The influence of Amatino Manucci and Luca Pacioli

The influence of Amatino Manucci and Luca Pacioli
Fenny Smith Friday 25 April 2008 Gresham College We’re going to start off the day by going back to the beginnings of double entry bookkeeping In mediaeval and Renaissance Italy. We going to look at two figures: Luca Pacioli published an encyclopaedic work – everything you ever needed to know about mathematics, entitled Summa de Arithmetica, Geometria, Proportione et Proportionalità Venice, 1494 And Amatino Manucci Partner in a Florentine merchant firm and kept the accounts for a small branch in a small town in the south of France – In order to get you into a mediaeval mindset, I’m going to start with a cameo that Pacioli gives of “a month in the life of” a Venetian merchant in the 1490’s

I’m going to have to read this part out to you (in English!).
So you have something to look at I have some pictures to confirm this mediaeval mood. Hope not too much like a modern TV documentary!

In Venice I buy 2400 loaves of sugar, net weight 7200 lbs, all for 1440 ducats. I pay 2% brokerage fees (sensaria) and a total of 2 ducats for carriage and public weighing. And then I spend for packaging [cases, cord, canvas, etc.] in all 8 ducats. And for the tax on sales made through brokers (messetaria), 1% of the first amount, and for customs, municipal duties on provisions, and export tax, in total 3 ducats percent. And for a seal and certificate for the crossing, in total 1 ducat. For a ship to Rimini 13 ducats. And for various tips for the armed boats, several times, 2 ducats. And food for myself and an assistant for a month, in all 6 ducats. And for several ferry trips to the mainland, here and there, for barbers, laundry, and shoes, a total for myself and attendants, 1 ducat. And when I arrive at Rimini I pay port duties to the captain of the port, £3 in Rimini money, and for porters to unload and transport to the warehouse, £5. And for the entry tax on provisions, 4 soldi (shillings) per item of baggage, of which there are 32, for that is the custom. And for the public warehouse fee, 4 soldi per item. And when I arrive at the market I find that £140 there are worth £100 in Venetian money. And £4 in their money make a ducat. I want to know, how much should I charge per hundredweight there in Rimini, in their money, in order to make a profit of 10%?

It may seem an extreme illustration of the kind of calculations a merchant may need to perform, but even when our merchant has worked out his 10%, in real life he would not have finished. Currency in short supply many customers may have wished to pay at least partly in goods, that is by bartering for example wool, cloth, linen or various kinds of spices (Pacioli’s examples often include hundredweights of cloves.) In this case, the merchant would need to inspect the goods for quality, and agree with his purchaser how much he would pay per unit of cloth etc, and then work out how much sugar that would equate to. Even when paying cash, his purchaser may only have had coin in other currencies to hand, and rates of exchange might need to be agreed - and the appropriate quantities calculated. When this was settled, the merchant might need to remember that he and his partners may have borrowed money to invest in their venture, and this would need to be paid back, perhaps with interest. Then what was left would need to be divided among himself and his partners, in proportion to the amounts of money and time (at a suitable rate) they had each invested in the partnership. And finally, the individual himself may have borrowed to raise his own share of the investment. When that had been paid back, he would be left with a wagon or two of assorted bales of cloth and sacks of wool and spices, and a couple of leather bags of money in various currencies would need to draw up some accounts to see whether or not he was really making a living from it all, and to show any interested parties that he was not committing fraud.

Pacioli’s Summa Intended to teach commercial skills
Part of a 300 year tradition Following Leonardo Fibonacci (1202) Treatises, schools, curricula No formal bookkeeping training Existing ledgers Pacioli’s Summa was intended to give the 15th century merchant the skills to make all of these calculations, and it was the culmination of a 300 year tradition of treatises and handbooks dealing with commercial arithmetic with the Arabic numerals, inspired by Leonardo Fibonacci’s “Liber Abaci” (1202), which introduced these numerals to the Italian merchant classes[1] along with their efficient use in commercial computation. The development of schools of arithmetic (and algebra) from the late 13th century and their flowering in the 15th, is well documented, along with their curriculum and evidence of almost universal attendance among young males[2]. But the two examples of a syllabus that we have do not mention methods of bookkeeping, and we have to imagine that such training, if it existed, was on the job, and the knowledge that we have of the earliest methods of bookkeeping comes from study of real, practical example, in such ledgers as have survived. [1] Van Egmond, “The commercial Revolution and the beginnings of Western mathematics in Renaissance Florence, ”, Ph.D. thesis, Indiana University, 1976. [2] ibid. and Michael Baxandall, Painting and experience in fifteenth century Italy, OUP, 1972

Mediaeval account books
Ephemeral Often reused Scraped and written over Incorporated into later books If preserved, not under good conditions Opportunities for such study are limited by the ephemeral nature of account books in the Middle Ages. Once the books were balanced and closed, and the business probably also dissolved, they were no longer thought worthy of preservation. Parchment was expensive, and the most efficient method of disposal was to scrape off the ink and use the parchment again. At least one valuable example of accountants’ ledgers has ended up, incomplete, as end papers bound into a subsequent book. Even if they were preserved, this would not be under ideal conditions, and dampness may have caused the pages to stick together so that when separated, the ink from one side could stick to the facing page.

