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symbolic

There are several symbolic acts descriptive of the siege.

18691There are several symbolic acts descriptive of the siege.

18392It will be shown later that all invariants, single or simultaneous, are expressible in terms of symbolic products.

4431It will be shown later that all invariants, single or simultaneous, are expressible in terms of symbolic products.

4330Stroh, from a knowledge of the results, was able to verify and extend the results by the symbolic method.

3524Stroh, from a knowledge of the results, was able to verify and extend the results by the symbolic method.

3424of the symbolic factors of the form are replaced by IA others in which new variables y1, y2 replace the old variables x1, x 2 .

3118We cannot even outline here the process of selection by which the symbolic meanings now stereotyped in the Roman Pontifical were arrived at.

2818The loculi were intact and the epitaphs still in their places, so that " they form a kind of museum, in which the development, the formulae, and the symbolic figures of Christian epigraphy, from its origin to the end of the 3rd or 4th century, can be notified and contemplated, not in artificial specimens as in the Lateran, but in the genuine and living reality of their original condition."

2619Still more original and remarkable, however, was that part of his system, fully stated in his Laws of Thought, which formed a general symbolic method of logical inference.

2521Early in 1886 he struck the public taste with precision in his wild symbolic tale of The Strange Case of Dr Jekyll and Mr Hyde.

2415Early in 1886 he struck the public taste with precision in his wild symbolic tale of The Strange Case of Dr Jekyll and Mr Hyde.

2415To express the function aoa2 - _ which is the discriminant of the binary quadratic aoxi -+-2a1x2x2-+a2x2 = ai =1, 1, in a symbolic form we have 2(aoa 2 -ai) =aoa2 +aGa2 -2 a1 ï¿½ al = a;b4 -}-alb?

2313Such a symbolic product, if its does not vanish identically, denotes an invariant or a covariant, according as factors az, bz, cz,...

2313Symbolic Identities.- For the purpose of manipulating symbolic expressions it is necessary to be in possession of certain simple identities which connect certain symbolic products.

2212and that thence every symbolic product is equal to a rational function of covariants in the form of a fraction whose denominator is a power of f x.

2212Symbolic Identities.- For the purpose of manipulating symbolic expressions it is necessary to be in possession of certain simple identities which connect certain symbolic products.

2212The waratah or native tulip, the magnificent flowering head of which, with the kangaroo, is symbolic of the country, is one of the Proteaceae.

2216It is clear from what has been said above that the liturgical vestments possessed originally no mystic symbolic meaning whatever; it was equally certain that, as their origins were forgotten, they would develop such a symbolic meaning.

2216Given any propositions involving any number of terms, Boole showed how, by the purely symbolic treatment of the premises, to draw any conclusion logically contained in those premises.

2110Two methods of treatment have been carried on in parallel lines, the unsymbolic and the symbolic; both of these originated with Cayley, but he with Sylvester and the English school have in the main confined themselves to the former, whilst Aronhold, Clebsch, Gordan, and the continental schools have principally restricted themselves to the latter.

2013A separation is the symbolic representation of a product of monomial symmetric functions.

2013To find the effect of linear transformation on the symbolic form of quantic we will disuse the coefficients a 111 a 12, a21, a22, and employ A1, Iï¿½1, A2, ï¿½2.

2013The identities are, in particular, of service in reducing symbolic products to standard forms. A symbolical expression may be always so transformed that the power of any determinant factor (ab) is even.

2013That the name also prevailed as that of a god among other Semitic races (or even These sacred arks were carried in procession accompanied by symbolic figures.

1912It is thus possible to study simultaneously all the theories which depend upon operations of the group. Symbolic Representation of Symmetric Functions.-Denote the s 8 s elementar symmetric function a s by al a 2 a3 ...at pleasure; then, Y y si,, si,...

1912with the amice, "Place on my head the helmet of salvation," &c. For the symbolic meanings of the various vestments see the separate articles devoted to them.

189with the amice, "Place on my head the helmet of salvation," &c. For the symbolic meanings of the various vestments see the separate articles devoted to them.

179may be the same or different, it is necessary that every product of umbrae which arises in the expansion of the symbolic product be of degree n, in a l, a 2; in the case of b,, b 2 of degree n 2; in the case of c 1, c 2 of degree n3; and so on.

1413(1 + a i x) (1+ = s i z we have the symbolic identity +02712+0.3x3+...

1420If we restrict ourselves to this set of symbols we can uniquely pass from a product of real coefficients to the symbolic representations of such product, but we cannot, uniquely, from the symbols recover the real form, This is clear because we can write n-1 n-2 2 2n-3 3 a1a2 =a l a 2, a 1 a 2 = a 1 a2 while the same product of umbrae arises from n n-3 3 2n-3 3 aoa 3 = a l .a a 2 = a a 2 .

137-2 _ ab 2an-2bn-2Crz z x () x x x, Each term on the right-hand side may be shown by permutation of a, b, c to be the symbolical representation of the same covariant; they are equivalent symbolic products, and we may accordingly write 2(ac) (bc)ai -1 bi -1 cx 2 =(ab)2a:-2b:-2c:, a relation which shows that the form on the left is the product of the two covariants n (ab) ay 2 by 2 and cZ.

1214-2 _ ab 2an-2bn-2Crz z x () x x x, Each term on the right-hand side may be shown by permutation of a, b, c to be the symbolical representation of the same covariant; they are equivalent symbolic products, and we may accordingly write 2(ac) (bc)ai -1 bi -1 cx 2 =(ab)2a:-2b:-2c:, a relation which shows that the form on the left is the product of the two covariants n (ab) ay 2 by 2 and cZ.

1214where the multiplications on the leftand right-hand sides of the equation are symbolic and unsymbolic respectively, provided that m P4, M P4 are quantities which satisfy the relation exp (M14+Moir+...+Mp4EpnP+...) =1+mic -Fmoif+...+mp,eng+...; where E, n are undetermined algebraic quantities.

1113by symbolic means," the definition, as developed by him, is one which would apply to the philosophy of Kant.

1011Every symbolic product, involving several sets of cogredient variables, can be exhibited as a sum of terms, each of which is a polar multiplied by a product of powers of the determinant factors (xy), (xz), (yz),...

98It has been shown by Gordan that every symbolic product is expressible as a sum of transvectants.

99If we have a symbolic product, which contains the symbol a only in determinant factors such as (ab), we may write x 2, -x 1 for a 1, a 2, and thus obtain a product in which (ab) is replaced by b x, (ac) by c x and so on.

76We have seen that transvection is equivalent to the performance of partial differential operations upon the two forms, but, practically, we may regard the process as merely substituting (ab) k, (OW for azbx, 4x t ' respectively in the symbolic product subjected to transvection.

710In common with other sciences, economics makes use of " abstractions"; but if for some problems we employ symbolic processes of reasoning, we must keep clearly in view the limits of their significance, and neither endow the symbols with attributes they can never possess, nor lose sight of the realities behind them.

69We write;L 22 = a 1 a 2 .b 1 n-2 b2s 3 n - 3 3 n-3 3 n-3 3 a 3 = a 1 a 2 .b 1 b 2 .c 1 c2, and so on whenever we require to represent a product of real coefficients symbolically; we then have a one-to-one correspondence between the products of real coefficients and their symbolic forms. If we have a function of degree s in the coefficients, we may select any s sets of umbrae for use, and having made a selection we may when only one quantic is under consideration at any time permute the sets of umbrae in any manner without altering the real significance of the symbolism.

57(ab)i(ac)j(bc)k..., that the symbolic product (ab)i(ac)j(bc)k..., possesses the invariant property.

57the i t " power of that appertaining to a x and b x multiplied by the j t " power of that appertaining to a x and c x multiplied by &c. If any two of the linear forms, say p x, qx, be supposed identical, any symbolic expression involving the factor (pq) is zero.

57the i t " power of that appertaining to a x and b x multiplied by the j t " power of that appertaining to a x and c x multiplied by &c. If any two of the linear forms, say p x, qx, be supposed identical, any symbolic expression involving the factor (pq) is zero.

57+P=n1, j+k+...+T =n3, It will also be a covariant if the symbolic product be factorizable into portions each of which satisfies these conditions.

46(multiplication symbolic) ?r1! ?2,ï¿½..

424For these only will the symbolic product be replaceable by a linear function of products of real coefficients.

35= t) 1 v ...axbxcx..., and assert that the symbolic product (ab)i(ac)'(bc)k...aibxc2...

351+Eaix+Esiy+ /al a2x 2 +Malt2xy -Z01023,2+ï¿½ï¿½ï¿½ The most general symmetric function to be considered is E 41 041 8424-3033..ï¿½ .conveniently written in the symbolic form (pigi p2g2 p3go...)ï¿½ Observe that the summation is in regard to the expressions obtained by permuting then suffixes I, 2, 3, ...n.

314But here too symbolic ideas must be taken into account.

20A sort of symbolic retaliation was the punishment of the offending member, seen in the cutting off the hand that struck a father or stole a trust; in cutting off the breast of a wet-nurse who substituted a changeling for the child entrusted to her; in the loss of the tongue that denied father or mother (in the Elamite contracts the same penalty was inflicted for perjury); in the loss of the eye that pried into forbidden secrets.

26= exp,udl where exp denotes (by the rule over exp) that the multiplication of operators is symbolic as in Taylor's theorem.

