1.
Portrait of Luca Pacioli
–
The Portrait of Luca Pacioli is a painting attributed to the Italian Renaissance artist Jacopo de Barbari, dating to around 1500 and housed in the Capodimonte Museum, Naples, southern Italy. The painting, which portrays the Renaissance mathematician Luca Pacioli, is mentioned for the first time in a 1631 inventory of the Ducal Palace of Urbino and it was later moved to Florence through Vittoria della Rovere-Medici, belonging to both the reigning dynasties of Urbino and Tuscany. The painting reappeared in the 19th century, as a property of the Ottaviano branch of the Medicis and it was subsequently acquired by the Italian state to prevent its being sold to England. The painting has been attributed to Jacopo de Barbari due to the presence of a cartouche with the inscription IACO. BAR. P.1495, with the presence of a fly above it. However, the attribution to the Venetian painter is now regarded as wrong. The painting has been attributed to Leonardo da Vinci, who had collaborated with Pacioli when he moved to Milan in 1496. The painting portrays the friar and mathematician with a filled with geometrical tools, slate, chalk, compass. A rhombicuboctahedron, half-filled with water and characterized by a detailed triple reflection effect of the Ducal Palace of Urbino, is suspended from the ceiling, Pacioli is demonstrating a theorem by Euclid written in an open book. The closed book, with the inscription LI. RI. LUC. BUR. is supposed to be his Summa de arithmetica, Luca Pacioli The enigmas in the Portrait of Luca Pacioli
2.
Jacopo de' Barbari
–
He moved from Venice to Germany in 1500, thus becoming the first Italian Renaissance artist of stature to work in Northern Europe. His few surviving paintings include the first known example of trompe loeil since antiquity and his twenty-nine engravings and three very large woodcuts were also highly influential. Since the earlier part of the range would have him achieve sudden prominence at the age of nearly fifty, there have also been suggestions he was of German extraction, but it now seems clear he was Italian, there are surviving documents of his in Italian addressed to Germans. He signed most of his engravings with a caduceus, the sign of Mercury, and he was probably not of the important Venetian Barbaro family as he was never listed in that familys genealogy. Nothing is known about his first decades, although Alvise Vivarini has been suggested as his master and he left Venice for Germany in 1500, and thereafter is better documented. In Germany he was known as Jacop Walch, probably from Wälsch meaning foreigner. He may have returned to Venice with Philip the Handsome of Burgundy, by March 1510 he was working for Philips successor Archduchess Margaret in Brussels and Mechelen. In January 1511 he fell ill and made a will, and in March the Archduchess gave him a pension for life, on account of his age and weakness. His earliest documented work is his huge and impressive aerial view Map of Venice, for which a privilege was granted to its publisher in 1500. This clearly drew on the work of many surveyors, but was a spectacular feat nonetheless and it was later updated by others to reflect major new building projects in a second state of the print. These may have also produced before 1500, they are clearly strongly influenced by Mantegna. He showed me a man and a woman which he had according to measure. Jacobus did not want to show his principles to me clearly, de Barberi spent a year in Nuremberg, where Dürer lived, in 1500–1, and influences flowed in both directions between him and Dürer for a number of years. None of his engravings are dated, so much of the dating of them depends on resemblances to dated prints by Dürer, five of his engravings were in an album of Hartmann Schedels, which was bound up in December 1504, which gives further evidence as to dating. De Barberi had probably made some engravings before leaving Italy, some of his paintings are dated as,1500,1503,1504,1508. Documents relating to his employment by Maximilian suggest his work was to include illuminating manuscripts and his only generally accepted drawing is a Cleopatra in the British Museum, apparently done as a study for an engraving which has not survived. His style is related to his master, Alvise Vivarini and to Giovanni Bellini. Apart from Dürer, the influence of Mantegnas technique also appears in what are probably the earlier engravings, done around the turn of the century and his engravings are mostly small, showing just a few figures
3.