Early examples Genoa 1340, commune stewards
Wealth of earlier manuscripts Particularly Florence and Tuscany Arrigo Castellani transcribed all extant pre-1300 prose texts from Florence 2 volumes 1952 Including many account book fragments Earliest fully attested examples of double entry are the accounts of the stewards or massari of the Genoese commune for 1340 technique would seem to have its origins in Tuscany, particularly in Florence. This perception may possibly be because there is much more material available from this area bulk of what is available is from Florence, thanks to transcriptions made by Arrigo Castellani.[1] In sum, most of the earliest ledgers that we have come from Florence, and Florentine companies. The example given above from Venice is typical of the Venetian custom of partners coming together for a single venture, after which the company would be dissolved, and other ventures initiated with perhaps different partners[2]. In Florence, partnerships would typically last for a few years, after which the books would be balanced and closed, and new partnerships formed as the partners changed. This had the advantage, for us, of more stable accounting, and a greater chance of survival of the ledgers used. [1] Castellani methodically and painstakingly transcribed almost all extant Florentine prose texts up to 1300, including a vast number of account book fragments in his Nuovi Testi Fiorentini del Dugento, 2 vols, Florence, 1952. [2] Geoffrey A. Lee, “The development of Italian bookkeeping ”, Abacus, 9, no. 2, December 1973, pp

Studies Federico Melis Raymond de Roover Basil S. Yamey
Geoffrey A. Lee Indebted to these guys, especially Geoffrey Lee

Lee’s survey of 13th C. ledgers and his 6 DE components
The business as an independent accounting entity Algebraic opposition Single monetary unit Proprietor’s equity Profit or loss as net equity change Measure of profit and loss over an accounting period Offers 6 components of DEB the individual proprietor or business partnership as an accounting entity whose books record its financial relationships with other economic agents algebraic opposition: firstly between increases and decreases in a physical holding of cash or goods; secondly between increases and decreases in the level of indebtedness by or to another economic agent or identity; thirdly between indebtedness by and to other entities in general; and fourthly between assets and liabilities of the entity accounted for a single monetary unit, to which amounts in other currencies are converted, thus making the entries additive overall proprietor’s equity, as the algebraic sum of assets and liabilities profit or loss, as the net increment or decrement to equity resulting from one or more acts of exchange between the entity and its economic environment (excluding the proprietors) the accounting period, over which profit or loss may be measured.

Early Florentine ledgers
Unknown Florentine Banking firm, 1211 Gualtieri dal Borgo, guardian of the sons of Rinieri Ugelletti, Two ledgers of Bene Bencivenni, and Estate of Baldovino, son of Jacopo Riccomanni, Gentile de’ Sassetti and Sons, Found proto elements of DEB in these

1211 fragments Transcribed by Pietro Santini 1887
two leaves of parchment reused as front and rear flyleaves of a 14th century manuscript of a legal work unknown firm of bankers that operated in Florence, Bologna, and Pisa in that year, and most of the entries pertain to loans and repayments. Each page is ruled down the middle, and each of the two columns is divided horizontally into 6-8 blocks.

1211 fragments Each block represents an account, with the details of the loan and repayments entered successively, and when the repayments were deemed sufficient to cover the loan, the account was struck through with oblique lines. In all, there are 42 blocks. This format has become known as the ‘paragraph format’ and is seen in most early Florentine ledgers. It was much more economical on parchment than the modern two sided arrangement, which began to emerge in the 14th century as paper became much cheaper. Lee discerns in these fragments the first three of his components: 1. the firm is clearly distinguished from outsiders; 2. there is algebraic offsetting of various kinds: increments and decrements to the same account balance as well as between loan and deposit account balances, and also complex transfers between different customers’ accounts in settlement of liabilities to third parties; 3. all entries are in Pisan currency with many intricate conversions in a variety of Italian and international coin.

1211 fragments The firm is clearly distinguished from outsiders
There is algebraic offsetting of various kinds All entries are in Pisan currency with many intricate conversions in a variety of Italian and international coin 1. the firm is clearly distinguished from outsiders; 2. there is algebraic offsetting of various kinds: increments and decrements to the same account balance as well as between loan and deposit account balances, and also complex transfers between different customers’ accounts in settlement of liabilities to third parties; 3. all entries are in Pisan currency with many intricate conversions in a variety of Italian and international coin.

