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卢卡·帕乔利

（1445-1517）

意大利数学家，世界会计之父。其《簿记论》被会计学界认为是会计发展史上的里程碑，是簿记理论专门而系统研究的历史起点。

以下两份来自网络的英文资料，可以提供更多对他的了解。

1.个人生平

Luca Pacioli

Born: 1445 in Sansepolcro, Italy

Died: 1517 in Sansepolcro, Italy

Luca Pacioli's father was Bartolomeo Pacioli, but Pacioli does not appear to have been brought up in his parents house. He lived as a child with the Befolci family in Sansepolcro which was the town of his birth. This town is very much in the centre ofItaly about 60 km north of the city of Perugia. As far as Pacioli was concerned, perhaps the most important feature of this small commercial town was the fact that Piero della Francesca had a studio and workshop in there and della Francesca spent quite some time there despite frequent commissions in other towns

Although we know little of Pacioli's early life, the conjecture that he may have received at least a part of his education in the studio of della Francesca in Sansepolcro must at least have a strong chance of being correct. One reason that this seems likely to be true is the extensive knowledge that Pacioli had of the work of Piero della Francesca and Pacioli's writings were very strongly influenced by those of Piero.

Pacioli moved away from Sansepolcro while he was still a young lad. He moved toVenice to enter the service of the wealthy merchant Antonio Rompiasi whose house was in the highly desirable Giudecca district of that city. One has to assume that Pacioli was already well educated in basic mathematics from studies in Sansepolcro and he certainly must have been well educated generally to have been chosen as a tutor to Rompiasi's three sons. However, Pacioli took the opportunity to continue his mathematical studies at a higher level while in Venice, studying mathematics under Domenico Bragadino. During this time Pacioli gained experience both in teaching, from his role as tutor, and also in business from his role helping with Rompiasi's affairs.

It was during his time in Venice that Pacioli wrote his first work, a book on arithmetic which he dedicated to his employer's three sons. This was completed in 1470 probably in the year that Rompiasi died. Pacioli certainly seemed to know all the right people for he left Venice and travelled to Rome where he spent several months living in the house of Leone Battista Alberti who was secretary in the Papal Chancery. As well as being an excellent scholar and mathematician, Alberti was able to provide Pacioli with good religious connections. At this time Pacioli then studied theology and, at some time during the next few years, he became a friar in the Franciscan Order.

In 1477 Pacioli began a life of travelling, spending time at various universities teaching mathematics, particularly arithmetic. He taught at the University of Perugiafrom 1477 to 1480 and while there he wrote a second work on arithmetic designed for the classes that he was teaching. He taught at Zara (now called Zadar or Jadera inCroatia but at that time in the Venetian Empire) and there wrote a third book on arithmetic. None of the three arithmetic texts were published, and only the one written for the students in Perugia has survived. After Zara, Pacioli taught again at the University of Perugia, then at the University of Naples, then at the Universityof Rome. Certainly Pacioli become acquainted with the duke of Urbino at some time during this period. Pope Sixtus IV had made Federico da Montefeltro the duke of Urbino in 1474 and Pacioli seems to have spent some time as a tutor to Federico's son Guidobaldo who was to become the last ruling Montefeltro when his father died in 1482. The court at Urbino was a notable centre of culture and Pacioli must have had close contact with it over a number of years.

In 1489, after two years in Rome, Pacioli returned to his home town of Sansepolcro. Not all went smoothly for Pacioli in his home town, however. He had been granted some privileges by the Pope and there was a degree of jealousy among the men from the religious orders in Sansepolcro. In fact Pacioli was banned from teaching there in 1491 but the jealousy seemed to be mixed with a respect for his learning and scholarship for in 1493 he was invited to preach the Lent sermons.

