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Of course, she had never been able to read the expressions on his face.

247From the tone in which the courtiers addressed him and the way Paulucci had allowed himself to speak of him to the Emperor, but above all from a certain desperation in Pfuel's own expressions, it was clear that the others knew, and Pfuel himself felt, that his fall was at hand.

222Two forms of Western Aramaic survive: the Jerusalem form of the dialect, in the Aramaic portions of Daniel and Ezra; and the Galilean, in isolated expressions in the Talmud (3rd century), and in a fragmentary 5th century translation of the Bible.

201The general type of problem is to find two, three or four numbers such that different expressions involving them in the first and second, and sometimes the third, degree are squares, cubes, partly squares and partly cubes, &c. E.g.

175The general type of problem is to find two, three or four numbers such that different expressions involving them in the first and second, and sometimes the third, degree are squares, cubes, partly squares and partly cubes, &c. E.g.

1751+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.

143A table may be formed expressing the k expressions Pa l), P(2),...P(1) as linear functions of the k expressions (m"`'smï¿½2smï¿½3s...), s =1, 2, ...k, and the numbers BSc occurring therein is 2s 3s possess row and column symmetry.

101Miss Sullivan never needlessly belittled her ideas or expressions to suit the supposed state of the child's intelligence.

91"If there is a point we don't see it, or it is not at all witty," their expressions seemed to say.

91The soldiers lifted the canteen lids to their lips with reverential faces, emptied them, rolling the vodka in their mouths, and walked away from the sergeant major with brightened expressions, licking their lips and wiping them on the sleeves of their greatcoats.

8524, the reader is left to recognize Enoch from his knowledge of the Biblical narrative.) In the second part of the book there is no expression of "messianic" hope; in the first part the picture of the national future agrees in general (if its expressions are to be taken literally) with that given in the book of Daniel: the Jews are to have dominion over the peoples (iii.

71For the most part, the facial expressions of those sitting around the table were sympathetic, but Dulce looked as if she was ready to break into tears.

62Their expressions were unusually sober.

53When Miss Keller speaks, her face is animated and expresses all the modes of her thought--the expressions that make the features eloquent and give speech half its meaning.

54In this way, she learns countless new expressions without any apparent effort.

54"Well, then, old chap, mon tres honorable Alphonse Karlovich," said Shinshin, laughing ironically and mixing the most ordinary Russian expressions with the choicest French phrases--which was a peculiarity of his speech.

44Papias actually confounds expressions of Jesus with verses from the Apocalypse of Baruch, referring to the amazing fertility of the days of the Messianic kingdom (Papias in Iren.

30Papias actually confounds expressions of Jesus with verses from the Apocalypse of Baruch, referring to the amazing fertility of the days of the Messianic kingdom (Papias in Iren.

30Language has crystallized them into certain definite notions and expressions, without which we cannot proceed a single step, but which we have accepted without knowing their exact meaning, much less their origin.

32The Gathas alone claim to be authentic utterances of Zoroaster, his actual expressions in presence of the assembled congregation.

21The Gathas alone claim to be authentic utterances of Zoroaster, his actual expressions in presence of the assembled congregation.

21All wore similar dreamy expressions to Toni's.

23He urged on the bill by which Catholics were prohibited from sitting in either House of Parliament, and was bitter in his expressions of disappointment when the Commons passed a proviso excepting James, against whom the bill was especially aimed, from its operation.

10The resistance found from the above expressions includes the components I, 2 and 4 of § 4.

10Another singular fact is that they often seemed to be totally unaware of the tendency if not the meaning of some of their own expressions: thus Macleay could write, and doubtless in perfect good faith (Trans.

10Another singular fact is that they often seemed to be totally unaware of the tendency if not the meaning of some of their own expressions: thus Macleay could write, and doubtless in perfect good faith (Trans.

10We find in the Meditations no speculations on the absolute nature of the deity, and no clear expressions of opinion as to a future state.

11It may be inquired what meaning is to be attached to these expressions, and what are the conditions and the nature of the changes assumed by them.

11To treat the actual forms of religion as expressions of our various human needs is a fruitful idea which deserves fuller development than it has yet received; but Feuerbach's treatment of it is fatally vitiated by his subjectivism.

11Expressions in Propertius (ii.

11Expressions in the Odes of Horace (ii.

11The Malay language abounds in idiomatic expressions, which constitute the chief difficulty in its acquisition.

11The authors of rectangular maps look upon the Tabernacle as an image of the world at large, and believe that such expressions as the " four corners of the earth " (Isa.

11" If the law simply consists of ordinary expressions and narratives, such as the words of Esau, Hagar, Laban, the ass of Balaam or Balaam himself, why should it be called the law of truth, the perfect law, the true witness of God ?

11Thus the values of the expressions a 2 /(i - a /V) (Rudolphi, Zeits.

11On the analogy between this case and that of the interface between two solutions, Nernst has arrived at similar logarithmic expressions for the difference of potential, which becomes proportional to log (P 1 /P 2) where P2 is taken to mean the osmotic pressure of the cations in the solution, and P i the osmotic pressure of the cations in the substance of the metal itself.

11Hence in all there are mn such systems. If, therefore, we have a third equation, and we substitute each system of values in it successively and form the product of the mn expressions thus formed, we obtain a function which vanishes if any one system of values, common to the first two equations, also satisfies the third.

11Symbolic Identities.- For the purpose of manipulating symbolic expressions it is necessary to be in possession of certain simple identities which connect certain symbolic products.

11When R =0, and neither of the expressions AC - B 2, 2AB -3C vanishes, the covariant a x is a linear factor of f; but, when R =AC - B 2 = 2AB -3C =0, a x also vanishes, and then f is the product of the form jx and of the Hessian of jx.

11It may be inquired what meaning is to be attached to these expressions, and what are the conditions and the nature of the changes assumed by them.

11To treat the actual forms of religion as expressions of our various human needs is a fruitful idea which deserves fuller development than it has yet received; but Feuerbach's treatment of it is fatally vitiated by his subjectivism.

11Symbolic Identities.- For the purpose of manipulating symbolic expressions it is necessary to be in possession of certain simple identities which connect certain symbolic products.

11All he had seen that day, all the significant and stern expressions on the faces he had seen in passing, were lit up for him by a new light.

11If a hollow sphere 7 of which the outer radius is R and the inner radius r is placed in a uniform field Ho, the field inside will also be uniform and in the same direction as Ho, and its value will be approximately 3 i - R 3 For a cylinder placed with its axis at right angles to the lines of force, 2 = Ho (41) 2 +4(-2)(i - R2) These expressions show that the thicker the screen and the greater its permeability o, the more effectual will be the shielding action.

13Only quizzical and sad expressions.

00For a moment they silently exchanged determined expressions.

00To endow the universal substance with moral attributes, to maintain that it is more than the metaphysical ground of everything, to say it is the perfect realization of the holy, the beautiful and the good, can only have a meaning for him who feels within himself what real not imaginary values are clothed in those expressions.

00On the 25th of November Cromwell charged Manchester with "unwillingness to have the war prosecuted to a full victory"; which Manchester answered by accusing Cromwell of having used expressions against the nobility, the Scots and Presbyterianism; of desiring to fill the army of the Eastern Association with Independents to prevent any accommodation; and of having vowed if he met the king in battle he would as lief fire his pistol at him as at anybody else.

0012, 45); though from the lips of slaves and other low persons in the plays we no doubt hear expressions which, while they are quite in keeping with the characters to whom they are allotted, would have shocked the ears of polite society in the 2nd century B.C.

00The book contains expressions such as daemones, angelica virtus, and purgatoria dementia, which have been thought to be derived from the Christian faith; but they are used in a heathen sense, and are explained sufficiently by the circumstance that Boetius was on intimate terms with Christians.

00Then a disappears from all the above expressions.

00Literature and affairs, science and statecraft, poetry and medicine, these various expressions of human nature and activity were so harmoniously balanced that they might be found in the possession of one and the same individual.

00Its foundation was probably certain expressions lamenting Scottish interference in English affairs.

00Before the rise of Neoplaton ism proper we meet with various mystical or semimystical expressions of the same religious craving.

00But the exact meaning which he attaches to such expressions is not quite clear; and they occur, moreover, only incidentally and with the air of current phrases mechanically repeated.

00It is not surprising that with such maxims as these in his mouth, unguarded in his expressions and careless of his reputation, he should have afforded room for the circulation of many stories to his disadvantage."

00AMMONIUS GRAMMATICUS, the supposed author of a treatise entitled IIEpc 6yoLwv Kai &acaopwv (On the Di f ferences of Synonymous Expressions), of whom nothing is known.

00With one symbol for an unknown, it will easily be understood what scope there is foradroit assumptions, for the required numbers, of expressions in the one unknown which are at once seen to satisfy some of the conditions, leaving only one or two to be satisfied by the particular value of x to be determined.

