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
Alpha is the first letter of the Greek alphabet. Together with Omega, the last letter of the Greek alphabet, is is sometimes used to signify the beginning and the end, or the first and the last of anything; also as a symbol of the Divine Being. Alpha and Omega were also formerly the symbol of Christianity, and engraved accordingly on the tombs of the ancient Christians. Research Alpha
Alphabet (from Alpha, and Beta, the two first letters of the Greek alphabet), is the series of characters used in writing a language, and intended to represent the sounds of which it consists.
The English alphabet, like most of those of modern Europe, is derived directly from the Latin, the Latin from the ancient Greek, and that from the Phoenician, which again is believed to have had its origin in the Egyptian hieroglyphics, the Hebrew alphabet also having the same origin. The names of the letters in Phoenician and Hebrew must have been almost the same, for the Greek names, which, with the letters, were borrowed from the former, differ little from the Hebrew. By means of the names we may trace the process by which the Egyptian characters were transformed into letters by the Phoenicians. Some Egyptian character would, by its form, recall the idea of a house, for example, in Phoenician or Hebrew beth. This character would subsequently come to be used wherever the sound b occurred. Its form might be afterwards simplified, or even completely modified, but the name would still remain, as beth still continues the Hebrew name for b, and beta the Greek. Our letter m, which in Hebrew was called mim, water, has still a considerable resemblance to the zigzag wavy line which had been chosen to represent water, as in the zodiacal symbol for Aquarius.
The letter o, of which the Hebrew name means eye, no doubt originally intended to represent that organ. While the ancient Greek alphabet gave rise to the ordinary Greek alphabet and the Latin, the Greek alphabet of later times furnished elements for the Coptic, the Gothic, and the old Slavic alphabets. The Latin characters are now employed by a great many nations, such as the Italian, the French, the Spanish, the Portuguese, the English, the Dutch, the German, the Hungarian, the Polish, etc, each nation having introduced such modifications or additions as are necessary to express the sound of the language peculiar to it. The Greek alphabet originally possessed only sixteen letters, though the Phoenician had twenty-two.
The original Latin alphabet, as it is found in the oldest inscriptions, consisted of twenty-one letters; namely, the vowels a, e, i, o, and u (v), and the consonants b, c, d, f, h, k, l, m, n, p, q, r, s, t, x, z. The Anglo-Saxon alphabet had two characters for the digraph th, which were unfortunately not retained in later English; it had also the character ae. It wanted j, v, y (consonant), and z. The German alphabet consists of the same letters as the English, but the sounds of some of them are different.
Anciently certain characters called Runic were made use of by the Teutonic nations, to which some would attribute an origin independent of the Greek and Latin alphabets. While the alphabets of the west of Europe are derived from the Latin, the Russian, which is very complete, is based on the Greek, with some characters borrowed from the Armenian, etc. Among Asiatic alphabets, the Arabian (ultimately of Phoenician origin) has played a part analogous to that of the Latin in Europe, the conquests of Mohammedanism having imposed it on the Persian, the Turkish, the Hindustani, etc. The Sanskrit or Devanagari alphabet is one of the most remarkable alphabets of the world. As now used it has fourteen characters for the vowels and diphthongs, and thirty-three for the consonants, besides two other symbols. Our alphabet is a very imperfect instrument for what it has to perform, being both defective and redundant. An alphabet is not essential to the writing of a language, since ideograms or symbols may be used instead, as in Chinese.
In the English language there are twenty-six letters, A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y and Z, these twenty-six letters occur in use most disproportionately. At the start of the 20th century the proportion of use was as follows, but this will vary as new words, particularly scientific names are added to the English language:
E - 1000 , T - 770, A - 728, I - 704, S - 680, O - 672, N - 670, H - 540, R - 528, D - 392, L - 360, U - 296, C - 280, M - 272, F - 236, W - 190, Y - 184, P - 168, G - 168, B - 158, V - 120, K - 88, J - 55, Q - 50, X - 46, Z - 22
However, as an initial letter, the proportionate use was very different, with the most popular initial letters being:
S - 1194, C - 937, P - 804, A - 574, T - 571, D - 505, B - 463, M - 439, F - 388, I - 377, E- 340, H - 308, L - 298 and R - 291.
The most commonly occurring end letters are R, S, T, and D. Research Alphabet
Antitype is that which is correlative to a type; by theological writers the term is employed to denote the reality of which a type is the prophetic symbol. Research Antitype
In philosophy, an attribute is a quality or property of a substance, as whiteness or hardness. A substance is known to us only as a congeries of attributes.
In the fine arts an attribute is a symbol regularly accompanying and marking out some personage. Thus the caduceus, purse, winged hat, and sandals are attributes of Mercury, the trampled dragon of St George. Research Attribute
Baphomet was the imaginary idol or symbol which the Templars were accused of employing in their mysterious rites, and of which little or nothing is known. Research Baphomet
Baptism (from the Greek baptizo, from bapto, to immerse or dip), is a rite which is generally thought to have been usual with the Jews even before Christ, being administered to proselytes. From this baptism, however, that of St John the Baptist differed, because he baptized Jews also as a symbol of the necessity of perfect purification from sin. Christ himself never baptizedy, but directed his disciples to administer this rite to converts; and baptism, therefore, became a religious ceremony among Christians, taking rank as a sacrament with all sects which acknowledge sacraments.
In the primitive church the person to be baptized was dipped in a river or in a vessel, with the words which Christ had ordered, generally adopting a new name to further express the change. Sprinkling, or, as it was termed, clinic baptism, was used only in the case of the sick who could not leave their beds. The Greek Church and Eastern schismatics retained the custom of immersion; but the Western Church adopted or allowed the mode of baptism by pouring or sprinkling, since continued by most Protestants. This practice can be traced back certainly to the third century, before which its existence is disputed.
