Painting of Luca Pacioli, attributed to Jacopo de' Barbari, 1495 (attribution controversial[1]). Table is filled with geometrical tools: slate, chalk, compass, a dodecahedron model. A rhombicuboctahedron half-filled with water is suspended from the ceiling. Pacioli is demonstrating a theorem by Euclid.

Fra Luca Bartolomeo de Pacioli (sometimes Paciolo) (1445–1514 or 1517) was an Italian mathematician and Franciscan friar, collaborator with Leonardo da Vinci, and seminal contributor to the field now known as accounting. He was also called Luca di Borgo after his birthplace, Borgo Santo Sepolcro, Tuscany. Image File history File links Pacioli. ... Image File history File links Pacioli. ... Jacopo de Barbari, sometimes known or referred to as: deBarbari, de Barberi, de Barbari, Barbaro, Barberino, Barbarigo or Barberigo etc. ... A dodecahedron is any polyhedron with twelve faces, but usually a regular dodecahedron is meant: a Platonic solid composed of twelve regular pentagonal faces, with three meeting at each vertex. ... The rhombicuboctahedron, or small rhombicuboctahedron, is an Archimedean solid with eight triangular and eighteen square faces. ... Euclid(Greek: ), also known as Euclid of Alexandria, was a Greek mathematician who flourished in Alexandria, Egypt, almost certainly during the reign of Ptolemy I (323–283 BC). ... Leonhard Euler is considered by many to be one of the greatest mathematicians of all time A mathematician is the person whose primary area of study and research is the field of mathematics. ... The Order of Friars Minor and other Franciscan movements are disciples of Saint Francis of Assisi. ... The Mona Lisa Leonardo di ser Piero da Vinci (April 15, 1452 – May 2, 1519) was an Italian polymath: scientist, mathematician, engineer, inventor, anatomist, painter, sculptor, architect, musician, and writer. ... It has been suggested that Accounting scholarship be merged into this article or section. ... San Sepolcro, or Borgo Santo Sepolcro, a town and episcopal see of Tuscany, Italy, in the province of Arezzo. ... Tuscany (Italian: ) is one of the 20 Regions of Italy. ...

Life

Luca Pacioli studied in Venice and Rome and became a Franciscan friar in the 1470s. He was a travelling mathematics tutor until 1497, when he accepted an invitation from Lodovico Sforza ("Il Moro") to work in Milan. There he collaborated with, lived with, and taught mathematics to Leonardo da Vinci. In 1499, Pacioli and Leonardo were forced to flee Milan when Louis XII of France seized the city and drove their patron out. After that, Pacioli and Leonardo frequently traveled together. Upon return to his hometown, Pacioli died of old age in 1517. The Order of Friars Minor and other Franciscan movements are disciples of Saint Francis of Assisi. ... Euclid, Greek mathematician, 3rd century BC, as imagined by by Raphael in this detail from The School of Athens. ... 1497 was a common year starting on Friday (see link for calendar) of the Gregorian calendar. ... Ludovico Sforza (Ludovico il Moro, The Moor) (July 27, 1452–May 27, 1508), a member of the Sforza dynasty of Milan, Italy, was the second son of Francesco Sforza, and was famed as patron of Leonardo da Vinci and other artists. ... Milan (Italian: ; Lombard: Milán (listen)) is the main city of northern Italy, located in the plains of Lombardy. ... The Mona Lisa Leonardo di ser Piero da Vinci (April 15, 1452 – May 2, 1519) was an Italian polymath: scientist, mathematician, engineer, inventor, anatomist, painter, sculptor, architect, musician, and writer. ... 1499 was a common year starting on Sunday (see link for calendar) of the Gregorian calendar. ... Louis XII the Father of the People (French: Louis XII le Père du Peuple) (June 27, 1462 – January 1, 1515) was King of France 1498 – January 1, 1515. ...

Work

The first printed illustration of a rhombicuboctahedron, by Leonardo da Vinci, published in De divina proportione.

Woodcut from De divina proportione illustrating the golden ratio as applied to the human face.

Pacioli published several works on mathematics, including: Image File history File links Download high resolution version (1000x1063, 362 KB) Summary The first ever printed version NOT of the icosidodecahedron, by Leonardo da Vinci as apeared in the Divina Proportione by Luca Pacioli 1509, Venise Correction: This is a rhombicuboctahedron not an icosidodecahedron. ... Image File history File links Download high resolution version (1000x1063, 362 KB) Summary The first ever printed version NOT of the icosidodecahedron, by Leonardo da Vinci as apeared in the Divina Proportione by Luca Pacioli 1509, Venise Correction: This is a rhombicuboctahedron not an icosidodecahedron. ... The rhombicuboctahedron, or small rhombicuboctahedron, is an Archimedean solid with eight triangular and eighteen square faces. ... The Mona Lisa Leonardo di ser Piero da Vinci (April 15, 1452 – May 2, 1519) was an Italian polymath: scientist, mathematician, engineer, inventor, anatomist, painter, sculptor, architect, musician, and writer. ... Image File history File links Download high resolution version (1000x1482, 210 KB) File links The following pages link to this file: Golden ratio Luca Pacioli Golden Mean ... Image File history File links Download high resolution version (1000x1482, 210 KB) File links The following pages link to this file: Golden ratio Luca Pacioli Golden Mean ... The golden section is a line segment sectioned into two according to the golden ratio. ... Euclid, Greek mathematician, 3rd century BC, as imagined by by Raphael in this detail from The School of Athens. ...