00Evidence in support of this view is sought for in the accounts in the Anglo-Saxon Chronicle and elsewhere, where the decisions of the witan were received with loud expressions of approval or of disapproval by an assembled crowd, and it is argued that this is a survival from an earlier age, when all the freemen attended the witan.

00If we are to follow von Sybel rather than Kugler, this saga of the First Crusade found one of its earliest expressions (c. 1120) in the prose work of Albert of Aix (Historia Hierosolymitana) - genuine saga in its 1 His somewhat legendary treatise, De liberatione civitatum Orientis, was only composed about 1155.

00a Mahommedan, as synonymous Religion expressions.

00As it is rich in specific expressions for the various aspects of certain ideas, it is requisite to employ always the most appropriate term suited to the particular aspect.

00both the translation and the original were publicly burnt by the common hangman on the 5th of May 1686, as containing "expressions scandalous to His Majesty the king of France."

00Alexander is said to have granted the Lydians to be " free " and " to use the laws of the ancient Lydians," whatever exactly these expressions may mean (Arr.

00and therefore of the product of those expressions.

00symbolically, to be the fundamental form of seminvariant of degree 0 and weight w; he observes that every form of this degree and weight is a linear lic expressions.

00The collected works of Hrabanus himself contain nothing new, but in some glosses on Aristotle and Porphyry, first exhumed by Cousin, there are several noteworthy expressions of opinion in a Nominalistic sense.

00Some of the expressions used by Anselm in controverting his position favour this idea.

00In the French Corps Legislatif, also, the vice-president, Forgade la Roquette, referred to his death, and warm expressions of esteem were repeated and applauded on every side.

00Logical in its derivatives and in its grammatical structure, the Magyar language is, moreover, copious in idiomatic expressions, rich in its store of words, and almost musical in its harmonious intonation.

00Expressions occur in Laplace's private letters inconsistent 3 Mee.

00The 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.

00This reaction has taken the form of a return to the alliance between algebra and geometry (ï¿½5), on which modern analytical geometry is based; the alliance, however, being concerned with the application of graphical methods to particular cases rather than to general expressions.

00The two expressions whose equality is stated by an equation or an identity are its members.

00- The calculation of the values of simple algebraical expressions for particular values of letters involved is a useful exercise, but its tediousness is apt to make the subject repulsive.

00Another useful set of graphs comprises those which give the relation between the expressions of a length, volume, &c., on different systems of measurement.

00Let X and Y be the related quantities, their expressions in terms of selected units A and B being x and y, so that X=x.A, Y = y.

00(ii.) By means of the commutative law we can collect like terms of a monomial, numbers being regarded as like terms. Thus the above expression is equal to 6a 5 bc 2, which is, of course, equal to other expressions, such as 6ba 5 c 2.

00It must, of course, be remembered (ï¿½ 23) that this is a statement of arithmetical equality; we call the statement an " identity," but we do not mean that the expressions are the same, but that, whatever the numerical values of a, b and c may be, the expressions give the same numerical result.

00is then an expression of the form a p b e c r d s, where p, q, r, s have the greatest possible values consistent with the condition that each of the given expressions shall be divisible by a p b e c r d s .

00is of the form a p b e c r d s, where p, q, r, s have the least possible values consistent with the condition that a P PC'd s shall be divisible by each of the given expressions.

00The principles of arithmetical transformation follow from those stated in ï¿½ï¿½ 15-18 by replacing X, A, B, m, M, x, n, a and p by any expressions involving or not involving the unknown quantity or number and representing positive numbers or (in the case of X, A, B and M) positive quantities.

00if B and C are expressions involving x which are different in form but are arithmetically equal for all values of x), then the statement A = C is an equation which is true for the same value of x for which A = B is true.

00(viii.) The quadratic equation is the equation of two expressions, monomial or multinomial, none of the terms involving any power of x except x and x 2 .

00The standard form is usually taken to be ax2+bx+c =0, from which we find, by transformation, (2 ax+b) 2 =b 2 - 4ac, 4 (}b 2 -4ac} -b and thence x = 2a (ii.) In an equation of the form Q=V, the expressions P, Q, U, V are usually numerical.

00Fractional Expressions.

00The expressions obtained in this way are called the first, second,.

00Thus we arrive at the differential coefficient of f(x) as the limit of the ratio of f (x+8) - f (x) to 0 when 0 is made indefinitely small; and this gives an interpretation of nx n-1 as the derived function of xn (ï¿½ 45)ï¿½ This conception of a limit enables us to deal with algebraical expressions which assume such forms as -° o for particular values of the variable (ï¿½ 39 (iii.)).

00Expressions of the form b1,1 - I and a-}-b A l - I, where a and b are real numbers, are then described as imaginary and complex numbers respectively; the former being a particular case of the latter.

00In the course of reducing such expressions as (AB)C, (AB){C(DE)} and the like, where a chain of multiplications has to be performed in a certain order, the multiplications may be all progressive, or all regressive, or partly, one, partly the other.

00Its great merit consists in the complete notation and symbolism, which avoided the cumbersome expressions of the earlier algebraists, and reduced the art to a form closely resembling that of to-day.

00A fantastic and elaborate doctrine of symbolism existed which comprised all nature; witchcraft, alchemy and medicine were its practical expressions.

00That state of mind was due to the fact that the groupings so recognized did not profess to be simply the result of scientific reasoning, but were necessarily regarded as the expressions of the " insight " of some more or less gifted persons into a plan or system which had been arbitrarily chosen by the Creator.

00In these expressions we are to replace p by ks/f, or rather, since the diffraction pattern is symmetrical, by kr/f, where r is the distance of any point in the focal plane from the centre of the system.

00If we put for shortness 7 for the quantity under the last circular function in (I), the expressions (i), (2) may be put under the forms u sin T, v sin (T - a) respectively; and, if I be the intensity, I will be measured by the sum of the squares of the coefficients of sin T and cos T in the expression u sin T +v sin (T - a), so that I =u 2 +v 2 +2uv cos a, which becomes on putting for u, v, and a their values, and putting f =Q .

00Expressions suitable for discussion when v is large were obtained 1 In experiment a line of light is sometimes substituted for a point in order to increase the illumination.

00Comparing the expressions for C, S in terms of M, N, and in terms of G, H, we find that G = z (cos u+sin u)-M, H = z (cos u-sin u) +N.

00Thus, though the psalms represent a great range of individual religious experience, they avoid such situations and expressions as are too unique to be used in acts of public devotion.

00These considerations, in addition to numerous phrases and expressions which cannot here be noticed, of which the full force can only be felt by those who have specially studied the Maccabaean period and those other portions of the Old Testament, such as Zechariah ix.

00Cicero frequently reproduces his expressions, applies passages in his plays to his own circumstances, and refers to his personages as typical representations of character.'

00Other expressions in his poem (e.g.

00The fragments of the old tragedian Pacuvius and of the satirist Lucilius show that Lucretius had made use of their expressions and materials.

00came to London on the 2nd of August 1274, when he was received with the wildest expressions of joy.

00Hero's expressions for the areas of regular polygons of from 5 to 12 sides in terms of the squares of the sides show interesting approximations to the values of trigonometrical ratios.

00A careful examination, however, of the "we" sections shows that words and expressions characteristic of the author of the third Gospel and the Acts are found in them to an extent which is very remarkable, and that in many instances they belong to the very texture of the passages.

00and ii., passim), and prolonged by the expressions of joy, the ascriptions of thanksgiving and praise, called forth by the words and works of Christ and the wonders of the cross and resurrection, which are peculiarly frequent and full (iv.

00bdo 7rpb 2 (u, b 2 a2 Uibb +¢z), and the difference X-X 1 is the component momentum of the liquid in the interspace; with similar expressions for Y and Y1.

00Kirchhoff's expressions for X, Y, Z, the coordinates of the centre of the body, FX=y 1 cos xY--y 2 cos yY-{-y 3 cos zY, (18) FY = -y l cos xX -Hy2 cos yX+y 3 cos zX, (Ig) G=y 1 cos xZ+y 2 cos yZ+y 3 cos zZ, (20) (21) F(X+Yi) = Fy3-Gx3+i /) X 3epi.

00While the so-called "barbaric laws" (leges barbarorum) of the continent, not excepting those compiled in the territory now called Germany, were largely the product of Roman influence, the continuity of Roman life was almost completely broken in the island, and even the Church, the direct heir of Roman tradition, did not carry on a continuous existence: Canterbury was not a see formed in a Roman province in the same sense as Tours or Reims. One of the striking expressions of this Teutonism is presented by the language in which the Anglo-Saxon laws were written.