26Symbolic Form.-Restricting consideration, for the present, to binary forms in a single pair of variables, we must introduce the symbolic form of Aronhold, Clebsch and Gordan; they write the form Iln n n-1 n-1 n n n aixi+a2x2) = 44+(1) a l a 2 x 1 x2+...+a2.x2=az wherein al, a2 are umbrae, such that n-1 n-1 n a 1, a 1 a 2, ...a 1 a 2, a2 are symbolical respreentations of the real coefficients ï¿½o, ai,...

27The weight of the function is bipartite and consists of the two numbers Ep and Eq; the symbolic expression of the symmetric function is a partition into biparts (multiparts) of the bipartite (multipartite) number Ep, Eq.

28Notice, therefore, that the symbolic product (ab)i(ac)j(bc)k...

210Some of them imitated the Hebrew prophets in the performance of symbolic acts of denunciation, foretelling or warning, going barefoot, or in sackcloth or undress, and, in a few cases, for brief periods, altogether naked; even women in some cases distinguished themselves by extravagance of conduct.

211She'd thought her role more spiritual or symbolic.

10For the substitution rr xl =A 11 +1 2 12, 52=A21+ï¿½2E2, of modulus A1 ï¿½i = (Alï¿½.2-A2ï¿½1) = (AM), A 2 ï¿½2 the quadratic form a k xi -1-2a 1 x i x 2 +a 2 4 = x =f (x), becomes A41 +2A1E16 =At = OW, where Ao = aoA i +2a1AiA2 +a2Az, _ _ A 1 = ao A lï¿½l +ai(A1/.22+A2ï¿½1) +7,2X2/22, A2 = aoï¿½l +2a1ï¿½1/ï¿½2 +a 2ï¿½2 ï¿½ We pass to the symbolic forms a:= (aixi+a2x2) 2, A 2 = (A 151+ A 26) 2/ by writing for ao, al, a2 the symbols ai, a 1 a 2, a?

10Its symbolic expression, to a numerical factor pres, is (Hbc) (Hbd) (Hcd) (bcd), and it is clearly of degree 6.

10We may write function of such symbolic + (1+ai)(1+alt)...(16e)=1+A2t 2 +A3E 3 +...+A0 °.

10If we expand the symbolic expression by the multinomial theorem, and remember that any symbolic product ai 1 a2 2 a3 3 ...

10Now the symbolic expression of the seminvariant can be expanded by the binomial theorem so as to be exhibited as a sum of products of seminvariants, of lower degrees if alai 0-2a2 +...+crea0 can be broken up into any two portions (alai -1-0-2a2-1-ï¿½ï¿½ï¿½ +asas) +(as+1as +1 +o-8+2as+2+ï¿½ï¿½ï¿½ +ooae), such that Q1 +a2+...

10We Have The Symbolic Expression Of A /?

10Since +xZ=x x we have six types of symbolic factors which may be used to form invariants and covariants, viz.

10The number of different symbols a, b, c,...denotes the the covariants are homogeneous, but not in general isobaric functions, of the coefficients of the original form or forms. Of the above general form of covariant there are important transformations due to the symbolic identities: - (ï¿½b) 2 2)2 = a b - a b; (xï¿½ = as a consequence any even power of a determinant factor may be expressed in terms of the other symbolic factors, and any uneven power may be expressed as the product of its first power and a function of the other symbolic factors.

00To assist us in handling the symbolic products we have not only the identity (ab) cx + (bc) a x + (ca) bx =0, but also (ab) x x+ (b x) a + (ax) b x = 0, (ab)a+(bc)a s +(ca)a b = 0, and many others which may be derived from these in the manner which will be familiar to students of the works of Aronhold, Clebsch and Gordan.

00There is no linear covariant, since it is impossible to form a symbolic product which will contain x once and at the same time appertain to a quadratic. (v.) is the Jacobian; geometrically it denotes the bisectors of the angles between the lines ax, or, as we may say, the common harmonic conjugates of the lines and the lines x x .

00The development of symbolic algebra by the use of general symbols to denote numbers is due to Franciscus Vieta (Francois Viete, 1540-1603).

00This study was inaugurated by George Peacock, who was one of the earliest mathematicians to recognize the symbolic character of the fundamental principles of algebra.

00The geometrical interpretation of imaginary quantities had a far-reaching influence on the development of symbolic algebras.

00But the whole style of the work, with its use of conventional apocalyptic forms, favours the more symbolic view.

00Shadows and reflections were ignored, and perspective, approximately correct for landscape distances, was isometrical for near objects, while the introduction of a symbolic sun or moon lent the sole distinction between a day and a night scene.

00And he admits (§ 63) that if we were compelled to choose between translating mental phenomena into physical and its converse, the latter would be preferable, seeing that the ideas of matter and motion, merely symbolic of unknowable realities, are complex states of consciousness built out of units of feeling.

00The boundarystones between properties (termini) were also the objects of cult at the annual festival of the Terminalia, and the "god Terminus," the symbolic boundary-stone, shares with Jupiter the great temple on the Capitol.

00His cult survived the metamorphosis of the ancient Vedic nature-worship into modern Hinduism, and there still are in India fire-priests (agnihotri) whose duty is to superintend his worship. The sacred fire-drill for procuring the temple-fire by friction - symbolic of Agni's daily miraculous birth - is still used.

00According to tradition in Hesse, he awaits resurrection, probably symbolic of the triumph of the sun over winter, within the Gudensberg (Hill of Odin).

00SACRAMENT, in religion, a property or rite defined in the Anglican catechism as " an outward and visible sign of an inward and spiritual grace"; if the grace be allowed to be inherent in the external symbolic thing or act as well as in the faithful who receive or do it, this definition holds good not only for the Latin Church, but for more primitive religions as well.

00Thus Berengar of Tours (999-1088) upheld the symbolic character of the Eucharist and the superiority of the Bible over tradition.

00While the scriptural statements imply a belief in the existence of spiritual beings intermediate between God, and men, it is probable that many of the details may be regarded merely as symbolic imagery.

00in the symbolic story, the moment for working the miracle; in the symbolized reality, the hour of His death, condition for the spirit's advent; and " what is there between Me and thee ?

00The kerubim might perhaps be symbolic representatives of the god Rakab'el or Rekub'el, probably equivalent to Hadad, whose sacred animal was the bull.

00That the figures symbolic of Rakab or Hadad were compounded or amalgamated by the Israelites with those symbolic of Nergal (the lion-god) and Ninib (the eagle-god), is not surprising.

00The signs or symbolic acts of the prophet probably originated in the actions of sympathetic magic. Thus in the vivid scene of r Kings xxii.

00magical act passes into sign or symbol, not however without the accompanying conception that underlies it still persisting that a mysterious effectuating potency belongs to the symbolic act.

00Although real historical personages - Gustavus Vasa, Olaus Petri the reformer and Gerdt the Anabaptist - figure as leading characters, they are made symbolic of the present-day forces of progress and reaction.

00For the great festival of Tezcatlipoca, the handsomest and noblest of the captives of the year had been chosen as the incarnate representative of the god, and paraded the streets for public adoration dressed in an embroidered mantle with feathers and garlands on his head and a retinue like a king; for the last month they married him to four girls representing four goddesses; on the last day wives and pages escorted him to the little temple of Tlacochcalco, where he mounted the stairs, breaking an earthenware flute against each step; this was a symbolic farewell to the joys of the world, for as he reached the top he was seized by the priests, his heart torn out and held up to the sun, his head spitted on the tzompantli, and his body eaten as sacred food, the people drawing from his fate the moral lesson that riches and pleasure may turn into poverty and sorrow.

00That the Lord's Supper was from the first a meal symbolic of Christian unity and commemorative of Christ's death is questioned by none.

00the Franks, we find the payment of a very small sum, which is often regarded as symbolic and as a relic of real purchase.

00In the West trine immersion was generally held to be symbolic of the triune name of "Father, Son and Holy Ghost."

00The story of the Creation in the book of Genesis is shown, from the point of view of chronology, to be a poetic or symbolic account by the discovery of civilizations of much greater antiguity.

00It has been suggested that this use is due to the custom of the symbolic use of flowers.

00The Wandering Jew has been regarded as a symbolic figure representing the wanderings and sufferings of his race.

00Plutarch in his treatise on Isis and Osiris well exemplifies this standpoint: for him every god and every rite is symbolic of some natural or moral truth.

00By the result of a symbolic discharge of arrows he informed the king of his coming success against Syria, and immediately thereafter he died.

00It is the prose epic of feudalism, and its romantic spirit, its high ideals, its fantastic gallantry, its ingenious adventures, its mechanism of symbolic wonders, and its flowing style have entranced readers of such various types as Francis I.

00Though the progress of his psychological thought compelled him to abandon the positive theology of the Moravians, he always retained an appreciation of its spiritual or symbolic significance.

00In both the patient was withdrawn from the multitude and the cure was wrought with the accompaniment of symbolic actions.

00The Baptist has pointed Him out to them in striking language, which recalls at once the symbolic ritual of the law and the spiritual lessons of the prophets: " Behold, the Lamb of God, which taketh away the sin of the world."

00When the idea, itself indefinite, gets no further than a struggle and endeavour for its appropriate expression, we have the symbolic, which is the Oriental, form of art, which seeks to compensate its imperfect expression by colossal and enigmatic structures.