Since the Reformation there have been various Protestant sects called Baptists, holding that baptism should be administered only by immersion, and to those who can make a personal profession of faith. The Montanists in Africa baptized even the dead, and in Roman Catholic countries the practice of baptizing church-bells - a custom of tenth-century origin - continues to this day. Being an initiatory rite, baptism is only administered once to the same person. The Roman and Greek Catholics consecrate the water of baptism, but Protestants do not. The act of baptism is accompanied only with the formula that the person is baptized in the name of the Father, Son, and Holy Ghost; but, among most Christians, it is preceded by a confession of faith made by the person to be baptized if an adult, and by his parents or sponsors if he be a child. The Roman Catholic form of baptism is far more elaborate than the Protestant. This church teaches that all persons not baptized are damned, even unbaptized infants are not admitted into heaven; but for those with whom the absence of baptism was the chief fault, even St. Augustine himself believed in a species of mitigated damnation. Protestants hold that though the neglect of the sacrament is a sin, yet the saving new birth may be found without the performance of the rite which symbolizes it. Naming the person baptized forms no essential part of the ceremony, but has become almost universal, probably from the ancient custom of renaming the catechumen. Research Baptism
The British Standards Institution (BSI) is an association founded in 1901 at London, which received a royal charter in 1929 and took its present name in 1931. Its function is to formulate standards for building, engineering, chemical, textile, and electrical products, ensuring that they maintain a specified quality. Products so standardised make use of the Kite mark logo as a symbol of quality. Manufacturers who use the Kite mark do so under licence from the BSI on condition that products are subject to regular inspection. Apart from maintaining quality standards in this way, the BSI attempts to ensure that the design of goods is restricted to a sensible number of patterns and sizes for one purpose, to avoid unnecessary variety. The BSI, which collaborates closely with the International Standards Organization, is also actively concerned in metrology, providing information on units of measurement and issuing glossaries defining technical words. Research British Standards Institution
The Broad Arrow is a symbol used as a royal mark on government stores. It was the cognisance of Viscount Sydney, Earl of Romney, who was the master- general of the Ordnance from 1693 to 1702. Research Broad Arrow
Catacombs ( derived from the Greek kata, meaning down, and kumbos, meaning a hollow or recess) are caves or subterranean places for the burial of the dead, the bodies being placed in graves or recesses hollowed out in the sides of the cave. Caves of this kind were common amongst the Phoenicians, Greeks, Persians, and many oriental nations.
In Sicily and Asia Minor numerous excavations have been discovered containing sepulchres, and the catacombs near Naples are remarkably extensive. Those of Rome, however, are the most important. The catacumbae is said to have been originally applied to the district near Rome which contains the chapel of St Sebastian, in the vaults of which, according to tradition, the body of St Peter was first deposited; but (besides its general application) it is now applied in a special way to all the extensive subterranean burial-places in the neighbourhood of Rome, which extend underneath the town itself as well as the neighbouring country, and are said to contain not less than 6,000,000 tombs. They consist of long narrow galleries usually about 2.4 metres high and 1.5 metres wide, which branch off in all directions, forming a perfect maze of corridors. Different stories of galleries lie one below the other. Vertical shafts run up to the outer air, thus introducing light and air, though in small quantity.
The graves or loculi lie longwise in the galleries. They are closed laterally by a slab, on which there is occasionally a brief inscription or a symbol, such as a dove, an anchor, or a palm-branch, and sometimes both. The earliest that can be dated with any certainty belongs to the year 111 AD. It is now regarded as certain that in times of persecution the early Christians frequently took refuge in the catacombs, in order to celebrate there in secret the ceremonies of their religion; but it is not less certain that the catacombs served also as ordinary places of burial to the early Christians, and were for the most part excavated by the Christians themselves.
In early times rich Christians constructed underground burying-places for themselves and their brethren, which they held as private property under the protection of the law. But in course of time, partly by their coming under the control of the church and partly by accidents of proprietorship, these private burying-grounds were connected with each other, and became the property, not of particular individuals, but of the Christian community. In the 3rd century AD there were already several such common burying-places belonging to the Christian congregations, and their number went on increasing until the time of Constantine, when the catacombs ceased to be used as burying-places.
From the time of Constantine down to the 8th century they were used only as places of devotion and worship. But their use as formal places of worship can only have been occasional, for the limited dimensions even of the largest rooms, and the extreme narrowness of the passages, must have made it impossible for any large number to take efficient part in the services at one time. But though the idea of the catacombs as regular places of worship may be carried too far, there is no doubt, from the episcopal chairs, altars, basins, etc, found within them, and from the subjects of the mosaics and carvings on the walls, that the rites of the church, and particularly the eucharist and the sacrament of baptism, were often celebrated there.
They could never have cerved as dwelling-places for any length of time to the Christians, residence in most of them for more than a short time being very dangerous to the health.
During the siege of Rome by the Lombards in the 8th century the catacombs were in part destroyed, and soon became entirely inaccessible, so that they were forgotten, and only the careful and laborious investigations of archaeologists, amongst whom De Rossi (Roma Sotterranea) and Parker (The Catacombs) may be mentioned, have thrown anything like a complete light on the origin and history of the catacombs.
There are extensive catacombs at Paris, consisting of old quarries from which has been obtained much of the material for the building of the city. In them are accumulated bones removed from cemeteries now built over. Research Catacomb
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