00The reign of !Ethelred, which witnessed the greatest national humiliation and the greatest crime in English history, is also marked by the most lavish expressions of religious feeling and the most frequent appeals to morality.

00Enactments about the pursuit of thieves, and the calling in of warrantors to justify sales of chattels, are other expressions of the difficulties attending peaceful intercourse.

00Such remains as there are of their language, a few expressions and the proper names of ancient chieftains still borne by certain families, connect it with the Berber dialects.

00His opposition to 'the philosophes had its strongest expressions in Fanatisme des philosophes (Geneva and Paris, 1764) and Histoire des revolutions de l'empire romain (Paris, 1766-1768).

00His appeal to Caesar involved a protracted process, and it is very difficult to put expressions like those e.g.

00The great undertaking was supported by liberal subscriptions, and Walton's political opinions did not deprive him of the help of the Commonwealth; the paper used was freed from duty, and the interest of Cromwell in the work was acknowledged in the original preface, part of which was afterwards cancelled to make way for more loyal expressions towards that restored monarchy under which Oriental studies in England immediately began to languish.

00Incidentally he introduces into his explanations the current German expressions for the things he is treating of, with the apology that Solomon had 1 In the oldest MSS.

00Even if there were no such unmistakable expressions as these, the most cursory glance into Saint-Simon's writings is enough to reveal the thread of connexion between the ingenious visionary and the systematic thinker.

00The terms trinomial, quadrinomial, multinomial, &c., are applied to expressions composed similarly of three, four or many quantities.

00The above expressions for the capacity of an ellipsoid of three unequal axes are in general elliptic integrals, but they can be evaluated for the reduced cases when the ellipsoid is one of revolution, and hence in the limit either takes the form of a long rod or of a circular disk.

00Let V be the potential at the centre of the prism, then the normal forces on the two faces of area dy.dx are respectively RI dx2 d xl and (dx 2 d x), dV d2 and similar expressions for the normal forces to the other pairs of faces dx.dy, dz.dx.

00Hence, multiplying these normal forces by the areas of the corresponding faces, we have the total flux parallel to the x-axis given by - (d 2 V/dx 2)dxdydz, and similar expressions for the other sides.

00We thus obtain the expressions dH = sdo +0 (dp I dO) dv = Sd0 - o (dv/do) dp..

00- The change of intrinsic energy E along any path is found by subtracting the work pdv from either of the expressions for dH.

00Since the two expressions (9) are the partial differential-coefficients of a single function E of the independent variables v and 0, we shall obtain the same result, namely d 2 E/d0dv, if we differentiate the first with respect to v and the second with respect to 0.

00If we also assume that they are constant with respect to temperature (which does not necessarily follow from the characteristic equation, but is generally assumed, and appears from Regnault's experiments to be approximately the case for simple gases), the expressions for the change of energy or total heat from 00 to 0 may be written E - Eo = s(0 - 0 0), F - Fo = S(0-00).

00(14) where (00,v), (e 0, vo) are any two points on the adiabatic. The corresponding expressions for the change of energy or total heat are obtained by adding the term 2as 0 (02-002) to those already given, thus: E - Eo = so (0-00) + 2 aso (02-002), F - Fo=S0(0-00) + zaso (02-002), where So= so+R.

00Many complicated expressions have been suggested by subsequent writers in the attempt to represent the continuity of the gaseous and liquid states in a single formula, but these are of a highly empirical nature, and beyond the scope of the present inquiry.

00Denoting by So, so, these constant limiting values at p=o, we may obtain the values at any pressure by integrating the expressions (27) and (28) from co to v and from o to p respectively.

00(29) (30) The expression for the change of entropy between any two states is found by dividing either of the expressions for dH in (8) by 0 and integrating between the given limits, since dH/B is a perfect differential.

00In the case of an ideal gas, dp/d9 at constant volume =R/v, and dvld6 at constant pressure =R/p; thus we obtain the expressions for the change of entropy 0-4)0 from the state poeovo to the state pev, log e e/eo+R logev/vo =S log e 9/00-R (32) In the case of an imperfect gas or vapour, the above expressions are frequently employed, but a more accurate result may be obtained by employing equation (17) with the value of the specific heat, S, from (29), which gives the expression 4-¢o = Sologe0/00 - R logep/po-n(cp/B-copo/Bo)

00Writing formulae (3r) and (33) for the energy and entropy with indeterminate constants A and B, instead of taking them between limits, we obtain the following expressions for the thermodynamic functions in the case of the vapour: " =Solog e 0 - R log e p - ncp/D+A".

00This simple result is generally true, and the corresponding expressions for G" and J" are valid, provided that c - b in formula (17) is a function of the temperature only.

00It is not necessary to suppose that c varies inversely as the nth power of the temperature, and that b is constant, as assumed in deducing the expressions for cp, E, and F.

00The early Montanists (the prophets themselves) used expressions which seem to indicate a Monarchian conception of the person of Christ.

00Every endeavour is made to gloss over, or modify, expressions which seemed derogatory to the ancestors of ' According to Zunz, Gottesdienstliche Vortrdge, 2nd ed., p. 80, its contents bear the following proportions to Genesis, z o o to Exodus, about 1 1 4 to Leviticus, s to Numbers, and 4 to Deuteronomy.

00He has most of the characteristic expressions of the Eastern creeds.

00Another of his works, Recensio canonica effectionum geometricarum, bears a stamp not less modern, being what we now call an algebraic geometry - in other words, a collection of precepts how to construct algebraic expressions with the use of rule and compass only.

00In commerce, however, other expressions are met with, as, for example, "pounds per cubic foot" (used for woods, metals, &c.), "pounds per gallon," &c. The standard substances employed to determine relative densities are: water for liquids and solids, and hydrogen or atmospheric air for gases; oxygen (as 16) is sometimes used in this last case.

00Nevertheless on her deathbed, when she was attended by the archbishop of Canterbury and the bishop of London, she used expressions which were construed as a declaration of Protestantism.

00In bookkeeping, in such expressions as "petty cash," "cash-book," and the like, it has the same significance, and so also in "cash-payment" or ready-money payment as opposed to "credit," however the payment may be made, by coin, notes or cheque.

006-21, together with some isolated expressions and all references to the Lamb.

00Fox, of the Central Laboratory of the International Council at Christiania, has investigated the relation of the atmospheric gases to sea-water by very exact experimental methods and arrived at the following expressions for the absorption of oxygen and nitrogen by sea-water of different degrees of concentration.

00He had read widely and deeply, and in his own writings we come across many expressions familiar to us in earlier systems. Yet his philosophy is no eclecticism.

00The numbers obtained by giving n any value in these expressions are of the first, second, third,.

00In 1408, however, the clergy of the city and archiepiscopal diocese of Prague laid before the archbishop a formal complaint against Huss, arising out of strong expressions with regard to clerical abuses of which he had made use in his public discourses; and the result was that, having been first deprived of his appointment as synodal preacher, he was, after a vain attempt to defend himself in writing, publicly forbidden the exercise of any priestly function throughout the diocese.

00His death, on the 17th of May 1838, called forth widespread expressions of esteem for the statesman who had rendered such great and varied services to his country.

00The government was frankly theocratic. Said Winthrop (1637): " We see not that any should have authority to set up any other exercises besides what authority bath already set up "; and a synod at Cambridge in 1637 catalogued eighty-two " opinions, some blasphemous, others erroneous and all unsafe," besides nine " unwholesome expressions," all of which were consigned " to the devil of hell from whence they came."

00The author maintains that the Graeco-Hebraic expressions must not be interpreted literally, but explained in terms intelligible to the modern mind.

00- The following are expressions for the areas of some simple figures; the expressions in (i) and (ii) are obtained arithmetically, while those in (iii) - (v) involve dissection and rearrangement.

00- The following are expressions for the volumes of some simple solid figures.

00Let u and x be the numerical expressions of the magnitudes of E and F.

00Thus we get two expressions for A + B -}- C, from which we can eliminate ug.

00The result of performipg both operations, in order to obtain the volume, is the result of the operation denoted by the product of these two expressions; and in this product the powers of E and of E' may be dealt with according to algebraical laws.

00The calculation of the expressions in brackets may be simplified by taking the pairs in terms from the outside; by finding the successive differences of uo + um, ill + um_l, ..., or of uI u i +umi, ..

00The expressions in square brackets are in each case to be taken as relating to the extreme values x =xo and x=xm, as in §§ 75 and 76.

00Either or both of the expressions K and L will have to be calculated by means of the formula of § 84; if this is applied to both expressions, we have a formula which may be written in a more general form f f 4 u4(x, y) dx dy = u dx dy.

00d The second and third expressions on the right-hand side represent areas of trapezettes, which can be calculated from the data; and the fourth expression represents the volume of a briquette, to be calculated in the same way as R above.