The other early Florentine ledgers
Gualtieri dal Borgo, guardian of the sons of Rinieri Ugelletti, Two ledgers of Bene Bencivenni, and Estate of Baldovino, son of Jacopo Riccomanni, Gentile de’ Sassetti and Sons, Gualtieri dal Borgo, guardian of the sons of Rinieri Ugelletti, Contain the earliest surviving account for a creditor or depositor Interest is also included in the body of the account proper cross referencing to other ledger folios (not extant) Some attempt at balancing Single unit of account, the new Florentine silver currency The domestic ledger ( ) of a wealthy Florentine, Bene Bencivenni, who died between 1296 and 1298. Mostly debtors’ accounts, but includes one large investment in a firm. No proper cross references, and no single monetary unit Do show the balancing every January of those debtors’ accounts that are still open. Administration ( ) of the estate of Baldovino (died 1272), son of Jacopo Riccomanni 9 leaves in all Single monetary unit, the silver florin Systematic annual balancing of the accounts in order to compute interest compounded annually. Cross referencing is less sophisticated than elsewhere. Accounts of Gentile de’ Sassetti and sons ( ). Mostly domestic Include a large investment in the family business. 27 leaves of debtors’ accounts from the front of the ledger, and five of creditors’ accounts from the back of it. No single currency unit and no systematic balancing First proven example of this debtor vs. creditor arrangement Account for rent receivable Only fully developed account for a partnership share which survives from this period. Another ledger ( ) of Bene Bencivenni Continuation of the first Earliest unmistakable instances of the writing off of bad debts Sentiment “I do not think that I shall ever get any money” appears at the end of several of the debt accounts

Amatino Manucci Partner in Florentine firm of Giovanni Farolfi
Based at Nîmes Branches in a number of towns in the area Including Salon Manucci kept the accounts We have those from

Salon a market town population in 1300 of two to three thousand about 45 miles from Nîmes, and 25 miles from each of Arles, Aix (the provincial capital), and Marseilles, the major port interesting times for the area after French religious wars of the 13th century Languedoc (including Nîmes) had fallen, in 1271 to the French crown formed much of the Languedoc province. Provence became, in 1246, a fief of the French crown The popes were to take up residence there in 1309, in Avignon, where they were to stay until 1376.

Salon As I say, based in Salon Market town
Centre for olive oil industry Fontaine Moussue Chateau de l’Empéri Where Rostang de Capre, Archbishop of Arles from often resided Farolfi company’s most important customer

Farolfi company Partners Giovanni Farolfi Compagno Franchi (Pagno)
Amatino (Matino) kept the books at Salon Bacchera Baldovino chief buyer Farolfi company, based in Nîmes Giovanni Farolfi himself, the senior partner, sometimes known as Giovanni Filippi, or Giovanni son of Ubaldino, with apparently second in command, Compagno (or Pagno), Franchi. Amatino (or Matino) kept the books in the Salon branch under its chief buyer, Bacchera Baldovini. A number of other partners are mentioned: Borrino (or Burrino) and Vitale Marsoppi, Ughetto Buonaguida, Francesco Cavalcante, and also possibly Tommasino Farolfi and Giometto Verdiglione. Major customers apart from de Capre were Guillaume de Lambesc (a village a few miles to the east), Gilles Vacquier, a draper in Salon, Ghilberto Doni, Gaetano (Tano) da Figliano (near Florence), Ischiatta della Fiorentina, based in Isle-sur-la-Sorgue, further north near Avignon, and one Giovanni Giuserani or Jean Jusserand, who may have been either Italian or Provençal. The Archbishop, Tano da Figliano, and Giuserani/Jusserand, were also suppliers, as were Tommasino Farolfi of Mondragon, north of Avignon, and Astruc Durand Loncontaire, who with his business partners formed part of a thriving Jewish community which had found sanctuary in the area under the Holy Roman Emperors.

Farolfi company Other partners
Borrino (or Burrino) and Vitale Marsoppi Ughetto Buonaguida Francesco Cavalcante also possibly Tommasino Farolfi Giometto Verdiglione A number of other partners are mentioned: Borrino (or Burrino) and Vitale Marsoppi Ughetto Buonaguida Francesco Cavalcante also possibly Tommasino Farolfi and Giometto Verdiglione.

Farolfi company Major customers Rostang de Capre Archbishop of Arles
Bertrand des Baux of Avellino to the north of Arles (not directly a customer of the company but often mentioned with the Archbishop in the accounts: good PR for the company) Major customers apart from de Capre were Guillaume de Lambesc (a village a few miles to the east), Gilles Vacquier, a draper in Salon, Ghilberto Doni, Gaetano (Tano) da Figliano (near Florence), Ischiatta della Fiorentina, based in Isle-sur-la-Sorgue, further north near Avignon, and one Giovanni Giuserani or Jean Jusserand, who may have been either Italian or Provençal. The Archbishop, Tano da Figliano, and Giuserani/Jusserand, were also suppliers, as were Tommasino Farolfi of Mondragon, north of Avignon, and Astruc Durand Loncontaire, who with his business partners formed part of a thriving Jewish community which had found sanctuary in the area under the Holy Roman Emperors.

Farolfi company Other major customers Guillaume de Lambesc (a village
a few miles to the east) Gilles Vacquier, a draper in Salon Ghilberto Doni Major customers apart from de Capre were Guillaume de Lambesc (a village a few miles to the east), Gilles Vacquier, a draper in Salon, Ghilberto Doni, Gaetano (Tano) da Figliano (near Florence), Ischiatta della Fiorentina, based in Isle-sur-la-Sorgue, further north near Avignon, and one Giovanni Giuserani or Jean Jusserand, who may have been either Italian or Provençal. The Archbishop, Tano da Figliano, and Giuserani/Jusserand, were also suppliers, as were Tommasino Farolfi of Mondragon, north of Avignon, and Astruc Durand Loncontaire, who with his business partners formed part of a thriving Jewish community which had found sanctuary in the area under the Holy Roman Emperors.

