Luca Pacioli

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Fra Luca Bartolomeo de Pacioli (sometimes Paciolo) (1445–1514) was an Italian mathematician and Franciscan friar. He was also called Luca di Borgo after his birthplace, Borgo San Sepolcro, Tuscany.

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 by Lodovico Sforza to work in Milan. There he collaborated with Leonardo da Vinci. Pacioli published several works on mathematics, including:

Summa de arithmetica, geometrica, proportioni et proportionalita (Venice 1494), a synthesis of the mathematical knowledge of his time.
Geometry (1509), a Latin translation of Euclid.
De divina proportione (Venice 1509), a work on mathematical and artistic proportion.

Summa de arithmetica... included 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 reported 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 assets (including receivables and inventories), liabilities, capital, income, and expense accounts. He demonstrated year-end closing entries and proposed that a trial balance be used to prove a balanced ledger. Also, his treatise alludes to a wide range of topics from accounting ethics to cost accounting.

Leonardo da Vinci drew the illustrations of the regular solids published in De divina proportione while he lived with and took mathematics lessons from Pacioli. The work discusses the mathematics of the golden ratio and its application in architecture. Da Vinci'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.

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

Pacioli, Luca. De divina proportione, Luca Paganinem de Paganinus de Brescia (Antonio Capella) 1509, Venice
Taylor, Emmet, R. No Royal Road: Luca Pacioli and his Times (1942)

External links

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