00Thus there is many " a pedagogue to Christ," and the Christian visible means and expressions are the culmination and measure of what, in various degrees and forms, accompanies every sincerely striving soul throughout all human history.

00If the loads on the right of the section are considered the expressions are similar and give the same results.

00Yet they do not really add much to what is there already, and they have the drawbacks of pseudonymity; they lack concrete and personal qualities; they are general expressions of tendencies which we cannot well locate or measure, save by means of the Apostolic Fathers themselves or of their earliest Catholic successors.

00They are after all personal expressions of Christianity, in which are discernible also specific types of local tradition.

00This "Palace language" appears to have come into existence from a desire to avoid the employment in the presence of royalty of downright expressions of vulgarity or of words which might be capable of conveying an unpleasant or indelicate idea other than the meaning intended.

00The work contains, in more or less alphabetical order, notes on well-known events and persons mentioned by the orators, and explanations of legal and commercial expressions.

00Ultimately, indeed, as sanctuaries were multiplied and the priests all over the land came to form one well-marked class, " Levite and legitimate priest became equivalent expressions, as is explained in the article Levites.

00In the first of these, entitled " Recherches sur l'attraction des spheroides homogenes," published in the Memoires of the Academy for 1785, but communicated to it at an earlier period, Legendre introduces the celebrated expressions which, though frequently called Laplace's coefficients, are more correctly named after Legendre.

00The former was now mixed with Latin and classical expressions; much of the literature consists of fulsome panegyric, verses written on the marriages and funerals of nobles, with conceits and fantastic ideas, devoid of all taste, drawn from their coats of arms. The poets of this period are, as may be imagined, in most cases mere rhymesters; there are, however, a few whose names are worth recapitulating, such as Waclaw Potocki (c. 1622 - c. 1696), now known to have been the author of the Wojna Chocimska, or "War of Khotin," the same campaign which afterwards formed the subject of the epic of Krasicki.

00The 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.

00The Proverbs of Jesus, the son of Sirach (c. 200 B.C.), which form now the apocryphal book Ecclesiasticus, were translated into Greek by the grandson of the author at about 130 B.C.; and in the preface prefixed by him to his translation he speaks of " the law, and the prophets, and the other books of our fathers," and again of " the law, and the prophets, and the rest of the books," expressions which point naturally to the same threefold division which was afterwards universally recognized by the Jews.

00The style of Deuteronomy, when once it had been formed, lent itself readily to imitation; and thus a school of writers, imbued with its spirit, and using its expressions, quickly arose, who have left their mark upon many parts of the Old Testament.

00The style of " P " is strongly marked - as strongly marked, in fact, as (in a different way) that of Deuteronomy is; numerous expressions not found elsewhere in the Hexateuch occur in it repeatedly.

00The date at which it was written is uncertain; there are features in it which point to its having been the work of a poet living in north Israel, and writing at an early date; but most recent scholars, on account chiefly of certain late expressions occurring in it, think that it cannot have been written earlier than the 4th or 3rd century B.C. In the graceful and tender idyll of Ruth, it is told how Ruth, the Moabitess, and a native consequently of a country hostile theocratically to Israel, adopted Israel's faith (i.

00(b) In determinations of volume which do not admit of a high degree of accuracy the cubic decimetre can be taken as equivalent to the litre; and in these determinations expressions of volumes based on the cube of the unit of linear measure can be substituted for expressions based on the litre as defined above.

00army corps, and Boulanger's expressions of gratitude and devotion on this occasion were remembered against him afterwards when, as war minister in M.

00The Latin original is a glossed version of the Vulgate, and in the English translation the words of the gloss are often substituted for the strong and picturesque expressions of the Biblical text;.

00He made many alterations in the Matthew Bible, characterized by critical acumen and a happy choice of strong and idiomatic expressions.

00The characteristics of Lelewel as an historian are great research and power to draw inferences from his facts; his style is too often careless, and his narrative is not picturesque, but his expressions are frequently terse and incisive.

00The second of these two expressions is generally given as the definition of dispersive power.

00This conception of a difference, of an internal structure in the absolute, finds other and not less obscure expressions in the mystical contributions of the Menschliche Freiheit and in the scholastic speculations of the Berlin lectures on mythology.

00The following table gives the values of this constant and several expressions involving it Useful fractional approximations are 22/7 and 355/113.

00Especially in this last he shows a tendency to epigram and often uses humorous and pathetic expressions.

00The irritation caused by the decision gradually subsided, but at the moment it led to strong expressions on the part of Sir Wilfrid Laurier and others in favour of securing for Canada a fuller power of making her own treaties.

00A text so transmitted must in the lapse of time be profoundly though insensibly modified, its forms and expressions modernized, and, if widely disseminated, local variations introduced into it.

00Proper names, technical expressions, quotations from foreign languages, and frequent change of subject, are all likely to cause difficulty to a scribe and error in his work.

00The elements of this Christian Latin language may be enumerated as follows: - (i.) it had its origin, not in the literary language of Rome as developed by Cicero, but in the language of the people as we find it in Plautus and Terence; (ii.) it has an African complexion; (iii.) it is strongly influenced by Greek, particularly through the Latin translation of the Septuagint and of the New Testament, besides being sprinkled with a large number of Greek words derived from the Scriptures or from the Greek liturgies; (iv.) it bears the stamp of the Gnostic style and contains also some military expressions; (v.) it owes something to the original creative power of Tertullian.

00Besides, all the extant works, though apparently didactic, are full of dialectical matter in the way of opinions (AEyo,cisva), difficulties and doubts (hiropi),uara, europiac), solutions (XimrELs), and of dialectical style in the way of conversational expressions.

00The chief works of Damiron, of which the best are his accounts of French philosophers, are the following: - An edition of the Nouveaux melanges philosophiques de Jouffroy (1842), with a notice of the author, in which Damiron softened and omitted several expressions used by Jouffroy, which were opposed to the system of education adopted by the Sorbonne, an article which gave rise to a bitter controversy, and to a book by Pierre Leroux, De la mutilation des manuscrits de M.

00After many expressions of regret at finding no method of giving effect to the proposal, the commission confined itself to recording its opinion that " a further examination of the question by the Powers would prove a great benefit to humanity."

00The general assembly, to which the case was appealed, suspended Dr Briggs in 1893, being influenced, it would seem, in part, by the manner and tone of his expressions - by what his own colleagues in the Union Theological Seminary called the " dogmatic and irritating " nature of his inaugural address.

00From these introductions we are able to judge of the style of Pappus's writing, which is excellent and even elegant the moment he is free from the shackles of mathematical formulae and expressions.

00On the whole there is clearly a presumption that where we have striking expressions which are known to us besides only in one of our Gospel-records, that particular record has been the source of it.

00With much reluctance the royal permission was given and the resignation accepted, on the 10th of May 1532, with many gracious expressions of goodwill on the part of the king.

00Sometimes he spoke of mind as an effect of matter; but, though his expressions may be careless, nothing is to be made of the difference, for he called it movement and effect indifferently in the same context.

00He divides phenomena into impressions and ideas, vivid and faint, object and subject, non-ego and ego, outer and inner, physical and psychical, matter and spirit; all of which are expressions of the same antithesis among phenomena.

00Af ter the 4th century other names or expressions come into use, such as mensa tremenda, sedes corporis et sanguinis Christi.

00Such a circumstance occurring at a time of general festivity, when devices, mottoes and conceits of all kinds were adopted as ornaments or badges of the habits worn at jousts and tournaments, would naturally have been commemorated as other royal expressions seem to have been by its conversion into a device and motto for the dresses at an approaching hastilude."

00It is one of the expressions used in the Targums in place of "God."

00Great care was taken by the scribes in these renderings to mitigate the anthropomorphic expressions applied to God in the Scriptures, and by paraphrase, the use of abstract terms and indirect phraseology, to prevent such expressions from giving rise to erroneous views as to God's personal manifestation in the popular mind.

00All expressions implying God's local presence are similarly rendered: thus e.g.

00Tears, dejection and passionate expressions of a despair "wishing only for death," bore fitful and variable witness to her first sense of a heavier yoke than yet had galled her spirit and her pride.

00Perhaps our knowledge of Johnson's sentiments regarding the Scots in general, and of his expressions regarding Hume and Smith in particular, may lessen our surprise at this vehemence.

00The quarrel which all the acquaintances of the two philosophers had predicted soon came, and no language had expressions strong enough for Rousseau's anger.

00Moreover, if we remain faithful to the fundamental conception that the contents of the mind are merely matters of experience, it is evident in the first place that as impressions are strictly individual, ideas also must be strictly particular, and in the second place that the faculties of combining, discriminating, abstracting and judging, which Locke had admitted, are merely expressions for particular modes of having mental experience, i.e.