Farolfi company Other major customers Gaetano (Tano) da Figliano
Ischiatta della Fiorentina Giovanni Giuserani or Jean Jusserand Gaetano (Tano) da Figliano (near Florence) Ischiatta della Fiorentina, based in Isle-sur-la-Sorgue, further north near Avignon, and one Giovanni Giuserani or Jean Jusserand, who may have been either Italian or Provençal.

Farolfi company Suppliers The Archbishop Tano da Figliano
Giuserani/Jusserand Tommasino Farolfi of Mondragon Astruc Durand Loncontaire Suppliers The Archbishop, Tano da Figliano Giuserani/Jusserand Tommasino Farolfi of Mondragon, north of Avignon Astruc Durand Loncontaire, who with his business partners formed part of a thriving Jewish community which had found sanctuary in the area under the Holy Roman Emperors. Like to think of a cosmopolitan group of merchants and traders

Farolfi company Commodities Wheat, barley, oats, wine, wool
Cloth, yarn, dyeing materials also: Exchange Lending of money Official ban on usury? wheat, barley, oats, wine, wool, as well as cloth, yarn, and dyeing materials. They also engaged in the exchange of and lending of money Archbishop happily borrowed from the Farolfi company at 15% per annum.

Here is a sample page. Struck most by neat writing, and oblique lines – accounts struck through when closed. Wide margin, columns of Roman numerals down RHS.

Diederne, dì 27 di febbraio anno novantanove; posto ove doveano avere, al Quaderno de le spese, ne l'8 carte - £26 17s 2d

Farolfi document Archivio di Stato in Florence
56 leaves, sequentially numbered Missing: 47 from beginning half a dozen in the run unknown number from the end Occasional pages stuck together Castellani had to use a mirror

Farolfi document The first half of the ledger contained accounts for
Debtors Expenditure Debit side of the head office account (the balance account) The first half of the surviving ledger contained the accounts for debtors and expenditure, and the debit side of the head office account (the balance account), while the creditors’ and profit accounts and the credit side of the balance account were in the second half. The two sides of the balance account were later compared, and ideally would have been equal.

Farolfi document The second half of the ledger contained accounts for
Creditors Profit Credit side of the balance account credit and debit would be compared for balancing The first half of the surviving ledger contained the accounts for debtors and expenditure, and the debit side of the head office account (the balance account), while the creditors’ and profit accounts and the credit side of the balance account were in the second half. The two sides of the balance account were later compared, and ideally would have been equal. The entries in this ledger, which may conveniently be called the General Ledger, show evidence of a multiple system of ledgers, all carefully cross-referenced.

The other ledgers White Ledger Similarly divided into two halves
General Ledger acting as a continuation No closing balance account General Ledger has no opening one. “White ledger” (quaderno bianco), which Lee shows was similarly divided into two halves, with the General Ledger acting as a continuation of the White one, which had no closing balance account, just as the General ledger has no opening one.

The other ledgers Red Book Main merchandise accounts
Similarly divided into two halves Purchases in the front, sales at the back Closing balances were transferred to the debit of the balance account in the General Ledger There was also a “Red book” (libro rosso), which is shown to have contained the main merchandise accounts (agricultural produce plus wool and yarn), debited with purchases in the front half and credited with sales at the back. Closing inventory balances were transferred to the debit of the balance account in the General Ledger. In the last pages of the latter would have been the Profits Account (avanzi). They do not survive but there are references to them in the General Ledger and Lee surmises that excesses of credits over debits would have been regularly transferred from the Red Book to the Profits account, just as the Current Expenses account would contain the debit excesses. The latter account is extant, and contains a debit entry, cross referenced to the Red Book, of £951/4/5d “which we lost on wheat that we purchased”.

The other ledgers Cloth Ledger Expenses Ledger Cash Book
Cloth analogy to the Red Book Expenses Ledger Accounts relative to fixtures Current expenses Cash Book There is one reference to a Cloth Ledger (quaderno dei panni), a cloth analogy to the Red Book, but its use seems inconsistent. The reference is in an account for Druggets (sargie - coarse woollen cloth), to which the debit and credit totals from this ledger have been transferred, along with further sales and a profit figure (credited to Profits), which Lee finds arithmetically wrong. The balance account in the General Ledger shows no debits for ending inventories of cloth. There are several other debits to customers for cloth sales with no cross references, although a number of notes were made that bills had been drawn up by “Maître Bertrand Arnaud (maestro Bertrano Arnaldi), notary of Salon”. Such bills appear quite often in the General Ledger, and usually without cross reference to another account book. The last book to which references are explicitly made is the Expenses Ledger (quaderno delle spese), which appears to have contained accounts relative to fixtures (masserize, i.e. furniture and household goods) and current expenses (spese corse), as mentioned above. There are corresponding entries in the General Ledger, to which were also transferred the closing totals of the Expenses ledger under Fixtures Account and Current Expenses Account, and further entries made there, as with the Cloth Ledger There must also have been a Cash Book, although no reference is made to it in the text, where numerous entries relate to cash paid and received. Lee surmises that it would have been in the standard Italian form for the period, with receipts at the front, payments at the back and periodic balancing of the totals. There would be no need for references in the General Ledger because the entries would be by date, but there would have been references in the Cash Book to the General Ledger.