00First comes architecture - in the main, symbolic art; then sculpture, the classical art par excellence; they are found, however, in all three forms. Painting and music are the specially romantic arts.

00Its commanding position gained it in 1634, by royal decree, the title of "Llave del Nuevo Mundo y Antemural de las Indias Occidentales" (Key of the New World and Bulwark of the West Indies), in reference to which it bears on its coat of arms a symbolic key and representations of the Morro, Punta and Fuerza.

00This is some symbolic object, stick or what not, which passes between the parties to a contract, the obligations under which, if not fulfilled by the contracting parties during their lives, become hereditary.

00Venn, in his Symbolic Logic, proposes the four forms, xy = o, xy = o, xy>o, xy> o (where y means " not-y "), but only as alternative to the ordinary forms. Bradley says that " ` S-P is real' attributes S-P, directly or indirectly, to the ultimate reality," and agrees with Brentano that " ` is ' never stands for anything but ` exists ' "; while Bosanquet, who follows Bradley, goes so far as to define a categorical judgment as " that which affirms the existence of its subject, or, in other words, asserts a fact."

00In quantitative judgments we may think x = y, or, as Boolero oses x = v ° p p y = - ° y, or, as Jevons proposes, x = xy, or, as Venn proposes, x which is not y=o; and equational symbolic logic is useful whenever we think in this quantitative way.

00The symbolic logic, which confuses " is " with " is equal to," having introduced a particular kind of predicate into the copula, falls into the mistake of reducing all predication to the one category of the quantitative; whereas it is more often in the substantial, e.g.

00Venn, Symbolic Logic (2nd ed., London, 1894); The Principles of Empirical or Inductive Logic (London, 1889); J.

00Hamilton's significance for the history of logic lies in the stimulus that he gave to the development of symbolic logic in England by his new analytic based upon his discovery or adoption of the principle of the quantification of the predicate.

00" It is not an algebra," said Kant 3 of his technical logic, and the kind of support lent recently to symbolic logic by the Gegenstandstheorie identified with the name of Alexius Meinong (b.

00The future of symbolic logic as coherent with the rest of logic, in the sense which the word has borne throughout its history seems to be bound up with the question of the nature of the analysis that lies behind the symbolism, and of the way in which this is justified in the setting of a doctrine of validity.

00Venn's Symbolic Logic (1881) gave a careful history and bibliography of that development.

00Wright, Biblical Studies (1886) argues ably for the symbolic theory.

00LIGHTS The ceremonial use of lights in the Christian Church, with which this article is mainly concerned, probably has a double origin: in a very natural symbolism, and in the adaptation of certain and Jewish rites and customs of which the paganJ symbolic meaning was Christianized.

00All this might very early, without the incentive of Jewish and pagan example, have affected the symbolic ritual of the primitive Church.

00in 180 B.C. and decorated with a combat of gods and giants, symbolic of the struggle between the Pergamene Greeks and the Gaulish barbarians.

00This gave them a symbolic or representative character as a closed body (cf.

00Cybele was usually worshipped in connexion with Attis, as Aphrodite with Adonis, the two being a duality interpreted by the philosophers as symbolic of Mother Earth and her vegetation.

00So carefully is this record of the visions arranged that the first two chapters of the second part of the book (vii.-viii.) were no doubt purposely made to appear in a symbolic form, in order that in the last two revelations (xi.-xii.), which were couched in such direct language as to be intelligible even to the modern student of history, the author might obtain the effect of a climax.

00Leo of Rome, Athanasius, Gregory of Nyssa, Theophylactus, Cyril of Jerusalem and others, trine immersion was regarded as being symbolic of the three days' entombment of Christ; and in the Armenian baptismal rubric this interpretation is enjoined, as also in an epistle of Macarius of Jerusalem addressed to the Armenians (c. 330).

00The work on [[Trigonometry]] and Double Algebra (1849) contains in the latter part a most luminous and philosophical view of existing and possible systems of symbolic calculus.

00In 1860 De Morgan endeavoured to render their contents better known by publishing a [[Syllabus]] of a Proposed System of Logic, from which may be obtained a good idea of his symbolic system, but the more readable and interesting discussions contained in the memoirs are of necessity omitted.

00These steps are symbolic of the rising, culminating and setting of the sun, or alternatively the course of the solar deity through the three divisions of the universe.

00The very various periods named make it probable that the periodical return of the phoenix belongs only to vulgar legend, materializing what the priests knew to be symbolic. Of the birds of the heron family the gorgeous colours and plumed head spoken of by Pliny and others would be least inappropriate to the purple heron (Ardea purpurea), with which, or with the allied Ardea cinerea, it has been identified by Lepsius and Peters (Alteste Texte des Todtenbuchs, 1867, p. 51).

00Its function could determine the meaning of the symbols, since the most ancient Immortal writing is based on a complex system of symbolic context.

00She'd thought her role more spiritual or symbolic.

00After a hiatus of fifty years, France had finally allowed the US to build a small, largely symbolic, NATO base.

00Morris rejects any symbolic meaning to the number of fish caught, believing there is no actual evidence to support the view.

00allegorical paintings that aimed to record the symbolic history of mankind.

00A young girl takes a trip through a metaphorical zoo gathering animals symbolic of her negative thoughts.

00It contains a film of a complete Symbolic Modeling session with on-screen annotation.

00Typical assembler directives tell the assembler where to locate a program and data in memory and equate symbolic names to actual values.

00Apart from Forth, the system ROM has a symbolic assembler enabling you to write machine code directly on the board.

00attach enormous symbolic importance to the act of voting.

00Others sported red berets, symbolic of the governing Fifth Republic Movement party.

00The symbolic transformation from old man to young man represents the continuity of proletarian struggle in the post-modern age blah blah blah!

00It had no symbolic significance, just bothersome disjointed sequences that lacked a relevant theme.

00A great catafalque had been built, housing a symbolic coffin.

00cauldronge caldron used to make pilaf had a special symbolic significance for the Janissaries, and was the focal point of each division.

00My tendency to get lost when trying to follow a mass of symbolic computations has long haunted me.

00The sun conjunct Regulus is therefore symbolic of Jesus in the Manger.

00Such slabs are often decorated with carved motifs including crosses and various symbolic or purely decorative elements.

00This hugely symbolic event was arguably a ritual act of public desecration which transgressed the most sacred site of communist public space.

00The shield incorporates elements symbolic of the three original wards constituted in 1879.

00It's the symbolic representation of a myth, a graphic depiction of something utterly abstract yet elemental.

00Five score years ago, a great American, in whose symbolic shadow we stand signed the Emancipation Proclamation.

00The white ermine is meant to be symbolic of chastity.

00On systems that don't support symbolic links, produces a fatal error at run time.

00etymology detail is called for here, which may include the etymologies of key words or elaboration of their special contextual or symbolic meaning.

00Also present in the show are some re-worked forms that he created in the 1980's when he first became involved with symbolic figuration.

00flesh and bloodloded planet gods be symbolic for the flesh-and-blood gods as well as the other way round?

00symbolic gestures, important in their time, no longer build trust.

00incorporates elements symbolic of the three original wards constituted in 1879.

00man-to-man combat between challengers for the favors of a woman usually ended in the symbolic death of an opponent.

00It relies heavily on the use of symbolic representations and deduction to apply quantum mechanics to a variety of situations.

00Explore the original story using mime, music, symbolic movement.

00Well, that's to totally misread this book: this number along with many of the numbers in Revelation is symbolic.

00Making people miss lectures has some symbolic value, making them contract mumps has none whatsoever.

00naive assumption of symbolic equivalence.

00This is yet another symbolic feature, the triad asking the percipient to join them to form a quaternity.

00The Sun Stone is a symbolic phallus on the physical level.

00This symbolic role functioned relative to notions of social organization, delineating or invoking the fundamental limits of social praxis.

00And avoid the potential infinite regress of symbolic meaning by being fully grounded in the real world.

00Reverse: symbolic representation of technological development from the Iron Age to the modern computer age.

00Abraham is a symbolic " returner " from " exile ", given a promise of land by the Persian shah.

00The ribbons were personally designed by King George VI and all have symbolic significance.

00It will focus in particular on functionalism, Marxism, symbolic interactionism, figurational sociology and feminism.

00The slippery finger may be less impressive than the metal speculum, but it is no less significant as an instrument of symbolic domination.

00President Armando Guebuza administered the first doses of the vaccine in the Maputo suburb of Mavalane as the symbolic launch of the campaign.

00symbolic of something, but it's not quite clear what.

00symbolic of the world, a world which is no friend of Grace.

00symbolic of peace, were laid in commemorative solidarity.

00symbolic in nature.

00symbolic gestures, important in their time, no longer build trust.

00symbolic Interactionism is concerned with social situations and the way people make sense of those situations.

00symbolic significance.

00symbolic computations has long haunted me.

00symbolic representations do not take kindly to Meta Model questions.

00symbolic meaning to the number of fish caught, believing there is no actual evidence to support the view.

00He was terrific if purely symbolic best country album.

00This hugely symbolic event was arguably a ritual act of public desecration which transgressed the most sacred site of communist public space.

00If it is only a symbol then it doesn't literally purify but is merely symbolic of purification.

00In practice, the legislation turned out to be largely symbolic.

00In a deeply symbolic action he chose twelve disciples one for each of the ancient tribes.

