''[[Divina proportione]]'',
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Fra Luca Bartolomeo de Pacioli (sometimes Paccioli or Paciolo; c. 1447 – 19 June 1517)^{ [3] } was an Italian mathematician, Franciscan friar, collaborator with Leonardo da Vinci, and an early contributor to the field now known as accounting. He is referred to as "The Father of Accounting and Bookkeeping" in Europe and he was the second person to publish a work on the double-entry system of book-keeping on the continent.^{ [4] }^{ [lower-alpha 1] } He was also called Luca di Borgo after his birthplace, Borgo Sansepolcro, Tuscany.
Luca Pacioli was born between 1446 and 1448 in the Tuscan town of Sansepolcro where he received an abbaco education. This was education in the vernacular (i.e., the local tongue) rather than Latin and focused on the knowledge required of merchants. His father was Bartolomeo Pacioli; however, Luca Pacioli was said to have lived with the Befolci family as a child in his birth town Sansepolcro.^{ [6] } He moved to Venice around 1464, where he continued his own education while working as a tutor to the three sons of a merchant. It was during this period that he wrote his first book, a treatise on arithmetic for the boys he was tutoring. Between 1472 and 1475, he became a Franciscan friar.^{ [6] } Thus, he could be referred to as Fra ('Friar') Luca.
In 1475, he started teaching in Perugia as a private teacher before becoming first chair in mathematics in 1477. During this time, he wrote a comprehensive textbook in the vernacular for his students. He continued to work as a private tutor of mathematics and was instructed to stop teaching at this level in Sansepolcro in 1491. In 1494, his first book, Summa de arithmetica, geometria, Proportioni et proportionalita , was published in Venice. In 1497, he accepted an invitation from Duke Ludovico Sforza to work in Milan. There he met, taught mathematics to, collaborated, and lived with Leonardo da Vinci. In 1499, Pacioli and Leonardo were forced to flee Milan when Louis XII of France seized the city and drove out their patron. Their paths appear to have finally separated around 1506. Pacioli died at about the age of 70 on 19 June 1517, most likely in Sansepolcro, where it is thought that he had spent much of his final years.^{ [6] }
Pacioli published several works on mathematics, including:
The majority of the second volume of Summa de arithmetica, geometria. Proportioni et proportionalita was a slightly rewritten version of one of Piero della Francesca's works. The third volume of Pacioli's Divina proportione was an Italian translation of Piero della Francesca's Latin book De quinque corporibus regularibus . In neither case did Pacioli include an attribution to Piero. He was severely criticized for this and accused of plagiarism by sixteenth-century art historian and biographer Giorgio Vasari. R. Emmett Taylor (1889–1956) said that Pacioli may have had nothing to do with the translated volume Divina proportione, and that it may just have been appended to his work. However, no such defense can be presented concerning the inclusion of Piero della Francesca's material in Pacioli's Summa.
Pacioli dramatically affected the practice of accounting by describing the double-entry accounting method used in parts of Italy. This revolutionized how businesses oversaw their operations, enabling improved efficiency and profitability. The Summa's section on accounting was used internationally as an accounting textbook up to the mid-16th century. The essentials of double-entry accounting have for the most part remain unchanged for over 500 years. "Accounting practitioners in public accounting, industry, and not-for-profit organizations, as well as investors, lending institutions, business firms, and all other users for financial information are indebted to Luca Pacioli for his monumental role in the development of accounting."^{ [10] }
The ICAEW Library's rare book collection at Chartered Accountants' Hall holds the complete published works of Luca Pacioli. Sections of two of Pacioli's books, 'Summa de arithmetica' and 'Divina proportione' can be viewed online using Turning the Pages, an interactive tool developed by the British Library.^{ [11] }
Luca Pacioli also wrote an unpublished treatise on chess, De ludo scachorum (On the Game of Chess). Long thought to have been lost, a surviving manuscript was rediscovered in 2006, in the 22,000-volume library of Count Guglielmo Coronini-Cronberg in Gorizia. A facsimile edition of the book was published in Pacioli's home town of Sansepolcro in 2008. Based on Leonardo da Vinci's long association with the author and his having illustrated Divina proportione, some scholars speculate that Leonardo either drew the chess problems that appear in the manuscript or at least designed the chess pieces used in the problems.^{ [12] }^{ [13] }^{ [14] }^{ [15] }
Double-entry bookkeeping, in accounting, is a system of book keeping where every entry to an account requires a corresponding and opposite entry to a different account. The double-entry system has two equal and corresponding sides known as debit and credit. The left-hand side is debit and the right-hand side is credit. In a normally debited account, such as an asset account or an expense account, a debit increases the total quantity of money or financial value, and a credit decreases the amount or value. On the other hand, for an account that is normally credited, such as a liability account or a revenue account, credits increase the account's value and debits decrease that value. In double-entry bookkeeping, a transaction always affects at least two accounts, always includes at least one debit and one credit, and always has total debits and total credits that are equal. This is to keep the accounting equation in balance. For example, if a business takes out a bank loan for $10,000, recording the transaction would require a debit of $10,000 to an asset account called "Cash", as well as a credit of $10,000 to a liability account called "Notes Payable".
