Symbols Sentence Examples

He studied the five symbols on the paper in his hand.

The symbols were useless to him.

Of the twenty symbols, I've figured out five.

Her own necklace had the same symbols surrounding five stars.

The cuneiform symbols on his back were purple, marking him as a servant to the Others.

In the very earliest centuries we find the episcopate, united in council,, drawing up symbols of faith, which every believer was bound to accept under pain of exclusion, condemning heresies, and casting out heretics.

Ostentatious avoidance of a fish-diet became, indeed, one of the outward symbols of militant Protestantism among the Puritans.

The next morning, she went to the game room after her sparring session and sat the entire day, learning more and more about the game and experimenting with how the symbols on the keyboard interacted with the images before her.

Brady gazed at the screen in front of him, unable to decipher the symbols and colors.

It was patrolled by guardsmen wearing the Others' symbols on their cloaks.

He showed Gabriel the drawing of the different symbols with a sketch of the sun on one end and the ground on the other.

He looked down and saw the arrow pointed towards one of the symbols.

One, can you read the symbols?

The two parties united under the act of 1729, which adopted the Westminster symbols "as being, in all the essential and necessary articles, good forms of sound words and systems of Christian doctrine."

The writing on the tablet was too faded to make out, and the symbols he did see looked nothing like those on the compass.

In 491 B.C. Aegina was one of the states which gave the symbols of submission ("earth and water") to Persia.

His principal characteristic was perfect confidence in any result obtained by the treatment of symbols in accordance with their primary laws and conditions, and an almost unrivalled skill and power in tracing out these results.

Thus, if x= horned and y = sheep, then the successive acts of election represented by x and y, if performed on unity, give the whole of the class horned sheep. Boole showed that elective symbols of this kind obey the same primary laws of combination as algebraical symbols, whence it followed that they could be added, subtracted, multiplied and even divided, almost exactly in the same manner as numbers.

Thus, 1 - x would represent the operation of selecting all things in the world except horned things, that is, all not horned things, and (1 - x) (1 - y) would give us all things neither horned nor sheep. By the use of such symbols propositions could be reduced to the form of equations, and the syllogistic conclusion from two premises was obtained by eliminating the middle term according to ordinary algebraic rules.

The court might go a journey to view the property and even take with them the sacred symbols on which oath was made.

But in Italy, although they were severally identified with the papal and imperial parties, they really served as symbols for jealousies which altered in complexion from time to time and place to place, expressing more than antagonistic political principles, and involving differences vital enough to split the social fabric to its foundation.

The fables of the phoenix and of the conduct of the wild ass and the ape at the time of the equinox owe their origin to astronomical symbols belonging to the.

The denotation of elements by symbols had been practised by the alchemists, and it is interesting to note that the symbols allotted to the well-known elements are identical with the astrological symbols of the sun and the other members of the solar system.

Such truth can be apprehended by the multitude only in symbols which guide the will through the imagination, and through historic facts which are embodiment of ideas.

Symbols like the letters of the alphabet have been found in European soil painted upon pebbles belonging to a stratum between the Palaeolithic and Neolithic age.

Both Umbrian and Oscan devised two new symbols.

The symbols denoting a number are called its digits.

In the meantime, he'd learn to use the compass better and decipher the symbols.

When substances in solution are dealt with, Thomsen indicates their state by affixing Aq to their symbols.

Since the distance of a body from the observer cannot be observed directly, but only the right ascension and declination, calling these a and 6 we conceive ideal equations of the form a = f (a, b, c, e, f, g, t) and 5=0 (a, b, c, e, f, g, t), the symbols a, b,.

Gold, the most perfect metal, had the symbol of the Sun, 0; silver, the semiperfect metal, had the symbol of the Moon, 0j; copper, iron and antimony, the imperfect metals of the gold class, had the symbols of Venus Mars and the Earth tin and lead, the imperfect metals of the silver class, had the symbols of Jupiter 94, and Saturn h; while mercury, the imperfect metal of both the gold and silver class, had the symbol of the planet,.

Compounds were represented by copulating simpler symbols, e.g.

Compounds were denoted by joining the symbols of the components, and by varying the manner of joining compounds of the same elements were distinguished The symbol V was used to denote a liquid, and a vertical line to denote a gas.

If two compounds combined, the + signs of the free compounds were discarded, and the number of atoms denoted by an Arabic index placed after the elements, and from these modified symbols the symbol of the new compound was derived in the same manner as simple compounds were built up from their elements.

He also introduced barred symbols, i.e.

A figure placed on the right of a symbol only affects the symbol to which it is attached, but when figures are placed in front of several symbols all are affected by it, thus 2H 2 SO 4 means H 2 SO 4 taken twice.

The distribution of weight in chemical change is readily expressed in the form of equations by the aid of these symbols; the equation 2HC1+Zn =ZnCl2+H2, for example, is to be read as meaning that from 73 parts of hydrochloric acid and 65 parts of zinc, 136 parts of zinc chloride and 2 parts of hydrogen are produced.

Usually, when the symbols of the elements are written or printed with a figure to the right, it is understood that this indicates a molecule of the element, the symbol alone representing an atom.

Thus, the symbols 14 2 and P4 indicate that the molecules of hydrogen and phosphorus respectively contain 2 and 4 atoms. Since, according to the molecular theory, in all cases of chemical change the action is between molecules, such symbols as these ought always to be employed.

Here also should be mentioned the sound sh, which, like th, is not a combination of sounds though written with two symbols.

Conventional signs and symbols are universally used in depicting these objects.

Latin letters are used throughout; the miniatures of older maps are superseded by symbols, and in the better-known countries the maps are fairly correct, but they fail lamentably when we follow their author into regions - the successful delineation of which depends upon critical combination of imperfect information.

The enclosing slab very often bears one or more Christian symbols, such as the FIG.

They are to be distinguished from Christian catacombs only by the character of their decorations, the absence of Christian symbols and the language of their inscriptions.