00As it was the International Year of the Mountains, to visit the greatest of them all seemed highly symbolic.

00A customary Champions of Europe, becoming increasingly symbolic all the time, led onto a better performance in the second half.

00As philosophers and physiologists have established, even physical reality can be considered as symbolic.

00The interrogation would have been a moment of truth in the case, a symbolic breakthrough after decades in which Pinochet was considered untouchable.

00In other words, the symbolic value of linguistic utterances is more important than the content of what one says.

00wanee zodiac worked as a symbolic calendar divided into twelve parts, like the of 12 moons waxing and waning in a year.

00Ezekiel's style is generally impetuous and vigorous, somewhat smoother in the consolatory discourses (xxxiv., xxxvi., xxxvii.); he produces a great effect by the cumulation of details, and is a master of invective; he is fond of symbolic pictures, proverbs and allegories; his " visions " are elaborate literary productions, his prophecies show less spontaneity than those of any preceding prophet (he receives his revelations in the form of a book, ii.

00The opening " vision " (i.), an elaborate symbolic picture, is of the nature of a general preface, and was composed probably late in the prophet's life.

00There follow a symbolic prediction of the exile (xii.) and a denunciation of non-moral prophets and prophetesses (xiii.) - though Yahweh deceive a prophet, yet he and those who consult him will be punished; and so corrupt is the nation that the presence of a few eminently good men will not save it (xiv.).

00The waratah or native tulip, the magnificent flowering head of which, with the kangaroo, is symbolic of the country, is one of the Proteaceae.

00In the 16th and 17th chapters of the Differential Equations we find, for instance, a lucid account of the general symbolic method, the bold and skilful employment of which led to Boole's chief discoveries, and of a general method in analysis, originally described in his famous memoir printed in the Philosophical Transactions for 1844.

00With the exception of Augustus de Morgan, Boole was probably the first English mathematician since the time of John Wallis who had also written upon logic. His novel views of logical method were due to the same profound confidence in symbolic reasoning to which he had successfully trusted in mathematical investigation.

00Still more original and remarkable, however, was that part of his system, fully stated in his Laws of Thought, which formed a general symbolic method of logical inference.

00Given any propositions involving any number of terms, Boole showed how, by the purely symbolic treatment of the premises, to draw any conclusion logically contained in those premises.

00A sort of symbolic retaliation was the punishment of the offending member, seen in the cutting off the hand that struck a father or stole a trust; in cutting off the breast of a wet-nurse who substituted a changeling for the child entrusted to her; in the loss of the tongue that denied father or mother (in the Elamite contracts the same penalty was inflicted for perjury); in the loss of the eye that pried into forbidden secrets.

00Whilst the oblations of Soma-juice, made thrice on each offering-day, amidst chants and recitations, constitute the central rites of those services, their ritual also requires numerous single oblations of the ishti kind, including at least three animal offerings, and in some cases the immolation of many hecatombs of victims. Moreover, a necessary preliminary to every Somasacrifice is the construction, in five layers, of a special fire-altar of large dimensions, consisting of thousands of bricks, formed and baked on the spot, to each, or each group, of which a: special symbolic meaning is attached.

00Among the symbolic conceits in which the authors of the Brahmanas so freely indulge, there is one overshadowing all others - if indeed they do not all more or less enter into it - which may be considered as the sum and substance of these speculations, and the esoteric doctrine of the sacrifice, involved by the Brahmanical ritualists.

00History Of Geographical Theory The earliest conceptions of the earth, like those held by the primitive peoples of the present day, are difficult to discover and almost impossible fully to grasp. Early generalizations, as far as they were made from known facts, were usually expressed in symbolic language, and for our present purpose it is not profitable to speculate on the underlying truths which may sometimes be suspected in the old mythological cosmogonies.

00It consisted essentially in the adoption of Delauny's final numerical expressions for longitude, latitude and parallax, with a symbolic term attached to each number, the value of which was to be determined by substitution in the equations of motion.

00That the name also prevailed as that of a god among other Semitic races (or even These sacred arks were carried in procession accompanied by symbolic figures.

00by symbolic means," the definition, as developed by him, is one which would apply to the philosophy of Kant.

00In common with other sciences, economics makes use of " abstractions"; but if for some problems we employ symbolic processes of reasoning, we must keep clearly in view the limits of their significance, and neither endow the symbols with attributes they can never possess, nor lose sight of the realities behind them.

00Constitutional formulae like these, in fact, are nothing more than symbolic expressions of the character of the compounds which they represent, the arrangement of symbols in a certain definite manner being understood to convey certain information with regard to the compounds represented.

00Some of them imitated the Hebrew prophets in the performance of symbolic acts of denunciation, foretelling or warning, going barefoot, or in sackcloth or undress, and, in a few cases, for brief periods, altogether naked; even women in some cases distinguished themselves by extravagance of conduct.

00The loculi were intact and the epitaphs still in their places, so that " they form a kind of museum, in which the development, the formulae, and the symbolic figures of Christian epigraphy, from its origin to the end of the 3rd or 4th century, can be notified and contemplated, not in artificial specimens as in the Lateran, but in the genuine and living reality of their original condition."

00It is clear from what has been said above that the liturgical vestments possessed originally no mystic symbolic meaning whatever; it was equally certain that, as their origins were forgotten, they would develop such a symbolic meaning.

00We cannot even outline here the process of selection by which the symbolic meanings now stereotyped in the Roman Pontifical were arrived at.

00Two methods of treatment have been carried on in parallel lines, the unsymbolic and the symbolic; both of these originated with Cayley, but he with Sylvester and the English school have in the main confined themselves to the former, whilst Aronhold, Clebsch, Gordan, and the continental schools have principally restricted themselves to the latter.

00A separation is the symbolic representation of a product of monomial symmetric functions.

00= exp,udl where exp denotes (by the rule over exp) that the multiplication of operators is symbolic as in Taylor's theorem.

00It is thus possible to study simultaneously all the theories which depend upon operations of the group. Symbolic Representation of Symmetric Functions.-Denote the s 8 s elementar symmetric function a s by al a 2 a3 ...at pleasure; then, Y y si,, si,...

00(1 + a i x) (1+ = s i z we have the symbolic identity +02712+0.3x3+...

001+Eaix+Esiy+ /al a2x 2 +Malt2xy -Z01023,2+Ã¯¿½Ã¯¿½Ã¯¿½ The most general symmetric function to be considered is E 41 041 8424-3033..Ã¯¿½ .conveniently written in the symbolic form (pigi p2g2 p3go...)Ã¯¿½ Observe that the summation is in regard to the expressions obtained by permuting then suffixes I, 2, 3, ...n.

00The weight of the function is bipartite and consists of the two numbers Ep and Eq; the symbolic expression of the symmetric function is a partition into biparts (multiparts) of the bipartite (multipartite) number Ep, Eq.

00where the multiplications on the leftand right-hand sides of the equation are symbolic and unsymbolic respectively, provided that m P4, M P4 are quantities which satisfy the relation exp (M14+Moir+...+Mp4EpnP+...) =1+mic -Fmoif+...+mp,eng+...; where E, n are undetermined algebraic quantities.

00(multiplication symbolic) ?r1! ?2,Ã¯¿½..

00Symbolic Form.-Restricting consideration, for the present, to binary forms in a single pair of variables, we must introduce the symbolic form of Aronhold, Clebsch and Gordan; they write the form Iln n n-1 n-1 n n n aixi+a2x2) = 44+(1) a l a 2 x 1 x2+...+a2.x2=az wherein al, a2 are umbrae, such that n-1 n-1 n a 1, a 1 a 2, ...a 1 a 2, a2 are symbolical respreentations of the real coefficients Ã¯¿½o, ai,...

00If we restrict ourselves to this set of symbols we can uniquely pass from a product of real coefficients to the symbolic representations of such product, but we cannot, uniquely, from the symbols recover the real form, This is clear because we can write n-1 n-2 2 2n-3 3 a1a2 =a l a 2, a 1 a 2 = a 1 a2 while the same product of umbrae arises from n n-3 3 2n-3 3 aoa 3 = a l .a a 2 = a a 2 .

00We write;L 22 = a 1 a 2 .b 1 n-2 b2s 3 n - 3 3 n-3 3 n-3 3 a 3 = a 1 a 2 .b 1 b 2 .c 1 c2, and so on whenever we require to represent a product of real coefficients symbolically; we then have a one-to-one correspondence between the products of real coefficients and their symbolic forms. If we have a function of degree s in the coefficients, we may select any s sets of umbrae for use, and having made a selection we may when only one quantic is under consideration at any time permute the sets of umbrae in any manner without altering the real significance of the symbolism.

00To express the function aoa2 - _ which is the discriminant of the binary quadratic aoxi -+-2a1x2x2-+a2x2 = ai =1, 1, in a symbolic form we have 2(aoa 2 -ai) =aoa2 +aGa2 -2 a1 Ã¯¿½ al = a;b4 -}-alb?

00To find the effect of linear transformation on the symbolic form of quantic we will disuse the coefficients a 111 a 12, a21, a22, and employ A1, IÃ¯¿½1, A2, Ã¯¿½2.