00The subscribers engaged by oath to maintain religion in the state in which it existed in 1580, and to reject all innovations introduced since that time, while professed expressions of loyalty to the king were added.

00When the formula cited is not used, other somewhat nebulous expressions are sometimes employed, as, for example, that.

00In the chapter (xx.) of that work where Hobbes dealt with the famous problem whose solution he thought he had found, there were left expressions against Vindex (Ward) at a time when the solutions still seemed to him good; but the solutions themselves, as printed, were allowed to be all in different ways halting, as he naively confessed he had discovered only when he had been driven by the insults of malevolent men to examine them more closely with the help of his friends.

00containing provisions to check attempts to undermine the loyalty of the soldiers, and making it a crime punishable with three years imprisonment to attack religion, monarchy, marriage, the family or property by abusive expressions in such a manner as to endanger public peace.

00On the other hand, expressions such as " Austrian citizens," " Austrian law " are found.

00Just as the prophet often misunderstood traditional traits of the sacred history, he may, as an unlearned man, likewise have often employed foreign expressions wrongly.

00Sprenger has rightly observed that Mahomet makes a certain parade of these foreign terms, as of other peculiarly constructed expressions; in this he followed a favourite practice of contemporary poets.

00It is the tendency of the imperfectly educated to delight in out-of-the-way expressions, and on such minds they readily produce a remarkably solemn and mysterious impression.

00The close connexion of the two expressions, it is true, makes it probable that Mahomet only added the adjective Rahim to the substantive Rahman in order to strengthen the conception.

00Their common discourse is full of asseverations and expressions respecting sacred things.

00It is clear that the basis which they chose for the new literature was the simplest language of daily life in the monasteries, charged as it was with expressions taken from Greek, pre-eminently the language of patristic Christianity.

00the expressions used in vv.

00The instructions given to them by the emperor were as follows: - they were to procure and peruse all the writings of all the authorized jurists (those who had enjoyed the jus respondendi); were to extract from these writings whatever was of most permanent and substantial value, with power to change the expressions of the author wherever conciseness or clearness would be thereby promoted, or wherever such a change was needed in order to adapt his language to the condition of the law as it stood in Justinian's time; were to avoid repetitions and contradictions by giving only one statement of the law upon each point; were to insert nothing at variance with any provision contained in the Codex constitutionum; and were to distribute the results of their labours into fifty books, subdividing each book into titles, and following generally the order of the Perpetual Edict.2 These directions were carried out with a speed which is surprising when we remember not only that the work was interrupted by the terrible insurrection which broke out in Constantinople in January 532, and which led to the temporary retirement from office of Tribonian, but also that the mass of literature which had to be read through consisted of no less than two thousand treatises, comprising three millions of sentences.

00In such work the painters of Upper Germany at this time, working in the spirit of the late Gothic style just before the dawn of the Renaissance, show considerable technical attainments, with a love of quaint costumes and rich draperies crumpled in complicated angular folds, some feeling for romance in landscape backgrounds, none at all for clearness or balance in composition, and in the attitudes and expressions of their overcrowded figures a degree of grotesqueness and exaggeration amounting often to undesigned caricature.

00No doubt there must have been some kind of foundation for Pirkheimer's charges; and it is to be noted that neither in Darer's early correspondence with this intimate friend, nor anywhere in his journals, does he use any expressions of tenderness or affection for his wife, only speaking of her as his housemate and of her helping in the sale of his prints,&c. That he took her with him on his journey to the Netherlands shows at any rate that there can have been no acute estrangement.

00Luther, though he had probably uttered in private certain expressions of dissatisfaction with Melanchthon, maintained unbroken friendship with him; but after Luther's death certain smaller men formed a party emphasizing the extremest points of his doctrine.'

00The reading of 15thand 16thcentury verse in the light of these will bring home the critical error of treating such poems as Burns's Collar's Saturday Night, the Address to the Deil, and Scotch Drink as entirely expressions of the later poet's personal predilection.

00" He was never tired of asserting his belief " that the Christian Church had not yet presented its final or its most perfect aspect to the world "; that " the belief of each successive age of Christendom had as a matter of fact varied enormously from the belief of its predecessor "; that " all confessions and similar documents are, if taken as final expressions of absolute truth, misleading "; and that " there still remained, behind all the controversies of the past, a higher Christianity which neither assailants nor defenders had fully exhausted."

00We are familiar enough in the West with similar classifications, summed up in such expressions as the Seven Deadly Sins, the Ten Commandments, the Thirty-nine Articles, the Four Cardinal Virtues, the Seven Sacraments and a host of others.

00The oldest verses are all lyrics, expressions either of emotion, or of some deep saying, some pregnant thought.

00The promotion was unexpected, and was accompanied by expressions from the king which made it still more honourable, as showing that if he had been in some things too subservient, it was from no abject, selfseeking policy of his own.

00Heresy was gaining ground in high places, especially after the king's marriage with Catherine Parr; and there seems to be some truth in the story that the queen herself was nearly committed for it at one time, when Gardiner, with the king's approbation, censured some of her expressions in conversation.

00This last sentence has led some modern writers to suppose that he made two different voyages; but this is improbable; the expressions of Polybius imply that his explorations in both directions, first towards the north and afterwards towards the east, formed part of the same voyage.

00Exquisite as he is in his special mode of execution, he undoubtedly falls far short, not only of his great naturalist contemporaries such as 1Vlasaccio and Lippo Lippi, but even of so distant a precursor as Giotto, in all that pertains to bold or life-like invention of a subject or the realization of ordinary appearances, expressions and actions - the facts of nature, as distinguished from the aspirations or contemplations of the spirit.

00The history of the Afghan countries under the Mongols is obscure; but that regime must have left its mark upon the country, if we judge from the occurrence of frequent Mongol names of places, and even of Mongol expressions adopted into familiar language.

00Plato's criticisms of the sophists are then, in the opinion of the present writer, no mere obiter dicta, introduced for purposes of literary adornment or dramatic effect, but rather the expressions of profound and reasoned conviction, and, as such, entitled at any rate to respect.

00Although these expressions were equivocal, the Republicans were satisfied and embarked on the vessels prepared for them.

00By Ohm'S Law, And By The Definition Of Difference Of Electric Pressure Or Potential, We Obtain The Following Alternative Expressions For The Quantity Of Heat H In Joules Generated In A Time T Seconds By A Current Of C Amperes Flowing In A Wire Of Resistance R Ohms, The Difference Of Potential Between The Ends Of The Wire Being E = Cr Volts: H=Ect=Crt=E Z T/R.

00Army to the minimum in order to strengthen his attack on the Isonzo, and in reply to Brusati's expressions of anxiety regarding the adequacy of his forces during this period Cadorna pointed out that the requirements of the Isonzo front made it necessary to reduce the numbers of the I.

00The expressions of them are simply the speech-signs for them.

00The consideration that mere double negation leaves us precisely where we were and not upon a higher plane where the dominant concept is richer, is, of course, fatal only to certain verbal expressions of Hegel's intent.

00The sum of two such lines (formed by adding together the real and the imaginary parts of two such expressions) can, of course, be expressed as a third directed line) - the diagonal of the parallelogram of which they are conterminous sides.

00If we write the expressions for the two lines in the form A+Bi, A'+B'i, the product is AA' - BB'+i(AB'+BA'); and the fact that the length of the product line is the product of those of the factors is seen in the form (A 2 + B 2) (A'2-{-B'2) = (AA' - BB')2+(AB'+BA')2.

00Neither of these men professed to employ the calculus itself, but they recognized fully the extraordinary clearness of insight which is gained even by merely translating the unwieldy Cartesian expressions met with in hydrokinetics and in electrodynamics into the pregnant language of quaternions.

00These works are lost; but their titles, combined with expressions in the letters of Synesius, who consulted her about the construction of an astrolabe and a hydroscope, indicate that she devoted herself specially to astronomy and mathematics.

00The leading thesis seems to have been that all the great religions of the world originated from the same supreme source, and that they were all to be regarded as so many divers expressions of one and the same fundamental truth, or "Wisdom Religion," in such form and dress as was best adapted to suit the times and the people for whose spiritual growth and development religious instruction was required.

00As thus the restless reason tests the emotions of the soul, criticizes the traditions to which they cling, rejects the ancient dogmas in which they have been defined, the Church slowly participates in the process: silently this position and that are forsaken, legends and beliefs once of prime importance are forgotten, or when forced into controversy many ways are found by which the old and the new are reconciled: the sharpness of distinctions can be rubbed off, expressions may be softened, definitions can be modified and half-way resting-places afforded, until the momentous transition has been made and the continuity of tradition is maintained.

00mous expressions Perez had used in connexion with his troubles, in Castile.