During this time in Sansepolcro, Pacioli worked on one of his most famous books theSumma de arithmetica, geometria, proportioni et proportionalita which he dedicated to Guidobaldo, the duke of Urbino. Pacioli travelled to Venice in 1494 to publish theSumma. The work gives a summary of the mathematics known at that time although it shows little in the way of original ideas. The work studies arithmetic, algebra, geometry and trigonometry and, despite the lack of originality, was to provide a basis for the major progress in mathematics which took place in Europe shortly after this time. As stated in [1] the Summa was:-

... not addressed to a particular section of the community. An encyclopaedic work(600 pages of close print, in folio) written in Italian, it contains a general treatise on theoretical and practical arithmetic; the elements of algebra; a table of moneys, weights and measures used in the various Italian states; a treatise on double-entry bookkeeping; and a summary of Euclid's geometry. He admitted to having borrowed freely from Euclid, Boethius, Sacrobosco, Fibonacci, ...

The geometrical part of Pacioli's Summa is discussed in detail in [6]. The authors write:-

The geometrical part of L Pacioli's Summa [Venice, 1494] in Italian is one of the earliest printed mathematical books. Pacioli broadly used Euclid's Elements, retelling some parts of it. He referred also to Leonardo of Pisa (Fibonacci).

Another interesting aspect of the Summa was the fact that it studied games of chance. Pacioli studied the problem of points, see [9], although the solution he gave is incorrect.

Ludovico Sforza was the second son of Francesco Sforza, who had made himself duke ofMilan. When Francesco died in 1466, Ludovico's elder brother Galeazzo Sforza became duke of Milan. However, Galeazzo was murdered in 1476 and his seven year old son became duke of Milan. Ludovico, after some political intrigue, became regent to the young man in 1480. With very generous patronage of artists and scholars, Ludovico Sforza set about making his court in Milan the finest in the whole of Europe. In 1482 Leonardo da Vinci entered Ludovico's service as a court painter and engineer. In 1494 Ludovico became the duke of Milan and, around 1496, Pacioli was invited by Ludovico to go to Milan to teach mathematics at Ludovico Sforza's court. This invitation may have been made at the prompting of Leonardo da Vinci who had an enthusiastic interest in mathematics.

At Milan Pacioli and Leonardo quickly became close friends. Mathematics and art were topics which they discussed at length, both gaining greatly from the other. At this time Pacioli began work on the second of his two famous works, Divina proportione and the figures for the text were drawn by Leonardo. Few mathematicians can have had a more talented illustrator for their book! The book which Pacioli worked on during 1497 would eventually form the first of three books which he published in 1509 under the title Divina proportione (see for example [3]). This was the first of the three books which finally made up this treatise, and it studied the 'Divine Proportion' or 'golden ratio' which is the ratio a : b = b : (a + b). It contains the theorems ofEuclid which relate to this ratio, and it also studies regular and semiregular polygons (see in particular [4] for a discussion of Pacioli's work on regular polygons). Clearly the interest of Leonardo in this aesthetically satisfying ratio both from a mathematical and artistic point of view was an important influence on the work. The golden ratio was also of importance in architectural design and this topic was to form the second part of the treatise which Pacioli wrote later. The third book in the treatise was a translation into Italian of one of della Francesca's works.

Louis XII became king of France in 1498 and, being a descendant of the first duke ofMilan, he claimed the duchy. Venice supported Louis against Milan and in 1499 the French armies entered Milan In the following year Ludovico Sforza was captured when he attempted to retake the city. Pacioli and Leonardo fled together in December 1499, three months after the French captured Milan. They stopped first at Mantua, where they were the guests of Marchioness Isabella d'Este, and then in March 1500 they continued to Venice. From Venice they returned to Florence, where Pacioli and Leonardo shared a house.

The University of Pisa had suffered a revolt in 1494 and had moved to Florence. Pacioli was appointed to teach geometry at the University of Pisa in Florence in 1500. He remained in Florence, teaching geometry at the university, until 1506. Leonardo, although spending ten months away working for Cesare Borgia, also remained in Florence until 1506. Pacioli, like Leonardo, had a spell away from Florence when he taught at the University of Bologna during 1501-02. During this time Pacioli worked with Scipione del Ferro and there has been much conjecture as to whether the two discussed the algebraic solution of cubic equations. Certainly Pacioli discussed this topic in the Summa and some time after Pacioli's visit to Bologna, del Ferro solved one of the two cases of this classic problem.