Piero della Francesca, originally named Piero di Benedetto, was an Italian painter of the Early Renaissance. To contemporaries he was also known as a mathematician and geometer. Nowadays Piero della Francesca is chiefly appreciated for his art. His painting is characterized by its serene humanism, its use of geometric forms and perspective. His most famous work is the cycle of frescoes The History of the True Cross in the church of San Francesco in the Tuscan town of Arezzo.
Leonardo da Vinci (1452–1519) was an Italian polymath, regarded as the epitome of the "Renaissance Man", displaying skills in numerous diverse areas of study. Whilst most famous for his paintings such as the Mona Lisa and the Last Supper, Leonardo is also renowned in the fields of civil engineering, chemistry, geology, geometry, hydrodynamics, mathematics, mechanical engineering, optics, physics, pyrotechnics, and zoology.
Events from the year 1509 in art.
Divina proportione, later also called De divina proportione is a book on mathematics written by Luca Pacioli and illustrated by Leonardo da Vinci, composed around 1498 in Milan and first printed in 1509. Its subject was mathematical proportions and their applications to geometry, to visual art through perspective, and to architecture. The clarity of the written material and Leonardo's excellent diagrams helped the book to achieve an impact beyond mathematical circles, popularizing contemporary geometric concepts and images.
De ludo scachorum, also known as Schifanoia, is a Latin-language manuscript on the game of chess written around 1500 by Luca Pacioli, a leading mathematician of the Renaissance. Created in the times when rules of the game were evolving to the ones known today, the manuscript contains over a hundred chess problems, to be solved – depending on the problem – using either the old or the modern rules.
Mathematics and art are related in a variety of ways. Mathematics has itself been described as an art motivated by beauty. Mathematics can be discerned in arts such as music, dance, painting, architecture, sculpture, and textiles. This article focuses, however, on mathematics in the visual arts.
The year 1537 in science and technology included many events, some of which are listed here.
The portrait of a man in red chalk in the Royal Library of Turin is widely, though not universally, accepted as a self-portrait of Leonardo da Vinci. It is thought that Leonardo da Vinci drew this self-portrait at about the age of 60. The portrait has been extensively reproduced and has become an iconic representation of Leonardo as a polymath or "Renaissance Man". Despite this, some historians and scholars disagree as to the true identity of the sitter.
De Prospectiva pingendi is the earliest and only pre-1500 Renaissance treatise solely devoted to the subject of perspective. It was written by the Italian master Piero della Francesca in the mid-1470s to 1480s, and possibly by about 1474. Despite its Latin title, the opus is written in Italian.
The year 1509 in science and technology included many events, some of which are listed here.
The Portrait of Luca Pacioli is a painting attributed to the Italian Renaissance artist Jacopo de' Barbari, dating to around 1500 and housed in the Capodimonte Museum, Naples, southern Italy. The painting portrays the Renaissance mathematician Luca Pacioli and may have been painted by his collaborator Leonardo da Vinci. The person on the right has not been identified conclusively, but could be the German painter Albrecht Dürer, whom Barbari met between 1495 and 1500.
John Mellis lived in the 16th century. Along with James Peele and John Dee, Mellis is one of the first authors who contributed to the accounting literature.
De arte supputandi libri quattuor was the first printed work on arithmetic published in England. Published in 1522, it was written by Cuthbert Tunstall, Bishop of London, and based on Luca Pacioli's Summa de arithmetica, geometria, proportioni et proportionalità. It is dedicated to Sir Thomas More.
The history of accounting or accountancy can be traced to ancient civilizations.
Summa de arithmetica, geometria, proportioni et proportionalita is a book on mathematics written by Luca Pacioli and first published in 1494. It contains a comprehensive summary of Renaissance mathematics, including practical arithmetic, basic algebra, basic geometry and accounting, written for use as a textbook and reference work.
Paganino Paganini, was an Italian printer and publisher from the Republic of Venice during the Renaissance. He was the original publisher of Luca Pacioli's mathematical works, Summa de arithmetica and De divina proportione, and of what is thought to be the first printed version of the Quran in Arabic.
The Alphabetum Romanum, by Felice Feliciano, published in 1463, was the first book demonstrating how to create Roman square capital letters geometrically based on the subdivision of a square.
De quinque corporibus regularibus is a book on the geometry of polyhedra written in the 1480s or early 1490s by Italian painter and mathematician Piero della Francesca. It is a manuscript, in the Latin language; its title means [the little book] on the five regular solids. It is one of three books known to have been written by della Francesca.
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