00The Eastern Church affirms belief in an intermediate state after death, but the belief is otherwise as vague as the expressions of the pre-Nicene fathers on the subject.

00If x, y, z be the rectangular co-ordinates of a masselement m, the expressions m5i, m~, m~ must be equal to the components of the total force on m, these forces being partly extraneous and partly forces exerted on m by other mass elements of the system.

00If we multiply theta by p, q, r, respectively, or again by Ap, Bq, Cr respectively, and add, we verify that the expressions Ap2 + Bqf + Cr1 and A1p2 + Bfqi + Ciri are both consta~it.

00By an obvious analogy, the expressions OTfO4r may be called the generalized components of momentum; they are usually denoted by Pr, thus = OT/aq,.

007 (1904), the qfiestion is investigated from a new mathematical point of view, and expressions for the whirling of loaded shafts are obtained without the necessity of any assumption of the kind stated above.

00raided south Palestine and Ethiopia, and at Semna beyond the second cataract set up a stela of conquest that in its expressions recalls the stelae of Sesostris in Herodotus: Sesostris may, therefore, be the highly magnified portrait of this Pharaoh.

00There is no proof that he was the author of any of these poems, but from expressions in the poems of Sir David Lindsay, who was on terms of intimacy with him, it appears that occasionally he wrote verses.

00As the Genesis begins with a line identical in meaning, though not in wording, with the opening of Cmdmon's Hymn, we may perhaps infer that the writer knew and used Cmdmon's genuine poems. Some of the more poetical passages may possibly echo Cmdmon's expressions; but when, after treating of the creation of the angels and the revolt of Lucifer, the paraphrast comes to the Biblical part of the story, he follows the sacred text with servile fidelity, omitting no detail, however prosaic. The ages of the antediluvian patriarchs, for instance, are accurately rendered into verse.

00This appears, on the one hand, in the use of expressions having a Modalistic ring about them - see especially the poems of Commodian, written about the time of Valerian - and, on the other hand, in the rejection of the doctrine that the Son is subordinate to the Father and is a creature (witness the controversy between Dionysius of Alexandria and Dionysius of Rome), as well as in the readiness of the West to accept the formula of Athanasius, that the Father and the Son are one and the same in substance (O,uoou6coc).

00The expressions " science of finance " and " public finance " have been suggested as suitable to delimit the last mentioned application.

00The expressions yr hwn, y neb, " the one," are mistaken for relatives by the old grammarians; the true relative follows: yr hwn a =" the one who."

00He was ignorant of the rules of grammar, confused genders and cases, and wrote in the vernacular Latin of his time, apart from certain passages which are especially elaborated and filled with poetical and elegant expressions.

00Two so-called friends endeavoured, on the plea of doubts of their own, to lead him into a theological discussion; and, some of Spinoza's expressions being repeated to the Jewish authorities, he was summoned to give an account of himself.

00Expressions for 00, 01, 132, ...

00The latter regarded dogmatic as stating in scientific connexion "the doctrine prevailing in a (single) Christian church at a given time" - as "not merely historical (geschichtlich)," but containing an "apologetic element" - as "not confined to the symbolical books, but" including all - even local expressions of the common faith which produce no breach of harmony - and as having for its "very business and task" to "purify and perfect" doctrine (Der christliche Glaube, § 19).

00His opponents, moreover, have preserved some expressions of his, with extracts from his principal work; so that our knowledge of Marcion's views is in part derived from the best sources.

00All private meetings and public gatherings, with the expressions of opinion and the class of subjects discussed, were to be controlled by the police.

00(i) They may be sym bolical of the light of God's presence, of Christ as " Light of Light," or of the children of Light in conflict with the powers of darkness; they may even be no more than expressions of joy on the occasion of great festivals.

00The words and phrases which are common to the pastorals and the rest of the Pauline epistles are neither so characteristic nor so numerous as those peculiar to the former, and the data of style may be summed up in the verdict that they point to a writer who, naturally reproducing Paul's standpoint as far as possible, and acquainted with his epistles, yet betrays the characteristics of his later milieu in expressions as well as in ideas.'

00His friend Naudee, however, declares that the expressions used by Campanella were wrongly interpreted as revolutionary.

00Owing probably to the fact that Makran was for many generations under the rule of the Persian kings, the Baluchi spoken on the west of the province, which is also called Makrani, is more largely impregnated with Persian words and expressions than the Eastern dialect.

00A full account of the principal trials, and of the various legislative measures for repressing the expressions of popular opinion for which he was more or less responsible, will be found in Twiss's Public and Private Life of the Lord Chancellor Eldon, and in the Lives of the Lord Chancellors, by Lord Campbell.

00With regard to the literary relation of this chapter with Ezekiel, it must be admitted that Ezekiel presents many striking parallels, and in particular makes use, in common with chap. xxvi., of several expressions which do not occur elsewhere in the Old Testament.

00We shall then have E 1 - Mixoi S f El E - 4 S 2 Adding these expressions, and dividing the second member by S, we obtain for the tension of the surface of contact of the two liquids T,.

00(3) The text must be retranslated into Hebrew in order to explain unintelligible expressions and restore the true text.

00This circumstance gave rise to a number of proverbial expressions, like Avriicbpas oe bei or "naviget Anticyram," and to frequent allusions in the Greek and Latin writers.

00Rabelais wrote a panegyrical memoir of Guillaume, which is lost, and the year before saw the publication of an edition of Gargantua and Pantagruel, book i., together (both had been repeatedly reprinted separately), in which some dangerous expressions were cut away.

00On the other hand, there are in the book, in the description of Gargantua's and Pantagruel's education, in the sketch of the abbey of Thelema, in several passages relating to Pantagruel, expressions which either signify a sincere and unfeigned piety of a simple kind or else are inventions of the most detestable hypocrisy.

00The effect is produced partly by the comments of the evangelist, which especially take the form of citations from the Old Testament; partly by the frequency with which certain expressions are used, and the prominence that is given in this and other ways to particular traits and topics.

00In his works written during this period (for instance, the Praeparatio evangelica and Demonstratio evangelica), as in the works of Origen himself and other anteNicene fathers, expressions occur looking in the direction of Arianism, and others looking in the opposite direction.

00The expressions "Chaldaea r" and "Chaldaeans" are frequently used in the Old Testament as equivalents for "Babylonia" and "Babylonians."

00Skeat has connected it with Old English lcietan, to let, which is very doubtful, though this is the origin of the use of the word in such expressions as "two-" "three-way leet," a place where cross-roads melt.

00It may be pointed out here that these expressions are defined by the act, the effect of the definitions being shortly that a drain is a conduit for the drainage of one building or of several within the same curtilage, while a sewer comprises every kind of drain except that which is covered by the definition of a drain as above stated.

00It has always been politic for powerful states to facilitate and hide schemes of aggrandizement under euphemistic expressions; to cloak subjection or dependence by describing it in words inoffensive or strictly applicable to other relations.

00He made some preliminary use of these expressions in 1817, in a paper on Kepler's Problem (Transactions Berlin Academy, 1816-1817, p. 49), and fully developed them seven years later, for the purposes of a research into planetary perturbations (Ibid.

00" one man," means 20, &c., &c. The existence of such expressions demonstrates that the people who use them had originally no spoken names for these numbers, but once merely counted them by gesture on their fingers and toes in low savage fashion, till they obtained higher numerals by the inventive process of describing in words these counting-gestures.

00This whole prophecy, which is perhaps the most interesting in the Book of Daniel, presents problems which can never be thoroughly understood, first because the author must have been ignorant of both history and chronology, and secondly, because, in his effort to be as mystical as possible, he purposely made use of indefinite and vague expressions which render the criticism of the passage a most unsatisfactory task.

00Strange shapes of hills and rocks, rare plants and animals, unusual faces and figures of men, questionable smiles and expressions, whether beautiful or grotesque, far-fetched objects and curiosities, were things he loved to pore upon and keep in memory.

00In 1490, the seventh year of his residence at Milan, after some expressions of impatience on the part of his patron, he had all but got his model ready for display on the occasion of the marriage of Ludovico with Beatrice d'Este, but at the last moment was dissatisfied with what he had done and determined to begin all over again.

00Judging by the accounts of those who saw it, and the fragmentary evidences which remain, the tumultuous medley of men -and horses, and the expressions of martial fury and despair, must have been conceived and rendered with a mastery not less commanding than had been the looks and gestures of bodeful sorrow and soul's perplexity among the quiet company on the convent wall at Milan.

00Frazer, The Golden Bough, ii (1900), pp. 160, 291, who regards the bull and goat form of Dionysus as expressions of his proper character as a deity of vegetation; F.

00The old familiar name Yahweh became a secret; its place was taken by such general expressions as the Holy, the Almighty, the Majesty on High, the King of Kings, and also by the simple word "Heaven."