During his time in Florence Pacioli was involved with Church affairs as well as with mathematics. He was elected the superior of his Order in Romagna and then, in 1506, he entered the monastery of Santa Croce in Florence. After leaving Florence, Pacioli went to Venice where he was given the sole rights to publish his works there for the following fifteen years. In 1509 he published the three volume work Divina proportione and also a Latin translation of Euclid's Elements. The first printed edition of Euclid's Elements was the thirteenth century translation by Campanus which had been published in printed form in Venice in 1482. Pacioli's edition was based on that of Campanus but it contained much in the way of annotation by Pacioli himself.

In 1510 Pacioli returned to Perugia to lecture there again. He also lectured again inRome in 1514 but by this time Pacioli was 70 years of age and nearing the end of his active life of scholarship and teaching. He returned to Sansepolcro where he died in 1517 leaving unpublished a major work De Viribus Quantitatis on recreational problems, geometrical problems and proverbs. This work makes frequent reference to Leonardo da Vinci who worked with him on the project, and many of the problems in this treatise are also in Leonardo's notebooks. Again it is a work for which Pacioli claimed no originality, describing it as a compendium.

Despite the lack of originality in Pacioli's work, his contributions to mathematics are important, particularly because of the influence which his book were to have over a long period. In [10] the importance of Pacioli's work is discussed, in particular his computation of approximate values of a square root (using a special case of Newton's method), his incorrect analysis of certain games of chance (similar to those studied by Pascal which gave rise to the theory of probability), his problems involving number theory (similar problems appeared in Bachet's compilation), and his collection of many magic squares.

In 1550 there appeared a biography of Piero della Francesca written by Giorgio Vasari. This biography accused Pacioli of plagiarism and claimed that he stole della Francesca's work on perspective, on arithmetic and on geometry. This is an unfair accusation, for although there is truth that Pacioli relied heavily on the work of others, and certainly on that of della Francesca in particular, he never attempted to claim the work as his own but acknowledged the sources which he used.

Article by: J J O'Connor and E F Robertson

July 1999

MacTutor History of Mathematics

[http://www-history.mcs.st-andrews.ac.uk/Biographies/Pacioli.html]

2.会计学之父：卢卡·帕乔利

The Father of Accounting: Luca Pacioli

The discipline and science of accounting is essential for the world economy to function well. Without an accurate way to keep track of investments, expenditures, depreciation, and more, there would be no way to understand the true financial picture of a company and no way to be confident in its prospects. This would kill commerce, capital investment, and other transactions that keep the economy running.

The history of accounting is more fascinating than many people probably imagine, and several figures have made key contributions to the science. One of the most important people in the history of accounting is Luca Pacioli, a Franciscan friar who lived during the fifteenth and sixteenth centuries, and who is today known as the “Father of Accounting.” This resource will provide a history of accounting and an overview of Pacioli’s contributions to the discipline.

History of Accounting

Most people are not likely to think of accounting when the topic of the “world’s oldest profession” is raised, but many experts believe that accounting fits that description to a tee. From the start, it was necessary for individuals to have a way to keep track of their business dealings even if they were largely self-sufficient, merely growing their own food and taking care of their other needs. As civilization progressed, ancient bookkeeping methods were developed. In the so-called “Fertile Crescent,” ancient bookkeepers would use clay tokens of different shapes and sizes to keep track of wealth. Each token could represent a different commodity — sheep, cattle, grain, and so forth. New technologies and recording methods developed over time, and as money was introduced to facilitate economic exchange, the token system was abandoned in the favor of written accounts.

During the medieval period, Italian merchants began to involve themselves in trade with other cities, first across the Mediterranean Sea and then in other parts of the world. The increasing complexity of these trade relationships required better record keeping, and the system of double-entry bookkeeping was invented. Luca Pacioli, an Italian Franciscan monk wrote Summa de Arithmetica, Geometrica, Proportioni et Proportionalita in 1494, and it was the first full description of this method of accounting.

During the Enlightenment and Industrial Revolution, Britain’s rise as the world’s chief economic power meant that accounting methods would have to advance as well. Men such as Josiah Wedgwood began implementing systems of cost accounting in their companies, and professional accountants began offering their services inLondon. Such methods were carried over to the United States, and large firms such as General Motors adopted these accounting methods as well. Today, standardized accounting practices are in use across the globe, helping companies around the world to stay afloat, attract investment, and keep the engine of the world economy running.

