Algebra is a kind of generalized arithmetic, in which numbers or quantities and operations, often also the results of operations, are represented by symbols. Algebra is an invaluable instrument in intricate calculations of all kinds, and enables operations to be performed and results obtained that by arithmetic would be impossible, and its scope is still being extended.
The beginnings of algebraic method are to be found in Diophantus, a Greek of the fourth century of our era, but it was the Arabians that introduced algebra to Europe and from them it received its name. The first Arabian treatise on algebra was published in the reign of the great Kaliph Al Mamun (813-833) by Mohammed Ben Musa. In 1202 Leonardo Fibonacci of Pisa, who had travelled and studied in the East, published a work treating of algebra as then understood in the Arabian school. From this time to the discovery of printing considerable attention was given to algebra, and the work of Ben Musa and another Arabian treatise, called the Rule of Algebra, were translated into Italian.
The first printed work treating on algebra (also on arithmetic, etc) appeared at Venice in 1494, the author being a monk called Luca Pacioli da Bergo. Rapid progress now began to be made, and among the names of those to whom advances are to be attributed are Tarfcaglia and Cardan. About the middle of the sixteenth century the German Stifel introduced the plus, minus and square root symbols, and Recorde the equals sign. Recorde wrote the first English work on algebra. Francois Vieta, a French mathematician (1540-1603), first adopted the method which has led to so great an extension of modern algebra, by being the first who used general symbols for known quantities as well as for unknown. It was he also who first made the application of algebra to geometry.
Albert Girard extended the theory of equations by the supposition of imaginary quantities. The Englishman Harriot, early in the seventeenth century, discovered negative roots, and established the equality between the number of roots and the units in the degree of the equation. He also invented the less than and greater than signs, and Oughthred that of the x multiplication symbol. Descartes, though not the first to apply algebra to geometry, has, by the extent and importance of his applications, commonly acquired the credit of being so. The same discoveries have also been attributed to him as to Harriot, and their respective claims have caused much controversy. He obtained by means of algebra the definition and description of curves. Since his time algebra has been applied so widely in geometry and higher mathematics that we need only mention the names of Fermat, Wallis, Newton, Leibnitz, De Moivre, MacLaurin, Taylor, Euler, D'Alembert, Lagrange, Laplace, Fourier, Poisson, Gauss, Horner, De Morgan, Sylvester, Cayley. Boole, Jevons, and others have applied the algebraic method not only to formal logic but to political economy. Research Algebra More information about Algebra
The Renaissance was that change in the outlook of Europe which took place during the centuries from the fourteenth to the sixteenth. In its broadest sense the Renaissance affected every department of human life. But in its narrower sense it refers to the revival of the learning of ancient Greece, and to the effects of that revival on the arts and literature of modern peoples. The Church in the Middle Ages had taught men to revere authority and to find in her teaching an answer to all the problems of life, whereas the Greeks taught men to inquire and to explore rather than to accept, and to enjoy rather than to suffer. It was this attitude of mind, more than anything else, which shook the medieval world to its foundations. The views of the ancient Greeks, now re-born into the world, were in sharp contrast with the ideals of the Middle Ages. From these ideals many men for a time turned with a feeling of contempt.
The Renaissance was a many-sided movement: it deeply influenced learning and education, art and architecture, science and invention, geography and exploration, and, above all, religion. After the fall of Rome, a knowledge of Greek had rapidly died out in the West and no provision was made for its teaching similar to that made for Latin. In Italy, owing to the closeness of its relations with the East, the number of scholars, monks, and others, who learnt some Greek was greater than elsewhere. It is not, surprising, therefore, that the revival of learning received its main impulse from Italy. From the time of Petrarch and Boccaccio, Italian scholars became more and more devoted to ancient studies, and they began to visit Constantinople, where Greek learning had been preserved. There they hunted out, copied, and eagerly studied the precious manuscripts of the past, and these opened up a new world of thought. Further, from the time that the Turks' crossed from Asia into Europe, some of the Greeks themselves began to travel westwards and to accept well-paid teaching posts in the wealthy Italian cities. And, though the revival began in Italy, the new ideas were rapidly circulated by the new printing presses invented at the time, and every nation in due course played its part in the Renaissance.