00For the substitution rr xl =A 11 +1 2 12, 52=A21+Ã¯¿½2E2, of modulus A1 Ã¯¿½i = (AlÃ¯¿½.2-A2Ã¯¿½1) = (AM), A 2 Ã¯¿½2 the quadratic form a k xi -1-2a 1 x i x 2 +a 2 4 = x =f (x), becomes A41 +2A1E16 =At = OW, where Ao = aoA i +2a1AiA2 +a2Az, _ _ A 1 = ao A lÃ¯¿½l +ai(A1/.22+A2Ã¯¿½1) +7,2X2/22, A2 = aoÃ¯¿½l +2a1Ã¯¿½1/Ã¯¿½2 +a 2Ã¯¿½2 Ã¯¿½ We pass to the symbolic forms a:= (aixi+a2x2) 2, A 2 = (A 151+ A 26) 2/ by writing for ao, al, a2 the symbols ai, a 1 a 2, a?

00(ab)i(ac)j(bc)k..., that the symbolic product (ab)i(ac)j(bc)k..., possesses the invariant property.

00Notice, therefore, that the symbolic product (ab)i(ac)j(bc)k...

00may be the same or different, it is necessary that every product of umbrae which arises in the expansion of the symbolic product be of degree n, in a l, a 2; in the case of b,, b 2 of degree n 2; in the case of c 1, c 2 of degree n3; and so on.

00For these only will the symbolic product be replaceable by a linear function of products of real coefficients.

00and we may suppose such identities between the symbols that on the whole only two, three, or more of the sets of umbrae are not equivalent; we will then obtain invariants of two, three, or more sets of binary forms. The symbolic expression of a covariant is equally simple, because we see at once that since AE, B, Ce,...

00= t) 1 v ...axbxcx..., and assert that the symbolic product (ab)i(ac)'(bc)k...aibxc2...

00+P=n1, j+k+...+T =n3, It will also be a covariant if the symbolic product be factorizable into portions each of which satisfies these conditions.

00that occur in the symbolic expression; the degree in the variables (i.e.

00The identities are, in particular, of service in reducing symbolic products to standard forms. A symbolical expression may be always so transformed that the power of any determinant factor (ab) is even.

00of the symbolic factors of the form are replaced by IA others in which new variables y1, y2 replace the old variables x1, x 2 .

00The operation of taking the polar results in a symbolic product, and the repetition of the process in regard to new cogredient sets of variables results in symbolic forms. It is therefore an invariant process.

00Every symbolic product, involving several sets of cogredient variables, can be exhibited as a sum of terms, each of which is a polar multiplied by a product of powers of the determinant factors (xy), (xz), (yz),...

00It has been shown by Gordan that every symbolic product is expressible as a sum of transvectants.

00We have seen that transvection is equivalent to the performance of partial differential operations upon the two forms, but, practically, we may regard the process as merely substituting (ab) k, (OW for azbx, 4x t ' respectively in the symbolic product subjected to transvection.

00If we have a symbolic product, which contains the symbol a only in determinant factors such as (ab), we may write x 2, -x 1 for a 1, a 2, and thus obtain a product in which (ab) is replaced by b x, (ac) by c x and so on.

00and that thence every symbolic product is equal to a rational function of covariants in the form of a fraction whose denominator is a power of f x.

00Making the substitution in any symbolic product the only determinant factors that present themselves in the numerator are of the form (af), (bf), (cf),...and every symbol a finally appears in the form.

00Such a symbolic product, if its does not vanish identically, denotes an invariant or a covariant, according as factors az, bz, cz,...

00Its symbolic expression, to a numerical factor pres, is (Hbc) (Hbd) (Hcd) (bcd), and it is clearly of degree 6.

00We may write function of such symbolic + (1+ai)(1+alt)...(16e)=1+A2t 2 +A3E 3 +...+A0 Ã‚°.

00If we expand the symbolic expression by the multinomial theorem, and remember that any symbolic product ai 1 a2 2 a3 3 ...

00Now the symbolic expression of the seminvariant can be expanded by the binomial theorem so as to be exhibited as a sum of products of seminvariants, of lower degrees if alai 0-2a2 +...+crea0 can be broken up into any two portions (alai -1-0-2a2-1-Ã¯¿½Ã¯¿½Ã¯¿½ +asas) +(as+1as +1 +o-8+2as+2+Ã¯¿½Ã¯¿½Ã¯¿½ +ooae), such that Q1 +a2+...

00We Have The Symbolic Expression Of A /?

00Since +xZ=x x we have six types of symbolic factors which may be used to form invariants and covariants, viz.

00The number of different symbols a, b, c,...denotes the the covariants are homogeneous, but not in general isobaric functions, of the coefficients of the original form or forms. Of the above general form of covariant there are important transformations due to the symbolic identities: - (Ã¯¿½b) 2 2)2 = a b - a b; (xÃ¯¿½ = as a consequence any even power of a determinant factor may be expressed in terms of the other symbolic factors, and any uneven power may be expressed as the product of its first power and a function of the other symbolic factors.

00To assist us in handling the symbolic products we have not only the identity (ab) cx + (bc) a x + (ca) bx =0, but also (ab) x x+ (b x) a + (ax) b x = 0, (ab)a+(bc)a s +(ca)a b = 0, and many others which may be derived from these in the manner which will be familiar to students of the works of Aronhold, Clebsch and Gordan.

00There is no linear covariant, since it is impossible to form a symbolic product which will contain x once and at the same time appertain to a quadratic. (v.) is the Jacobian; geometrically it denotes the bisectors of the angles between the lines ax, or, as we may say, the common harmonic conjugates of the lines and the lines x x .

00cvii.) and inscriptions preserve the knowledge that the mystic, sacratus, passed through seven degrees, which probably corresponded to the seven planetary spheres traversed by the soul in its progress to wisdom, perfect purity, and the abode of the blest: Corax, Raven, so named because the raven in Mithraic mythology was the servant of the Sun; Cryphius, Occult, a degree in the taking of which the mystic was perhaps hidden from others in the sanctuary by a veil, the removal of which was a solemn ceremonial; Miles, Soldier, signifying the holy warfare against evil in the service of the god; Leo, Lion, symbolic of the element of fire; Perses, Persian, clad in Asiatic costume, a reminiscence of the ancient origin of the religion; Heliodromus, Courier of the Sun, with whom Mithras was identified; Pater, Father, a degree bringing the mystic among those who had the general direction of the cult for the rest of their lives.

00The development of symbolic algebra by the use of general symbols to denote numbers is due to Franciscus Vieta (Francois Viete, 1540-1603).

00This study was inaugurated by George Peacock, who was one of the earliest mathematicians to recognize the symbolic character of the fundamental principles of algebra.

00The geometrical interpretation of imaginary quantities had a far-reaching influence on the development of symbolic algebras.

00These algebras were essentially geometrical, and it remained, more or less, for the American mathematician Benjamin Peirce to devise systems of pure symbolic algebras; in this work he was ably seconded by his son Charles S.

00sons, whose names he regarded as, together with his own, symbolic by divine appointment of certain decisive events or religious truths - Isaiah (Yesha'-yahu), meaning "Salvation - Yahweh"; Shear-Yashub, "a remnant shall return"; and Maher-shalal-hash-baz, "swift (swiftly cometh) spoil, speedy (speedily cometh) prey" (vii.

00But the whole style of the work, with its use of conventional apocalyptic forms, favours the more symbolic view.

00This would also explain the absence of explicit scriptural citations generally, though knowledge both of the Old Testament and of several New Testament books - including the congenially symbolic Gospel of John - is clear (cf.

00Shadows and reflections were ignored, and perspective, approximately correct for landscape distances, was isometrical for near objects, while the introduction of a symbolic sun or moon lent the sole distinction between a day and a night scene.

00And he admits (§ 63) that if we were compelled to choose between translating mental phenomena into physical and its converse, the latter would be preferable, seeing that the ideas of matter and motion, merely symbolic of unknowable realities, are complex states of consciousness built out of units of feeling.

00The boundarystones between properties (termini) were also the objects of cult at the annual festival of the Terminalia, and the "god Terminus," the symbolic boundary-stone, shares with Jupiter the great temple on the Capitol.

00(I) In the Spring (it must be remembered that the old Roman calendar began the year with March) we have ceremonials of anticipation and prayer for the crops to come: prominent among them are the Fordicidia, with its symbolic slaughter of pregnant cows, addressed to Tellus, the Cerealia, a prayer-service to Ceres for the corn-crop, and the most important of the rustic celebrations of lustration and propitiation, the Parilia, the festival of Pales.

00His cult survived the metamorphosis of the ancient Vedic nature-worship into modern Hinduism, and there still are in India fire-priests (agnihotri) whose duty is to superintend his worship. The sacred fire-drill for procuring the temple-fire by friction - symbolic of Agni's daily miraculous birth - is still used.

00According to tradition in Hesse, he awaits resurrection, probably symbolic of the triumph of the sun over winter, within the Gudensberg (Hill of Odin).

00SACRAMENT, in religion, a property or rite defined in the Anglican catechism as " an outward and visible sign of an inward and spiritual grace"; if the grace be allowed to be inherent in the external symbolic thing or act as well as in the faithful who receive or do it, this definition holds good not only for the Latin Church, but for more primitive religions as well.

00Thus Berengar of Tours (999-1088) upheld the symbolic character of the Eucharist and the superiority of the Bible over tradition.

00While the scriptural statements imply a belief in the existence of spiritual beings intermediate between God, and men, it is probable that many of the details may be regarded merely as symbolic imagery.

