The figure of Luca Pacioli is certainly crucial in this century. His biography, by itself, allows us to understand many of the traits of Monaco Borgo Sansepolcro, born into a family of modest economic conditions around 1445.
's father was Bartolomeo Pacioli Luca Pacioli, but it seems that Luke did not live with his family, he was instead Sasepolcro, but with the family Befolci. As for Pacioli, the most important component of this market town was the study of Piero della Francesca, who spent much time at his studio in Sansepolcro, intent to follow the many orders received. The hypothesis that has received part of his education in the study of Piero della Francesca is very likely. One of the main reasons why you believe this is that Pacioli seemed to be very knowledgeable on the subject of the works of Piero della Francesca and Pacioli's works seem to be much influenced by his presence.
At the end of the studies conducted in the schools of abacus, Sansepolcro Pacioli left to move to Venice (1464) to be in the service of the wealthy merchant Antonio Rompiansi who lived nel quartiere malfamato della Giudecca. Bisogna supporre che dovesse certamente avere una buona educazione riguardo alla matematica di base grazie ai suoi studi a Sansepolcro e sicuramente doveva avere una buona educazione letteraria per essere stato assunto come tutore dei tre figli di Rompiansi. Ad ogni modo, durante il suo soggiorno a Venezia colse l'occasione per approfondire ulteriormente i suoi studi matematici avendo come maestro Domenico Bragadino. Durante questo periodo Pacioli prese confidenza sia con l'insegnamento, grazie al suo lavoro di tutore, sia con gli affari, grazie al suo ruolo nell'aiutare Rompiansi con i suoi commerci.
Fu proprio durante questo soggiorno a Venezia che Pacioli scrisse la sua prima opera: un libro di matematica arithmetic which he dedicated to his employer. This was completed in 1470, probably the year he died Rompiansi. After leaving Venice, to Rome as the guest of tarsferì Leone Battista Alberti, who was secretary in the Papal Court. Alberti was able to provide Pacioli many religious contacts. During this time Pacioli became a theologian and a few years later became a Franciscan friar in the order.
In 1447 Pacioli began a life of travel, spending time in universities to teach mathematics, especially arithmetic. I teach at the University of Perugia dall'1477 all'1480 and stayed there while writing his second book on arithmetic for the classes they teach. I teach in Zadar e durante il suo soggiorno scrisse la sua terza opera sull'aritmetica. Nessuno di questi libri fu pubblicato e solamente quello scritto per gli studenti a Perugia ci è arrivato. Dopo Zara, Pacioli insegnò alle università di Perugia, per una seconda volta, a Napoli e a Roma. Sicuramente Pacioli conobbe Federico di Montefeltro duca di Urbino durante questo periodo, a cui venne attribuito questo titolo dal papa Sisto IV nel 1474, e sembra che Pacioli abbia insegnato al figlio Guidobaldo di Montefeltro, l'ultimo regnante della famiglia Montefeltro dopo la morte del padre nel 1482. La corte di Urbino era un famoso centro culturale e Pacioli aveva contatti con gente importante per molti anni. Nel 1489, dopo due anni trascorsi a Roma, Pacioli tornò a Sansepolcro. However not all went for the best in his city. The Pope had allowed certain privileges and religious men of the small town were jealous of him. In fact, Pacioli was forbidden to teach there in 1491, but the jealousy seemed to be attached to respect for his wisdom and numeracy, and in 1493 he was invited to preach sermons in Lent.
