mathematics were for him the exact science par excellence.

When, in the course of his reflections, he came to unite theology and science, his amazement was unlimited. So much so that, speaking about sole proportion in three terms, he says it is divine, comparing it to the Holy Trinity with the one and only God in three persons. Further, being in ecstasies over the mathematical virtues of this same proportion — superior for him to all others — he compares it to Christ’s law, coming to perfect and not to abolish the ancient law.

That serious-minded people may speak of naivety is of no importance to him. You have only to see the unyielding face of Pacioli to understand that it is useless to waste time in discus-sion.

It is likely that his uncompromising personality was not irrelevant to some adverse reaction from the monks of Borgo. What happened circa 1509 in the Franciscan monastery when a papal bull sent Pacioli there with the responsibility for the res-toration of good order?

As you might expect, he was unwelcome. As a last straw to the friars’ fury, Pacioli, old and perhaps in poor health, was permitted to be served his meals in his room and was exempted from singing in the choir. It was war: the keys were refused to Luca, who was naturally upset. The Director-General of the Or-der tried to intervene without success. The intervention of the Borgo Captain of the Guards was necessary, not to reconcile both parties, but to come to an agreement.

One is always at a disadvantage when one treads — even unintentionally — on the toes of someone else. And the monks’ feet, bare in sandals, must have been that much more sensitive. Was this resentment, forsaking Christian charity, the starting point of calumnies touching Pacioli’s intellectual honesty? One has the right to pose the question.

However that may be, the life of Luca Pacioli was pursued with the rigor of a straight line. Born at Borgo around 1447 as he was, we can only make suppositions on his early education.
One day a solution must be found to quash the legend propagated by the bitter pen of Vasary, writing that our author owed his mathematical knowledge to Piero della Francesca. This theory does not consider that at the time Pacioli was old enough to learn, the painter, in complete maturity of his own powers, was kept far from his native town because of the commissions he received. It would be more logical to believe that Uncle Benedetto, called “Biardo,” a soldier by profession and consequently of a scientific bent, was capable of introducing Luca to the rudiments of calculation.

We know, however, that as an adolescent Luca was an ap-prentice in the family of Folco di Belfolci — who was well versed in business. Business knowledge leads to accounting knowledge. It is worth noting that for a long time mathematical books had devoted a large section to business problems. The books of Pacioli do not violate this tradition. They were destined — as agreeably said by Pellos the Nicean — for “merchants and honest people.” Luca, however, did not remain long at this stage, and around the age of 17, he went to Venice to perfect his mathematical training.

In the meantime, he certainly learned Latin, since all scien-tific books of this period — from Euclid’s Elements onwards — were written only in that language. Having become aware of this difficulty, Pacioli was later to write in the Italian vernacular, so as to be understood by the majority.

It was again by a businessman (and rich merchant), Rompiasi, that Pacioli was boarded and received like a son. In return, he served as tutor for the sons of the house. On account of this merchant, Pacioli also travelled on ships carrying goods, as he has told us. It was job training, apprenticeship on the site, that he remembered much later when he was to write on bookkeeping.

From this period, three constants take shape that we shall discover in Pacioli’s character. First, an unlimited intellectual curiosity. Second, his passion for work. Of that he makes no bones: “From my earliest years,” he said, “I have been so habituated to study that I have never done anything else from my cradle days.” And third, the enthusiastic desire to make profitable to others the knowledge acquired by himself through hard work.

FIRST WORK, 1470

Pacioli acquired algebra skills when he was just 23 years old. This algebra, which resolved many of his problems, was the subject of his first work (unfortunately, lost today). This book was for the use of his cherished pupils, Bartolo Francesco and Paulo Rompiasi. It seems obvious that his sojourn in Venice with a businessman laid the foundation of the 1494 treatise on Double Entry.

Those who claim that this text not only may have been inspired, but even copied from pre-existing works, have certainly not taken the pains to read our author and to appreciate, so to speak, his very particular style. Some headings are based on knowledge certainly acquired only from direct experience. For example, the inventory drawn up at the beginning of the specimen accounts matches too precisely those used by a certain type of merchant and thus does not resemble the accounts which appeared in the Rompiasi books. Because nothing equals the text itself for appreciating Pacioli’s patient explanations, let us seek his counsels:

To begin with, the merchant must make diligent inven-tory, in the following manner: he writes on a sheet of paper or in a special book all that he has in this world — his personal belongings, household goods and estate. He begins with the things that are more valuable and easier to lose, such as ready cash, jewels, silver, because his estate, such as house, lands, lagoons, valleys, fishponds and the like, cannot be mislaid as can personal belongings and household goods. The possessions must be written down one by one. The inventory must always mention first the date, the place and the merchant’s name.