00in the symbolic story, the moment for working the miracle; in the symbolized reality, the hour of His death, condition for the spirit's advent; and " what is there between Me and thee ?

00John's last and greatest symbolic sign replaces those historic motives, since here it is the raising of Lazarus which determines the hierarchs to kill Jesus (xi.

00II suggests a mystic or symbolic explanation by its statement " the life of the flesh is in the blood; and I have given it to you upon the altar to make atonement for your lives: 3 for it is the blood that maketh atonement by reason of the life."

00The kerubim might perhaps be symbolic representatives of the god Rakab'el or Rekub'el, probably equivalent to Hadad, whose sacred animal was the bull.

00That the figures symbolic of Rakab or Hadad were compounded or amalgamated by the Israelites with those symbolic of Nergal (the lion-god) and Ninib (the eagle-god), is not surprising.

00The signs or symbolic acts of the prophet probably originated in the actions of sympathetic magic. Thus in the vivid scene of r Kings xxii.

00magical act passes into sign or symbol, not however without the accompanying conception that underlies it still persisting that a mysterious effectuating potency belongs to the symbolic act.

00Although real historical personages - Gustavus Vasa, Olaus Petri the reformer and Gerdt the Anabaptist - figure as leading characters, they are made symbolic of the present-day forces of progress and reaction.

00For the great festival of Tezcatlipoca, the handsomest and noblest of the captives of the year had been chosen as the incarnate representative of the god, and paraded the streets for public adoration dressed in an embroidered mantle with feathers and garlands on his head and a retinue like a king; for the last month they married him to four girls representing four goddesses; on the last day wives and pages escorted him to the little temple of Tlacochcalco, where he mounted the stairs, breaking an earthenware flute against each step; this was a symbolic farewell to the joys of the world, for as he reached the top he was seized by the priests, his heart torn out and held up to the sun, his head spitted on the tzompantli, and his body eaten as sacred food, the people drawing from his fate the moral lesson that riches and pleasure may turn into poverty and sorrow.

00That the Lord's Supper was from the first a meal symbolic of Christian unity and commemorative of Christ's death is questioned by none.

00the Franks, we find the payment of a very small sum, which is often regarded as symbolic and as a relic of real purchase.

00In the West trine immersion was generally held to be symbolic of the triune name of "Father, Son and Holy Ghost."

00The story of the Creation in the book of Genesis is shown, from the point of view of chronology, to be a poetic or symbolic account by the discovery of civilizations of much greater antiguity.

00Amongst the best known of these symbolic impressions are banshees, corpse lights, phantom funeral processions, ominous animals or sounds and symbolic dreams (e.g.

00He shows at any rate that some sort of a theology existed in his day; particularly interesting is his description of the symbolic figure of Cronus with eyes before and behind and six wings open and folded (Fr.

00It has been suggested that this use is due to the custom of the symbolic use of flowers.

00The Wandering Jew has been regarded as a symbolic figure representing the wanderings and sufferings of his race.

00Plutarch in his treatise on Isis and Osiris well exemplifies this standpoint: for him every god and every rite is symbolic of some natural or moral truth.

00By the result of a symbolic discharge of arrows he informed the king of his coming success against Syria, and immediately thereafter he died.

00It is the prose epic of feudalism, and its romantic spirit, its high ideals, its fantastic gallantry, its ingenious adventures, its mechanism of symbolic wonders, and its flowing style have entranced readers of such various types as Francis I.

00Though the progress of his psychological thought compelled him to abandon the positive theology of the Moravians, he always retained an appreciation of its spiritual or symbolic significance.

00In both the patient was withdrawn from the multitude and the cure was wrought with the accompaniment of symbolic actions.

00The Baptist has pointed Him out to them in striking language, which recalls at once the symbolic ritual of the law and the spiritual lessons of the prophets: " Behold, the Lamb of God, which taketh away the sin of the world."

00When the idea, itself indefinite, gets no further than a struggle and endeavour for its appropriate expression, we have the symbolic, which is the Oriental, form of art, which seeks to compensate its imperfect expression by colossal and enigmatic structures.

00First comes architecture - in the main, symbolic art; then sculpture, the classical art par excellence; they are found, however, in all three forms. Painting and music are the specially romantic arts.

00Its commanding position gained it in 1634, by royal decree, the title of "Llave del Nuevo Mundo y Antemural de las Indias Occidentales" (Key of the New World and Bulwark of the West Indies), in reference to which it bears on its coat of arms a symbolic key and representations of the Morro, Punta and Fuerza.

00This is some symbolic object, stick or what not, which passes between the parties to a contract, the obligations under which, if not fulfilled by the contracting parties during their lives, become hereditary.

00Venn, in his Symbolic Logic, proposes the four forms, xy = o, xy = o, xy>o, xy> o (where y means " not-y "), but only as alternative to the ordinary forms. Bradley says that " ` S-P is real' attributes S-P, directly or indirectly, to the ultimate reality," and agrees with Brentano that " ` is ' never stands for anything but ` exists ' "; while Bosanquet, who follows Bradley, goes so far as to define a categorical judgment as " that which affirms the existence of its subject, or, in other words, asserts a fact."

00In quantitative judgments we may think x = y, or, as Boolero oses x = v Ã‚° p p y = - Ã‚° y, or, as Jevons proposes, x = xy, or, as Venn proposes, x which is not y=o; and equational symbolic logic is useful whenever we think in this quantitative way.

00The symbolic logic, which confuses " is " with " is equal to," having introduced a particular kind of predicate into the copula, falls into the mistake of reducing all predication to the one category of the quantitative; whereas it is more often in the substantial, e.g.

00Venn, Symbolic Logic (2nd ed., London, 1894); The Principles of Empirical or Inductive Logic (London, 1889); J.

00Hamilton's significance for the history of logic lies in the stimulus that he gave to the development of symbolic logic in England by his new analytic based upon his discovery or adoption of the principle of the quantification of the predicate.

00" It is not an algebra," said Kant 3 of his technical logic, and the kind of support lent recently to symbolic logic by the Gegenstandstheorie identified with the name of Alexius Meinong (b.

00The future of symbolic logic as coherent with the rest of logic, in the sense which the word has borne throughout its history seems to be bound up with the question of the nature of the analysis that lies behind the symbolism, and of the way in which this is justified in the setting of a doctrine of validity.

00Venn's Symbolic Logic (1881) gave a careful history and bibliography of that development.

00Wright, Biblical Studies (1886) argues ably for the symbolic theory.

00LIGHTS The ceremonial use of lights in the Christian Church, with which this article is mainly concerned, probably has a double origin: in a very natural symbolism, and in the adaptation of certain and Jewish rites and customs of which the paganJ symbolic meaning was Christianized.

00All this might very early, without the incentive of Jewish and pagan example, have affected the symbolic ritual of the primitive Church.

00in 180 B.C. and decorated with a combat of gods and giants, symbolic of the struggle between the Pergamene Greeks and the Gaulish barbarians.

00This gave them a symbolic or representative character as a closed body (cf.

00Cybele was usually worshipped in connexion with Attis, as Aphrodite with Adonis, the two being a duality interpreted by the philosophers as symbolic of Mother Earth and her vegetation.

00But here too symbolic ideas must be taken into account.

00So carefully is this record of the visions arranged that the first two chapters of the second part of the book (vii.-viii.) were no doubt purposely made to appear in a symbolic form, in order that in the last two revelations (xi.-xii.), which were couched in such direct language as to be intelligible even to the modern student of history, the author might obtain the effect of a climax.

00Lessons in Logic, c. xxiii.), John Venn (see his Symbolic Logic, 2nd ed., 18 94, p. 135), and Allan Marquand (see American Academy of Arts and Sciences, 188 5, pp. 303-7, and Johns Hopkins University Studies in Logic, 1883).

00Leo of Rome, Athanasius, Gregory of Nyssa, Theophylactus, Cyril of Jerusalem and others, trine immersion was regarded as being symbolic of the three days' entombment of Christ; and in the Armenian baptismal rubric this interpretation is enjoined, as also in an epistle of Macarius of Jerusalem addressed to the Armenians (c. 330).

00The work on [[Trigonometry]] and Double Algebra (1849) contains in the latter part a most luminous and philosophical view of existing and possible systems of symbolic calculus.

00In 1860 De Morgan endeavoured to render their contents better known by publishing a [[Syllabus]] of a Proposed System of Logic, from which may be obtained a good idea of his symbolic system, but the more readable and interesting discussions contained in the memoirs are of necessity omitted.

00These steps are symbolic of the rising, culminating and setting of the sun, or alternatively the course of the solar deity through the three divisions of the universe.

00Nor can the esoteric and pantheistic theories of priests (according to which the various beast-gods were symbolic manifestations of the divine essence) be received as an historical account of the origin of the local animal-worships.

00The very various periods named make it probable that the periodical return of the phoenix belongs only to vulgar legend, materializing what the priests knew to be symbolic. Of the birds of the heron family the gorgeous colours and plumed head spoken of by Pliny and others would be least inappropriate to the purple heron (Ardea purpurea), with which, or with the allied Ardea cinerea, it has been identified by Lepsius and Peters (Alteste Texte des Todtenbuchs, 1867, p. 51).

00And avoid the potential infinite regress of symbolic meaning by being fully grounded in the real world.

00Reverse: Symbolic representation of technological development from the Iron Age to the modern computer age.