The walls are in many places coated with stucco adorned with frescoes, including palms, doves, labara and other Christian symbols.

A group of signs carved on some rocks near Visegrad have been regarded as cuneiform writing, but are probably medieval masonic symbols.

They teach further the solution of problems leading to equations of the first and second degree, to determinate and indeterminate equations, not by single and double position only, but by real algebra, proved by means of geometric constructions, and including the use of letters as symbols for known numbers, the unknown quantity being called res and its square census.

Each part of the partition is a bipartite number, and in representing the partition it is convenient to indicate repetitions of parts by power symbols.

If 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 .

In other words, B, b may be regarded as different or alternative symbols to A, a.

If the forms be identical the sets of symbols are ultimately equated, and the form, provided it does not vanish, is a covariant of the form ate.

In particular, when the product denotes an invariant we may transform each of the symbols a, b,...to x in succession, and take the sum of the resultant products; we thus obtain a covariant which is called the first evectant of the original invariant.

The second evectant is obtained by similarly operating upon all the symbols remaining which only occur in determinant factors, and so on for the higher evectants.

To obtain the real form we multiply out, and, in the result, substitute for the products of symbols the real coefficients which they denote.

The coefficients of the symbols must then present themselves n 1, n 2, n 3 ...times respectively.

Of these thirteen sections, the first contains a simple description of the more prominent phenomena, without mathematical symbols or numerical data.

The first column contains the symbols of the various elements which were added to the iron, and the second the percentage proportion in which each element was present; the sample containing 0.03% of carbon was a specimen of the best commercial iron, the values obtained for it being given for comparison.

The distinction between algebraical and arithmetical reasoning then lies mainly in the fact that the former is in a more condensed form than the latter; an unknown quantity being represented by a special symbol, and other symbols being used as a kind of shorthand for verbal expressions.

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

To say, for instance, that X is equal to A -B, is the same thing as to say that X is a quantity such that X and B, when added, make up A; and the above five statements of necessary connexion between two statements of equality are in fact nothing more than definitions of the symbols -, m of, =,, and loga.

We therefore represent them by separate symbols, in the same way that we represent the unknown quantity in an equation by a symbol.

These constructed symbols may be called positive and negative coefficients; or a symbol such as (- p) may be called a negative number, in the same way that we call 3 a fractional number.

A special algebra is one which differs from ordinary algebra in the laws of equivalence which its symbols obey.

Even when the formal evolution of the science was fairly complete, it was taken for granted that its symbols of quantity invariably stood for numbers, and that its symbols of operation were restricted to their ordinary arithmetical meanings.

The progress of analytical geometry led to a geometrical interpretation both of negative and also of imaginary quantities; and when a " meaning " or, more properly, an interpretation, had thus been found for the symbols in question, a reconsideration of the old algebraic problem became inevitable, and the true solution, now so obvious, was eventually obtained.

They are (a+b)-?-c=a+(b+c) (A) (aXb)Xc=aX(bXc) (A') a+b=b+a (c) aXb=bXa (c') a(b c) =ab-Fac (D) (a - b)+b=a (I) (a=b)Xb=a (I') These formulae express the associative and commutative laws of the operations + and X, the distributive law of X, and the definitions of the inverse symbols - and =, which are assumed to be unambiguous.

The special symbols o and I are used to denote a - a and a=a.

But the symbols of ordinary algebra do not necessarily denote numbers; they may, for instance, be interpreted as coplanar points or vectors.

It is remarkable that Mobius employs the symbols AB, ABC, Abcd In Their Ordinary Geometrical Sense As Lengths, Areas And Volumes, Except That He Distinguishes Their Sign; Thus Ab = Ba, Abc= Acb, And So On.

From A Merely Formal Point Of View, We Have In The Barycentric Calculus A Set Of " Special Symbols Of Quantity " Or " Extraordinaries " A, B, C, &C., Which Combine With Each Other By Means Of Operations And Which Obey The Ordinary Rules, And With Ordinary Algebraic Quantities By Operations X And =, Also According To The Ordinary Rules, Except That Division By An Extraordinary Is Not Used.

From these are derived symbols of the type A i = ales+a2e2+...

Associated with these new units there is a system of extensive quantities of the second species, represented by symbols of the type = Ei 121 [i=I, 2,...zn(n - I)].

The outer and inner products of two extensive quantities A, B, are in many ways analogous to the quaternion symbols Vab and Sab respectively.

The algebras discussed up to this point may be considered as independent in the sense that each of them deals with a class of symbols of quantity more or less homogeneous, and a set of operations applying to them all.

But when an algebra is used with a particular interpretation, or even in the course of its formal development, it frequently happens that new symbols of operation are, so to speak, superposed upon the algebra, and are found to obey certain formal laws of combination of their own.

For instance, there are the symbols A, D, E used in the calculus of finite differences; Aronhold's symbolical method in the calculus of invariants; and the like.

Sir Isaac Newton introduced the term Universal Arithmetic, since it is concerned with the doctrine of operations, not affected on numbers, but on general symbols.

In it he mentions many earlier writers from whom he had learnt the science, and although it contains very little that cannot be found in Leonardo's work, yet it is especially noteworthy for the systematic employment of symbols, and the manner in which it reflects the state of mathematics in Europe during this period.

His symbols for greater than and less than ("3 and .) have been completely superseded by Harriot's signs.

The embodiment of political and religious supremacy displayed in the high priest's authority, clothing and symbols can only reflect exilic or rather post-exilic conditions.'

His pages abound in symbols representing unknown functions, the form of the function being left to be ascertained by observation of facts, which he does not regard as a part of his task, or only some known properties of the undetermined function being used as bases for deduction.

In his Principes de la theorie des richesses (1863) he abandoned the mathematical method, though advocating the use of mathematical symbols in economic discussions, as being of service in facilitating exposition.

