Luca Pacioli Research Articles

Pacioli’s and Galileo’s ship

The works of Luca Pacioli, in addition to being a compendium of all the 15th-century mathematical knowledge, are a precious testimony of “scientific” culture in a broad sense. In his De viribus quantitatis, the “magic” character of mathematics manifests itself through a very rich series of parlour tricks, but also through some applications in the field of physics. Here we unexpectedly find a Pacioli devoted to the “learned” physics of an Aristotelian imprint with some echoes of the 14th-century Parisian school, which disseminated “practical” physics, useful to everybody, and a “home-made” physics, done with humble everyday materials, with amazement as its main goal. Everything is part of Pacioli’s programme to promote “mathematical disciplines” in the cultural field, asserting their usefulness for everyday and professional life, as well as their “divine” and “supernatural” character.

“Italian or Empirical Accounting…” by Ivan Akhmatov: Analysis and history of its creation

This article represents the first biography of Ivan Akhmatov (1766–1829), an analysis of his works on Accounting and History. Until now all the Russians encyclopaedias stated that Akhmatov the professor and author of the accounting book, and Akhmatov the historian were different persons with the same surname. However, the results of archive research show that it was one person. This article also contains a detailed review of Akhmatov’s book, Italian of Empirical Accounting. Its sources were studied in detail. In particular, it was proven that Akhmatov did not copy de la Porte’s La science des negocians et teneurs de livres in full, but added some corrections and amendments to it based on the first publication of Pierre Bouchet’s book in 1800, and not on the second one as it was stated by Russian bibliographies. Moreover, Akhmatov included in his book other Russian sources as well as his own thoughts. This article contains a description of the book’s structure, content and its main ideas. It proves that Akhmatov was the first one, in Russian accounting literature, to call Luca Pacioli, the founder of the science of accounting. It examines Akhmatov’s proposals regarding the classifications of accounts and bookkeeping rules. It also considers Akhmatov’s own proposal to use a double-entry system in government institutions. Finally, it discusses the opinions of Russian historians of accounting in Russia on Akhmatov. This article describes the creation by Akhmatov of the first historical atlas of Russia. This atlas was reissued many times. It also analyses the atlas’ funding sources. It presents Akhmatov’s biography: studies, works, life in retirement. Finally, it establishes that Ivan Akhmatov was the first person in Russia to be appointed as professor of accounting at the university.

"A difficult case": Pacioli and Cardano on the Chinese Rings

Abstract The Chinese rings puzzle is one of those recreational mathematical problems known for several centuries in the West as well as in Asia. Its origin is diffcult to ascertain but is most likely not Chinese. In this paper we provide an English translation, based on a mathematical analysis of the puzzle, of two sixteenth-century witness accounts. The first is by Luca Pacioli and was previously unpublished. The second is by Girolamo Cardano for which we provide an interpretation considerably different from existing translations. Finally, both treatments of the puzzle are compared, pointing out the presence of an implicit idea of non-numerical recursive algorithms.

The Early Practices of Financial Statements Formation in Medieval Italy

ABSTRACTIn 1494, Luca Pacioli was the first to describe the accounting statements that he called the “bilancio del libro” and “summa summarum.” While the “bilancio del libro,” or trial balance, never raised doubts as to its usefulness, the obscure interpretation of the summa summarum in the treatise and the inclusion of both statements by Pacioli led to varied perceptions of the value and meaning of this section of his treatise. This paper presents the results of many years of research in the archives of the merchant of Prato, Francesco Datini's companies between 1363 and 1410. It reports the finding of the earliest known example of a “bilancio del libro” inside the Ledger in 1395 when, in one accounting cycle, the company simultaneously formed both documents. The bilancio del libro served as a trial balance and the summa summarum was used as a statement to be transmitted to the head office. The research method employed was logical and analytical modeling.

The Capital Structure: Is Debt just a Policy or Requerement?

