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 Council of Trent was a general Council of the Roman Catholic Church held at Trent between 1545 and 1563. Its origins have historical significance. A comprehensive definition of dogma and strong internal reforms were needed to enable the Roman Church to show an undivided front against the growing strength of the Reformed doctrines. The popes generally had resisted appeals for general councils, e.g. that made by the university of Paris in 1518. In 1530 the Protestant estates demanded a 'council of Christendom' and the emperor, Charles V, was strongly convinced of the necessity of reform. After various delays and postponements between 1537 and 1544, a council was summoned to Trent by pope Paul III, in 1545. Over 200 fathers attended, and the sittings continued, broken partly by political developments, under Popes Julius III and Pius IV, the last of the 25 sessions being held in December 1563.
Among the matters dealt with by the council (the Tridentine decrees), the most important were: the joint value of Scripture and the tradition of the Church as standards of Divine revelation; the interpretative authority of the Church Fathers; original sin; the authority of the Vulgate, 1546; the Divine origin and forms of the sacraments of baptism and confirmation, 1547; the Eucharist and penance, 1551; communion in both kinds and the sacrifice of the Mass, 1562; orders and the regulation of the hierarchy; the sacrament of matrimony; veneration of saints, indulgences, index of prohibited books, 1563. The decrees were confirmed by Pius IV in 1564.
The Council of Trent was of great importance as guiding the main lines of Roman Catholic development in Post-Reformation times. The catechism of the council, summarising its decrees and definitions, was edited by the Dominican scholars, and in 1564 the Roman Congregation of the Council was established to safeguard its decisions and facilitate their practice. Research Council Of Trent
Criminal law is the law relating to crimes. The general theory of the common law is, that all wrongs are divisible into two species: first, civil or private wrongs or torts; secondly, criminal or public wrongs. The former are to be redressed by private suits or remedies instituted by the parties injured. The latter are redressed by the state acting in its sovereign capacity.
The general description of the private wrongs is, that they comprehend those injuries which affect the rights and property of the individual, and terminate there; that of public wrongs or offences being, that they comprehend such acts as injure, not merely individuals, but the community at large, by endangering the peace, the comfort, the good order, the policy, and even the existence of society. In the first, therefore, so far as the law is concerned, the compensation of the individual whose rights have been infringed is held to be a sufficient atonement; but in the second class of offences it is demanded that the offender make satisfaction to the community as acting prejudicially to its welfare. The exact boundaries between these classes are not, however, always easy to be discerned, even in theory; for there are few private wrongs which do not exert an influence beyond the individual whom they directly injure. The divisions, torts and crimes, are thus not necessarily mutually exclusive, cases sometimes occurring in which the person injured obtains damages, while at the same time the criminal is subjected to punishment, not as against the individual, but as against the state. It is, moreover, obvious that legal criminality is not in any strict sense the measure of the morality of actions, though the legal enactment tends to enforce itself as a moral law. In large part it is only an approximate expression of the current sense of justice, this expression being both aided and hindered by the historical and constantly reflexive character of legal method.
The basis of the criminal law of Great Britain is to be found in a series of loose definitions and descriptions, of which many, and those among the more important, date from the 13th century. The irregular superstructure reared upon these consists mainly of parliamentary enactments which originated in the 18th century, but have been twice re-enacted in the 19th century - the first time between 1826 and 1832, and the second time in 1861, with an intermediary attempt at amendment in 1837. The laws as formulated, however, by no means always represent the law as interpreted, the whole system being further complicated by a mass of judicial comments and particular constructions. Thus while there is a statutory division of crimes into treasons, felonies, and misdemeanours, the distinctions between them are so uncertain that it is possible to regard the first head as merely the isolation of a sub-case of felony; while in respect of the second and third classes, the distinction can only be clearly marked by an enumeration of the crimes arbitrarily assigned to each in the common law and judges' decisions.
Even in severity of punishment a misdemeanour may rank as high as a felony. The Criminal Statutes Consolidation Acts - the result of a series of commissions extending over thirty years - accomplished little more in the way of systematization than the introduction of greater exactitude into the definition of certain individual offences and the gradation of penalties. The aim of criminal law as at present constituted, and since the end of the 19th century, is both retributive and preventive - in its former aspect being based upon the primitive passion of retaliation, in the latter primarily upon the fundamental instinct of self-preservation. The prevention of crime may, however, be effected in a threefold manner: by imposing a penalty which shall operate by fear to deter people from committing crimes, or by rendering it physically impossible for a person of known criminal tendency to repeat an offence, or by the reformation of the criminal. With the higher evolution of society the principle of retaliation has fallen into theoretic disrepute, though still a practical legal factor; and the problems of penology are made to turn almost exclusively upon the principle of prevention in these three aspects, and especially on the two last. The discovery in the 19th century that fear of a penalty only operated up to a certain point, beyond which an excessive punishment exercised a brutalizing tendency, led to a large mitigation of penal severity accompanied by a wide desire for the abolition of capital punishment, though this took almost one hundred years to be realised in Great Britain; while, on the other hand, various schemes have been devised for making punishment reformatory. These original changes in criminal law date in a large measure from the publication of Beccaria's Dei Delitti e delle Pene (On Offences and Penalties) in 1764. Research Criminal Law
A definition is a brief and precise description of a thing by its properties; an explanation of the signification of a word or term, or of what a word is understood to express. Logicians distinguish definitions into nominal and real. A nominal definition explains the meaning of a term by some equivalent word or expression supposed to be better known. A real definition explains the nature of the thing. A real definition is again accidental, or a description of the accidents, as causes, properties, effects, etc; or essential, which explains the constituent parts of the essence or nature of the thing. An essential definition is, moreover, metaphysical or logical, defining 'by the genus and difference', as it is called; as, for example, 'a plant is an organized being, destitute of sensation', where the part first of the definition states the genus (organized being), and the latter the difference (destitute of sensation, other organisms/beings possessing sensation); or physical, when it distinguishes the physical parts of the essence; thus, a plant is distinguished by the leaves, stalk, root, etc. A strictly accurate definition can be given of only a few objects. The most simple things are the least capable of definition, from the difficulty of finding terms more simple and intelligible than the one to be defined. Research Definition
An epic is a poetical narrative of heroic achievements. It is largely dramatic in character, but embraces a greater area and admits many incidents, each of which might serve as a dramatic plot.