The Life of Luca Pacioli

Luca Pacioli was born in 1445 in Tuscany, Italy, where he received an education in the ways of medieval merchants and commerce. Over time, his interest in mathematics led him to become an expert tutor in the subject, and he wrote a textbook on mathematics to help instruct his students. During the years 1472–1475, Pacioli became a Franciscan friar, but he did not end his tutoring career.

In 1494, Pacioli published his most famous work —Summa de Arithmetica, Geometria, Proportioni et Proportionalita. In addition to providing instruction in standard mathematics, this work would also describe double-entry bookkeeping completely for the very first time, which has earned for him the title “father of accounting.” It was also the first textbook on algebra that was written in the vernacular language of northern Italy. Eventually, Pacioli would travel to Milan, where he became an associate of Leonardo da Vinci. Da Vinci actually learned a lot about mathematics from Pacioli, and the knowledge he gained would help Da Vinci create some of the excellent anatomical drawings for which he is known today.

Much of Pacioli’s work in mathematics was not original or unique, but his writings had a large influence in Italy, allowing for information that was formerly the possession merely of the elite to be disseminated among the general populace. Pacioli died in 1517, the same year that Martin Luther’s 95 Theses in Germany would help spark the Protestant Reformation.

Friar Luca’s Contributions to Accounting

Pacioli did not actually invent double-entry bookkeeping, nor did ever claim to have done so. He gave credit to one Bendetto Cotrugli for coming up with the system, as he relied on an unpublished by Cotrugli for the portion of his work on accounting in his own Summa. Nevertheless, Pacioli’s summation of the method was incredibly important for the history of accounting, as it was one of the first descriptions of double-entry bookkeeping to be distributed on a large-scale.

Double-entry bookkeeping allows for a company or individual to keep track of credits and debits and thereby keep accounts in balance. Every financial transaction is recorded in two columns, debits in the left and credits in the right, ensuring that the ways in which each transaction affects every aspect of the company’s finances is properly recorded. For example, a company that takes payment for a specific service will record a debit in the cash account and a credit in the revenue account, allowing them to keep track of the real impact of the payment on the company’s bottom line.

Double-entry bookkeeping itself may not sound all that exciting, but without it, most experts would confess that the industrial revolution and growth of free-market capitalism could never have happened. Luca’s description of double-entry bookkeeping ensured that the process would become widely adopted across the Western world and would encourage the rise of Europe and the United States as global powers.

Without the work of an otherwise obscure Franciscan friar in the fifteenth and sixteenth centuries, the economy as we know it today could not exist. Pacioli’s description of double-entry bookkeeping led to the rise of modern accounting, accurate record keeping, and the overall growth of industry and trade. Understanding his role in accounting history is important for understanding Western history and the way in which the economy functions today.

Additional Resources

Accounting History — The Nevada Society of Certified Public Accountants offers this short history of accounting.

Birth of Double-Entry — Indian River State College details the history of double entry bookkeeping and Luca Pacioli’s important contributions to it.

Bookkeeping Dictionary — Knowing the accounting terms in this dictionary is helpful to understanding the history of accounting.

Engines of Ingenuity — The importance of double-entry bookkeeping in the history of civilization is explained on this page.

Cliffs Notes: Double Entry Bookkeeping — A simple explanation of double-entry bookkeeping, the accounting method that Luca Pacioli pioneered, is found here.

Dictionary of Scientific Biography — The Dictionary of Scientific Biography has this entry on the life and influence of Luca Pacioli.

History of Double Entry Bookkeeping — A history of double entry bookkeeping and Luca Pacioli’s contributions to it can be found here.

Little Known but Great: Luca Pacioli — This biography of Luca Pacioli explains why he was a great man even though he remains little known to most people.

Luca Pacioli (1445–1517) — A fuller biography of Luca Pacioli is found on this UK-based webpage.

Luca Pacioli: The Father of Accounting — Texas A&M University makes this short biography of Luca Pacioli available to web surfers.