1. Introduction The presence of debt started when Luca Pacioli introduced his accounting equation in interpretation that firms are obtaining their assets by using liabilities and equities. After years, debt always show up in most of firm's financial reports and generally attracting the investors in capital market. The existence of debt inflicting some questions in context of capital structure, such as is debt a requirement for most of firms in term to finance their investment activities in objective to achieve the target profit? or is debt just a policy for other intentions?. These issues about capital structure of the firms are still in debate around academicians especially in context of trade off theory and pecking order theory since debt has playing its own role which makes the capital structure still a puzzle (Myers, 1984; Nechaev and Antipina, 2016; Thalassinos et al., 2010; Vovchenko et al., 2017; Fetai, 2015). Myers (2001) proposes two conditional theories of capital structure for explaining why firms obtaining debt, which are trade off and pecking order. According to Myers (2001), in perspective of trade off, firms as tax payers generally shall look for optimum debt in term to get tax shield, while in perspective of pecking order, firms shall avoid debts if their internal fund such as retained earnings sufficient for financing their expenditures or investments (Boldeanu and Tache, 2016). In contrast, the findings by Baker and Wurgler (2002), Klein, O'Brien, and Peters (2002), Hovakimian, Hovakimian, and Tehranian (2004), Alti (2006), Elliott, Kant, and Warr (2008), Thalassinos et al. (2015), Allegret et al. (2016), Duguleana and Duguleana (2016) and Brendea (2012) show that the market timing hypothesis can become an alternative explanation about capital structures of the firms, where the valuations by investors for share prices in capital market shall trigger the effects of pecking order or trade off in flexible. As developing country, the Indonesia has many firms with various debt. Limited to the samples, based on data from Indonesia Stock Exchange (www.idx.co.id) the trends of average total debts to total assets ratio are 52.33% for year of 2011, 48.06% for year of 2012, 49.88% for year of 2013, 48.99% for year of 2014, and 50.25% for year of 2015. The trends show that the average of debt to asset ratios for firms in period of 2011 to 2015 are fluctuate in range of almost or even half by their total assets which means most assets of these firms are financed by debts. The study proceeds the next sections as follows, section 2 reviews the relevant literatures and hypothesis development. Section 3 presents the samples, variable definitions and the regression models. Section 4 presents the result and discuss the findings, and finally section 5 concludes the findings. 2. Literature Review 2.1. Trade off theory and pecking order theory Similar to Myers (2001), Elliott, Kant, and Warr (2008) propose that, the model of capital structure can be viewed in perspectives of two main theories which are trade off theory and pecking order theory. Moreover, Elliott, Kant, and Warr (2008) explain that, in perspective of pecking order theory, the firms shall choose the equities with lower cost of capital which implies that the firms shall finance their investments by use their internal funds then by external funds, while in perspective of static trade off theory, the firms in periodically shall adjust their capital structure until it reach the optimum portion. Sunder and Myers (1999) prove empirically that, the mature firms tend to adopt pecking order model in term to determine their capital structure rather than trade off model. Sunder and Myers (1999) also explain that, although debts shall give tax benefit to firms but the over debts shall make the firms bear the financial distress costs. According to Cheng and Shiu (2007), in view of pecking order theory, the existence of asymmetry information between insiders and outsiders makes firms use their internal fund rather than debts in term for financing the investments, and that why pecking order assumes the firms tend to decrease their debts when they get profit. …

Pacioli's Lens: God, Humanism, Euclid, and the Rhetoric of Double Entry

ABSTRACTThis paper investigates why, in 1494, the Franciscan friar and teacher of mathematics, Luca Pacioli, published an instructional treatise describing the system of double entry bookkeeping. In doing so, it also explores the rhetoric and foundations of double entry through the lens of Pacioli's treatise. Recent findings on Pacioli's life and works, his writings, and the medieval accounting archives are combined to identify how he was inspired by his faith and his humanist beliefs to give all merchants access to the practical mathematics and the bookkeeping they required. The paper finds that Pacioli's teaching method was inspired by Euclid, his Franciscan education, and his humanist beliefs, and that Pacioli reveals a simplicity in the then-unrecognized axiomatic foundation of double entry that has been largely overlooked. The findings represent a paradigm shift in how we perceive Pacioli, his treatise, and double entry.