Subsidiary ledgers Plush Book Memorandum Ledger
partner Borrino Marsoppi business expenses total debited to Expenses and credited to Borrino’s account Memorandum Ledger Similarly for the other partners There were at least two subsidiary books, one which Lee translates as the “Plush Book” (libro piloso), and a Memorandum Ledger (quaderno memoriale). The former was kept by the partner Borrino Marsoppi, presumably to record his business expenses, which were periodically summarised, the total being debited to Expenses and credited to Borrino’s account. Since the other ledger relates to out of pocket expenses of partners other than Borrino, it most probably served a similar purpose for them

Rent Four accounts for prepaid rent on various premises
£16 was paid to Pierre Guillaume on 17 May 1299 Four years’ rent in advance for a warehouse Sum transferred from the White Ledger to the debit of the rent account There are four accounts for prepaid rent on various premises, which are treated in an impressively sophisticated way. For example, £16 was paid to Pierre Guillaume on 17 May 1299, for four years’ rent in advance for a warehouse, the sum being transferred from the White Ledger to the debit of the rent account. One year later, on 17 May, one year’s rent, £4, was credited to the rent account and debited to Current Expenses. The other rentals were treated in the same way: for advance rent of £12 for a shop, £3 written off after a year; for £1/10/- for one year for another warehouse, all written off; and for £12 paid in advance for three years on 6 October 1297 for a second shop, the remaining balance of £4 was transferred in the same way.

Rent One year later on 17 May One year’s rent: £4
Credited to the rent account and debited to Current Expenses There are four accounts for prepaid rent on various premises, which are treated in an impressively sophisticated way. For example, £16 was paid to Pierre Guillaume on 17 May 1299, for four years’ rent in advance for a warehouse, the sum being transferred from the White Ledger to the debit of the rent account. One year later, on 17 May, one year’s rent, £4, was credited to the rent account and debited to Current Expenses. The other rentals were treated in the same way: for advance rent of £12 for a shop, £3 written off after a year; for £1/10/- for one year for another warehouse, all written off; and for £12 paid in advance for three years on 6 October 1297 for a second shop, the remaining balance of £4 was transferred in the same way.

Other rent For advance rent of £12 for a
shop, £3 written off after a year For £1/10/- for one year for another warehouse, all written off For £12 paid in advance for three years on 6 October 1297 for a second shop Remaining balance of £4 was transferred in the same way There are four accounts for prepaid rent on various premises, which are treated in an impressively sophisticated way. For example, £16 was paid to Pierre Guillaume on 17 May 1299, for four years’ rent in advance for a warehouse, the sum being transferred from the White Ledger to the debit of the rent account. One year later, on 17 May, one year’s rent, £4, was credited to the rent account and debited to Current Expenses. The other rentals were treated in the same way: for advance rent of £12 for a shop, £3 written off after a year; for £1/10/- for one year for another warehouse, all written off; and for £12 paid in advance for three years on 6 October 1297 for a second shop, the remaining balance of £4 was transferred in the same way.

Sophistication Extensive cross referencing Accounts are “Personal”
“Real” Goods and for Rent “Nominal” Fixtures Current Expenses Expenses of Eating and Drinking These records taken together show a considerable sophistication, even though they refer only to one branch of the company. Looking at Manucci’s scheme as a whole, with reference to the six concepts (page 3 above), Lee is satisfied that it forms a double entry system. The ledger allows for “real” and “nominal” as well as “personal” accounts. Apart from the Druggets account, the other goods accounts that appear in the General Ledger are for purchase and resale of individual packhorses. The nominal accounts are for Fixtures (with purchases debited and sale proceeds credited, both brought forward to the General from the Expenses ledger) and Current Expenses, as we have seen, and also for Expenses of Eating and Drinking.

Balancing and equity Evidence that Manucci balanced accounts
We can’t check: Only debit side extant References to credit side show that it followed straight after extant pages Lee did a lot of detective work on existing entries Clear that Manucci’s system had the means for checking There is an obstacle to the checking of Manucci’s balancing of the accounts, in that only the debit side is extant: the references to the credit side show that it occupied the pages immediately following the last of the extant leaves. Nevertheless, Lee navigates all existing references with great skill and perseverance, and with minute checking and correction of a number of errors, both arithmetical and of principle, and subtle detective work on a number of credit and debit entries which are not cross referenced to corresponding debits and credits, he manages to get the accounts of 1300 to balance. There are gaps and errors which cannot be investigated, but it is clear not only that Manucci himself had officially balanced the accounts, but also that his system had allowed him the means to do so. Lot more detail in the transcript, but now we turn to Luca Pacioli

Luca Pacioli Lots of information about this chap

Luca Pacioli Born around1445 In Borgo San Sepolcro
Piero della Francesca younger compatriot of the artist/mathematician Piero della Francesca, he was born around 1445 in the little town of Borgo San Sepolcro near Arezzo in Tuscany.