Round the rim was a cuneiform legend, and in the field a Hittite figure with six Hittite symbols engraved twice over on either hand of it.

These, now almost sixty in number (excluding seals), are all in a pictographic character which employed symbols somewhat elaborately depicted in relief, but reduced to conventional and " shorthand " representations in the incised texts.

The objects represented by these symbols have been certainly identified in only a few instances.

A certain number are heads (human and animal) detached from bodies, in a manner not known in the Egyptian hieroglyphic system, with which some of the other symbols show obvious analogies.

His system, however, like all others, is built in the main upon hypotheses incapable at present of quite satisfactory verification, such, for example, as the conjectural reading " Gargamish " for a group of symbols which recurs in inscriptions from Jerablus and elsewhere.

Other conjectural identifications of groups of symbols with the place-names Hamath, Marash, Tyana are bases of Sayce's system.

Convinced of being divinely inspired, he had begun to see visions, and discovered in the Apocalypse symbols of the heavenly vengeance about to overtake this sin-laden people.

But such traces of prehistoric letters as are supposed to have been found seem to be corruptions of the Korean alphabet rather than independent symbols.

Chamberlain, the necessity of committing to memory two syllabaries, one of which has many variant forms, and at least two or three thousand Chinese ideographs, in forms standard and cursive ideographs, too, most of which are susceptible of three or four different readings according to circuinstance,add, further, that all these kinds of written symbols are apt to be encountered pell mell on the same page, and the task of mastering Japanese becomes almost Herculean.

Such pictures partake largely of the impressionist character, but they attain much beauty in the hands of the Japanese artist with his extensive repertoire of suggestive symbols.

Though represented in English by two symbols this is a single sound, which may be either interdental or, as frequently in English, produced "by keeping the tongue loosely behind the upper front teeth, so that the breath escapes partly between the tongue and the teeth, and partly, if the teeth are not very closely set, through the interstices between them" (Jespersen).

It is, however, to be regretted that English has not kept the old symbols for sounds which are very characteristic of the language.

Substituting these symbols in the expression for the area, the relation becomes H=o(p' - p„)(v„_v')/(o' - o").

In this case the condition of flow is simply that of constant total heat, or in symbols, d(E+pv) =0.

This does not mean, what is often alleged, that nobody before him had ever thought of choosing symbols different from numerals, such as the letters of the alphabet, to denote the quantities of arithmetic, but that he made a general custom of what until his time had been only an exceptional attempt.

The symbols and myths in these are not the creation of the writer, but borrowed from the past, and in not a few instances the materials are too foreign to his subject to lend themselves to his purpose without the help of artificial and violent expedients.

Like the Arabian logicians, and some of the scholastics, who held that ideas existed in a threefold form - ante res, in rebus and post res - he laid down the principle that the archetypal ideas existed metaphysically in the ultimate unity or intelligence, physically in the world of things, and logically in signs, symbols or notions.

If the interpretation of the Maya calculiform glyphs be trustworthy, these people had carried their numeral system into the hundreds of thousands and devised symbols for recording such high numbers.

Figure of the god Texcatlipoca, surrounded by the 20 day symbols of the sacred cycle of 260 days, tonalanaatl.

These mythological ideas and symbols of the American aborigines were woven in their textiles, painted on their robes and furniture, burned into their pottery, drawn in sand mosaics on deserts, and perpetuated in the only sculptures.

In late post-exilic times, however, foreign tales, even if of mythical origin, naturally came into favour, especially as religious symbols.

The earlier Greek writers - Eudoxus, Eratosthenes, Hipparchus - knew of only eleven zodiacal symbols, but made one do double duty, extending the Scorpion across the seventh and eighth divisions.

Both the famous zodiacs of Dendera display their symbols, unmistakably identified by Lepsius.

The " zodiac of labours " was replaced in French castles and hotels by a " zodiac of pleasures," in which hunting, hawking, fishing and dancing were substituted for hoeing, planting, reaping and ploughing.8 It is curious to find the same sequence of symbols employed for the same decorative purposes in India as in Europe.

The hieroglyph of Leo, for instance, occurs among the symbols of the Mithraic worship."

Their dogmatic symbols are usually said to include nine separate creeds which together form the Book of Concord (Liber Concordiae).

The General Council, a secession from the General Synod, was organized in 1867, and accepts the "unaltered" (invariata) Augsburg Confession in its original sense, and the other Lutheran symbols as explanatory of the Augsburg Confession.

The greatest philologist of antiquity was, however, his successor, Aristophanes of Byzantium (195), who reduced accentuation and punctuation to a definite system, and used a variety of critical symbols in his recension of the Iliad and Odyssey.

As a mathematician he occupied himself with many branches of his favourite science, more especially with higher algebra, including the theory of determinants, with the general calculus of symbols, and with the application of analysis to geometry and mechanics.

The mastery which he had obtained over the mathematical symbols was so complete that he never shrank from the use of expressions, however complicated - nay, the more complicated they were the more he seemed to revel in them - provided they did not sin against the ruling spirit of all his work - symmetry.

Finally, sacred formulas, names and symbols are of the highest importance among the Gnostic sects.

Hence, a principal item in their religious practice consisted in communications about the being, nature and names of the Seven (or of any other hostile daemons barring the way to heaven), the formulas with which they must be addressed, and the symbols which must be shown to them.

None of them were written except through the use of ideographs, in the making of which the Aztecs used colours with much skill, while the Mayas used an abbreviated form, or symbols.

The Aztec numerals, which were vigesimal or reckoned by scores, were depicted by dots or circles up to 20, which was represented by a flag, 400 (a score of scores) by a feather, and 8000 (a score of scores of scores) by a purse; but for convenience these symbols might be halved and quartered, so that 534 might be shown by one feather, one quarter of a feather, one flag, one-half of a flag, and four dots.

It was not until the 13th century that the symbolical meaning of the cross began to be elaborated, and this was still further accentuated from the 14th century onward by the increasingly widespread custom of adding to it the figure of the crucified Christ and other symbols of the Passion.