The great and wealthy city of Florence was the centre of the Italian Renaissance. Cosimo de Medici, a merchant prince who became ruler of the city, was a patron of the New Learning, and he encouraged Greek scholars to settle in Florence. His grandson, Lorenzo de Medici, known as The Magnificent, loved to gather round him the learned men of the day; he spent 60,000 pounds a year on books; and he caused 200 rare manuscripts to be brought from the East to the Medici library. Rome was second only to Florence as a centre of the New Learning. The Popes themselves became great patrons of learning. Nicholas V founded the Vatican Library. When the son of Lorenzo de Medici became Pope as Leo X, the Renaissance in Rome reached its highest point. Leo made Rome, as he said, ' the capital of the world in literature, as it is in everything else'. He provided a hundred professors for his Greek college in Rome, and he brought his father's library to the Holy City. The library was afterwards restored to Florence by his cousin Clement VII, another member of this remarkable Medici family. The New Learning influenced England from the time of Edward IV, and it made great headway in the reigns of Henry VII and Henry VIII when the scholars known as the Oxford Reformers were flourishing.
The first Englishman to bring Greek manuscripts to England was William Selling. One of his pupils was Thomas Linacre, who went to Florence and shared the instruction given to the young Medici princes; he read in the Vatican Library, and made the acquaintance of Aldo at Venice. Another Oxford teacher who drew his inspiration from Italian sources was William Grocyn, one of the first men to give lectures on Greek literature at his University.
One of Grocyn's pupils was John Colet, who visited Italy in 1496 and returned to lecture on the Gospels in the Greek original at Oxford. He and Sir Thomas More, were friends of Erasmus, a Dutch scholar of international fame. Lady Margaret Beaufort, mother of Henry VII, was herself a patroness of the New Learning. She founded two Cambridge colleges, Christ's and St. John's, and two Lady Margaret Professorships of Divinity, one at Oxford and one at Cambridge. The Revival of Learning was one aspect of the Renaissance; the outburst of artistic energy in the fifteenth and sixteenth centuries was another. The painters of the new period broke away from the conventional art of the Middle Ages and began again to draw from living models. As with the artists, so with the sculptors. Donatello 'went straight with his mighty chisel to original sources - to youth and manhood, and the love of living'. The great figures of that age - Botticelli, Leonardo da Vinci, Michelangelo, Raphael, Titian - still dominate the history of European art. Examples of their works, and of many other Italian artists of the Renaissance, as well as of the Northern artists - Holbein, Durer, and others - are to be seen in the magnificent collection at the National Gallery.
It was natural that men who sought their inspiration from the Greeks should turn with renewed interest to classical architecture. The ruins of ancient Rome provided examples ready to hand; and soon churches planned like classical temples were rising in every city in Italy. St. Peter's, Rome, was designed by Bramante, and the famous dome added by Michelangelo. But great as was the enthusiasm for this architecture Renaissance architecture did not establish itself in England until the end of the reign of Queen Elizabeth I, though Henry VII's tomb at WestminsterAbbey is an example of the Florentine art of the period.
The Renaissance period, filled as it was with a love of experiment, naturally produced a renewed interest in science. With the exception of isolated geniuses like Friar Roger Bacon, there were no medieval scientists worthy of the name. Practically no scientific discoveries had been made for centuries. Modern Science begins its history with the Renaissance and owes a good deal to Leonardo da Vinci. He was the first of a long line of experimenters whose work has continued to the present day. The greatest shock to the medieval notions of the universe was given by Copernicus. For two thousand years mankind with few exceptions had believed that the earth was the centre of the universe, and that the sun revolved round our planet every twenty-four hours. Such had been the teaching of Ptolemy, the Greek scientist. Another Greek, Pythagoras, had questioned it, and advanced the extraordinary notion that the sun, not the earth, was the centre of the universe; but there were few who accepted his theory until Copernicus turned his attention to the 'solar system'. Through slits cut in the walls of his house, Copernicus watched the movements of the planets. Just before he died in 1543 he published a book - 'The Revolutions of the Heavenly Bodies' - giving to the world the results of his observations.
Twenty years later the famous Galileo was born at Pisa, and it was he who perfected the telescope. He lived to popularise the theory of Copernicus, but he was nearly put to death for his pains and was forced by the Court of Inquisition to recant. The Italian Galileo, and the English Newton who discovered the laws of gravity, were the two greatest scientists of the seventeenth century. In the realm of geographical discovery, no age in the world' s history was more momentous than the Age of the Renaissance. Columbus, who discovered America; Vasco De Gama, who found the Cape Route to India; Cabot, Cartier, and Cortez, the discoverers of Newfoundland, Canada, and Mexico; Balboa, who first sailed on the Pacific; Magellan, whose ship was the first to sail round the world - all these and many more make the fifteenth and sixteenth centuries an era without parallel in the annals of discovery.