During this period in Sansepolcro, Pacioli worked on one of his most famous: the Summa de Arithmetica, geometry, proportions proportional er which he dedicated to Guidobaldo then Duke of Urbino. Pacioli went to Venice in 1494 to publish the Summa. This book provides a summary of the mathematics known at that tempo anche se mostra poco per quanto riguarda idee originali. L'opera studia l'aritmetica, l'algebra, la geometria e la trigonometria e, nonostante mancasse di originalità, avrebbe fornito una base per il più grande progresso nella matematica che avvenne in Europa poco dopo la sua morte. Come detto nella Summa era:
… non indirizzato ad alcuna particolare parte della comunità. Un'opera enciclopedica scritta in italiano, contiene un trattato generale sull'aritmetica teorica e pratica; elementi di algebra; una tavola di monete, pesi, e misure usati nei vari stati italiani; un trattato sull'amministrazione delle entrate e delle uscite; e un riassunto della geometria euclidea. He freely admitted to using the concepts of Euclid, Boethius, Holy Boasco, Fibonacci ...
The geometric part of Pacioli's Summa is discussed in detail in Section 6:
The geometric part of the sum of Pacioli [Venice, 1494] written in Italian is one of the first books printed in mathematics. Pacioli broadly used Euclid's Elements some rewriting. Also referred to Leonardo of Pisa (Fibonacci).
Another interesting aspect of the Summa is the fact that he studied the play of chance. Pacioli studied the problem of points even if the solution he gave is incorrect.
Ludovico Sforza was the second son of Francesco Sforza, who had proclaimed himself Duke of Milan. When Francis died in 1466, the elder brother of Louis, Galeazzo Sforza became Duke of Milan. Later, Galeazzo was murdered in 1476 and her son seven years became Duke of Milan. Ludovico, after some political intrigue, became tutor to the young man in 1480. With a very generous patronage of artists and scholars, Ludovico Sforza set the stage to make his court in Milan the best in Europe. In 1482 Leonardo da Vinci was taken at the service of Ludovico as a painter and engineer of the court. In 1494 Ludwig became Duke of Milan, around 1496, Pacioli was invited by Ludovico to go to Milan to teach mathematics to his court. This call could have been done at the request of Leonardo who had an interest enthusiasm for mathematics .
Ludovico Sforza was the second son of Francesco Sforza, who had proclaimed himself Duke of Milan. When Francis died in 1466, the elder brother of Louis, Galeazzo Sforza became Duke of Milan. Later, Galeazzo was murdered in 1476 and her son seven years became Duke of Milan. Ludovico, after some political intrigue, became tutor to the young man in 1480. With a very generous patronage of artists and scholars, Ludovico Sforza set the stage to make his court in Milan the best in Europe. In 1482 Leonardo da Vinci was taken at the service of Ludovico as a painter and engineer of the court. In 1494 Ludwig became Duke of Milan, around 1496, Pacioli was invited by Ludovico to go to Milan to teach mathematics to his court. This call could have been done at the request of Leonardo who had an interest enthusiasm for mathematics .
At Milan Pacioli and Leonardo became fast friends. Art and mathematics were subjects on which they discussed long and hard, learning a lot each other. In recent years Pacioli began work on the second of his two most famous works: The Divine Proportione illustration which were designed by Leonardo, Pacioli's book on which he worked during 1497 was later to form the first of three books in 1509 that public with the title Divina Proportione. This was the first of three great books that made up the treated and studied the Divine Proportion also called the Golden Section, which is the proportion a: b = b (a + b). It contains the theorems of Euclid that have to do with this proportion, and also studies regular and semiregular polygons. Clearly, Leonardo's interest in this proportion to be aesthetically pleasing from the mathematical point of view that art was an important influence on the work. The golden section was also important in architectural design and this topic would have composed the second part of the Treaty Pacioli wrote later. The third book of the treatise is a translation into Italian of works by Piero della Francesca.
became King Louis XII of France in 1498 and, being a descendant of the first Duke of Milan, claimed the duchy. Louis argued against Milan and Venice in 1499 the French army entered Milan. In the following year Ludovico Sforza was captured in an attempt to regain the city. Leonardo and Pacioli fled together in December of 1499 three months after the capture of Milan. They stopped in Mantua, where they were guests of the Marchesa Isabella d'Este, and in March 1500 went to Venice, then returned to Florence, where the two shared a house.