One smote the threshold with an axe, another with a pestle, the third swept it with a broom - three symbols of culture (for trees were hewn down with the axe, grain pounded with the pestle, and the fruits of the field swept up with the broom) which Silvanus could not endure.

In the West, Augustine, like Eusebius and Theodoret, calls the elements signs or symbols of the body and blood signified in them; yet he argues that Christ " took and lifted up his own body in his hands when he took the bread."

The elements, he said, remain physically what they were, but are spiritually raised as symbols to a higher power.

The work consists solely of a list of symbols of the various scales and modes, and is probably only a fragment.

The swine seems to have been the animal sacred to him, or to have been one of the symbols under which he is represented.

C. Haddon's Fetichism and Magic. in which the god really lived, and which were no mere images or symbols of him.

According to him, whatever inferences we make, certain or uncertain, are mere economies of thought, adapting ideas to sensations, and filling out the gaps of experience by ideas; whatever we infer, whether bodies, or molecules, or atoms, or space of more than three dimensions, are all without distinction equally provisional conceptions, things of thought; and " bodies or things are compendious mental symbols for groups of sensations - symbols which do not exist outside thought."

At the Reformation the altars in churches were looked upon as symbols of the unreformed doctrine, especially where the struggle lay between the Catholics and the Calvinists, who on this point were much more radical revolutionaries than the Lutherans.

But he does speak of certain sacred symbols which he defines elsewhere as figures of wild beasts.

The latter was the chief town; its coins are found in considerable number, the types being sometimes the Athenian goddess and her owl, sometimes native religious symbols, the caps of the Dioscuri, Apollo, &c. Few coins of Myrina are known.

The Tyrian coins of the period, stamped with native, Greek and Egyptian symbols, illustrate the traditional relations of the city and the range of her ambitions.

At Salem he was a member of the congregation of Roger Williams, whom he resolutely defended in his trouble with the New England clerical hierarchy, and excited by Williams's teachings, cut the cross of St George from the English flag in token of his hatred of all symbols of Romanism.

The bishop is consecrated, after taking the oath of fidelity to the Holy See, and subscribing the profession of faith, by a bishop appointed by the pope for the purpose, assisted by at least two other bishops or prelates, the main features of the act being the laying on of hands, the anointing with oil, and the delivery of the pastoral staff and other symbols of the office.

Berzelius, although by common consent it was much simpler and more convenient than his cumbersome system of circular symbols.

In works of art Triptolemus appears mounted on a chariot (winged or drawn by dragons, symbols of the fruitfulness of the earth), with Demeter and Persephone handing him the implements of agriculture.

The "Melancolia," numbered "1" as though intended to be the first of a series, with its brooding winged genius sitting dejectedly amidst a litter of scientific instruments and symbols, is hard to interpret in detail, but impossible not to recognize in general terms as an embodiment of the spirit of intellectual research (the student's "temperament" was supposed to be one with the melancholic), resting sadly from its labours in a mood of lassitude and defeat.

The advantage of numerical marks is that they are more easily manipulated than symbols; the disadvantage, that they produce the false impression that merit can be estimated with mathematical accuracy.

To reinterpret all these features as mere symbols, the lumber of ancient days, is to avoid the problem of their introduction into the Temple, and to assume an advance of popular thought which is not confirmed by the retention and fresh developments of the old ideas both in the pseudepigraphical literature and in the literature of Rabbinical Judaism.'

These belts or scarves were symbols of authority and power and were surrendered on defeat in battle.

Thus rotation is now expressed in symbols at least as simply as it can be exhibited by means of a model.

Expressed in symbols, the relation may be written H' - H"=S(8'-0")..

Among his symbols was a serpent coiled round a staff, and physicians were for long wont to place this at the head of their prescriptions.

In St Paul we find the beginnings of explanation, indeed of two explanations, and in the Epistle to the Hebrews the whole sacrificial system is found to culminate in Christ, of whom all priests and sacrifices are symbols, so that they are abolished with the coming of the great reality.

By the word alphabet, derived from the Greek names for the first two letters - alpha and beta - of the Greek alphabet, is meant a series of conventional symbols each indicating a single sound or combination of sounds.

Symbols for a combination of sounds are not necessary, though they may be convenient as abbreviations.

The resemblances between some Egyptian symbols and some symbols of the Phoenician alphabet are striking; in other cases the differences are no less remarkable.

Elsewhere several series of such symbols resembling inscriptions have been found scratched on bones of the same period s For the history of writing these may be important, but for the history of the alphabet, as we know it, they are not in question.

As already mentioned, the twenty-two symbols of the Phoenician alphabet indicate consonantal sounds only.

That the alphabet was borrowed and adapted independently by different places not widely separated, and that the earliest Greek alphabets did not spread from one or a few centres in Greek lands, seem clear (a) from the different Greek sounds for which the Phoenician symbols were utilized; (b) from the different symbols which were employed to represent sounds which the Phoenicians did not possess, and for which, therefore, they had no symbols.

On the other hand, a table of Greek alphabets 2 will show how widely different the symbols for the same sound were.

Different views with regard to some of these symbols are expressed by Lidzbarski, Ephemeris far semitische Epigraphik, ii.

For the history of the additional symbols which are not Phoenician, we must begin with y.

But as Dr Evans has found a form like the digamma among his most recent types of symbols, and as we have no intermediate forms which will prove the development of from Y, though the form found at Oaxos in Crete, viz.

Such progress is more easily indicated by changes in the symbols among a people whose acquaintance with the art is not of long standing nor very familiar.

The history of the symbols 4 and x is altogether unknown.

On the other hand, if we remember the large number of symbols belonging to the prehistoric script, it will seem at least as easy to believe that the persons who, by adding new letters to the Phoenician alphabet, attempted to bring the symbols more into accordance with the sounds of the Greek language, may have borrowed from this older script.