00Some liberal Christians do not accept a literal bodily resurrection, [3] seeing the story as richly symbolic and spiritually nourishing myth.

00It is a broad collection of numerical and symbolic calculation and visualization tools with a familiar scratchpad interface.

00Abraham is a symbolic " returner " from " exile ", given a promise of land by the Persian shah.

00The ribbons were personally designed by King George VI and all have symbolic significance.

00Colin Wills, the last tin miner in St. Agnes will strike a symbolic sledgehammer blow linking the past with the present.

00It will focus in particular on functionalism, Marxism, symbolic interactionism, figurational sociology and feminism.

00The slippery finger may be less impressive than the metal speculum, but it is no less significant as an instrument of symbolic domination.

00President Armando Guebuza administered the first doses of the vaccine in the Maputo suburb of Mavalane as the symbolic launch of the campaign.

00Doubtlessly this is massively symbolic of something, but it 's not quite clear what.

00The land of Egypt, in scripture, is often symbolic of the world, a world which is no friend of Grace.

00White flowers, symbolic of peace, were laid in commemorative solidarity.

00But icons as understood in the Orthodox Church since that date are partly symbolic in nature.

00Symbolic Interactionism is concerned with social situations and the way people make sense of those situations.

00Blades of grass dyed with manganese were woven into the baskets in geometric patterns with a symbolic significance.

00Symbolic representations do not take kindly to Meta Model questions.

00He was terrific if purely symbolic best country album.

00If it is only a symbol then it doesn't literally purify but is merely symbolic of purification.

00In practice, the legislation turned out to be largely symbolic.

00In a deeply symbolic action he chose twelve disciples one for each of the ancient tribes.

00As it was the International Year of the Mountains, to visit the greatest of them all seemed highly symbolic.

00A customary Champions of Europe, becoming increasingly symbolic all the time, led onto a better performance in the second half.

00As philosophers and physiologists have established, even physical reality can be considered as symbolic.

00The symbolic aliens are frequently replaced by a savage authoritarian regime trampling on freedom.

00The interrogation would have been a moment of truth in the case, a symbolic breakthrough after decades in which Pinochet was considered untouchable.

00In other words, the symbolic value of linguistic utterances is more important than the content of what one says.

00The zodiac worked as a symbolic calendar divided into twelve parts, like the of 12 moons waxing and waning in a year.

00Most people agree, however, that baptism is a symbolic act.

00Whether used for symbolic purposes or simply because of its pleasing design, the fleur de lis can be found in countless homes, used in all sorts of different ways.

00It was symbolic of Napoleon’s strength and the liberation his Napoleonic Code offered.

00Named for the castle ruins of Le Chateau de Lancome, Mr. Petitjean found the symbolic splendor of the rose an ideal for the beauty of a woman.

00Designed for the extroverted mature woman, it is symbolic of J.

00Included in the kit are angel cutouts sitting on large clouds, which provides enough room to add a symbolic element, reminiscent of your baby.

00One look through a gallery of wedding cake topper pictures will show any couple that there is a wide range of styles for this symbolic wedding figurine.

00Because lucky bamboo plants are often used for feng shui and other symbolic decorations, the number of shoots used in wedding favor arrangements can be very significant.

00Wedding favor frames in symbolic shapes, such as the popular castle or the pumpkin carriage.

00Photos of white wedding picture frames can beautifully depict wedding in a symbolic and wonderful way.

00Chat with your fiancé, wedding party, and other close friends and family members to brainstorm ideas and pick out things that are symbolic for you as a couple.

00If you use the Aster in your wedding flowers you will be pleased to know that this particular flower is symbolic of love and faith.

00Wear a simple and inexpensive white dress in a symbolic TTD photo shoot.

00As threat displays became more symbolic than practical, some societies have developed penis sheaths for different occasions, from ceremonial use to everyday wear.

00A necklace can be a symbolic and meaningful gift, and none are more heartfelt and personal than mother necklaces.

00Celtic knots are delicate and highly symbolic designs with different twists representing the connections between nature, life, and spiritualism.

00Because the knots themselves are highly symbolic - often embodying particular beliefs or family patterns - using symbolic gems adds another layer of meaning to the jewelry.

00Claddagh bracelet silver Celtic jewelry makes highly symbolic, richly meaningful gifts between friends, lovers, or anyone who shares a special relationship.

00It is a symbolic keepsake that is certain to become a treasured family heirloom as it is handed down through the generations.

00A stone with such a legendary history would appeal to a person searching for symbolic jewelry.

00In Western culture monkeys are symbolic of many things.

00To others they are symbolic of cunningness, mimicry or mischievousness.

00It is these symbolic meanings of the monkey that makes it a desirable fashion accessory for many people worldwide.

00People who are searching for symbolic or inspirational jewelry should consider this necklace.

00Tiffany & Co. created a variety of jewelry with the symbolic stone over the years.

00Moonstone's mystical lore and luminous beauty make it a natural choice for symbolic jewelry.

00Check out small stores on college campuses that sell folk jewelry, symbolic jewelry or metaphysical items.

00Jewelry friendship pendants can be made extra special by personalizing the piece to be more symbolic of your enduring relationship.

00Many jewelry stores offer a limited selection of friendship pendants, though they will have a larger range of basic pendants that can be just as symbolic when given to a friend.

00Admirers of inspirational and symbolic jewelry will love Chalice Well pendants and the jewelry's connection to both Christianity and Arthurian legend.

00A gift of religious jewelry can become one of the child's most treasured objects due to its symbolic nature.

00Beyond these typical pieces of jewelry you can also find pocket watches, earrings, bracelets, necklaces, and rings designed with religious motifs and symbolic icons.

00Later, the Rose of Sharon was interpreted to be symbolic of Christ.

00The pearl circle of life pendant is an elegant design that will appeal to those who like symbolic jewelry.

00Today many jewelry shoppers simply associate pearls with formal dress rather than a symbolic message.

00Jewelry shoppers who want a symbolic pendant for a personal statement or as a special gift to a loved one may find the pearl circle of life pendant perfect.

00Consider a men's Celtic knot cross necklace if you are looking for a cross that is highly symbolic and fashionable.

00The rich history and lore surrounding opals also will appeal to men looking for historic and symbolic rings.

00And by directly touching, not using a symbolic button for an action.

00A roogle is symbolic of their efforts, and a fine bit of international cooperation it is.

00Wetherby, Amy, et al. Communication and Symbolic Behavior Scales: Developmental Profile.

00Cultural values can also affect artistic expression and development, influencing content, art media, style, and symbolic meaning as represented in the child's view of the world.

00Because there are no rules in symbolic play, the child can use this play to reinforce, learn about, and imaginatively alter painful experiences.

00Symbolic play may be used by children to cope with fear of separation when they go to school or to the hospital.

00Also, a child's self-awareness deepens as he explores an event through role-playing or symbolic play.

00Other children may draw pictures that are symbolic of death (an airplane crashing, boats sinking, burning buildings, or children in graves).

00Some symbolic (language) abilities are developed at the end of this stage.

00The child makes perceptual discriminations involving color, shape, size, use, number, missing parts, and symbolic material.

00Material symbols such as kimonos, fans, and towels are given rich symbolic importance as the rehearsal space is changed into a sacred and special room separate from the worries of the outside world.

00The symbolic bears of the Grateful Dead can be found in many places and on many things.

00Both men and women wore these symbolic items, and wore face masks as well.

00This is symbolic of the close contact with the earth that is required at the funeral.

00The decision for the memorial included an Outdoor Symbolic Memorial and 30,000 square foot interactive memorial museum.

00The Outdoor Symbolic Memorial is 3.3 acres and has 168 chairs with glass bases representative of the lives lost.

00The color red is the first color most people think of as symbolic of fire.

00From art posters and tee shirts to artist prints and tattoos, an art dragon yang yin is not only beautiful to look at, it is also rich with symbolic meaning.

00In the Taoist belief the five elements are symbolic of five elemental energies that combine, in a multitude of ways, to produce the ten thousand things, which encompasses everything that exists in the world.

00Each element has an assigned color because it is a symbolic representation of the element.

00In feng shui, peonies are not just symbolic but also enhancers often used to bring abundance to the couple in love and to strengthen their bonds of love.

00These have become symbolic with love and many use them as symbols of love and in the love sector of homes.

00The eye of each teardrop is symbolic of the constant watchful eye of the koi.

00Mathematics is amongst the more complicated subjects for students because the language of math is often seen as largely symbolic.

00For a birthday, Valentine's Day, or First Anniversary, the rose is symbolic of a great range of emotion, from warmth and happiness to love and romance.

00Since fire is symbolic of the "spark of life," people with fire signs are passionate, assertive, spontaneous, and energetic.

00Families honor these gods by burning symbolic money to pay for their traveling expenses.

00Candle holders with dragonfly designs have different significance and symbolic meaning to individuals depending on their culture and spiritual beliefs.

00Whether your holiday will have a modern, traditional or a vintage Christmas theme, include angel Christmas decorations and ornaments for an enchanting, symbolic touch.

00Saviodsilva.com provides love quizzes based on the symbolic meaning of your answers.

00An engagement ring is the ultimate symbol of a couple's relationship, and nothing is more symbolic than three stone engagement rings that represent the different stages of that relationship.

00To emphasize the symbolic significance of the three stone arrangement, most three stone engagement rings utilize a prong setting, and the center stone may be slightly elevated.