Details on the mathematical interplay between Leonardo da Vinci and Luca Pacioli

Leonardo da Vinci (1452–1519) maintained a strong relationship with mathematics, but the benefits of this connection unfortunately had little impact in his time. His meeting with Luca Pacioli (1445–1517) in Milan in 1496 was crucial: the two men would become friends and a deep mutual respect would preside over Leonardo da Vinci's improving his mathematical knowledge while contributing to the drawings of Pacioli's De divina proportione (Milano, 1496–98) (Pacioli 1509a). Based on my recent works on the relationship between mathematics and physics during the Renaissance, here I resume some results on the conceptual mathematical frameworks between two Italian scholars.

Pacioli's double entry – part of an intellectual and social movement

ABSTRACTOur research contains unashamedly speculations about Pacioli, and his Renaissance heroes. It seeks to codify prior research which has speculated on many aspects of Fra Luca Pacioli's (1445–c.1517) life. Regarding teaching, not surprisingly, most students are less than enthused by the experience of being taught double-entry bookkeeping (DEB) as a mechanical exercise. The focus on control in many research papers has misplaced emphasis on the origins of DEB, generally ignoring the socio-economic and intellectual contexts in which it was forged. This study speculates on DEB's intellectual foundations, namely perspective, proportionality, harmony, order and balance captured in the Venetian form of DEB. By emphasising DEB's recourse to these aspects, it is placed in Renaissance Italy's fifteenth- and sixteenth-century intellectual and social movement. Academics including Bryer have suggested that a broader notion of financial accountability is appropriate. We concur. Accountability is generally a missing dimension in DEB teaching and related research. A major complaint in the aftermath of the Global Financial Crisis (GFC) levelled at the banks, and their shadow banking arms in particular, is that their group accounting failed ‘to tell it how it actually was’ – that is, it failed to truly account. Companies were unaccountable. The ‘morality’ of audited accounting with a lack of corporate accountability, namely its recourse to truth, balance, proportionality of the kind the Renaissance players sought, was certainly absent during the GFC.

Contributions of early Muslim scholars to originality of bookkeeping-system

We explored the early Muslim scholars’ contributions to the originality of the Bookkeeping system by comparing the contributions of Western academics with those of Muslim scholars. We investigated, also, the knowledge transfer between East and West and how the early Muslims scholars’ contributions were part of the fundamentals of the Bookkeeping System. A surveying most of essays that concentrating on developments in the historical bookkeeping literature as well as reviewing historical literature about transfer knowledge between East and West. We found that Muslim scholars’ contributions to the originality of the Bookkeeping system could be divided into three stages. Firstly, it began with the foundation of Islam in 610; this sets up the basics of the Bookkeeping System. Secondly, Al-Khwarizmi sets up a comprehensive Bookkeeping System in 976. Thirdly, during the period 1332 to 1418, Al-Nuwayri and Al-Qalqashandi completed the structure of the Bookkeeping System. We found, also, that, from the 8th to the 15th centuries, Muslim scholars represented a knowledge bridge for the West suggesting that Luca Pacioli’s work was the outcomes of the Muslim scholars’ contributions. It is the first study that links the originality of Bookkeeping system with transfer knowledge between East and West. It is the first research that compare between East and West’ contributions towards Bookkeeping’ pyramid

THE EARLIEST KNOWN TREATISE ON DOUBLE ENTRY BOOKKEEPING BY MARINO DE RAPHAELI

Historians of the origins of modern accounting have generally accepted that the earliest known instructional treatise on double entry bookkeeping was the one published by Luca Pacioli in 1494. This paper dispels that view, presenting detailed evidence of an earlier bookkeeping manual from 1475 that has hitherto remained virtually unknown. Using evidence gathered from the text, the paper on which it is written, and the handwriting, this paper speculates on its origins. It also presents an overview of the material taught in that book and compares it with other texts on double entry published up to the mid-16th century. In the course of doing so, a generic bookkeeping curriculum for the period is identified and specialist topics included in the manual from 1475 are noted and discussed. Finally, this paper considers the place of this text in the history of accounting, accounting practice, and accounting education. It concludes that this manual is of major significance in providing insights into how accounting was taught in 15th century Venice, and of which aspects of business it was felt that instruction in double entry was of fundamental importance at that time.