Sansepolcro
–
Sansepolcro, formerly Borgo Santo Sepolcro, is a town and comune in Tuscany, Italy, in the province of Arezzo. Situated on the reaches of the Tiber river, the town is the birthplace of the painters Piero della Francesca, Raffaellino del Colle, Santi di Tito. It was also the birthplace of the Italian mathematician Luca Pacioli, and of Matteo Cioni, today, the economy is based on agriculture, industrial manufacturing, food processing and pharmaceuticals. It is the home of Buitoni pasta, founded by Giulia Buitoni in 1827, according to tradition, the town was founded around 1000 AD by two pilgrims, Arcanus and Aegidius, who brought a stone from the Church of the Holy Sepulchre with them from the Holy Land. They founded an oratory dedicated to Saint Leonard, on the site of the current Cathedral, the first historical mentions of Sansepolcro are slightly later, referring to the Benedictine Abbey, the Badia, around which the walled commune clustered. During the conflicts between Guelfs and Ghibellines, the factions were headed by prominent local families, including the Pichi, Bercordati, Graziani. The main church is the Cathedral, built in Gothic-Romanesque style in 1012–49, other churches of note are San Francesco and San Lorenzo. The latter church has a Deposition by Rosso Fiorentino, the English writer Aldous Huxley described the Resurrection by Piero della Francesca, which is in the Museo Civico, as the greatest painting in the world. The museum collection includes three works by Piero della Francesca and many other treasures including paintings by Santi di Tito, Raffaellino del Colle. Diocese of Sansepolcro Eduino Francini St. Quentin Teatro Dante Sansepolcro is twinned with, Neuchâtel, Switzerland Neuves-Maisons, France Sinj, Croatia
4.
Republic of Florence
–
The Republic of Florence, also known as the Florentine Republic, was a medieval and early modern state that was centered on the Italian city of Florence in Tuscany. The republic originated in 1115, when the Florentine people rebelled against the Margraviate of Tuscany upon the death of Matilda, the Florentines formed a commune in her successors place. The republic was ruled by a council, known as the signoria, the signoria was chosen by the gonfaloniere, who was elected every two months by Florentine guild members. The republic had a history of coups and counter-coups against various factions. The Medici faction gained governance of the city in 1434, upon Cosimo de Medicis counter-coup against the faction that had sent him into exile the previous year, the Medici kept control of Florence until 1494. Giovanni de Medici re-conquered the republic in 1512, Florence repudiated Medici authority for a second time in 1527, during the War of the League of Cognac. The Medici re-assumed their rule in 1531, after an 11-month siege of the city, the republican government was disestablished in 1532, when Pope Clement VII appointed Alessandro de Medici Duke of the Florentine Republic, making the republic a hereditary monarchy. The city of Florence was established in 59 B. C. by Julius Caesar, the city had been part of the Marquisate of Tuscany before the death of Margravine Matilda in 1115. The city did not submit readily to her successor, Rabodo, the first official mention of the republic was in 1138 when several cities around Tuscany formed a league against Henry X of Bavaria. The country was part of the Holy Roman Empire. Florence prospered in the 12th century, trading extensively with foreign countries and this, in turn, provided a platform for demographic growth of the city. The growth of Florences population mirrored the rate of construction, many churches and this prosperity was shattered when Emperor Frederick I Barbarossa invaded the Italian peninsula in 1185. The Margraves of Tuscany re-acquired Florence and its townlands, the Florentines re-asserted their independence when Holy Roman Emperor Henry VI died in 1197. Florences population continued to grow into the 13th century, reaching 30,000 inhabitants, as has been said, the extra inhabitants supported the citys trade and vice versa. Several new bridges and churches were built, most prominently the cathedral of Santa Maria del Fiore, the buildings from the era serve as Florences best example of Gothic Architecture. Politically, Florence was barely able to maintain peace between factions, the precarious peace that existed at the beginning of the century was destroyed in 1216 when two factions known as the Guelphs and the Ghibellines began to war. The Ghibellines were the rulers of Florence. The Ghibellines, who under Frederick of Antioch had ruled the city since 1244, were deposed in 1250 by the Guelphs, the Guelphs led Florence to prosper further
5.