Luca even gives in Chapter III a model inventory with all the necessary explanations:

In the name of God, on the 8th day of November, 1493 in Venice. The following is the inventory of myself N … of Venice, street of the Apostles. I have written by my own hand — or have had written down by so-and-so — this inventory of all my possessions, personal belongings, household goods, estate, debts and credits which I possess on the day mentioned above. In the first place, I confirm that I have in cash, between gold and silver coins, so many ducats, of which so many are gold Venetian and so many gold Hungarian; so many Papal, so many Sienese and so many Florentine florins. The remainder is composed of silver and copper coins of various kinds, i.e., troni, marcelli, carlini (of both the Pope and the King), Florentine grossi and Milanese testoni etc.

So we see, passing before our eyes, one by one, all the possessions and all the debts of our merchant, with all the detail necessary to identify them.

On the style of living of these rich merchants, a proof which seems quite natural for Luca is given further on in the book:

If you lend some jewels or gold or silver table services to some friend for 8 or 15 days, particulars of same must not be put into the ledger, but must be recorded in a book of reminders, because in a few days they are to be returned. Thus also, if things of a similar kind were lent to you, they must not be placed in the ledger, but make a note of the matter in the reminders book, because you have to return them very soon.

At this time, a Venetian merchant was not just anyone, even when — after the taking of Byzantium (Constantinople) by the Turks in 1453 — relations with the Orient were inevitably modified. I have given in a previous article the list of goods shown in the ledger of Giacomo Badoer, a Venetian merchant circa 1439. In that inventory, very similar to the one given by Luca, one can however find an item which has, fortunately, disappeared in Summa. In the middle of spices, skins and pelts, textiles and gems, and ginger, slaves appear — counted by heads like cattle. This business was so prosperous that it constituted a third of the turnover.

As for the manner in which Badoer kept his ledger, it con-forms to those described by Giovanni Antonio Tagliente in his Luminario di Arithmetica of 1525 (two years after the second edition of Summa), suppressing the memorial and the journal. The transposition was made directly — with all desired details — in both accounts of the ledger, connecting one to the other. Certainly these accounts are by double-entry, but the absence of the journal leads to readjustments which would have shaken our friend Pacioli.

Absence of biographical documents concerning Piero della Francesca leads historians to make suppositions which are al-most impossible to transform into certainty. Were Piero and Alberti well-known to each other? Did they even meet? One common point alone is certain between these two geniuses: the Court of Urbino, which made use of their talents. Apart from that, nothing is sure.

Even at the period of the Renaissance, a man such as Alberti is rare. Descended from Florentine aristocracy, his scientific knowledge was immeasurable. Handsome as a young god, he excelled in all sports, while he took the classical studies with unbridled ardor. He did so much that, at 20, his health was affected. He had to rest. He did so by writing a comedy in the antique style, with such a pen that scholars for a long time believed it to be an original from Latin antiquity.

After that, the architect of Malatesta’s Temple at Rimini consecrated himself to mathematics, and that led him to codify the rules of perspective and to the editing of his de re oedificatoria written in Latin, an epitome of knowledge on architecture, both ancient and modern.

Such a man most assuredly would not have associated himself with — and above all entertained at home — an ordinary student. It can be presumed that it was on the recommendation of Piero that Luca was allowed this honor. Surely he found great profit from it.

It is at this time that Pacioli rejoins two of his brothers in the Order of Franciscans. And a little later (circa 1475) we shall see him — as we have said — under the portrayal of St. Peter the Martyr in the “Pale of Brera” by Piero della Francesca. This is also the period when the University of Perugia appointed Pacioli to the Chair of Mathematics.
That was the occasion for Luca to write a second work, dedicated to his new students. This text is that much more precious in that it is the only manuscript we have from Pacioli before Sumtna, this text provides, therefore, a direct approach to analyzing Summa.

SECOND WORK, 1476

The book, the author says, discusses mathematics and particularly algebra, but in a way less elaborate than the manuscript of 1470. The work contains, however, 396 pages which deal with rules of three and of companies, baratti or barter, false position, meriti or interest, business transactions and currency. Without entering into details, the problems of companies are those in which several merchants participate in making a purchase, each of them taking shares in a more or less considerable part of the capital, in proportion to which the profit is to be divided.