帕乔利的故乡，意大利 Borgo Sansepolcro 小镇

故乡小镇上的帕乔利纪念馆

帕乔利雕像

帕乔利诞辰500周年纪念邮票

帕乔利讲学图

《数学大全》封面

帕乔利设计的棋

两位大师合作的著作——《神圣比例》（帕乔利撰文，达芬奇绘制插图）

（1445-1517）

意大利数学家，世界会计之父。其《簿记论》被会计学界认为是会计发展史上的里程碑，是簿记理论专门而系统研究的历史起点。

以下两份来自网络的英文资料，可以提供更多对他的了解。

1.个人生平

Luca Pacioli

Born: 1445 in Sansepolcro, Italy

Died: 1517 in Sansepolcro, Italy

Luca Pacioli's father was Bartolomeo Pacioli, but Pacioli does not appear to have been brought up in his parents house. He lived as a child with the Befolci family in Sansepolcro which was the town of his birth. This town is very much in the centre ofItaly about 60 km north of the city of Perugia. As far as Pacioli was concerned, perhaps the most important feature of this small commercial town was the fact that Piero della Francesca had a studio and workshop in there and della Francesca spent quite some time there despite frequent commissions in other towns

Although we know little of Pacioli's early life, the conjecture that he may have received at least a part of his education in the studio of della Francesca in Sansepolcro must at least have a strong chance of being correct. One reason that this seems likely to be true is the extensive knowledge that Pacioli had of the work of Piero della Francesca and Pacioli's writings were very strongly influenced by those of Piero.

Pacioli moved away from Sansepolcro while he was still a young lad. He moved toVenice to enter the service of the wealthy merchant Antonio Rompiasi whose house was in the highly desirable Giudecca district of that city. One has to assume that Pacioli was already well educated in basic mathematics from studies in Sansepolcro and he certainly must have been well educated generally to have been chosen as a tutor to Rompiasi's three sons. However, Pacioli took the opportunity to continue his mathematical studies at a higher level while in Venice, studying mathematics under Domenico Bragadino. During this time Pacioli gained experience both in teaching, from his role as tutor, and also in business from his role helping with Rompiasi's affairs.

It was during his time in Venice that Pacioli wrote his first work, a book on arithmetic which he dedicated to his employer's three sons. This was completed in 1470 probably in the year that Rompiasi died. Pacioli certainly seemed to know all the right people for he left Venice and travelled to Rome where he spent several months living in the house of Leone Battista Alberti who was secretary in the Papal Chancery. As well as being an excellent scholar and mathematician, Alberti was able to provide Pacioli with good religious connections. At this time Pacioli then studied theology and, at some time during the next few years, he became a friar in the Franciscan Order.

In 1477 Pacioli began a life of travelling, spending time at various universities teaching mathematics, particularly arithmetic. He taught at the University of Perugiafrom 1477 to 1480 and while there he wrote a second work on arithmetic designed for the classes that he was teaching. He taught at Zara (now called Zadar or Jadera inCroatia but at that time in the Venetian Empire) and there wrote a third book on arithmetic. None of the three arithmetic texts were published, and only the one written for the students in Perugia has survived. After Zara, Pacioli taught again at the University of Perugia, then at the University of Naples, then at the Universityof Rome. Certainly Pacioli become acquainted with the duke of Urbino at some time during this period. Pope Sixtus IV had made Federico da Montefeltro the duke of Urbino in 1474 and Pacioli seems to have spent some time as a tutor to Federico's son Guidobaldo who was to become the last ruling Montefeltro when his father died in 1482. The court at Urbino was a notable centre of culture and Pacioli must have had close contact with it over a number of years.

In 1489, after two years in Rome, Pacioli returned to his home town of Sansepolcro. Not all went smoothly for Pacioli in his home town, however. He had been granted some privileges by the Pope and there was a degree of jealousy among the men from the religious orders in Sansepolcro. In fact Pacioli was banned from teaching there in 1491 but the jealousy seemed to be mixed with a respect for his learning and scholarship for in 1493 he was invited to preach the Lent sermons.