Summa de arithmetica
–
Summa de arithmetica, geometria, proportioni et proportionalita is a book on mathematics written by Luca Pacioli and first published in 1494. It contains a summary of Renaissance mathematics, including practical arithmetic, basic algebra, basic geometry and accounting. The Summa is the first printed work on algebra in a vernacular language, the Summa de arithmetica as originally printed consists of ten chapters on a series of mathematical topics, collectively covering essentially all of Renaissance mathematics. The first seven chapters form a summary of arithmetic in 222 pages, the eighth chapter explains contemporary algebra in 78 pages. The ninth chapter discusses various topics relevant to business and trade, including barter, bills of exchange, weights and measures and bookkeeping, the tenth and final chapter describes practical geometry in 151 pages. The work was dedicated to Guidobaldo da Montefeltro, Duke of Urbino, paciolis work likewise teaches through examples, but it also develops arguments for the validity of its solutions through reference to general principles, axioms and logical proof. In this way the Summa begins to reintegrate the logical methods of classical Greek geometry into the discipline of algebra. The business chapter also introduces the rule of 72 for predicting a future value. The book was published in Venice in 1494 by Paganino Paganini. While the Summa contained little or no original work by Pacioli. Its thoroughness and clarity made it a point of reference for European mathematicians through the sixteenth century. It includes the first printed example of a set of plus and minus signs that were to standard in Italian Renaissance mathematics, p with a tilde above for plus. In 1994 Italy issued a 750-lira postage stamp honoring the 500th anniversary of the Summas publication, depicting Pacioli surrounded by mathematical, the image on the stamp was inspired by the Portrait of Luca Pacioli, and contains many of the same elements
6.
De divina proportione
–
De divina proportione is a book on mathematics written by Luca Pacioli and illustrated by Leonardo da Vinci, composed around 1498 in Milan and first printed in 1509. Its subject was mathematical proportions and their applications to geometry, visual art through perspective, the clarity of the written material and Leonardos excellent diagrams helped the book to achieve an impact beyond mathematical circles, popularizing contemporary geometric concepts and images. The book consists of three manuscripts, which Pacioli worked on between 1496 and 1498. The first part, Compendio divina proportione, studies the golden ratio from a perspective and explores its applications to various arts. The second part, Trattato dellarchitettura, discusses the ideas of Vitruvius on the application of mathematics to architecture in twenty chapters, the text compares the proportions of the human body to those of artificial structures, with examples from classical Greco-Roman architecture. The third part, Libellus in tres partiales divisus, is mainly an Italian translation of Piero della Francescas Latin writings On Five Regular Solids and mathematical examples. In 1550 Giorgio Vasari wrote a biography of della Francesca, in which he accused Pacioli of plagiarism and claimed that he stole della Francescas work on perspective, on arithmetic, Leonardo drew the illustrations of the regular solids while he lived with and took mathematics lessons from Pacioli. Leonardos drawings are probably the first illustrations of skeletonic solids which allowed an easy distinction between front and back, Pacioli produced three manuscripts of the treatise by different scribes. He gave the first copy with a dedication to the Duke of Milan, Ludovico il Moro, a second copy was donated to Galeazzo da Sanseverino and now rests at the Biblioteca Ambrosiana in Milan. The third, which has gone missing, was given to Pier Soderini, on 1 June 1509 the first printed edition was published in Venice by Paganino Paganini, it has since been reprinted several times. The book was displayed as part of an exhibition in Milan between October 2005 and October 2006 together with the Codex Atlanticus, the M logo used by the Metropolitan Museum of Art in New York is adapted from one in De divina proportione. Full text of original edition Full text of 1509 edition Title page of a reprint in Vienna,1889 A video featuring a 1509 edition on display at Stevens Institute of Technology
7.
Double-entry bookkeeping system
–
Double-entry bookkeeping, in accounting, is a system of bookkeeping so named because every entry to an account requires a corresponding and opposite entry to a different account. For instance, recording earnings of $100 would require making two entries, an entry of $100 to an account named Cash and a credit entry of $100 to an account named Revenue. Deciding which account has to be debited and which account has to be credited is accomplished using the equation which is expressed as. This equation serves as a detection tool, if at any point the sum of debits for all accounts does not equal the corresponding sum of credits for all accounts. It follows that the sum of debits and the sum of the credits must be equal in value, Double-entry bookkeeping is no guarantee that errors have not been made, for example, the wrong ledger account may have been debited or credited, or the entries completely reversed. The oldest record of a complete system is the Messari accounts of the Republic of Genoa in 1340. By the end of the 15th century, the bankers and merchants of