This is how his compatriots remembered him in 1878

Biography As he mentions in a short biographical paragraph on f. 67v. of the Summa began his career as tutor to the three sons of a rich Venetian merchant, Antonio Rompiasi. While there, he attended the mathematics classes of Domenico Bragadino at the Rialto and showed, in 1470, an early sign of a pedagogical vocation by dedicating to the Rompiasi brothers his first book on arithmetic and algebra, which has unfortunately not survived. In the same year he travelled to Rome, where he stayed as a guest of Leon Battista Alberti. Some time between 1470 and 1477 Pacioli became a member of the mendicant order of Franciscan Friars, and, as is consistent with Franciscan principles, began a long career as an itinerant teacher of mathematics. Taught in most towns and cities in Italy, and even in Zadar in Croatia Associated with court of Montefeltro at Urbino

Biography Urbino Piero della Francesca
had a close connection, along with Piero della Francesca, with the court at Urbino, where he is thought to have tutored the young Guidobaldo da Montefeltro, son of the condottiero Duke Federigo Piero’s Nativity Prolific writer. Long list of books in the transcript Most famous for Urbino Piero della Francesca

Biography In 1494 he was in Venice, supervising the publication of the Summa, and from he was in Milan at the court of Ludovico Sforza, where he worked closely with Leonardo da Vinci on the De Divina Proportione Pacioli was a prolific writer, and his works include: 1470 Treatise on arithmetic and algebra, Venice, not extant, referred to in the Summa 1478 Treatise on arithmetic and algebra, Perugia, now in Vatican Library. 1481 Treatise for pupils in Zadar, not extant, referred to in the Summa 1494 Summa de arithmetica, geometria, proportione, at proportionalita, Venice. Second edition 1523, Tuscolano. 1497 “De Divina Proportione”, MSS now in Geneva and Milan n.d. Italian translation of Euclid, not extant, referred to in the introduction to “De viribus quantitatis”. n.d. “La Schifanoia”, treatise on games including chess, referred to in the introduction to “De viribus quantitatis”. Long thought to be missing, it turned up in 2006, and is in the possession of the Coronini Cronberg Foundation. Between 1496 and 1508, “De viribus quantitatis”, University of Bologna Library 1509 De Divina Proportione, Venice. 1509 Edition of Euclid, Venice.

Historical Perspective
300 year tradition since 1202 Leonardo Fibonacci’s “Liber abaci” adopted by Italian merchants maestri d’abaco, libri d’abaco Late 13th C 15 from the 14th C over 100 from the 15th 300 years of what has been called the abacus tradition Nothing to do with the ancient practice of calculating by means of a bead frame or counting board, although method remained in continuous use, especially in Northern Europe, until the 18th century. The term stems from the title “Liber abaci” chosen by Leonardo Fibonacci (Leonardo of Pisa) for his encyclopaedic introduction to the use of the Hindu Arabic numerals for basic calculation and commercial computation, which he compiled in 1202. This was quickly adopted by Italian merchants, who abandoned their counting boards and sponsored a thorough grounding of children in the new techniques by teachers (maestri d’abaco), who wrote manuscript textbooks which together with merchants’ manuals form a vernacular body known as the books of the abacus, or libri d’abaco. The earliest extant Italian abacus dates from the late 13th century. At least 15 survive from the 14th century and over 100 from the 15th. A few appear in print around that time, with over 200 printed by the end of the 16th century.

Abacus books Treviso 1478 Filippo Calandri 1491 Pacioli 1478
Some examples. All slightly different, but all covered much the same material, with many overlaps of arithmetical examples used – same numerical examples, solutions usually different. E.g. arithmetic, algebraic, more/less explanation, corrections, etc

Northern Europe Still using counters in 18th C
Continuous use since ancient times First printed arithmetics teach both counters and figures: Robert Recorde 1544 Adam Riese from 1522 Things were not so forward in Northern Europe, where people were not so ready to give up the old trusted techniques. Calculating with counters is simple and intuitive. While Shakespeare makes plentiful reference to calculation with counters, the first printed arithmetics in England and Germany taught reckoning both ‘on the line’ and ‘with the pen’. Special counters, often called jetons, continued to be minted until the late 18th century, and the practice only died out along with increased formal education in the ‘three R’s’, such as had begun to take place in Italy some centuries before.

Things were not so forward in Northern Europe, where people were not so ready to give up the old trusted techniques[1]. Calculating with counters is simple and intuitive. While Shakespeare makes plentiful reference to calculation with counters, the first printed arithmetics in England and Germany taught reckoning both ‘on the line’ and ‘with the pen’[2]. Special counters, often called jetons, continued to be minted until the late 18th century, and the practice only died out along with increased formal education in the ‘three R’s’, such as had begun to take place in Italy some centuries before.