During this time in Sansepolcro, Pacioli worked on one of his most famous books theSumma de arithmetica, geometria, proportioni et proportionalita which he dedicated to Guidobaldo, the duke of Urbino. Pacioli travelled to Venice in 1494 to publish theSumma. The work gives a summary of the mathematics known at that time although it shows little in the way of original ideas. The work studies arithmetic, algebra, geometry and trigonometry and, despite the lack of originality, was to provide a basis for the major progress in mathematics which took place in Europe shortly after this time. As stated in [1] the Summa was:-

... not addressed to a particular section of the community. An encyclopaedic work(600 pages of close print, in folio) written in Italian, it contains a general treatise on theoretical and practical arithmetic; the elements of algebra; a table of moneys, weights and measures used in the various Italian states; a treatise on double-entry bookkeeping; and a summary of Euclid's geometry. He admitted to having borrowed freely from Euclid, Boethius, Sacrobosco, Fibonacci, ...

The geometrical part of Pacioli's Summa is discussed in detail in [6]. The authors write:-

The geometrical part of L Pacioli's Summa [Venice, 1494] in Italian is one of the earliest printed mathematical books. Pacioli broadly used Euclid's Elements, retelling some parts of it. He referred also to Leonardo of Pisa (Fibonacci).

Another interesting aspect of the Summa was the fact that it studied games of chance. Pacioli studied the problem of points, see [9], although the solution he gave is incorrect.

Ludovico Sforza was the second son of Francesco Sforza, who had made himself duke ofMilan. When Francesco died in 1466, Ludovico's elder brother Galeazzo Sforza became duke of Milan. However, Galeazzo was murdered in 1476 and his seven year old son became duke of Milan. Ludovico, after some political intrigue, became regent to the young man in 1480. With very generous patronage of artists and scholars, Ludovico Sforza set about making his court in Milan the finest in the whole of Europe. In 1482 Leonardo da Vinci entered Ludovico's service as a court painter and engineer. In 1494 Ludovico became the duke of Milan and, around 1496, Pacioli was invited by Ludovico to go to Milan to teach mathematics at Ludovico Sforza's court. This invitation may have been made at the prompting of Leonardo da Vinci who had an enthusiastic interest in mathematics.

At Milan Pacioli and Leonardo quickly became close friends. Mathematics and art were topics which they discussed at length, both gaining greatly from the other. At this time Pacioli began work on the second of his two famous works, Divina proportione and the figures for the text were drawn by Leonardo. Few mathematicians can have had a more talented illustrator for their book! The book which Pacioli worked on during 1497 would eventually form the first of three books which he published in 1509 under the title Divina proportione (see for example [3]). This was the first of the three books which finally made up this treatise, and it studied the 'Divine Proportion' or 'golden ratio' which is the ratio a : b = b : (a + b). It contains the theorems ofEuclid which relate to this ratio, and it also studies regular and semiregular polygons (see in particular [4] for a discussion of Pacioli's work on regular polygons). Clearly the interest of Leonardo in this aesthetically satisfying ratio both from a mathematical and artistic point of view was an important influence on the work. The golden ratio was also of importance in architectural design and this topic was to form the second part of the treatise which Pacioli wrote later. The third book in the treatise was a translation into Italian of one of della Francesca's works.

Louis XII became king of France in 1498 and, being a descendant of the first duke ofMilan, he claimed the duchy. Venice supported Louis against Milan and in 1499 the French armies entered Milan In the following year Ludovico Sforza was captured when he attempted to retake the city. Pacioli and Leonardo fled together in December 1499, three months after the French captured Milan. They stopped first at Mantua, where they were the guests of Marchioness Isabella d'Este, and then in March 1500 they continued to Venice. From Venice they returned to Florence, where Pacioli and Leonardo shared a house.

The University of Pisa had suffered a revolt in 1494 and had moved to Florence. Pacioli was appointed to teach geometry at the University of Pisa in Florence in 1500. He remained in Florence, teaching geometry at the university, until 1506. Leonardo, although spending ten months away working for Cesare Borgia, also remained in Florence until 1506. Pacioli, like Leonardo, had a spell away from Florence when he taught at the University of Bologna during 1501-02. During this time Pacioli worked with Scipione del Ferro and there has been much conjecture as to whether the two discussed the algebraic solution of cubic equations. Certainly Pacioli discussed this topic in the Summa and some time after Pacioli's visit to Bologna, del Ferro solved one of the two cases of this classic problem.