Florence, Genoa, Venice, however, the double-entry accounting method was said to be developed independently earlier in Korea during the Goryeo dynasty when Kaesong was a center of trade and industry at that time. The Four-element bookkeeping system was said to be originated in the 11th or 12th century, the earliest extant accounting records that follow the modern double-entry system in Europe come from Amatino Manucci, a Florentine merchant at the end of the 13th century. Manucci was employed by the Farolfi firm and the ledger of 1299-1300 evidences full double-entry bookkeeping. Giovannino Farolfi & Company, a firm of Florentine merchants headquartered in Nîmes, acted as moneylenders to the Archbishop of Arles, some sources suggest that Giovanni di Bicci de Medici introduced this method for the Medici bank in the 14th century. Historical records show that since the second caliphate, AD 634-644, critics of claims that Muslims invented double-entry bookkeeping accept that several features of pre-double-entry accounting were used in the Muslim world before they were used in the West. Pacioli is often called the father of accounting because he was the first to publish a description of the double-entry system, thus enabling others to study. In pre-modern Europe, double-entry bookkeeping had theological and cosmological connotations, in the double-entry accounting system, at least two accounting entries are required to record each financial transaction. These entries may occur in asset, liability, equity, expense, recording of a debit amount to one or more accounts and an equal credit amount to one or more accounts results in total debits being equal to total credits for all accounts in the general ledger. If the accounting entries are recorded without error, the balance of all accounts having Debit balances will be equal to the aggregate balance of all accounts having Credit balances. The rules for formulating accounting entries are known as Golden Rules of Accounting, the accounting entries are recorded in the Books of Accounts. Regardless of which accounts and how many are impacted by a given transaction, there are two different ways to memorize the effects of debits and credits on accounts in the double entry system of bookkeeping. They are the Traditional Approach and the Accounting Equation Approach, irrespective of the approach used, the effect on the books of accounts remains the same, with two aspects in each of the transactions
8.
Italy
–
Italy, officially the Italian Republic, is a unitary parliamentary republic in Europe. Located in the heart of the Mediterranean Sea, Italy shares open land borders with France, Switzerland, Austria, Slovenia, San Marino, Italy covers an area of 301,338 km2 and has a largely temperate seasonal climate and Mediterranean climate. Due to its shape, it is referred to in Italy as lo Stivale. With 61 million inhabitants, it is the fourth most populous EU member state, the Italic tribe known as the Latins formed the Roman Kingdom, which eventually became a republic that conquered and assimilated other nearby civilisations. The legacy of the Roman Empire is widespread and can be observed in the distribution of civilian law, republican governments, Christianity. The Renaissance began in Italy and spread to the rest of Europe, bringing a renewed interest in humanism, science, exploration, Italian culture flourished at this time, producing famous scholars, artists and polymaths such as Leonardo da Vinci, Galileo, Michelangelo and Machiavelli. The weakened sovereigns soon fell victim to conquest by European powers such as France, Spain and Austria. Despite being one of the victors in World War I, Italy entered a period of economic crisis and social turmoil. The subsequent participation in World War II on the Axis side ended in defeat, economic destruction. Today, Italy has the third largest economy in the Eurozone and it has a very high level of human development and is ranked sixth in the world for life expectancy. The country plays a prominent role in regional and global economic, military, cultural and diplomatic affairs, as a reflection of its cultural wealth, Italy is home to 51 World Heritage Sites, the most in the world, and is the fifth most visited country. The assumptions on the etymology of the name Italia are very numerous, according to one of the more common explanations, the term Italia, from Latin, Italia, was borrowed through Greek from the Oscan Víteliú, meaning land of young cattle. The bull was a symbol of the southern Italic tribes and was often depicted goring the Roman wolf as a defiant symbol of free Italy during the Social War. Greek historian Dionysius of Halicarnassus states this account together with the legend that Italy was named after Italus, mentioned also by Aristotle and Thucydides. The name Italia originally applied only to a part of what is now Southern Italy – according to Antiochus of Syracuse, but by his time Oenotria and Italy had become synonymous, and the name also applied to most of Lucania as well. The Greeks gradually came to apply the name Italia to a larger region, excavations throughout Italy revealed a Neanderthal presence dating back to the Palaeolithic period, some 200,000 years ago, modern Humans arrived about 40,000 years ago. Other ancient Italian peoples of undetermined language families but of possible origins include the Rhaetian people and Cammuni. Also the Phoenicians established colonies on the coasts of Sardinia and Sicily, the Roman legacy has deeply influenced the Western civilisation, shaping most of the modern world
9.