In the problems of barter, the merchant gives wool in exchange for cloth or spices, and the calculations of interest concern money invested or borrowed for a short or long time period, at a low and a high rate of interest.

There are also numerous pages concerning geometry and algebra, and “subtle questions” and mathematical games, before ending with the “merchant tariff which is of great utility.”
Compared to the content of Summa, one can see that the manuscript of 1471 constitutes a projection of it already very advanced. You have here a proof of the coherent and compre-hensive spirit that has been identified as being one of the con-stants of Pacioli’s character. He does not detour — as many others of his time did — to astronomy and still less to astrology. He preserves in his first research efforts and always extends them with the aim of being useful to all, rendering knowledge accessible to the greatest number of readers.
One may be surprised to observe a monk, having taken a vow of poverty, preoccupied with business and commerce. That would be to misunderstand Pacioli badly. Assuredly, more than gold and silver, tor him the most enviable wealth consists in the knowledge of mathematics — the science without which nothing can exist. It is with mathematics that the Great Architect created the universe, this world being represented by five regular bodies. This science is naturally indispensable, as much to philosophy as to fine arts, to the art of war as to commerce.
It is for this reason, as Pacioli says in the beginning of his Divina Proportione, that “God having endowed him with this science, and having himself been engaged in it since the age of his tender nails [this expression is his own] he shall be its en-thusiastic apostle. I shall be the professor par excellence.” It is notable that this is the only title he assumes, whereas — with an admirable modesty — (and all due respect to his detractors) he declares all his working to be compilation. He is accordingly writing in the common vernacular in order to be read by those whom the failure to understand Latin would have barred from the knowledge.

That was not without disadvantages for his style, for which style purists have naturally reproached him. If it is true that fifteenth century Italy had a language, it is also true that dialects were numerous. Add to that the fact that he was writing, transposing, and translating from Latin texts, Pacioli was often obliged to forge his own words or to slip in terms since fallen into disuse.

Finally, and particularly, he is the master writing for his pupils, in the same matter that he spoke to them, with — alas — the same repetitions. Unceasingly, he announces his preoccupation of being brief, but incessantly his style marches from sentence to sentence, with the desire not to omit anything.

Here are some lines about merchants which will give you a taste of this very particular style:

Useful exhortations and beneficial advice on being a good merchant:

As I have said, you shall diligently take note of all the things you have in belongings and estate, one by one, even if they number ten thousand, mentioning their condition and nature, if deposited in a bank, or if placed in loans. All must be named in good order in the inventory, giving all the marks, name, surname, as detailed as possible, because things can never be too clear to a merchant on account of the quantity of cases that might occur in business, as he who daily works in business knows. The proverb is right when it says that more points are required to make a good merchant than a Doctor in Laws.

Who can enumerate the cases in which the merchant must intervene, at sea, on land, in time of peace and plenty, in time of war and famine, in time of comfort and in time of loss?
In those circumstances, he must know what path to take in the markets and at fairs, which are held in one place, or in another.

For these reasons, it is correct to say that the perfect merchant must resemble a cock, which is the most watchful creature in existence and keeps its nocturnal vigils in winter or in summer, never resting. It is said of the nightingale that it sings all through the night, but this can be verified only in summer during hot weather, and not in winter, as experience is ready to show. It is also said the head of the merchant must have a hundred eyes, yet these are not enough to give him fair warning of what he must say or do.
Annibal Caro describes with humor this style as “ash pan,” but he adds immediately afterwards that this ash contains also much gold. Witness the emphatic evidence of the great math-ematician, Cardan, insisting that without Pacioli, his own work would not be what it was. Thanks are due, therefore, to this remarkable teacher who was at the true take-off of the math-ematical revival in Italy and surrounding countries.

It is worth noting the care he took to precede his works with a detailed table of contents, which facilitated searching in his abstruse discourse, permitting the reader to arrive easily at the desired chapter. The table of distinctio 9 of the treatise alone requires a good two pages. If there are some who find that longish, it is, for Pacioli, only work done conscientiously.

In the introduction of his Divina Proportione, he explains his point of view:

.. . how praiseworthy it is by God and men that one who, having received as a gift some particular natural talent, should convey it willingly to others, because he awakens love in them and merits eulogy and honor, taking for his own the sacred motto: “What I have learned without a model I communicate willingly and cheerfully. The significance of these gentle words,” he adds, “is graven in my mind as durably as in marble.” It was natural for me to act thus with all and particularly when it concerns the faculties which I have received from God in the noble and necessary science of mathematics.