Symbols exactly like k, X, and (a), X, are found in the Carian alphabet, and transliterated by Professor Sayce 1 as v (and ii), h and kh respectively.

The development of symbols for the long vowels o and w was also the work of the Ionians.

In the Chalcidian alphabet the symbol for x was placed after the symbols common to all Greek alphabets, a position which X retains in the Latin (and also in the Faliscan) alphabet.

It is certain from the symbols which they develop or drop that the people of Campania and Samnium borrowed their alphabet from the Etruscans, who held dominion in Campania from the 8th to the 5th century B.C. Previous to the Punic wars Campania had reached a higher stage of civilization than Rome.

Oscan, in order to represent D, introduced later a form SJ, thus creating confusion between the symbols for d and for r.

Below are (t) the transliteration of the symbols; (2) the Greek words, both like the Cyprian reading from right to left.

The Greek alphabet, with which it was most Symbols of Ogam Alphabet.

That some symbols are like Persian only shows that Mesrob was not able to rid himself of the influences under which he lived.

The symbols become longer and thinner; in fact, cease to be the script of monuments and become the script of a busy trading people.

It has twenty-nine symbols, whereby it is enabled to differentiate certain sounds which are not distinguished from one another in the writing of the northern Semites.

For it can only depend on the mass m of the bob, the length 1 of the string, and the value of g at the place in question; and the above expression is the only combination of these symbols whose dimensions are those of a time, simply.

In symbols, if v be the velocity and p the perpendicular from 0 to the tangent to the path, pv=h, (1)

To prove these relations, we replace the symbols A1, A1 A,, in (5) by ai, a2,.

Wilson remarks," notwithstanding the acknowledged purport of this worship, it is but justice to state that it is unattended in Upper India by any indecent or indelicate ceremonies, and it requires a rather lively imagination to trace any resemblance in its symbols to the objects they are supposed to represent."In spite, however, of its wide diffusion, and the vast number of shrines dedicated to it, the worship of Siva has never assumed a really popular character, especially in northern India, being attended with scarcely any solemnity or display of emotional spirit.

For a syllogism consists of propositions, propositions of words, and words are the symbols of notions.

Babylonian speculation embraced the world in a triad of divine powers, Anu the god of heaven, Bel of earth and Ea of the deep; and these became the symbols of the order of nature, the divine embodiments of physical law?

These symbols were laid upon a couch (lectus), the left arm resting on a cushion (pulvinus, whence the couch itself was often called pulvinar) in the attitude of reclining.

In Europe it was confined to the countries under the domination of Rome.2 In Christianity, from the very first, fire and light are conceived as symbols, if not as visible manifestations, of the divine nature and the divine presence.

At every liturgical service, and especially at Mass and at choir services, there must be at least At two lighted tapers on the altar, 2 as symbols of the presence of God and tributes of adoration.

As symbols of light and joy a candle is held on each side of the deacon when reading the Gospel at Mass; and the same symbolism underlies the multiplication of lights on festivals, their number varying with the importance of the occasion.

Finally, lights are placed round the bodies of the dead and carried beside them to the grave, partly as symbols that they still live in the light lights.

His own college (Christ's) would have chosen him for the mastership; but a party opposition led to the election of Valentine Cary, who had already quarrelled with Ames for disapproving of the surplice and other outward symbols.

This explanation of the action of the solid is equivalent to that by which Gauss afterwards supplied the defect of the theory of Laplace, except that, not being expressed in terms of mathematical symbols, it does not indicate the mathematical relation between the attraction of individual particles and the final result.

Christian symbols have been discovered in the southern towns of Chinese Turkestan by Sven Hedin.

But, to use words in themselves unmeaning, as symbols by which to conduct and convey the complex intellectual processes in which mental conceptions are suggested, compared, combined, and even analysed, and new ones created - this is a faculty which is scarcely to be traced in any lower animal.

The obvious answer is, that the power of using words as signs to express thoughts with which their sound does not directly connect them, in fact as arbitrary symbols, is the highest grade of the special human faculty in language, the presence of which binds together all races of mankind in substantial mental unity.

His symbols from the animal kingdom were the bull (perhaps a totemistic attribute and identified with him), the panther, the lion, the tiger, the ass, the goat, and sometimes also the dolphin and the snake.

Pashas are of three grades, formerly distinguished by the number of horse-tails (three, two and one respectively) which they were entitled to display as symbols of authority when on campaign.

If 0 be the angle of tilt of the machine, and the other symbols be as before, it may be shown that the additional weight, w FIG.

Using the symbols of the diagram, it can be shown that the effect of placing the weight W at E instead of F is to cause the end of the beam to descend, as if under the action of an additional weight, w, at F such that w Wa(ml - l +tan 0)/h.

In the East various other symbols were used.

The second method consists in taking a series of names or symbols for the first few numbers, and then repeating these according to a regular system for successive numbers, so that each number is defined by reference to the number immediately preceding it in the series.

We therefore only require a definite law for the formation of the successive names or symbols.

We can, however, attach to the o's the same symbols, I, 2,.

Any particular I object is then defined completely by the combination 2 of the symbols last written down in each series; and 3 this combination of symbols can equally be used to denote the number of objects up to and including the last one (§ Io).

There are no single symbols for two, three, &c.; but numbers are represented by combinations of symbols for one, five, ten, fifty, one hundred, five hundred, &c., the numbers which have single symbols, viz.

The Roman system, except for the use of symbols for five, fifty, &c., is also in the denary scale, though expressed in a different way.

The introduction of these other symbols produces a compound scale, which may be called a quinarybinary, or, less correctly, a quinary-denary scale.

The figures used in the Hindu notation might be used to express numbers in any other scale than the denary, provided new symbols were introduced if the base of the scale exceeded ten.

The letters or symbols descriptive of each denomination are usually placed after or (in actual calculations) above the figures denoting the numbers of the corresponding units; but in a few cases, e.g.