During his time in Florence Pacioli was involved with Church affairs as well as with mathematics. He was elected the superior of his Order in Romagna and then, in 1506, he entered the monastery of Santa Croce in Florence. After leaving Florence, Pacioli went to Venice where he was given the sole rights to publish his works there for the following fifteen years. In 1509 he published the three volume work Divina proportione and also a Latin translation of Euclid's Elements. The first printed edition of Euclid's Elements was the thirteenth century translation by Campanus which had been published in printed form in Venice in 1482. Pacioli's edition was based on that of Campanus but it contained much in the way of annotation by Pacioli himself.

In 1510 Pacioli returned to Perugia to lecture there again. He also lectured again inRome in 1514 but by this time Pacioli was 70 years of age and nearing the end of his active life of scholarship and teaching. He returned to Sansepolcro where he died in 1517 leaving unpublished a major work De Viribus Quantitatis on recreational problems, geometrical problems and proverbs. This work makes frequent reference to Leonardo da Vinci who worked with him on the project, and many of the problems in this treatise are also in Leonardo's notebooks. Again it is a work for which Pacioli claimed no originality, describing it as a compendium.

Despite the lack of originality in Pacioli's work, his contributions to mathematics are important, particularly because of the influence which his book were to have over a long period. In [10] the importance of Pacioli's work is discussed, in particular his computation of approximate values of a square root (using a special case of Newton's method), his incorrect analysis of certain games of chance (similar to those studied by Pascal which gave rise to the theory of probability), his problems involving number theory (similar problems appeared in Bachet's compilation), and his collection of many magic squares.

In 1550 there appeared a biography of Piero della Francesca written by Giorgio Vasari. This biography accused Pacioli of plagiarism and claimed that he stole della Francesca's work on perspective, on arithmetic and on geometry. This is an unfair accusation, for although there is truth that Pacioli relied heavily on the work of others, and certainly on that of della Francesca in particular, he never attempted to claim the work as his own but acknowledged the sources which he used.

Article by: J J O'Connor and E F Robertson

July 1999

MacTutor History of Mathematics

[http://www-history.mcs.st-andrews.ac.uk/Biographies/Pacioli.html]

2.会计学之父：卢卡·帕乔利

The Father of Accounting: Luca Pacioli

The discipline and science of accounting is essential for the world economy to function well. Without an accurate way to keep track of investments, expenditures, depreciation, and more, there would be no way to understand the true financial picture of a company and no way to be confident in its prospects. This would kill commerce, capital investment, and other transactions that keep the economy running.

The history of accounting is more fascinating than many people probably imagine, and several figures have made key contributions to the science. One of the most important people in the history of accounting is Luca Pacioli, a Franciscan friar who lived during the fifteenth and sixteenth centuries, and who is today known as the “Father of Accounting.” This resource will provide a history of accounting and an overview of Pacioli’s contributions to the discipline.

History of Accounting

Most people are not likely to think of accounting when the topic of the “world’s oldest profession” is raised, but many experts believe that accounting fits that description to a tee. From the start, it was necessary for individuals to have a way to keep track of their business dealings even if they were largely self-sufficient, merely growing their own food and taking care of their other needs. As civilization progressed, ancient bookkeeping methods were developed. In the so-called “Fertile Crescent,” ancient bookkeepers would use clay tokens of different shapes and sizes to keep track of wealth. Each token could represent a different commodity — sheep, cattle, grain, and so forth. New technologies and recording methods developed over time, and as money was introduced to facilitate economic exchange, the token system was abandoned in the favor of written accounts.

During the medieval period, Italian merchants began to involve themselves in trade with other cities, first across the Mediterranean Sea and then in other parts of the world. The increasing complexity of these trade relationships required better record keeping, and the system of double-entry bookkeeping was invented. Luca Pacioli, an Italian Franciscan monk wrote Summa de Arithmetica, Geometrica, Proportioni et Proportionalita in 1494, and it was the first full description of this method of accounting.

During the Enlightenment and Industrial Revolution, Britain’s rise as the world’s chief economic power meant that accounting methods would have to advance as well. Men such as Josiah Wedgwood began implementing systems of cost accounting in their companies, and professional accountants began offering their services inLondon. Such methods were carried over to the United States, and large firms such as General Motors adopted these accounting methods as well. Today, standardized accounting practices are in use across the globe, helping companies around the world to stay afloat, attract investment, and keep the engine of the world economy running.