• Summa de arithmetica, geometrica, proportioni et proportionalita (Venice 1494), a synthesis of the mathematical knowledge of his time, is also notable for including the first published description of the method of keeping accounts that Venetian merchants used during the Italian Renaissance, known as the double-entry accounting system. Although Pacioli codified rather than invented this system, he is widely regarded as the "Father of Accounting". The system he published included most of the accounting cycle as we know it today. 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 (including receivables and inventories), liabilities, capital, income, 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. Also, his treatise touches on a wide range of related topics from accounting ethics to cost accounting.
• De viribus quantitatis (Ms. Università degli Studi di Bologna, 1496–1508), a treatise on mathematics.
• Geometry (1509), a Latin translation of Euclid.
• De divina proportione (written in Milan in 1496–98, published in Venice in 1509). 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, especially the mathematics of the golden ratio and its application in architecture. Leonardo da Vinci drew the illustrations of the regular solids in De divina proportione while he lived with and took mathematics lessons from Pacioli. Leonardo's drawings are probably the first illustrations of skeletonic solids, which allowed an easy distinction between front and back. The work also discusses the use of perspective by painters such as Piero della Francesca, Melozzo da Forlì, and Marco Palmezzano. As a side note, the "M" logo used by the Metropolitan Museum of Art in New York City is taken from De divina proportione.

Venice (Italian: Venezia, Venetian: Venezsia) is the capital of region Veneto, and has a population of 271,663 (census estimate January 1, 2004). ... 1494 was a common year starting on Monday (see link for calendar) of the Gregorian calendar. ... Double-entry accounting system is the standard practice for recording financial transactions. ... In formal bookkeeping and accounting, a balance sheet is a statement of the book value of a business or other organization or person at a particular date, at the end of a period such as a fiscal year, as distinct from an income statement, also known as a profit and... Income statements for companies indicate how Net Revenue (money received from the sale of products and services before expenses are taken out, also known as the top line) is transformed into Net Income (the result after all revenues and expenses have been accounted for, also known as the bottom line... 1509 was a common year starting on Friday (see link for calendar) of the Gregorian calendar. ... 1509 was a common year starting on Friday (see link for calendar) of the Gregorian calendar. ... The golden section is a line segment sectioned into two according to the golden ratio. ... The Parthenon on top of the Acropolis, Athens, Greece Architecture (from Latin, architectura and ultimately from Greek, αρχιτεκτων, a master builder, from αρχι- chief, leader and τεκτων, builder, carpenter) is the art and science of designing buildings and structures. ... The Mona Lisa Leonardo di ser Piero da Vinci (April 15, 1452 – May 2, 1519) was an Italian polymath: scientist, mathematician, engineer, inventor, anatomist, painter, sculptor, architect, musician, and writer. ... The Baptism of Christ, 1442 (National Gallery, London) Piero della Francesca (c. ... Melozzo da Forlì Melozzo da Forlì (Forlì, Italy, c. ... Marco Palmezzano was an Italian painter and architect, born in Forlì, Italy around 1459 and who died in 1539. ... Metropolitan Museum of Art New York Elevation The Metropolitan Museum of Art, often referred to simply as The Met, is one of the worlds largest and most important art museums. ...

Translation of Piero della Francesca's work

The third volume of Pacioli's De divina proportione was an Italian translation of Piero della Francesca's Latin writings on Five Regular Solids, but it did not include an attribution to Piero. He was severely criticized for that by sixteen-century art historian and biographer Giorgio Vasari. On the other hand, R. Emmett Taylor (1889–1956) said that Pacioli may have had nothing to do with that volume of translation, and that it may just have been appended to his work. The Baptism of Christ, 1442 (National Gallery, London) Piero della Francesca (c. ... Giorgio Vasaris selfportrait Wikimedia Commons has media related to: Giorgio Vasari Giorgio Vasari (Arezzo, Tuscany July 3, 1511 - Florence, June 27, 1574) was an Italian painter and architect, mainly known for his famous biographies of Italian artists. ...

Quote

The Ancients, having taken into consideration the rigorous construction of the human body, elaborated all their works, as especially their holy temples, according to these proportions; for they found here the two principal figures without which no project is possible: the perfection of the circle, the principle of all regular bodies, and the equilateral square.

– from De divina proportione

References

• Bambach, Carmen (2003). Leonardo, Left-Handed Draftsman and Writer. New York: Metropolitan Museum of Art. Retrieved on 2006-09-02.
• Pacioli, Luca. De divina proportione (English: On the Divine Proportion), Luca Paganinem de Paganinus de Brescia (Antonio Capella) 1509, Venice
• Taylor, Emmet, R. No Royal Road: Luca Pacioli and his Times (1942)

For the Manfred Mann album, see 2006 (album). ... September 2 is the 245th day of the year (246th in leap years) in the Gregorian calendar. ...

External links

• Luca Pacioli: The Father of Accounting
• Full Biography of Pacioli (St.Andrews)
• The Enigma of Luca Pacioli's Portrait
• Outline of Pacioli's Treatise - PARTICULARIS DE COMPUTIS ET SCRIPTURIS1
• Lucas Pacioli - Catholic Encyclopedia article