The earliest Greek system of notation was similar to the Roman, except that the symbols for 50, 500, &c., were more complicated.

Later, a system similar to the Hebrew was adopted, and extended by reproducing the first nine symbols of the series, preceded by accents, to denote multiplication by moo.

The failure to observe the distinction between an identity and an equality often leads to loose reasoning; and in order to prevent this it is important that definite meanings should be attached to all symbols of operation, and especially to those which represent elementary operations.

When sculptured decorations were added they frequently took the form of imitations of the actual festoons with which it was usual to ornament altars, or of symbols, such as crania and horns of oxen, referring to the victims sacrificed.

It is doubtful whether any opposition between crescent and cross, as symbols of Islam and Christianity, was ever intended by the Turks; and it is an historical error to attribute the crescent -to the Saracens of crusading times or the Moors in Spain.

The curious will find in them many reminiscences of Hindu and Buddhist legend; and the antiquary must notice the distinctive symbols assigned to each, in order to recognize the statues of the different Jinas, otherwise identical, in the different Jain temples.

Burke's conservatism was, as such a passage as this may illustrate, the result partly of strong imaginative associations clustering round the more imposing symbols of social continuity, partly of a sort of corresponding conviction in his reason that there are certain permanent elements of human nature out of which the European order had risen and which that order satisfied, and of whose immense merits, as of its mighty strength, the revolutionary party in France were most fatally ignorant.

The rationalist wing resolve Incarnation and still more Atonement into symbols of philosophical truth.

But, when this programme is carried out, there is no small danger lest the relations traced out between God and men should collapse into dust, the facts of Christ transform themselves into symbols, and the idealistic theology of the right wheel to the left.

As children of the summer they are symbols of the warmth of the sun, to which.

Examples are preserved of the various forms of spoons used by the ancient Egyptians of ivory, flint, slate and wood, many of them carved with the symbols of their religion.

By the second general method the moon's co-ordinates are obtained in terms of the time by the direct integration of the differential equations of motion, retaining as algebraic symbols the values of the various elements.

The third method seeks to avoid the difficulty by using the numerical values of the elements instead of their algebraic symbols.

In the mystery of the Supper Christ is truly exhibited to us by the symbols of bread and wine; and so His body and blood, in which He fulfilled all obedience for the obtaining of righteousness for us, are presented.

Muller frankly recognizes that not only are animals symbols of deity and its attributes, not only are they companions and messengers of deity (as in the period of anthropomorphic religion), but they have been divine beings in and for themselves during the earlier stages of thought.

But to indicate this opposition in the qualities of the reals A+B, we must substitute for these symbols others, which, though only "contingent aspects" of A and B, i.e.

In their numerous allusions to the subtle mercury, which the one makes when treating of a means of measuring time by the efflux of the metal, and the other in a treatise on the transit of the planet, we see traces of the school in which they served their first apprenticeship. Huygens, moreover, in his great posthumous work, Cosmotheoros, seu de terris coelestibus, shows himself a more exact observer of astrological symbols than Kircher himself in his Iter exstaticum.

Its organization was both curious and mysterious, and had a fantastic ritual full of symbols taken from the Christian religion, as well as from the trade of charcoal-burning, which was extensively practised in the mountains of the Abruzzi and Calabria.

His proofs are generally long and clumsy; this is accounted for in some measure by the absence of symbols and technical terms. Apollonius was ignorant of the directrix of a conic, and although he incidentally discovered the focus of an ellipse and hyperbola, he does not mention the focus of a parabola.

Nilus, the disciple and defender of Chrysostom, permitted the symbol of the cross in churches and also pictorial delineations of Old and New Testament history, but deprecated other symbols, pictures of martyrs, and most of all the representation of Christ.

When no other mark is appended the whorls are supposed to be alternate; but if it is desired to mark the position of the whorls special symbols are employed.

He held that "freedom from symbols and articles is abstractedly the highest state of Christian communion," but was "the peculiar privilege of the primitive Church."

He walked until he recognized the Guardians' station, a single story house nestled between two similar houses and marked by a star and an arrow – the White God's symbols – in the corner of one window.

Tamer, Rhyn's half-brother and the least friendly member of the Council, had deciphered five of the twenty symbols on the compass.

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

The symbols were from the time-before-time, an era of chaos he barely remembered.

Certain symbols pulled up certain features of the ships or angles of battle, similar to how picture-symbols in her video games on earth brought up different functions, allowing her to maneuver characters in the game or review the armament and skills of her opponents.

The gifting of the necklace was like a proposal, only much more to the Guardians who gave the symbols of their families and histories to their chosen suitors.

The story pointed out several auspicious symbols.

It was one of the bewildering assortment of coded letters and symbols that appear in chat room messages.

Mandarin birds and kingfisher covers are symbols of conjugal affection.

Unlike some other regular expression languages, there are no backslashed symbols that are n't alphanumeric.

Complex arguments were reduced to simple symbols, and thus more rapidly assimilated.

When only allele symbols are displayed an asterisk should precede them.

Some, like Staff of Kingship are inspired by symbols of African royalty, others like New Fine Trail and Shell by Indonesian batiks.

They were subjected to unprecedented press scrutiny which included criticism of their later role as symbols of 1960s youth counterculture.

A way to cross cultural divides is to use universal symbols.

These threats to agriculture are replaced by cypress and myrtle, symbols of God's powerful transformation of the wilderness.

Hindu counting system was purely decimal and distinct symbols for the numbers 1 - 9 existed already.

The Great Seal of the United States is not a Masonic emblem, nor does it contain hidden Masonic symbols.

These playing card-sized map symbol flashcards have been carefully designed to teach map symbols and map reading skills.

Again, these symbols indicate the nature of the transformations when moving from a hexagram in one quadrant to a hexagram in one quadrant to a hexagram in another.

All symbols and tablets of humanity contain one hieroglyph, the sacred prayer - Peace and Unity.