00One consideration that couples may want to acknowledge before choosing black jewels for an engagement ring is the symbolic superstition associated with black.

00Heart shaped diamond engagement rings are beautiful, nostalgic options for couples interested in a symbolic ring that is more unique than classic diamond shapes.

00Both styles have a loop that represents infinity and has a symbolic meaning when given as a special gift.

00Of course, all diamonds are symbolic of love, commitment, and timelessness, but adding yellow to the stone gives it even deeper meaning.

00Claddagh Rings: These highly symbolic Irish engagement rings are a great alternative to traditional designs but still represent the strong, deep meaning of a relationship.

00This makes Hollywood jewelry, particularly engagement rings, highly symbolic, not only because they represent the characters' nuptial commitment, but because the rings are designed to symbolize deeper themes in the movie itself.

00Prior Marriage: If a bride has been previously married, most surveys found that she preferred a more expensive ring for her second wedding, perhaps as a symbolic upgrade to a better relationship.

00Claddagh: Claddagh rings are highly symbolic, representing love, friendship, and fidelity with the heart, hands, and crown design.

00Every culture has unique ways to design engagement rings, and honoring one's culture with a symbolic ring can be a lovely and meaningful gesture.

00Ruby is also the designated July birthstone, and birthstone engagement rings can be a highly symbolic and sentimental options for July-born brides or couples whose nuptials will take place at the height of summer.

00With so many promise ring meanings to choose from, this type of symbolic jewelry can be a delightful gift for many different occasions and relationships.

00Religious promise rings are a strongly symbolic way for individuals to demonstrate their faith, spirituality, and commitment.

00A Christian purity promise ring is a highly symbolic and sacred token of a personal vow deeply rooted in one's religious beliefs.

00These unique wedding rings carry symbolic meanings in their intricate designs.

00While it's easy to choose a gemstone if you wish to go with your own birthstone, the birthstone of your significant other, or the birthstone of your child, there are other ways to choose gemstones that are equally symbolic.

00As more men embrace the beauty of diamonds as symbolic of their marriage, some designers are creating three stone diamond anniversary rings with a masculine touch.

00Edwardian: Edwardian engagement rings embrace the romance and spirituality of the Edwardian era with symbolic designs and superior craftsmanship.

00Choosing matching promise rings is a symbolic way for a couple to show off the promise they share, whether it is a promise of a future relationship to one another or if it is a shared commitment to chastity or Christian purity.

00Birthstone Rings: A birthstone engagement ring is highly symbolic, and that same symbolism is popular for his and hers promise rings.

00Celtic Rings: Celtic rings feature intricately woven, highly symbolic knots and other symbols that can easily be worn by men and women, making them popular choices for promise rings.

00A promise may be priceless, but finding cheap promise rings is essential for couples on a budget who still want this symbolic token of their commitment.

00A couple could exchange simple matching promise rings such as plain bands, while Claddagh rings are a highly symbolic and lovely option that can be had more cheaply than many gemstone rings.

00A double heart diamond ring is a lovely symbolic piece of jewelry that can be used for many special occasions.

00Exchanging Valentine's promise rings can be a wonderful way for a couple to commit to one another when they aren't quite ready to get engaged but they want to show their devotion in a strongly symbolic way.

00Rubies can also be a highly symbolic gift for couples who were married in July, since the ruby is July's birthstone.

00If the couple has a child born in July, or themselves have July birthdays, a ruby band is similarly sentimental and symbolic.

00A ruby anniversary band is a beautiful and highly symbolic choice to celebrate a long lasting marriage or any special July anniversary, or even if rubies are just a favorite jewel.

00Fortunately, there are many ways that a couple can find an engagement ring that is low in cost and high in symbolic value.

00Damascus wood grain wedding rings are a great choice for a couple searching for modern and symbolic wedding bands.

00The Damascus wedding ring is highly symbolic because it represents the blending of different metals into one work of art.

00Platinum Celtic engagement rings are good option for couples who like traditional symbolic jewelry or wish to honor their Celtic heritage.

00The Everlon jewelry collection appeals to couples looking for symbolic engagement, wedding and anniversary rings.

00The affordable price of the symbolic ring makes it a perfect promise ring.

00Bella's engagement ring will remain a popular item for Twilight fans who desire a symbolic engagement or promise ring.

00The simple beauty of traditional Jewish wedding rings can be meaningful to a couple who wants symbolic wedding jewelry.

00Throughout history, Jewish engagement and wedding jewelry had both social and symbolic meanings.

00The Jewish wedding ring's plain fashion is highly symbolic.

00The symbolic ring has a rich history that appeals to couples who want to honor the tradition and heritage of their faith.

00For symbolic jewelry, a groom may choose an aquamarine engagement ring for his bride's birthstone or a husband might mark his 19th wedding anniversary by gifting his wife with an aquamarine eternity ring.

00Couples searching for symbolic rings with rich history should consider Celtic wedding bands.

00These patterns are often symbolic so that the design has more meaning than mere decoration.

00The circular nature of knots is also highly symbolic because it involves an unbroken circle where two ends meet as one like a wedding ring.

00Celtic wedding bands offer many options to couples who want symbolic wedding jewelry or to celebrate a heritage.

00Getting engaged on Valentine's Day is very symbolic of your love for each other because it is a holiday that honors expressing love.

00These types of rings are usually all metal and feature a pattern, some of which are symbolic.

00When couples select a DNA2Diamonds ring made from the carbon signatures in their hair, they are selecting a piece of jewelry uniquely their own through DNA and symbolic of their union in marriage.

00Asteroids & Chiron ($25): This is a full natal chart analysis of the symbolic meanings, in your life, of asteroids and a planetoid.

00For an added element of fun and symbolic end to the academic year, let kids rip out used pages in their workbooks for their paper balls.

00Telling the tale of the late 19th century, classic western movies usually explain how the West was won while wearing a symbolic cowboy hat on the way to the saloon.

00Typically, this is the most difficult of the psychic gifts to interpret because the information is almost all symbolic in nature.

00Frequently, psychics can't shift their focus and reassess their perceptions as potentially symbolic rather than literal.

00The meanings behind these symbolic tattoos is as diverse as the people who have them, but they all begin from the same basic form.

00While one partner gets the locked heart, his or her significant other gets a tattoo of the symbolic keys to that heart.

00Fairies have a rich symbolic history and their size, detail, symbolism and colorful nature make them ideal for tattoos.

00Fairy-based tattoos can be beautiful, symbolic, detailed and interesting choices for body ink.

00The dolphin is also symbolic of a variety of things, in addition to being the cutest brainiac in the ocean.

00As you can see, the beauty of koi fish makes them a natural choice for tattoo inspiration, but the fact that these designs hold symbolic meanings really dovetails with what tattoos are all about.

00Every Aztec tattoo was done in a specific symbolic pattern, depending on the god being honored.

00Next, the heart is pierced by a thorn or may be wrapped in a crown of thorns, symbolic of the crown forced on Christ at his crucifixion.

00However, people have attached symbolic meanings to different flower species, which can be a good guide to choosing your floral tattoo.

00There are more flowers out there than just the typical rose, and many have beautiful symbolic meanings.

00For example, a cross is symbolic of two things to Christians: the crucifixion of Jesus and Christianity as a whole religion.

00Many famous authors are known for using symbolic speech in their novels and stories.

00Some novels and works of literature, such as the popular The DaVinci Code by Dan Brown spend an entire story explaining and relating to symbolic meaning.

00Tattooists must show a lot of meaning in a small image, so they often use symbolic messages to do this.

00One extreme form of symbolic tattoos can be seen in Russian jail tattoos, where different pictures have specific meanings.

00While kanji is the most popular form of tattoo in the world, there is much to be said for other types of symbolic Japanese ink.

00Katakana is a symbolic method for writing things out; this form of writing and tattooing is used to create a sense of urgency and deeper emphasis on the meaning of the original word.

00The use of a symbolic language makes the meaning unique, original and adds and air of mystery.

00The pearl is also considered symbolic of a closed lotus blossom.

00Tiger tattoos are both beautiful just as they are as well as symbolic, because of the many qualities assigned to this animal.

00Yes, butterflies are considered symbolic of rebirth, and certain flowers have meanings, but generally speaking, these designs are fairly innocuous.

00The points can also be symbolic of the four elements: Earth, Wind, Fire and Water.

00Fairies, pixies or whatever you choose to call them are all symbolic of the youthfulness that still lives deep within us all.

00As discussed above, roses can be very symbolic, but you don't have to follow any of these preconceived notions.

00This is basically symbolic of the fact that the Airborne Division is always ready for rapid deployment, and since that usually means being dropped into areas of active fighting, death is a constant companion.

00Butterflies have many beautiful legends and symbolic meanings attached to them.

00These tats can be small and symbolic, or they can be done as an entire back mural.

00The Middle East is filled with many ceremonies that hold a strong symbolic meaning to its people.

00It can also warm and heat a person and be symbolic of the fire and passion that burns within.

00It is a very popular ornamental tattoo; thousands of women have adorned their skin with this stunning symbolic creature.

00For those looking for a symbolic tattoo, a representation of the equinox with images of the sun and the planet Earth itself can be a great way of illustrating the constellation.

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The word usage examples above have been gathered from various sources to reflect current and historial usage. They do not represent the opinions of YourDictionary.com.