Mathematician
–
A mathematician is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems. Mathematics is concerned with numbers, data, quantity, structure, space, models, one of the earliest known mathematicians was Thales of Miletus, he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, the number of known mathematicians grew when Pythagoras of Samos established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was All is number. It was the Pythagoreans who coined the term mathematics, and with whom the study of mathematics for its own sake begins, the first woman mathematician recorded by history was Hypatia of Alexandria. She succeeded her father as Librarian at the Great Library and wrote works on applied mathematics. Because of a dispute, the Christian community in Alexandria punished her, presuming she was involved, by stripping her naked. Science and mathematics in the Islamic world during the Middle Ages followed various models and it was extensive patronage and strong intellectual policies implemented by specific rulers that allowed scientific knowledge to develop in many areas. As these sciences received wider attention from the elite, more scholars were invited and funded to study particular sciences, an example of a translator and mathematician who benefited from this type of support was al-Khawarizmi. A notable feature of many working under Muslim rule in medieval times is that they were often polymaths. Examples include the work on optics, maths and astronomy of Ibn al-Haytham, the Renaissance brought an increased emphasis on mathematics and science to Europe. As time passed, many gravitated towards universities. Moving into the 19th century, the objective of universities all across Europe evolved from teaching the “regurgitation of knowledge” to “encourag productive thinking. ”Thus, seminars, overall, science became the focus of universities in the 19th and 20th centuries. Students could conduct research in seminars or laboratories and began to produce doctoral theses with more scientific content. According to Humboldt, the mission of the University of Berlin was to pursue scientific knowledge. ”Mathematicians usually cover a breadth of topics within mathematics in their undergraduate education, and then proceed to specialize in topics of their own choice at the graduate level. In some universities, a qualifying exam serves to test both the breadth and depth of an understanding of mathematics, the students, who pass, are permitted to work on a doctoral dissertation. Mathematicians involved with solving problems with applications in life are called applied mathematicians. Applied mathematicians are mathematical scientists who, with their knowledge and professional methodology. With professional focus on a variety of problems, theoretical systems
10.
Franciscans
–
The Franciscans are a group of related mendicant religious orders within the Catholic Church, founded in 1209 by Francis of Assisi. These orders include the Order of Friars Minor, the Order of Saint Clare, Francis began preaching around 1207 and traveled to Rome to seek approval from the Pope in 1209. The original Rule of Saint Francis approved by the Pope disallowed ownership of property, the austerity was meant to emulate the life and ministry of Jesus Christ. Franciscans traveled and preached in the streets, while boarding in church properties, Saint Clare, under Franciss guidance, founded the Poor Clares in 1212, which remains a Second Order of the Franciscans. The extreme poverty required of members was relaxed in final revision of the Rule in 1223, the degree of observance required of members remained a major source of conflict within the order, resulting in numerous secessions. The Order of Friars Minor, previously known as the Observant branch, is one of the three Franciscan First Orders within the Catholic Church, the others being the Capuchins and Conventuals. The Order of Friars Minor, in its current form, is the result of an amalgamation of smaller orders completed in 1897 by Pope Leo XIII. The latter two, the Capuchin and Conventual, remain distinct religious institutes within the Catholic Church, observing the Rule of Saint Francis with different emphases, Franciscans are sometimes referred to as minorites or greyfriars because of their habit. In Poland and Lithuania they are known as Bernardines, after Bernardino of Siena, the name of original order, Friars Minor, means lesser brothers, and stems from Francis of Assisis rejection of extravagance. Francis was the son of a cloth merchant, but gave up his wealth to pursue his faith more fully. Francis adopted of the tunic worn by peasants as the religious habit for his order. Those who joined him became the original Order of Friars Minor and they all live according to a body of regulations known as the Rule of St Francis. First Order The First Order or the Order of Friars Minor are commonly called simply the Franciscans and this Order is a mendicant religious order of men, some of whom trace their origin to Francis of Assisi. Their official Latin name is the Ordo Fratrum Minorum, St. Francis thus referred to his followers as Fraticelli, meaning Little Brothers. Franciscan brothers are informally called friars or the Minorites and they all live according to a body of regulations known as the Rule of St Francis. These are The Order of Friars Minor, known as the Observants, most commonly simply called Franciscan friars, official name, the Order of Friars Minor Capuchin or simply Capuchins, official name, Friars Minor Capuchin. The Conventual Franciscans or Minorites, official name, Friars Minor Conventual, Second Order The Second Order, most commonly called Poor Clares in English-speaking countries, consists of religious sisters. The order is called the Order of St. Clare, but in the century, prior to 1263, this order was referred to as The Poor Ladies, The Poor Enclosed Nuns