Pacioli the man is encapsulated in full in these last two sentences.

THIRD MANUSCRIPT, 1481

Leaving Perugia for Zara about 1480, he wrote in that town a third manuscript, the loss of which is particularly unfortunate. Speaking of this work in his Summa, he tells us, in fact, that the work of Zara is composed of difficult problems requiring deep comprehension.

This seems to be the case in the Libellus, the text printed in 1509 at the end of the Divina Proportione, which is the cause of the most serious accusations made against Luca Pacioli. The fact that some persist — even without proof — in declaring this text about bookkeeping not to be original is of little importance, since the author himself does not claim it as an original work, but only one of compilation. On the other hand, the text of the Libellus is, in the vernacular, exactly the same as that of the Quinque corporibus regularibus written, or rather translated, into Latin, and offered by Piero della Francesca, after 1482, to the young Duke of Urbino.

This text is a group of geometrical problems, solved mostly by algebra and calling for very difficult calculations because they are so complicated. An example will give you an idea: — the volume of a body of 72 bases is obtained by the sum of 13 square roots diminished by the sum of 5 square roots. When one sees that those roots require 9 or 10 numbers, followed by fractions which count the same quantity of numbers of the de-nominator and of the numerator, because at that time, one could not use decimals, much less calculating machines, finding the solution is baffling. One is especially amazed at the man who was capable of devising such a treatise. One thinks also of the “difficult cases requiring deep comprehension” and above all of a brain accustomed to these disconcerting calculations. To credit a painter, even a great painter, who says of himself that he is aged and in poor health with this sort of exercise is, to say the least, incredible.
Because the “Pale di Brera” was finished — and badly fin-ished — by Berrugete, Piero was probably coming to grips with some serious infirmity. He gave a text to the Duke of Urbino, who is placed prominently in the picture, which was neither dedicated nor signed. It was astonishing because it avoided color in favor of geometry. It was written in the common vernacular, but the figures were very well finished, as you would expect from the hand of a great painter.

Seven years later, the Duke of Urbino, protector of Piero, died when his so a and heir was 10 years old. It was to this child that Piero offered a text written in Latin with a dedication, so that everyone would know the author, though the first half of this dedication was an exact copy of the introduction to chapter III of Vitruvius. In the second half, Piero asserts as his own the Prospectiva Pingendi given to the young Duke. It is on that work that Vasary — and others after him — founded their opinion that Luca had appropriated the work of his great elder, taking advantage of ease of access he would have at the Urbino library, where he could have purely and simply copied it.

Was not the opposite more plausible? Perhaps, to assist the aged and abandoned painter, this young compatriot, still proud to have been included in a painting by the Master, could have translated Piero’s Zara manuscript to permit him to recommend himself to the good offices of his protectors?

If Luca was dishonest, why did he not “lose” a text which I do not suppose would figure among the library’s treasures, given its highly specialized contents? Indeed, where and from whom could Piero, at this time, acquire the necessary knowl-edge for the composition of a text bristling with difficulties? How can one reconcile the work required to effect interminable calculations with the fact that the painter said himself he was weakened with age? How, above all, could the master painter of perspective, Piero, only succeed in illustrating his manuscript with false figures, constructed crookedly? On the other hand, the drawing of both regular and irregular bodies was for Luca Pacioli a problem more difficult than calculations. This is evident in Summa.

Later, in 1496, Luca’s meeting with Leonardo de Vinci re-moved all difficulties in the representation of solid bodies in Divina Proportione. Beforehand, since 1489, Luca had himself constructed his solid bodies, and Leonardo probably drew from those models.

Nevertheless, the accusation brought against Pacioli, dis-seminated by Vasary in the sixteenth century, and by others too, particularly by Mancini in the twentieth century, do not agree with the most elementary logic. These humorless detractors think they know better. To be fair, Luca has also happily found reliable defenders.
The limit of absurdity in the calumnies came from an anonymous and undated Abaco, assigned by Mancini to Piero, because there are in it problems from the Libellus and also the whole of the problems which end Summa. This Abaco, if it is not signed is, however, presented like this (I translate word for word):

Having been persuaded, by a person to whom I can refuse nothing, to write something about the mathematics necessary for merchants, I shall do it, not through presumption, but to obey, trying with God’s help to satisfy Him, that is to say write something concerning barter, interest and companies, beginning with the rule of three and the rule of position and, if it please God, to satisfy Him, something on algebra.