The new ideas which came surging into the world during the Renaissance acted in many respects as disruptive forces. This was particularly true in the realm of religion. An unquestioning acceptance of authority - i.e. of the teaching of the Catholic Church - was the keynote of the medieval attitude to life, but an eager, inquiring generation began to question this attitude. Men, too, were shocked by the moral decay of the Church and of the Papacy; voices were raised demanding reforms. Some reformers, like Colet and Erasmus, tried to reconcile the new ideas with the Church of Rome and worked to reform it; others, of whom Luther was the greatest, rejected altogether its authority.
The revolution in European history known as the Reformation was an indirect result of the Renaissance - of the New Learning which invited comparison between the present and the past; of the invention of printing which scattered broadcast the new ideas; and again, of the growing idea of the Nation and with it the supremacy of the State. Research Renaissance
Andreas Caesalpinus was an Italian botanist. He was born in 1519 at Arezzo and died in 1603. He became professor of botany at Pisa and was the first to attempt a comprehensive classification of plants upon a natural system. Research Andreas Caesalpinus
Benozzo Gozzoli was an Italian painter. He was born in 1424 at Florence and died some time after 1496. He was a pupil of Fra Angelico, and worked at Florence, Rome, Orvieto, and Pisa. His name is specially identified with the great series of mural paintings in the Campo Santo, at Pisa, consisting of twenty-four subjects from the Old Testament, from the Invention of Wine by Noah to the Visit oi the Queen of Sheba to Solomon. Research Benozzo Gozzoli
Bonaparte was the French form which the great Napoleon was the first to give to the original Italian name Buona-parte, borne by his family in Corsica. As early as the 12th and 13th centuries there were families of this name in Northern Italy, members of which reached some distinction as governors of cities (podesta), envoys, etc. But the connection between the Corsican Bonapartes and these Italian families is not clearly established, though probably the former descended from a Genoese branch of the family, which transplanted itself about the beginning of the 16th century to Corsica, an island then under the jurisdiction of Genoa. From that time the Buona-partes ranked as a distinguished patrician family of Ajaccio.
About the middle of the 18th century there remained three male representatives of this family at Ajaccio, viz. the archdeacon Luciano Bonaparte, his brother Napoleon, and the nephew of both, Carlo, the father of the Emperor Napoleon I. Carlo or Charles Buonaparte, born in 1746, studied law at Pisa University, and on his return to Corsica married Letizia Ramolino. He fought under Paoli for the independence of Corsica, but when further resistance was useless he went over to the side of the French, and was included by Louis XV amongst the 400 Corsican families who were to have rights in France as noble. In 1777 he went to Paris, where he resided for several years, procuring a free admission for his second son Napoleon to the military school of Brienne. He died in 1785 at Montpellier. By his marriage with Letizia Ramolino he left eight children: Giuseppe, or Joseph, king of Spain; Napoleon I, emperor of the French; Lucien, prince of Canino; Maria Anna, afterwards called Elise, princess of Lucca and Piombino, and wife of Prince Bacciocchi, Luigi, or Louis, king of Holland; Garlotta, afterwards named Marie Pauline, princess Borghese, Annunciata, afterwards called Caroline, wife of Murat king of Naples; and Girolamo, or Jerome, king of Westphalia. Research Bonaparte
Doria was one of the most powerful families of Genoa, became distinguished about the beginning of the twelfth century, and shared with three other leading families, the Fieschi, Grimaldi, and Spinola, the early government of the republic. Amongst the older heroes of this family are Oberto Doria, who in 1284 commanded the Genoese fleet which at Meloria annihilated the power of Pisa; Lamba Doria, who in 1298 defeated the Venetian Dandolo at the naval battle of Curzola; Paganino Doria, who in the middle of the fourteenth century distinguished himself by great victories over the Venetians.
But the greatest name of the Dorias is that of Andrea Doria, born at Oneglia in 1466, of a younger branch of the family. After serving some time as a condottiere with the princes of Southern Italy, he was entrusted by the Genoese with the reconstruction of their fleet. Disagreement with the Genoese factions drove him to take service with Francis I of France, in which he highly distinguished himself, and in 1527 he took Genoa in name of the French king. But being displeased with the projects of Francis for reducing Genoa to a place of secondary importance he went over to the service of Charles V in 1529, carrying with him the whole influence and resources of Genoa. He reestablished order in Genoa, reorganized the government, and although refusing the title of doge practically controlled its affairs to the end of his life. As imperial admiral he performed many services for Charles, clearing the seas of Moorish pirates and assisting the emperor in his expeditions to Tunis and Algiers. In 1547 his authority was threatened by the conspiracy of Fieschi, and he narrowly escaped assassination in the tumult. He died in 1560. Research Doria
Eugenius III was a pope. He was born at Pisa and was a disciple of St. Bernard of Olairvaux. He was raised to the popedom in 1145, was obliged to quit Rome in 1146 in consequence of the commotions caused by Arnold of Brescia. He returned by the help of King Roger of Sicily in 1150, and died in 1153. Research Eeugenius III
Galileo Galilee was an Italian physicist. He was born in 1564 at Pisa and died in 1642. The son of a Florentine nobleman, his father intended him to go into medicine and procured for him an excellent education in literature and the arts, and in 1581 he entered the University of Pisa.