Margarita Philosophica
Here is a piece of blatant propaganda from 16th C: Margarita Philosophica of Gregor Reisch (1508) (printed in Germany) Boethius  Pythagoras Who know’s what sum P is doing, but B is engaged in some kind of division sum. Advantage – could check your calculations

De Scripturis There are many published editions and translations of the de Scripturis Only a summary with a flavour of the content and style will be given here As with the Summa as a whole, the bookkeeping treatise contains many exhortations, admonitions, and homilies; and proverbs abound Dedicated to the Duke of Urbino Expressed intention of giving his subjects all necessary guidance in the successful conduct of business. Recommends double entry bookkeeping In particular the Venetian method, which surpasses all the others. Moreover, if one is familiar with this, one is equipped to understand any other method. He advises his reader to be a good accountant and ready mathematician, and to arrange all affairs systematically.

Contents Inventory Memorandum Journal Ledger
How to enter various transactions in the books Various other accounts Closing or balancing Brief summary

Inventory Given with an example Should be completed in one day
As detailed as possible This helps the merchant to be vigilant about his business transactions “There are more bridges to cross to make a good businessman than to make a Doctor of Laws” “The Law helps those that are awake, not those that sleep” A description of the Inventory is given with an example (dated Venice November 1493) Warnings and helpful advice, for example that the inventory must be completed in one day, and it should be as detailed as possible for this will help the merchant to be vigilant about his business transactions. Here Pacioli observes that, “There are more bridges to cross to make a good businessman than to make a Doctor of Laws”, and that “The Law helps those that are awake, not those that sleep”.

The three books Memorandum, Journal and Ledger Described with examples
Warning: Have the books officially examined For many people keep duplicate sets of books, and show one set to the buyer and the other to the seller The term Disposition covers the three principal books, Memorandum, Journal and Ledger, which are all described with a few examples. The reader is urged to have the books officially examined and sealed by a Commerce Officer, so that they can be attested as authentic, “for many people keep duplicate sets of books. They show one set to the buyer and the other to the seller”.

Entering transactions
Different ways of purchasing goods cash, time, exchange of goods, and by draft various combinations of these Dealing with public offices Municipal Bank in Venice Office of Exchange Keep careful accounts with banks as the clerks can sometimes mix up the accounts Advice is given on how to enter various aspects of business in the books, for example the different ways of purchasing goods, i.e. by cash, time, exchange of goods, and by draft, and various combinations of these. Among other subjects treated are dealing with public offices, such as the Municipal Bank in Venice, and the Office of Exchange. The merchant is advised to keep careful accounts with banks as the clerks can sometimes mix up the accounts, although a malicious clerk can be punished by the Venetian High Signoria.

Office of Exchange Brokerage fee
Split between the buyer and the seller Worked example on recording in the books, using 4% as the fee Proverb: “If you do nothing, you make no mistakes, and if you make no mistakes you do not learn” Dealing with the Office of Exchange involved paying a brokerage fee, which would be split between the buyer and the seller, and advice is given on how this should be recorded in the books. A worked example is given using 4% as the fee, and it is presumably because this is complicated that Pacioli offers a common proverb: “if you do nothing, you make no mistakes, and if you make no mistakes you do not learn”.

More guidance business trips separate stores
payment by draft or through the bank or both: safer to deliver the draft first, and then to settle through the bank exchange of goods bills of exchange Advice is given on how keep the accounts for business trips, for separate stores, and how to make the entry for a payment by draft or through the bank, or partly through each. Here the reader is advised that it is much safer to deliver the draft first, and then to settle through the bank. There is help with making the entries for exchange of goods, bills of exchange,

Partnerships Record all details in the Memorandum:
partnership’s objective how long it is intended to last who is to be employed the partners’ respective investments and shares assets and liabilities assumed by the partnership careful segregation of the partnership in the Ledger and for partnerships, with all the details of the arrangement recorded in the Memorandum, e.g. the partnership’s objective, and how long it is intended to last, who is to be employed, the partners’ respective investments and shares, the assets and liabilities assumed by the partnership, and careful segregation of the partnership in the Ledger.

Different expense accounts
Ordinary and extraordinary household accounts Business expenses Employees’ wages Ordinary expenses: Food, wine, clothing, services, household goods Extraordinary expenses: What you might spend in gaming, or money that might be lost or stolen, or lost at sea or through fires Different expense accounts are advised, for example, ordinary and extraordinary household accounts, business expenses, and employees’ wages. The ordinary household expenses are for everyday costs such as food and wine, fuel, clothes, footwear, tailoring, barbers, bakers, and water carriers, and all kitchen equipment down to glasses, tubs, and casks. The extraordinary expenses cover such things as what ‘you might spend in gaming, or money that might be lost or stolen, or lost at sea or through fires.’

Other essentials Income and Expense account Profit and Loss account
carrying books forward correcting mistakes closing or balancing of accounts the trial balance interim transactions Various other accounts are considered, such as the Income and Expense, and Profit and Loss accounts, and various essential details such as carrying books forward when they are full, correcting mistakes, and finally the closing or balancing of accounts, including the trial balance, and recording of interim transactions.