00His public expressions of opinion were hostile in tone to the policy pursued by Mr Chamberlain and Sir Alfred Milner.

00Mr Schreiner, in reply, used expressions which called down upon him the severest censure and indignation, both in the colony and in Great Britain.

00The shock to the public, to the House of Commons, to his party, and to Mr. Lloyd George was great; and genuine expressions of regret were heard on every side.

00is only an arithmetical statement in so far as each of the three expressions denotes a numerical quantity (§ II).

00The points of the compass might similarly be expressed by numbers in a binary scale; but the numbers would be ordinal, and the expressions would be analogous to those of decimals rather than to those of whole numbers.

00The expressions 4 r are then fractional numbers, their relation to n' n' n' ' ' ordinary or integral numbers being that /2 n times n times is equal to p times.

00While at Berlin in1824-1825he was thrown into prison, either on some ill-defined political charge at the instance of the French police, or on account of certain incautious expressions which he had let fall in conversation.

00The word the Jains use for soul is jiva, which means life; and there is much analogy between many of the expressions they use and the view that the ultimate cells and atoms are all, in a more or less modified sense, alive.

00In deciding on war the British government relied on the capacity of its fleet, which was entrusted to the command of Sir Charles Napier, to strike a great blow in the Baltic. The fleet was despatched with extraordinary rejoicings, and amidst loud and confident expressions of its certain triumph.

00In every portion of the globe the sixtieth anniversary of the queens reign excited interest; in every country the queens name was mentioned with affection and respect; while the people of the United States vied with the subjects of the British empire in praise of the queens character and in expressions of regard for her person.

00a property independent of the particular axes of co-ordinates used in the representation of the curve by its equation; for instance, the curve may have a node, and in order to this, a relation, say A = o, must exist between the coefficients of the equation; supposing the axes of co-ordinates altered, so that the equation becomes u' = o, and writing A' = o for the relation between the new coefficients, then the relations A = o, A' = o, as two different expressions of the same geometrical property, must each of them imply the other; this can only be the case when A, A' are functions differing only by a constant factor, or say, when A is an invariant of u.

00It is a form of the theorem for the case D = r, that the coordinates x, y, z of a point of the bicursal curve, or in particular the co-ordinates of a point of the cubic, can be expressed as proportional to rational and integral functions of the elliptic functions snu, cnu, dnu; in fact, taking the radical to be r -0 2 .r - k 2 0 2, and writing 8 =snu, the radical becomes = cnu, dnu; and we have expressions of the form in question.

00Burke, no doubt, in the course of that unparalleled trial showed some prejudice; made some minor overstatements of his case; used many intemperances; and suffered himself to be provoked into expressions of heat and impatience by the cabals of the defendant and his party, and the intolerable incompetence of the tribunal.

00The chief liturgical expressions of this cult are the institution of a feast of the Sacred Heart and public representations of it by statues and pictures.

00Scattered expressions of anti-Trinitarian opinion appear here early.

00By the recognition of this law the church was constituted as an ordered community, essentially distinct from the State; the distinction between the two was emphasized by the withdrawal of the early Christians from civic life, to avoid the performance of idolatrous ceremonies imposed as official expressions of loyalty, and by the persecutions which they had to endure, when the spread of an association apparently so hostile to the framework of ancient society had at length alarmed the imperial government.

00&c.), which overlook the essential distinction between what is and what ought to be; and even in one or two expressions to overleap this distinction extravagantly, as (e.g.) in saying that the man who " wilfully acts contrary to justice wills things to be what they are not and cannot be."

00Moral judgments, then, are expressions of the complex normal sympathy of an impartial spectator with the active impulses that prompt to and result from actions.

00It was believed that the vernacular could not be raised to the dignity of a literary language, and that literature and science needed words and expressions which were entirely lacking in the common language.

00Moreover, as a third advantage, these expressions are entirely free from those difficulties and ambiguities which are met with in every attempt to express the laws of motion in ordinary language.

00The solution of these equations would lead to expressions of the form a= 41(x,y,x',y',t) b= (x,y,x',y',t) (4) &c. &c.

00We first conceive of the planets as moving in invariable elliptic orbits, and thus obtain approximate expressions for their positions at any moment.

00With these expressions we express their mutual action, or their pull upon each other at any and every moment.

00Knowing these variations it becomes possible to represent by integration the value of the elements as algebraic expressions containing the time, and the elements with which we started.

00The computations are, as a general rule, simpler, and the algebraic expressions less complex, than when the computations of the longitude itself are calculated.

00The longitudes, latitudes and radii vectores of a planet, being algebraically expressed as the sum of an infinite periodic series of the kind we have been describing, it follows that the problem of finding their co-ordinates at any moment is solved by computing these expressions.

00The expressions for the longitude, latitude `and parallax appear as an infinite trigonometric series, in which the coefficients of the sines and cosines are themselves infinite series proceeding according to the powers of the above small numbers.

00Wherever the noblest expressions of her mind are honoured, wherever the large conceptions of Pericles command the admiration of statesmen, wherever the architect and the sculptor love to dwell on the masterpieces of Ictinus and Pheidias, wherever the spell of ideal beauty or of lofty contemplation is exercised by the creations of Sophocles or of Plato, there it will be remembered that the spirit which wrought in all these would have passed sooner from among men, if it had not been recalled from a trance, which others were content to mistake for the last sleep, by the passionate breath of Demosthenes.

00Along with strong expressions of empiricism we find him holding doctrines absolutely irreconcilable with empiricism in any form.

00Many of the wilder myths are the expressions of the sportive and humorous faculties.

00Nifo had edited the works of Averroes (1495-1497); but his expressions gave offence to the dominant theologians, and he had to save himself by distinguishing his personal faith from his editorial capacity.

00Virtue is the perfect conformity of the will with the moral ideas; of this the single virtues are but special expressions.

00The general expressions for the rectangular components of a vector transverse to the direction of propagation (z) in the case of waves of length X travelling with speed v are: - u= a cos (T - a), v=b cos (T - (3), where T= 27r(vt - z)/h.

00The expressions for the intensity of the refracted light may be obtained from those relating to the reflected light by the principle of energy.

00Now Fresnel's formulae were obtained by assuming that the incident, reflected and refracted vibrations are in the same or opposite phases at the interface of the media, and since there is no real factor that converts cos T into cos (T+p), he inferred that the occurrence of imaginary expressions for the coefficients of vibration denotes a change of phase other than 7r, this being represented by a change of sign.

00Formulae for metallic reflection may be obtained from Fresnel's expressions by writing the ratio sin i / sin r equal to a complex quantity, and interpreting the imaginary coefficients in the manner explained above.

00His appointment was three times renewed, on each occasion with the expressions of the highest esteem on the part of the governing body, and his yearly salary was progressively raised from 180 to l000 florins.

00Returning again to the equations already given in § i i for an elementary thermocouple, we have the following equivalent expressions for the E.M.F.

00But the two expressions are equivalent, and give the same results.

00Neglecting" conduction, all the expressions which he gives are equivalent to the equations of Thomson.

00The sole argument, though a very weighty one, is found in the undeniable relation, revealed in an astonishing similarity both in expressions and composition, which exists between these forgeries and some other documents certainly fabricated at Le Mans, under the episcopate of Aldric (832-856), notably the Actus Pontificum Cenomanis in urbe degentium, in which there is no lack of forged documents.

00From certain expressions used in astrological texts that are earlier than the 7th century B.C. it would appear, indeed, that the beginnings at least of the calculation of sun and moon eclipses belong to the earlier period, but here, too, the chief work accomplished was after 400 B.e., and the defectiveness of early Babylonian astronomy may be gathered from the fact that as late as the 6th century B.C. an error of almost an entire month was made by the Babylonian astronomers in the attempt to determine through calculation the beginning of a certain year.

00In the case of the expressions bien or mal lune, well or ill mooned, avoir un quartier de lune dans la tete, to have the quarter of the moon in one's head, the German mondsiichtig and the English moonstruck or lunatic, the fundamental idea lies in the strange opinions formerly held about the moon.

00are ignored in the narratives of the relations between David and Saul, of whose first meeting two 1 Characteristic expressions of Deuteronomic writers are found in r Sam.

00violent and bitter expressions" for which he afterwards became so conspicuous as to provoke the saying of Harry Marten (the regicide) that, "if the world was emptied of all but John Lilburn, Lilburn would quarrel with John, and John with Lilburn."

00The striking similarity between Kant's expressions in this Essay and the remarks with which Hume introduces his analysis of the notion of cause has led to the supposition that at this period of his philosophical career Kant was definitely under the influence of the earlier empirical thinker.

00The postulates of experience are general expressions of the significance of existence in the experience of a conscious subject.