At nineteen the swinging of a lamp in Pisacathedral led him to investigate the laws of the oscillation of the pendulum, which he subsequently applied in the measurement of time; and in 1586 the works of Archimedes suggested his invention of the hydrostatic balance. He now devoted his attention exclusively to mathematics and natural science, and in 1589 was made professor of mathematics in the University of Pisa.
In 1592 he was appointed professor of mathematics in Padua, where he continued eighteen years, and his lectures acquired European fame. Here he made the important discovery that the spaces through which a body falls, in equal times, increase as the numbers 1, 3, 5, 7. If he did not invent he improved the thermometer, and made some interesting observations on the magnet. To the telescope, which in Holland remained not only imperfect but useless, he gave a new importance. He noted the irregularity of the moon's surface, and taught his scholars to measure the height of its mountains by their shadow.
A particular nebula he resolved into individual stars, and conjectured that the Milky Way might be resolved in the same manner. His most remarkable discovery was that of Jupiter's satellites in 1610, and he observed, though imperfectly, the ring of Saturn. He also detected the sun's spots, and inferred, from their regular advance from east to west, the rotation of the sun, and the inclination of its axis to the plane of the ecliptic.
In 1610 Cosmo II, grand-duke of Tuscany, appointed him grand-ducal mathematician and philosopher, and with increased leisure he lived sometimes in Florence, and sometimes at the country seat of his friend Salviata, where he gained a decisive victory for the Copernican system by the discovery of the varying phases of Mercury, Venus, and Mars. In 1611 he visited Rome for the first time, where he was honourably received; but on his return to Florence he became more and more involved in controversy, which gradually took a theological turn.
The, monks preached against him, and in 1616 he found himself again obliged to proceed to Rome, where he is doubtfully said to have pledged himself to abstain from promulgating his astronomical views. In 1623 Galileo replied to an attack upon him in his Saggiatore, a masterpiece of eloquence, which drew upon him the fury of the Jesuits. In 1632, with the permission of the pope, he published a dialogue expounding the Copernican system as against the Ptolemaic. A congregation of cardinals, monks, and mathematicians, all sworn enemies of Galileo, examined his work, condemned it as highly dangerous, and summoned him before the tribunal of the Inquisition. The veteran philosopher was compelled to go to Rome early in 1633, and was condemned to renounce upon his knees the truths he had maintained. At the moment when he arose, he is said (but this is doubtful) to have exclaimed, in an undertone, stamping his foot, 'E pur si muove!' (and yet it moves!). Upon this he was sentenced to the dungeons of the Inquisition for an indefinite time, and every week, for three years, was to repeat the seven penitential psalms of David. After a few days' detention his sentence of imprisonment was commuted to banishment to the villa of the Grand-duke of Tuscany at Rome, and then to the archiepiscopal palace at Sienna.
He was afterwards allowed to return to his residence at Arcetri, near Florence, where he employed his last years principally in the study of mechanics and projectiles. The results are found in two important works on the laws of motion, the foundation of the present system of physics and astronomy. At the same time he tried to make use of Jupiter's satellites for the calculation of longitudes; and though he brought nothing to perfection in this branch, he was the first who reflected systematically on such a method of fixing geographical longitudes. He was at this time afflicted with a disease in his eyes, one of which was wholly blind and the other almost useless, when, in 1637, he discovered the libration of the moon.
Domestic troubles and disease embittered the last years of Galileo's life. After his death his remains were ultimately deposited in the church of Sta. Croce, at Florence. Research Galileo
Gherardesca were a family of Tuscan origin which played an important part in the history of the Italian republics of the middle ages. Historically the most prominent member of the family is Ugolino, whose death, and that of his two sons and grandsons, by starvation in the 'Tower of Hunger,' is described in one of the celebrated passages of Dante's Divina Commedia. Ugolino had made himself master of Pisa, and had behaved in the most cruel and arbitrary manner for four years, when, in 1288, he was overthrown by a conspiracy. Research Gherardesca
Giambattista Donati was an Italian astronomer. He was born in 1826 at Pisa and died in 1873. He began his career in the Florence observatory making a study of the spectra of the stars, and in 1858 he discovered a comet now named after him (Donati's Comet). Research Giambattista Donati
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