Last essentials Ledgers should be closed every year
“Frequent accounting makes for lasting friendship” Keeping of correspondence Summary of the rules for keeping a ledger Important kinds of transactions to be entered in the Memorandum recorded in the Journal posted to the Ledger It is advised that the ledgers should be closed every year. As Pacioli observes, “Frequent accounting makes for lasting friendship”. The treatise concludes with advice on the keeping of correspondence, a summary of the rules for keeping a ledger, and the important kinds of transactions that should be entered in the Memorandum, recorded in the Journal, and posted to the Ledger.

Assessment Many inconsistencies Not an ideal first text for a learner
No sample set of accounts But: Second edition 1523 Copied (and acknowledged) by Cardano and Tartaglia As the work of a highly respected practitioner and teacher of mathematics, who was widely known in his time, the Summa was widely dispersed, and went into a second edition in 1523, along with the de Scripturis. Just as the Summa, which contained the first printed account of algebra, became the standard for algebra in the 16th century, so the first printed account of double entry bookkeeping contained within it became a standard for this subject too, despite many inconsistencies and the fact that it is certainly not an ideal first text for a learner Both Cardano (1539) and Tartaglia (1546) base their accounts on the Summa, and many other writers defer to it

Dependencies on De Scripturis
Domenico Manzoni Quaderno doppio (Venice, 1540) based to a large extent on Pacioli’s tidied up how to correct badly kept account books set of illustrative accounts Domenico Manzoni’s Quaderno doppio (Venice, 1540) included a much needed set of illustrative accounts. Although the text is based to a large extent on Pacioli’s, Manzoni omitted nonessential and extraneous material, improved the explanation and added, among other new information, a chapter explaining how to correct account books that had previously been badly kept.

Jan Ympyn Nieuwe instructie (Antwerp1543) kept closely to the de Scripturis Improved treatment illustrative set of account books Editions in French (1543) English version by Grafton (1547) Domenico Manzoni’s Quaderno doppio (Venice, 1540) included a much needed set of illustrative accounts. Although the text is based to a large extent on Pacioli’s, Manzoni omitted nonessential and extraneous material, improved the explanation and added, among other new information, a chapter explaining how to correct account books that had previously been badly kept. Jan Ympyn, in his Nieuwe instructie (Antwerp1543), although he also improved the treatment, kept closely to the de Scripturis, and also included an illustrative set of account books, possibly based on his own experience in Antwerp. This treatise also appeared in French in the same year, and in 1547 an English version was published by Richard Grafton as A notable and very excellente woorke.

Hugh Oldcastle’s A profitable treatyce (1543) borrows very closely from de Scripturis does not contain a model set of accounts Schweicker’s Zwifach Buchhalten (1549) derivative of Manzoni’s work and he nce indirectly on the de Scripturis Also published in 1543, Hugh Oldcastle’s A profitable treatyce borrows very closely from de Scripturis, and does not contain a model set of accounts. In Germany, Schweicker’s Zwifach Buchhalten (1549), is derivative of Manzoni’s work and hence indirectly on the de Scripturis. It is interesting to note that neither Manzoni nor Oldcastle acknowledged any debt to Pacioli, and Ympyn’s position is ambiguous.

Later treatises on accounting
Increased in number Showed increasing variety in subject matter and treatment Pacioli’s name continued to be remembered 19th century: ‘ the father of double entry bookkeeping Pacioli 2000 – late 1990’s software Later treatises on accounting, as well as increasing in number, showed increasing variety in subject matter and treatment, but Pacioli’s name continued to be remembered, so that by the 19th century he had come to be known as the ‘Father of Double Entry Bookkeeping’. Such is his fame that not only were many translations of de Scripturis published, mostly in the 20th century, but he also inspired a set of accounting software that appeared on the marketing the 1990s. With his penchant for disseminating all that was newest and best in mathematics and accounting, one feels that he would have been pleased. [1] Basil Yamey, “Four centuries of books on book-keeping and accounting”. , as well as increasing in number, showed increasing variety in subject matter and treatment, but Pacioli’s name continued to be remembered, so that by the 19th century he had come to be known as the ‘Father of Double Entry Bookkeeping’. Such is his fame that not only were many translations of de Scripturis published, mostly in the 20th century, but he also inspired a set of accounting software that appeared on the marketing the 1990s. With his penchant for disseminating all that was newest and best in mathematics and accounting, one feels that he would have been pleased.

Conclusion Two important figures in the history of double entry bookkeeping Neither can be credited with its invention Both had their part to play Manucci was a steady practitioner Pacioli was a flamboyant teacher Conclusion We have considered two important figures in the history of double entry bookkeeping. Neither can be credited with its invention, which must have developed gradually over the preceding years, but both had their part to play. Manucci was a steady practitioner, who presumably adopted the most useful and applicable of the skills available to him, possibly developing some of his own, and who formed part of a body of accountants who acted similarly, and who together improved the techniques to the point of fully developing the double entry system. Pacioli was a flamboyant and well travelled teacher, whose aim was to promulgate all that was best in mathematics, and especially to provide as complete an account as possible of everything that would be of use in commercial circles.

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The influence of Amatino Manucci and Luca Pacioli

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The influence of Amatino Manucci and Luca Pacioli

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