The University of Pisa had been a revolt in 1494 and moved to Florence. Pacioli was appointed to teach geometry at the University of Pisa to Florence in 1500. He stayed there until 1506. Leonardo, although past ten months out of the city working for Cesare Borgia, he also remained in Florence until 1506.
became King Louis XII of France in 1498 and, being a descendant of the first Duke of Milan, claimed the duchy. Louis argued against Milan and Venice in 1499 the French army entered Milan. In the following year Ludovico Sforza was captured in an attempt to regain the city. Leonardo and Pacioli fled together in December of 1499 three months after the capture of Milan. They stopped in Mantua, where they were guests of the Marchesa Isabella d'Este, and in March 1500 went to Venice, then returned to Florence, where the two shared a house.
The University of Pisa had been a revolt in 1494 and moved to Florence. Pacioli was appointed to teach geometry at the University of Pisa to Florence in 1500. He stayed there until 1506. Leonardo, although past ten months out of the city working for Cesare Borgia, he also remained in Florence until 1506.
During his years in Florence, Pacioli was also involved in the affairs of the church. He was elected superior of his order in 1506 and entered the monastery of Santa Croce in Florence. When he left Florence, Pacioli went to Venice where they were granted rights to the publication of his works for the next fifteen years.
In 1510 Pacioli returned to Perugia to teach. He taught again in Rome in 1514 but had 70 years and was already close to his life of teaching and research. He returned to Sansepolcro where he died in 1517 without having published the great work De Viribus amanuensis geometric problems of leisure and proverbs. This work makes frequent references to Leonardo da Vinci who worked with him on this PROJECT, and many of the problems of this treaty are also in Leonardo's notes. Also in this work there is no originality, and the same Pacioli describes it as a compendium.
Despite the lack of original works of Pacioli his contribution to mathematics is particularly important because the influence of his books would last a long time. Pacioli in the importance of the work is discussed, in particular its approximate calculation of the value of the square root (using Newton's method), the incorrect analysis some games of chance (similar to those studied by Pascal), problems concerning the theory of numbers, and his collection of many square "magic". In 1550 was published a biography of Piero della Francesca, written by Giorgio Vasari. This biography accused Pacioli Pacioli of plagiarism and claimed that he had stolen the work of della Francesca on perspective, on arithmetic and geometry. This is an unjust accusation, because although there is some truth in saying that Pacioli took major inspiration from the work of others and certainly that of della Francesca in particular, he never attempted to proclaim His work of others but always quoted the sources he used.
Luca Pacioli is worthy of consideration in the history of mathematics, precisely because the route of "mathematization" of science and technology promoted in all the works of the friar from Sansepolcro and throughout his long career.
The cultural value of his work, however, should not be reduced to the listing of knowledge gathered ee subsequently used in the following centuries, but we must bear in mind the project for the dissemination of mathematics that innervates the tireless work of a teacher and , exerted by Pacioli in the course of its existence. The centrality of mathematics to human knowledge, real innovation in education and humanities in university curricula of the fifteenth century, depends, according to Pacioli, the necessity of the use of proportion in every field of human knowledge. In this context, the proportions are not only the universal language of science and technology, but also the basis on which the Creator has shaped the world.
In Pacioli's books can be traced the origin of the idea of \u200b\u200bmaking the queen of the sciences of mathematics and of making it the foundation of human knowledge, as will also be represented graphically in a clear and compelling by Nicolo Tartaglia on the front Nova's scent.
The idea of \u200b\u200bconsidering the proportions as the universal language of mathematics knowledge and image of the world that emerges from the Platonic cosmology revisited alal cvostituiranno light of divine proportion, in fact, two elements that often occur in the works of the main protagonists of the revolution sceientifica.
And we can not fail to mention the new consideration of the mechanical arts, techniques and crafts that emerges from the books. The math on the one hand provides technical rules to the other provides the scientific legitimacy of those rules, thanks to the logical proofs based on classical geometry (Euclid).
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