Luca Pacioli

Luca Pacioli (* 1445 in Borgo San Sepolcro (now Sansepolcro ), Tuscany, † 1514 or 1517 in Rome) was an Italian mathematician and Franciscan. He is known in economics, because he was the first double-entry bookkeeping to completely describe 1494.

Life

From 1477 he was a professor in Perugia, Rome, Naples, Pisa, Venice, Milan and Florence. Pacioli has probably studied mathematics with Piero della Francesca. After his death in 1492 he had at least two of the three mathematical writings, which he worked in his own works, especially the treatise on the Abacus (probably written before 1460 ). The younger Leonardo da Vinci received from him mathematics teaching, was friends with him and encouraged Pacioli in 1509 for its laid treatise on the golden section, the da Vinci was also illustrated by Leonardo. He argues that the perspectivity make the painting into a mathematical discipline as the music. The well-known representation of the people in da Vinci's square and circle (homo ad quadratum et Circulum ) finds in it an interpretation based on the pursuit of (finite) people for knowledge of the ( infinite) of God. Albrecht Dürer was influenced by the work. The human body, especially the human hand, but also architectural harmony and that of the letters of Roman inscriptions he regarded as the " divine proportion ".

Pacioli's action is based ( completed and printed in 1494, 2nd edition 1523 1487 ), which is the first printed book of a mathematician and probably was used according to much especially in his book Summa de Arithmetica, Geometria, Proportioni et Proportionality. It offers little independent ideas, but brings together the most important mathematical knowledge, on the basis, inter alia, the Liber Abbaci of Leonardo Fibonacci, 1202, 2nd ed 1228, which the solutions had been handed down for equations of first and second order of Al- Khwarizmi, but that was until revisiting by Pacioli hardly known. Pacioli also processes the works of Jordanus Nemorarius, 1236, and John de Sacrobosco, 1256th These skills were taught to the then Italian abacus schools for merchants. The book contains the first complete presentation of the " Venetian " method ( double-entry bookkeeping ), as it was probably used at this time by the Venetians and the Medici. However, he also mentioned the use of the same in the books of the financial officers of Genoa and is, contrary to many opinions, not the inventor of double-entry bookkeeping. This is probably a native of Ragusa dealer Benedetto Cotrugli. The book was, however, translated into many languages ​​and copied by other authors, which helped the double entry to their breakthrough. Pacioli did not find any solution for cubic equations ( x ³ mx = n or x ³ n = mx ) and concludes his work by claiming that they were the state of the science so little generally be solved as the quadrature of the circle; However, there was reason to hope that future solutions would be found. So it was, in fact, stimulated by these observations, first in the solution paths, Scipione del Ferro and Nicolo of Brescia ( " Tartaglia " called ) found. Also discussed Pacioli the division problem.

In 1500, Pacioli wrote, probably together with Leonardo da Vinci, a book about the game of chess, which was often cited in the literature: De ludo scacchorum called Schifanoia. The famous manuscript was considered lost until the book historian Duilio Contin 2006 in the library of the Palazzo Coronini Cronberg Foundation to Gorizia now discovered the only known copy.

In a work De viribus quantitatis next mathematical jokes and tricks and explanations of magic tricks are included. This trick instructions, based mostly on utilization of scientific knowledge are considered the oldest book on magic.

He also published ( 1509 in Venice) an improved version by John Campanus of Novara's translation of Euclid's Elements.

Works

• De divina proportione. Scriptorium, Sassari 1998 ( first edition Venice 1509 ); hg. and introduced by Giuseppina Masotti Biggiogero in the Fontes Ambrosiani, Vol 31, Officina Bodoni, Verona 1956; engl. Divine Proportion, Norwalk, CT 2001; Italian translator's Andrea Masini, in: Arnaldo Bruschi, inter alia, ( Eds. ): Scritti di architettura rinascimentali, Milan 1978, pp. 23-244.
• Summa de arithmetica, geometria, proportioni et proportionalitä, ed. Enrico Giusti, Abrizzi, Venice 1994, ISBN 88-317-6008-4 (reprint of the first edition of Paganini, Venice 1494).
• De viribus quantitatis. First major collection of mathematical puzzles and tricks, 1508th
• De ludo scacchorum detto Schifanoia, manuscript. Facsimile reprint: Aboca Museum di Sansepolcro, 2007