As the one of the main buildings of the communitiy, workhouses became symbols of class hostility and the obvious places to attack.

The Raven Stone A class one Pictish stone showing the Sea Eagle and notched rectangle with z rod symbols the black infill is recent.

Love and friendship intertwined in the Celtic symbols on the ring have relevance to every couple contemplating marriage.

The extent of the symbols permitted in a document remains as specified in the license issued by the commercial owner.

This Unicode text includes both IPA symbols and Japanese katakana.

The Great Seal of the United States is not a Masonic emblem, nor does it contain hidden Masonic emblem, nor does it contain hidden Masonic symbols.

It contains 15 well known jazz tunes with piano accompaniment written in single stave notation with chord symbols.

For double-stranded nucleic acids Table 2 permits the allocation of symbols to the complementary strand.

Also most of the symbol pages are A4 pages with 20 symbols on the page.

Furthermore, women characters are presented as symbols of hope in deeply patriarchal societies by possessing strong, dominant qualities.

Textiles were also tangible standards of value that were used as currency, as payment of taxes, and as symbols of imperial patronage.

Although this seems obvious, many peptidases are still named in just this way, most notably by use of gene symbols as names.

Even in the most ancient sources, the female personification of cities is associated with symbols of weddings.

Pictish symbols were added in the years around AD800.

The symbols && and || also have equal precedence.

Adding symbols for profiling and debugging Profiling is a method of identifying sections of code that consume large portions of execution time.

Indeed the symbols in the implemented program don't have any causal powers in addition to those of the implementing medium.

For non-Europeans from imperially subjugated countries, the symbols of subordination were even more extensive than those applied to European proletarians.

The brackets [] are used in this book to mark all symbols indicating pronunciation.

Among these symbols the serpent has appeared throughout Davie's long career, whilst images of crosses and of the ankh are also recurrent.

Other symbols - such as the Crown Jewels and coronation regalia - are unique objects which exert a powerful fascination.

The back of the crucifix contains an empty reliquary with a sliding lid carved with symbols of the Passion.

The Chi-Rho or Crook Inevitably, the Church adopted so-called pagan ritualism and its symbols.

To him we owe the symbols for and, a 2 and a 3, and the cube root sign.

Druids hold the land sacred, and honor the trees as symbols of the beauty and strength of creation.

Some common symbols in Ancient Egyptian religious jewelry include the scarab (beetle ), lotus, serpent, falcon, and the eye.

The 15-foot high pillar's sides are covered with high quality carved runes, vine scrolls, knot patterns, and sacred symbols.

Class II are relief carved slabs bearing symbols in addition to a cross.

Rosslyn's vaulted soffit features hundreds of small stone cubes, intricately carved with mysterious symbols.

I had thought about the possibility of simply using a stenographer to transmit the phonetic symbols to the television screen.

Thus the filter object can be used to select a subset of the symbols provided by the object name.

Those symbols can give you traction when you're thinking about broad swaths of experience.

The British Standards Organization, for example, specifies graphical symbols for process measurement and control.

Without the -u option, there are no unresolved references or undefined symbols to cause ld to search the archive library.

Each pack contains 30 attractive cards, including number cards (0-20 ), instructional cards and mathematical symbols.

The wallet has six international currency symbols on one side, and the same six symbols on the opposite side.

Smile Have you noticed how the smiley symbols in Haloscan comments have all received spray tans?

There are also special warning symbols to alert you to potentially toxic herbs.

It had become trendy to shoot signage and or other iconic symbols, and, well basically it was fast becoming trite.

Discarded shopping trolleys are incorporated into techno-industrial gothic as hidden symbols of our times.

The g77 compiler appends an underscore to symbols, or two if the name contained an underscore.

Also included is a comprehensive explanation of the chord symbols as well as a sample voicings chart.

Christianity 1, key figures, sacred writings, ceremonies and symbols.

The synod of New York and Philadelphia, which in 1781 had organized the presbytery of Redstone, the first of western Pennsylvania, in 1788 resolved itself into a General Assembly, which first met in Philadelphia in 1789, and after revising the chapters on Church and state, adopted the Westminster symbols as to their constitution, "as containing the system of doctrine taught in the Holy Scriptures," and they made them unalterable without the consent of two-thirds of the presbyteries and the General Assembly.

He did not regard logic as a branch of mathematics, as the title of his earlier pamphlet might be taken to imply, but he pointed out such a deep analogy between the symbols of algebra and those which can be made, in his opinion, to represent logical forms and syllogisms, that we can hardly help saying that logic is mathematics restricted to the two quantities, o and 1.

By unity Boole denoted the universe of thinkable objects; literal symbols, such as x, y, z, v, u, &c., were used with the elective meaning attaching to common adjectives and substantives.

He wandered from village to village and town to town, preaching to enormous audiences, always in the open air; the earnestness and straightforward eloquence with which he insisted that true repentance came from the heart, that pious pilgrimages and the absolution of the Church were mere outward symbols, appealed to all classes.

By combining the four symbols A, B, X, Y, according to their presence or absence, Garrod got a considerable number of formulae, each of which was overruled, so to speak, by the two categories of the presence or absence of the ambiens muscle.

That which among Catholics is most commonly regarded in its aspect as an offering and spoken of as the "mass" is usually regarded in its aspect as a participation in the symbols of Christ's death and spoken of as the "communion."

The most conspicuous of the many symbols and signs of his transgression was the golden eagle which he had placed over the great gate of the Temple; its destruction was the obvious means to adopt for the quickening and assertion of Jewish principles.

To emphasize the superiority of this imperium over that of the consuls, the dictator might be preceded by twenty-four lictors, not by the usual twelve; and, at least in the earlier period of the office, these lictors bore the axes, the symbols of life and death, within the city walls.

