Fra Luca Bartolomeo de Pacioli was an Italian mathematician, Franciscan friar, collaborator with Leonardo da Vinci, 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, he was 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 rather than Latin and focused on the knowledge required of merchants. His father was Bartolomeo Pacioli, 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. Thus, he could be referred to as Fra 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, 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, lived with Leonardo da Vinci. In 1499, Pacioli and da Vinci were forced to flee Milan when Louis XII of France seized the city and drove out their patron, their paths appear to have separated around 1506. Pacioli died at about the age of 70 on 19 June 1517, most in Sansepolcro, where it is thought that he had spent much of his final years. Pacioli published several works on mathematics, including: Tractatus mathematicus ad discipulos perusinos, a nearly 600-page textbook dedicated to his students at the University of Perugia where Pacioli taught from 1477 to 1480.
The manuscript was written between December 1477 and 29 April 1478. It contains 16 sections on merchant arithmetic, such as barter, profit, mixing metals, algebra, though 25 pages from the chapter on algebra are missing. A modern transcription was published by Calzoni and Cavazzoni along with a partial translation of the chapter on partitioning problems. Summa de arithmetica, geometria. Proportioni et proportionalita, a textbook for use in the schools of Northern Italy, it was a synthesis of the mathematical knowledge of his time and contained the first printed work on algebra written in the vernacular. It is notable for including one of the first published descriptions of the bookkeeping method that Venetian merchants used during the Italian Renaissance, known as the double-entry accounting system; the system he published included most of the accounting cycle. He described the use of journals and ledgers and warned that a person should not go to sleep at night until the debits equalled the credits.
His ledger had accounts for assets, capital and expenses — the account categories that are reported on an organization's balance sheet and income statement, respectively. He demonstrated year-end closing entries and proposed that a trial balance be used to prove a balanced ledger. Additionally, his treatise touches on a wide range of related topics from accounting ethics to cost accounting, he introduced the Rule of 72, using an approximation of 100*ln 2 more than 100 years before Napier and Briggs. De viribus a treatise on mathematics and magic. Written between 1496 and 1508, it contains the first reference to card tricks as well as guidance on how to juggle, eat fire, make coins dance, it is the first work to note. De viribus quantitatis is divided into three sections: Mathematical problems and tricks, along with a collection of proverbs and verses; the book has been described as the "Foundation of modern magic and numerical puzzles," but it was never published and sat in the archives of the University of Bologna, where it was seen by only a small number of scholars during the Middle Ages.
The book was rediscovered after David Singmaster, a mathematician, came across a reference to it in a 19th-century manuscript. An English translation was published for the first time in 2007. Geometry, a Latin translation of Euclid's Elements. Divina proportione. Two versions of the original manuscript are extant, one in the Biblioteca Ambrosiana in Milan, the other in the Bibliothèque Publique et Universitaire in Geneva; the subject was mathematical and artistic proportion the mathematics of the golden ratio and its application in architecture. Leonardo da Vinci drew the illustrations of the regular solids in Divina proportione while he lived with and took mathematics lessons from Pacioli. Leonardo's drawings are the first illustrations of skeletal solids, which allowed an easy distinction between front and back; the work discusses the use of perspective by painters such as Piero della Francesca, Melozzo da Forlì, Marco Palmezzano. The majority of the second volume of Summa de arithmetica, geometria.
Proportioni et proportionalita was a rewritten v
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