The Life of Luca Pacioli

Luca Pacioli was born in 1445 in Tuscany, Italy, where he received an education in the ways of medieval merchants and commerce. Over time, his interest in mathematics led him to become an expert tutor in the subject, and he wrote a textbook on mathematics to help instruct his students. During the years 1472–1475, Pacioli became a Franciscan friar, but he did not end his tutoring career.

In 1494, Pacioli published his most famous work —Summa de Arithmetica, Geometria, Proportioni et Proportionalita. In addition to providing instruction in standard mathematics, this work would also describe double-entry bookkeeping completely for the very first time, which has earned for him the title “father of accounting.” It was also the first textbook on algebra that was written in the vernacular language of northern Italy. Eventually, Pacioli would travel to Milan, where he became an associate of Leonardo da Vinci. Da Vinci actually learned a lot about mathematics from Pacioli, and the knowledge he gained would help Da Vinci create some of the excellent anatomical drawings for which he is known today.

Much of Pacioli’s work in mathematics was not original or unique, but his writings had a large influence in Italy, allowing for information that was formerly the possession merely of the elite to be disseminated among the general populace. Pacioli died in 1517, the same year that Martin Luther’s 95 Theses in Germany would help spark the Protestant Reformation.

Friar Luca’s Contributions to Accounting

Pacioli did not actually invent double-entry bookkeeping, nor did ever claim to have done so. He gave credit to one Bendetto Cotrugli for coming up with the system, as he relied on an unpublished by Cotrugli for the portion of his work on accounting in his own Summa. Nevertheless, Pacioli’s summation of the method was incredibly important for the history of accounting, as it was one of the first descriptions of double-entry bookkeeping to be distributed on a large-scale.

Double-entry bookkeeping allows for a company or individual to keep track of credits and debits and thereby keep accounts in balance. Every financial transaction is recorded in two columns, debits in the left and credits in the right, ensuring that the ways in which each transaction affects every aspect of the company’s finances is properly recorded. For example, a company that takes payment for a specific service will record a debit in the cash account and a credit in the revenue account, allowing them to keep track of the real impact of the payment on the company’s bottom line.

Double-entry bookkeeping itself may not sound all that exciting, but without it, most experts would confess that the industrial revolution and growth of free-market capitalism could never have happened. Luca’s description of double-entry bookkeeping ensured that the process would become widely adopted across the Western world and would encourage the rise of Europe and the United States as global powers.

Without the work of an otherwise obscure Franciscan friar in the fifteenth and sixteenth centuries, the economy as we know it today could not exist. Pacioli’s description of double-entry bookkeeping led to the rise of modern accounting, accurate record keeping, and the overall growth of industry and trade. Understanding his role in accounting history is important for understanding Western history and the way in which the economy functions today.

Additional Resources

Accounting History — The Nevada Society of Certified Public Accountants offers this short history of accounting.

Birth of Double-Entry — Indian River State College details the history of double entry bookkeeping and Luca Pacioli’s important contributions to it.

Bookkeeping Dictionary — Knowing the accounting terms in this dictionary is helpful to understanding the history of accounting.

Engines of Ingenuity — The importance of double-entry bookkeeping in the history of civilization is explained on this page.

Cliffs Notes: Double Entry Bookkeeping — A simple explanation of double-entry bookkeeping, the accounting method that Luca Pacioli pioneered, is found here.

Dictionary of Scientific Biography — The Dictionary of Scientific Biography has this entry on the life and influence of Luca Pacioli.

History of Double Entry Bookkeeping — A history of double entry bookkeeping and Luca Pacioli’s contributions to it can be found here.

Little Known but Great: Luca Pacioli — This biography of Luca Pacioli explains why he was a great man even though he remains little known to most people.

Luca Pacioli (1445–1517) — A fuller biography of Luca Pacioli is found on this UK-based webpage.

Luca Pacioli: The Father of Accounting — Texas A&M University makes this short biography of Luca Pacioli available to web surfers.

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