A great advance was made by Dalton, who, besides introducing simpler symbols, regarded the symbol as representing not only the element or compound but also one atom of that element or compound; in other words, his symbol denoted equivalent weights.4 This system, which permitted the correct representation of molecular composition, was adopted by Berzelius in 1814, who, having replaced the geometric signs of Dalton by the initial letter (or letters) of the Latin names of the elements, represented a compound by placing a plus sign between the symbols of its components, and the number of atoms of each component (except in the case of only one atom) by placing Arabic numerals before the symbols; for example, copper oxide was Cu +0, sulphur trioxide S+30.

Compounds are in like manner represented by writing the symbols of their constituent elements side by side, and if more than one atom of each element be present, the number is indicated by a numeral placed on the right of the symbol of the element either below or above the line.

When chemical change is expressed with the aid of molecular formulae not only is the distribution of weight represented, but by the mere inspection of the symbols it is possible to deduce from the law of gaseous combination mentioned above, the relative volumes which the agents and resultants occupy in the state of gas if measured at the same temperature and under the same pressure.

Constitutional 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.

Although the distinction is one which cannot be ultimately maintained, it is convenient to classify the signs of algebra into symbols of quantity (usually figures or letters), symbols of operation, such as +, i, and symbols of distinction, such as brackets.

They behave exactly like the corresponding symbols in arithmetic; and it follows from this that whatever " meaning " is attached to the symbols of quantity, ordinary algebra includes arithmetic, or at least an image of it.

The inverse symbols -, = are ambiguous, and in fact are rarely used.

From every proposition in this algebra a reciprocal one may be deduced by interchanging + and X, and also the symbols o and i.

Vieta, who does not avail himself of the discoveries of his predecessors - the negative roots of Cardan, the revised notation of Stifel and Stevin, &c. - introduced or popularized many new terms and symbols, some of which are still in use.

Its frequent explanation, however, of incompatible symbols by the doctrines of phonetic variation and interchange, or by alternative values of the same symbol used as ideograph, determinative or phonetic complement, and the occasional use of circular argument in the process of " verification," do not inspire confidence in other than its broader results.

The song and the hat named after him (the latter a broad slouch hat with a feather) became famous as the symbols of the middle-classes in revolt.

It is true that tradition largely fixes the form of figures and symbols in apocalyptic. Yet each new apocalypse is to some extent a reinterpretation of traditional material, which the writer uses not wholly freely but with reverence from the conviction that they contained the key to the mysteries of the present and the past.

The deity of the Son was believed to carry with it that of the Spirit, who was associated with Father and Son in the baptismal formula and in the current symbols, and so the victory of the Nicene Christology meant the recognition of the doctrine of the Trinity as a part of the orthodox faith (see especially the writings of the Cappadocian fathers of the late 4th century, Gregory of Nyssa, Basil and Gregory Nazianzen) .

He was sincerely religious; but his wellmeant efforts to unite the Lutheran and Reformed Churches, in celebration of the tercentenary of the Reformation (1817), revealed the limits of his paternal power; eleven years passed in vain attempts to devise common formulae; a stubborn Lutheran minority had to be coerced by military force, the confiscation of their churches and the imprisonment or exile of their pastors; not till 1834 was outward union secured on the basis of common worship but separate symbols, the opponents of the measure being forbidden to form communities of their own.

His views, in his chapter on the Laws of Motion, that the physicist forms a conceptional model of the universe by aid of corpuscles, that these corpuscles are only symbols for the component parts of perceptual bodies, and that force is a measure of motion, and not its cause, are the views of Mach.

The agitation, however, on the Catholic question had quickened the sense of the wrongs of Ireland, and the Irish Catholics were engaged ere long in a crusade against tithes and the established church, the most offensive symbols of their inferiority in the state.

At this stage we are as much concerned with speech-forms as the thought-forms of which they are conventional symbols, with Plato's analysis, for instance, into a noun and a verb, whose connotation of time is as yet a difficulty.

The Greek names of the letters, their forms, and the order of the symbols show that the Greek alphabet as we know it must have been imported by or from a Semitic people, and there is no evidence to contradict ancient tradition that this people was the Phoenicians.

They were, however, fated to fall far short of such a consummation; and at all times orthodox Brahmanism has had to wink at, or ignore, all manner of gross superstitions and repulsive practices, along with the popular worship of countless hosts of godlings, demons, spirits and ghosts, and mystic objects and symbols of every description.

In the first part of our own investigation we shall adhere to the symbols used by Laplace, as we shall find that an accurate knowledge of the physical interpretation of these symbols is necessary for the further investigation of the subject.

The fundamental principles of his system (see Scholasticism) are that "Essentia non sunt multiplicanda praeter necessitatem" ("Occam's Razor"), that nouns, like algebraical symbols, are merely denotative terms whose meaning is conventionally agreed upon (suppositio), and that the destructive effect of these principles in theological matters does not in any way destroy faith (see the Centilogium Theologicum, Lyons, 1495, and Tractatus de Sacramento Altaris).

Both Mr. Keith and I were distressed and full of forebodings for the morrow; but we went over to the college a little before the examination began, and had Mr. Vining explain more fully the American symbols.

Suddenly, it is as if those symbols of reactionary nationalism have had all their teeth pulled.

Read a lovely story about the meaning behind the symbols of Christmas Did you know?

These materials focus around the story of the nativity and use black and white rebus symbols.

Among these symbols the serpent has appeared throughout Davie 's long career, whilst images of crosses and of the ankh are also recurrent.

Many of the dishes made at this time are served because they are regarded as symbols of good luck.

They are the basic visual symbols and relics of all civilization.

They recognize that elements and compounds can be represented by symbols and formulae.

Some runes symbols are likely to have been acquired from other alphabets, such as the Greek, Etruscan, and the Early Roman.

Some common symbols in Ancient Egyptian religious jewelry include the scarab (beetle), lotus, serpent, falcon, and the eye.

The 15-foot high pillar 's sides are covered with high quality carved runes, vine scrolls, knot patterns, and sacred symbols.