Some authorities widen the definition of an epic so as to include not only long narrative poems of romantic or supernatural adventure, but also those of a historical, legendary, mock-heroic, or humorous character. An epic is distinguished from a drama in so far as the author frequently speaks in his own person as narrator; and from lyrical poetry by making the predominant feature the narration of action rather than the expression of emotion.
Among the more famous epics of the world's literature may be noted: Homer's Iliad and Odyssey; Virgil's AEneid; the German Nibelungenlied; the Anglo-Saxon poem of Beowulf; the French Song of Roland; Dante's Divina Commedia; Tasso's Gierusalemme Liberata; Ariosto's OrlandoFurioso; Milton's Paradise Lost; Spenser's Fairy Queen; Camoens' Lusiads (Portuguese); and Firdusi's Shah Nameh (Persian). Hesiod's Theogony; the poetic Edda; the Finnish Kalewala; the Indian Mahabharata may be described as collections of epic legends. The historical epic has an excellent representative in Barbour's Bruce; and specimens of the mock-heroic and humorous epic are found in The Battle of the Frogs and Mice; Reynard the Fox; Butler's Hudibras; and Pope's Rape of the Lock. Research Epic
An idea, as used by Plato, is the metaphysical equivalent for the concept or definition, on whose importance in philosophy his master Socrates laid so much stress in ethics. In contrast with the sensible and particular thing or phenomenon, which is apprehended by ordinary perception, the idea is thus supersensible, and belongs to a higher order of reality, an intelligible world, apprehended by thought. In modern philosophy the term was used, at first by the Cartesians, and thence onwards until the time of Kant, in the psychological sense from which the popular use is derived, and which has remained, with some modification, the prevalent sense of the term in English philosophy.
Megilp is a substance added to graining colour to prevent it from flowing together and to help it to retain its sharpness of definition after it has been combed or figured. Skilled grainers often prepare their own meglip to secret recipes. Research Megilp
Terrorism is the systematic use of violence and intimidation to coerce a government or a community into adopting certain specific political ends, such as national independence for a region, or reunification or self-government, or even the adoption of a political system more sympathetic to another country's economic interests. The term terrorism was first coined in England referring to the French revolution, the agents of which were called 'terrorists' by the hostile English press, particularly the Daily Telegraph. Terrorism is so called because of the employment of 'terror' tactics, typically the bombing of property and the murder of civilians which leads to general unrest and pressure from the public onto a government or encourages the public to remove a leader. Within this definition, resistance fighters - civilians who take up arms against another country's uniformed soldiers occupying their country - are not terrorists, but a country which bullies another country with threats of war unless political changes occur within the country, perhaps the adoption of a government more sympathetic to the bullying country's economic interests, clearly is an example of terrorism. Recent examples of terrorism included the Republican terrorists of northern Ireland which sought reunification with the Republic of Ireland through making attacks on the British people in an attempt to coerce the British government into agreeing to their terms. The Islamic fundamentalist attack on the Twin Towers on September the 11th 2001 were not seeking a stated political end, and as such were not a terrorist attack, but were a criminal act of murder and destruction. America's threats to the country of Iraq unless they change their leader - President Saddam Hussein - could be construed as terrorism as the alternative for the Iraqi people is clearly all out war, in which many civilians would be killed and lose their property. A clear use of intimidation for political ends. Research Terrorism
The Vatican Council was a council of the Roman Catholic Church, summoned by Pius IX in 1868. The encyclical convoking it, was issued on June the 29th, 1868, just over 300 years after the dissolution of the Council of Trent and at a time judged by many Roman Catholics to be inopportune Pius IX was determined, however, and the council met at St Peter's, on December the 8th, 1869. There were over 700 prelates present, including 49 cardinals, 121 archbishops, and 479 bishops. Several sessions were devoted to restating theological points before the real subject of the council was reached, but on July the 18th, 1870, the definition was made of papal infallibility. Although little, if any, doubt was expressed as to the doctrine itself, many of the prelates felt grave doubts as to the opportuneness of its definition. The outbreak of the Franco-Prussian War and the capture of Rome by the Italians necessitated an adjournment, on October the 20th, 1870. Research Vatican Counil
A hound is a name generally given to hunting dogs, but restricted by scientific writers to such dogs as hunt by scent, a definition which excludes the greyhound. There are several varieties including the bloodhound, staghound, foxhound, harrier and beagle. Hounds are distinguished not only by their fineness of scent, but by docility and sagacity. Of the rough-haired and smooth-haired varieties the former manifest the greatest affection for people. Research Hound
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