The game theory in thoracic surgery: from the intuitions of Luca Pacioli to the operating rooms management.

Game theory is a formal way to analyze the interactions among groups of subjects who behave each other. It has historically been of great interest in the economic fields in which decisions are made in a competitive environment. Game theory has fascinating potential if applied in the medical science. Few papers have been written about the application of game theory in surgery. The majority of scenarios of game theory in surgery fall into two main groups: cooperative and no cooperative games.

Accounting History: Definition and Relevance

This work traces the history of accounting and how merchants developed a system of keeping record using what is known as the Bollac. The stages of development of accounting, from the Mesopotamia 3500 B.C to the 21st century accounting. This study also talked about the Father of Accounting – Luca Pacioli and his contributions in the development of double entry bookkeeping and finally the relevance of accounting history to today’s world.

Masters, questions and challenges in the abacus schools

The mathematical scenario in Italy during the Late Middle Ages and the Renaissance is mainly dominated by the treatises on the abacus, which developed together with the abacus schools. In that context, between approximately the last thirty years of the fourteenth century and the first twenty years of the sixteenth century, the manuscript and printed tradition tell us of queries and challenges, barely known or totally unknown, in which the protagonists were abacus masters. We report in this work on the most significant examples and draw out interesting cues for thoughts and remarks of a scientific, historical and biographical nature. Five treatises, written in the fifteenth and sixteenth century, have been the main source of inspiration for this article: the Trattato di praticha d’arismetricha and the Tractato di praticha di geometria included in the codices Palat. 573 and Palat. 577 (c. 1460) kept in the Biblioteca Nazionale of Florence and written by an anonymous Florentine disciple of the abacist Domenico di Agostino Vaiaio; another Trattato di praticha d’arismetrica written by Benedetto di Antonio da Firenze in 1463 and included in the codex L.IV.21 kept in the Biblioteca Comunale of Siena; the Tractatus mathematicus ad discipulos perusinos written by Luca Pacioli between 1477 and 1480, manuscript Vat. Lat. 3129 of the Biblioteca Apostolica Vaticana; and Francesco Galigai’s Summa de arithmetica, published in Florence in 1521.

Leonardo’s Vitruvian Man Drawing: A New Interpretation Looking at Leonardo’s Geometric Constructions

Generally speaking, today’s scientific community considers that the famous figure drawn by Leonardo da Vinci at the end of the fifteenth century was made using the Golden ratio. More specifically, the relationship established between the circle’s diameter and the side of the square is a consequence of the geometric relationship probably discovered by Euclid, but made famous by Luca Pacioli in his De Divina proportione. Aware of the close working relationship between Leonardo and Pacioli, namely in the writing of this last book, the theory that establishes a close relationship between these two figures, making use of this remarkable mathematical relationship, has gained credibility. In fact, the use of the Divina proporzione, despite being a very stimulating construction on an intellectual level, presents too great a margin of error, especially for such a competent geometrician as Leonardo da Vinci was. For that reason, the relationship between these two figures (square and circle) is grounded on a much simpler geometric relationship than the one found at the base of the definition, for instance, of Le Corbusier’s Modulor.

Rethinking Managerial Reporting

Rethinking Managerial Reporting

Pacioli’s Innovation in Accounting: Business or Academic Affairs

According to the accounting literature there is no evidence for earlier use of “doubleentry”, as documented by Luca Pacioli in his Summa de Arithmetica Geometrica Proportioni et Proportionalita (1494), before the 13th century AD. Littleton’s popular thesis links doubleentry to the increased intensity in modern times (as compared with in antiquity) of two (all inclusive) groups of economic and technical “antecedents”, while Hoskin and Macve (1986) explain the articulation of double-entry in early Renaissance as an aspect of the new way of writing the text (“new textuality”), that was being developed around same time in Europe by scholars who saw in it (and in accounting, albeit with no particular interest in double-entry itself then) the potential of new power-knowledge relationships. In this study we attempt to explore if double entry, the innovative method for the accounting technology, is business or academic affairs.