Beyond the fact that there is no mention of geometry, can you imagine merchants asking a painter to instruct them in the necessary mathematics for their trade! With great seriousness, but without an ounce of good sense, Margaret Daly Davis has, again in our time, defended this undefensible supposition.
The contemporaries of Pacioli were fortunately more per-spicacious. Luca’s university career was continuing at Perugia, Zara and Rome, and he went to Venice in 1494 to work on the proofs being printed for Summa.

FOURTH WORK, 1494

This Summa, which well merits its name, contains Distinctio 9 Treatise, a chapter on bookkeeping, but the author warns that before studying this section it is necessary to have learned, thanks to preceding chapters, to be a fast calculator. “In order to be able to possess this qualification,” he says, ” I have given in the other sections of this book the rules and canons necessary for each operation, so that each diligent reader can learn them by himself. For anyone who has not assimilated them, it will be useless to study what follows.” That is clear! But if the reader must make some effort, the author too will have taken great trouble to relate in detail the entries in the Memorial, the Journal and the Ledger, with multiple examples.

For those who are interested in the history of accounting, the reading of Luca Pacioli’s treatise on double-entry bookkeeping is indeed the first thing to undertake. As this text is today available in most languages, no difficulty will be encountered.

I will, for my part, merely recall the sentence which comes nearly at the end of the chapter on bookkeeping:
With attentive and devoted study, make the effort to become a good bookkeeper. I have amply shown you in this excellent work how to become one. I have given you all the rules, and the places where you can easily find them are indicated in the table of contents which is given at the beginning of this treatise. And think to pray to God for me, so that I can, for His praise and glory, continue to work to the best of my ability.

These prayers were probably heard, since, two years after the appearance of Summa, Pacioli was called by Ludovico Sforza to the court of Milan, as a commentator on Euclid. It is there that he met Leonardo da Vinci. These two men, outwardly so opposite, were in fact admirably complementary. From their collaboration, not to say their friendship, emerged Divina Proportione, Luca’s fifth text, prepared in manuscript for the Duke of Milan, with illustrations representing the solid diagrams drawn by Leonardo. The arrival of French armies in Italy drove both our friends to Mantua. Evidence is missing on their subsequent relationship.

LATE WORKS, 1509-1512

As for Luca, he was teaching at Pisa, Perugia, Bologna and Florence (where, it seems, he mostly resided), and at Rome before becoming occupied in 1509 with the printing of his last works. These were a translation of Euclid, which replaced that of Campanus, but enriched with remarkable commentaries; and the printed edition of the Divina Proportione, dedicated this time to Soderini. This edition contains not only the text of the 1498 manuscript, but also a treatise on architecture very close to Vitruvius, of whom some passages are quoted in full, a very good “alphabet” and the famous Libellus, of which we have spoken. A lost text, de Viribus quantitatis, written by Pacioli around 1512 remained in manuscript.

We know little about the last years of this man who wrote that he was often tired, exhausted by work and staying up late. In 1514, the Pope offered him a chair of mathematics at the Sapienza in Rome. It seems that Pacioli was more often at the monastery in Borgo.

He died in 1517. This date has been found recently by Japanese accounting historians. After this, who may venture to say that the accounting influence of Luca Pacioli does not extend, even to the present, to the far corners of the earth?

1894-1994

The four hundred year anniversary of the printing of Summa was not a very great success. Very few accounting historians were active at that time. Carl Peter Kheil, the most important of them, translated into Czech the chapter of Summa relating to bookkeeping. This work was printed in 1894, the anniversary year of the publication of Summa.
It may be presumed that, pressed by time to publish his translation in the year of the 400th anniversary, Carl Peter Kheil hurried the work a little. On reading the printed text, he decided not to distribute it, this translation being, in his opinion, unsatisfactory.

We realized, my colleagues Robert Haulotte and myself, when we undertook the translation of the work of Luca Pacioli into French, how it is sometimes difficult to understand the numerous abbreviations of which the author made use, or to define the meaning of some words chosen to represent things that exist no more.

However, Kheil’s manuscript and some copies of his trans-lation have been conserved. That has allowed author Hugo Raulich, former teacher at Kheil’s private school, to transcribe in 1933 in Czech an expurgated translation of Luca Pacioli’s accounting work, based on the one undertaken by Kheil. That translation was published in 1940 in the technico-commercial Czech lexicon pxiblished under the direction of Joseph Fuska.

Shall we see other translations in other languages on the occasion of the five hundred year anniversary? That is not im-possible. In any case, to see the present activity of some ac-counting historians’ groups to fittingly honor this half millennial, one can be sure that their combined efforts will be successful.