Observations about Leonardo's drawings for Luca Pacioli

Three versions of Luca Pacioli's ‘De divina proportione’ remain: a manuscript held in Milan, another in Geneva and a printed version edited in Venice. A recent book, ‘Antologia della divina proporzione’, has all three in one volume, allowing an easy comparison of the different versions. The present paper proposes some observations about these drawings, generally said to be of Leonardo da Vinci's hand.

Were Early Modern Architects Neoplatonists? The Case of François Blondel

What was the status of Neoplatonism among early modern architects? What relationship did they see between their designs and the ‘design’ of nature? What, if anything, guaranteed the aesthetic claims for specific numerical ratios or geometrical forms? Did early modern architects even require such a guarantee? We have little direct evidence to answer these questions. It has generally been assumed, since the publication of Wittkower’s Architectural Principles, that practitioners held to stronger or weaker versions of Renaissance Platonism. Music, bodies, and buildings, according to this notion, shared a structural affinity with the order of the heavens, because they depended on the same basic numerical ratios. It is worth pointing out, however, that Wittkower himself adduces only circumstantial evidence for such beliefs. Alberti and Palladio, while suggestive, are both very terse on this point, obliging Wittkower to supplement his case with further evidence drawn from philosophers and mathematicians, in particular Luca Pacioli, Francesco Giorgi, and Nicolas of Cusa. It is this set of circumstances that makes François Blondel’s extensive response to Claude Perrault, in their famous debate over the efficacy of proportion, so important. The twenty chapters that Blondel devoted to this issue in the final volume of the Cours d’architecture (1675–1683) represent a rare historical testimony: an explicit, self-conscious, and theoretically elaborate justification of proportion by a Renaissance practitioner. Blondel’s interpretation of this tradition, too, is noteworthy. What these pages show is not an orthodox expression of Platonic doctrine, but rather an attempt to adapt the age-old principle of cosmic symmetria to a new, modern context.

120 let od (ne)vydání českého překladu knihy "Pojednání o účetnictví" od Luca Pacioliho

První tištěná učebnice podvojného účetnictví na světě, Pojednání o účetnictví Luca Pacioliho, vyšla jako část matematické učebnice Summa de arithmetica, geometria, proportii et proportionalita v Benátkách v roce 1494, letos je to tedy již 520 let. Zásluhou českých účetních historiků, K. P. Kheila ml. (1843-1908) a H. Raulicha (1866-1940) má český čtenář a zájemce o účetní historii dnes k dispozici vedle originálního textu, dále italské, německé, anglické a ruské verze, rovněž české verze Pacioliho Pojednání. Cesta k českým překladům nebyla jednoduchá. V případě Kheilova překladu zůstalo dokonce u ne zcela dokončené podoby překladatelské práce. Vzpomínáme letos především 120. výročí příprav vydání Kheilova překladu tiskem; vydání, které se nakonec neuskutečnilo.

Historia rachunkowości - jednej z najstarszych dyscyplin ekonomicznych

It is possible to find signs of accounting as far back as prehistoric times, when it constituted the essence of the then contemporary economic thought and solved problems involved in joint labour. This publication presents the history of accounting from the first bookkeeping account through Luca Pacioli's work that is so crucial to the history of accounting and, finally, the evolution of the bill of charges that was created for the needs of the first capitalists. Research on the system of accounting is presented, as are deceitful financial reporting and the establishment of the profession of Chartered Accountants. The history of accounting shows that it is one of the oldest disciplines of economic studies and, most importantly, the foundations of accounting have stood the test of time. The structure of a bookkeeping account with a Dt and Ct page has remained unchanged for over five thousand years.