00These conditions, the postulates of practical reason, are the concrete expressions of the three transcendental ideas, and in them we have the full significance of the ideas for reason.

002), though in the majority of Old Testament passages such expressions are merely verbal (e.g.

00(2) We have meaningless expressions which are really mistranslations of the Hebrew.

00The Greek in turn is derived from the Hebrew, for unintelligible expressions in the Syriac can be explained and the text restored by retranslation into Hebrew.

00For the most part, the facial expressions of those sitting around the table were sympathetic, but Dulce looked as if she was ready to break into tears.

00They watched her with matching troubled expressions, asking the same questions and getting the same answer.

00She had the artless expressions of a human, an endearing trait that made him want to wrap his arms around her.

00Of course, she had never been able to read the expressions on his face.

00Their expressions were unusually sober.

00She saw their expressions change as they got a whiff of her blood.

00Only quizzical and sad expressions.

00For a moment they silently exchanged determined expressions.

00All wore similar dreamy expressions to Toni's.

00The expressions "4" and "8/2" have the same denotation; but, they express different senses and different ways of conceiving the same number.

00ESL students are often confused by slang expressions that do not appear in an English dictionary.

00That problem is inherent in the discipline and process of creating of fresh expressions of loyalty.

00Facial expressions can have many nuances, with even a slightly raised eyebrow speaking volumes.

00Public expressions of anger were met with the ' repressive state apparatus ' in the form of riot police.

00The linguistic characteristics of natural argumentation, including discourse markers, sentence format, referring expressions, and style.

00Demetrius's use of proper names and characteristic expressions match the Septuagint, the Greek Bible, not the Hebrew scriptures.

00Expressions of interest on Ian Gunn's collected space-time buccaneers can be e-mailed to: UK.. .

00These calculations not only involved difficult mathematical expressions but also dealt with heavy arithmetical calculations.

00They should be familiar with the series expressions for the virial coefficients for a Lennard-Jones potential.

00cognate expressions.

00collectible figurines with their open expressions and smiling faces.

00Students are given incomplete collocations and semi-fixed expressions that appeared in the texts and try to complete them from memory.

00logical And Binary " and " returns the logical conjunction of the two surrounding expressions.

00They were often expressions of amorous dalliance, votive images given by a knight to his lady in pledge of devotion.

00decrement operators can only be applied to variable expressions to which a value can be assigned.

00The linguistic forms of this pointing are called deictic expressions, deictic expressions, deictic markers or deictic words; they are also sometimes called indexicals.

00But visual cues ¿ facial expressions, gestures, pupil dilation etc ¿ make up a massive 55% of your credibility rating.

00To facilitate the discovery of morphemes, the words in the Word Collection can also be filtered using regular expressions.

00disjunction of the two surrounding expressions.

00Other expressions are " he that doeth the truth " (cf.

00The animals ' expressions seem almost ecstatic, swept away by the moment until it is too late and the deed is done.

00All these willingly embraced changes are not a million miles away from the language of Fresh Expressions.

00All these willingly embraced changes are not a million miles away from the language of Fresh Expressions.

00equivocal expressions, of metaphorical phrases, or of eccentric words.

00expressions of dissatisfaction with a mark will vary across departments; you should seek advice from your tutor.

00expressions of interest is the 3rd April 2006.

00expressions of opinion will never be published.

00At this stage we would like to invite expressions of interest from anyone wishing to attend, contribute to or host panels.

00This gives us an unambiguous way of evaluating expressions.

00His facial expressions are sketched in my memory for life.

00The Church of England is desperate to give birth to fresh expressions of church.

00arithmetic expressions Operands are linked by operators: + - / * ^ which can be binary or unary.

00extensible mechanism for defining SQL expressions for your specific needs.

00facial expressions are sketched in my memory for life.

00Regular expressions can get quite fiendish to read at times.

00Very few animal lovers are not familiar with our collectible figurines with their open expressions and smiling faces.

00insolvency glossary of Terms - Jargon Buster Brief Definitions of Insolvency and Bankruptcy Terms and Expressions for England and Wales.

00only hermeneutic translation - the translation of meanings - reveals in its end result truly equivalent words, structures and expressions.

00You could tell by their body postures and facial expressions, they found the discussion awkward, but the atmosphere felt honest.

00honorific expressions have fundamental role (cf.

00idiomatic expressions taught in the text, with sentences showing their use in a new context.

00impute improper motives or use offensive expressions in reference to any Members of the Authority.

00indecipherable expressions abound.

00Insolvency glossary of Terms - Jargon Buster Brief Definitions of insolvency glossary of Terms - Jargon Buster Brief Definitions of Insolvency and Bankruptcy Terms and Expressions for England and Wales.

00frequent interruptions and expressions of approval and disapproval were noticeable features as the members entered the Chamber.

00intolerant society where public expressions of faith are banned by law.

00bilingual lexicographers translate words and expressions, rather than defining them.

00marshmallow man particularly has some great, angry facial expressions which contradict his fluffy, cute appearance.

00microscopy primer from the Molecular Expressions site.

00obsessive-compulsive symptoms (OCD; GTS with OCB) showed impaired recognition of facial expressions of disgust.

00His main research interest is the molecular pathology of cancer particularly the differential expressions of proteins.

00It also has a fun section where members can exchange expressions and slang by creating, playing and discussing phrasal Hangman word games.

00Expressions in Wood I specialize in hand carving bowls, platters, dishes and abstract sculptures mostly from native grown hardwoods.

00postfix expressions is that they are very easy to evaluate.

00It has been accepted in post-Gricean pragmatics that communicators convey more information than is contained in the expressions they utter.

00preponderater can any fair-minded observer discount the preponderating influence exerted by religion on the vital expressions of civilization.

00The site is part of an optical microscopy primer from the Molecular Expressions site.

00Factorizing quadratics An essential skill in many applications is the ability to factorize quadratic expressions.

00rapt, anxious expressions of the group are most striking.

00It is for this reason that the expressions toner and new paper cannot provide referents for it.

00There are expressions like +, - but also relational ones like =, and!= .

00It was the expressions on the faces, frozen at the moment of death, that caused the greatest revulsion.

00This proliferation makes rather risible the Guardian's expressions of expletive fatigue in relation to Gordon Ramsay's television appearances.

00sexagesimal values in expressions are followed.

00The current portfolio offers over 80 different single malts and more than 450 expressions aged between five and sixty years.

00Mathematical Expressions use the solidus whenever possible in preference to built-up fractions.

00tedious to write out all of those instanceof expressions, and you're right.

00tonality have tonalities that say " don't bother me right now " and tonalities combined with facial expressions that indicate something is wrong.

00Traditional models generally assume very simple functional forms for f i, in order to have analytically tractable expressions for g t.

00His facial expressions, moves and gestures were wonderfully underplayed and he gave a great first impression of " the underdog " .

00Five blank black visors looked down at him, masking the wearers ' expressions.

00The King was bold, excellent facial expressions, and a good speaking voice.

00Language has crystallized them into certain definite notions and expressions, without which we cannot proceed a single step, but which we have accepted without knowing their exact meaning, much less their origin.

00To endow the universal substance with moral attributes, to maintain that it is more than the metaphysical ground of everything, to say it is the perfect realization of the holy, the beautiful and the good, can only have a meaning for him who feels within himself what real not imaginary values are clothed in those expressions.

00He urged on the bill by which Catholics were prohibited from sitting in either House of Parliament, and was bitter in his expressions of disappointment when the Commons passed a proviso excepting James, against whom the bill was especially aimed, from its operation.

00They are no clamorous expressions of anger at the discrepancies and contrasts of humanity, but plain, solemn pictures of conditions of life, which neither the politician nor the moralist can deny to exist, and which they are imperatively called upon to remedy.

00On the 25th of November Cromwell charged Manchester with "unwillingness to have the war prosecuted to a full victory"; which Manchester answered by accusing Cromwell of having used expressions against the nobility, the Scots and Presbyterianism; of desiring to fill the army of the Eastern Association with Independents to prevent any accommodation; and of having vowed if he met the king in battle he would as lief fire his pistol at him as at anybody else.

00Towards the morning of the 3rd of September he again spoke, "using divers holy expressions, implying much inward consolation and peace," together with "some exceeding self-debasing words, annihilating and judging himself."

00The inconsistency of his attitude is shown by his use, side by side, of the contemptuous expressions barbarus (applied to the Romans) and pergraecari (applied to the Greeks).

0012, 45); though from the lips of slaves and other low persons in the plays we no doubt hear expressions which, while they are quite in keeping with the characters to whom they are allotted, would have shocked the ears of polite society in the 2nd century B.C.

00We find in the Meditations no speculations on the absolute nature of the deity, and no clear expressions of opinion as to a future state.

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.

00The book contains expressions such as daemones, angelica virtus, and purgatoria dementia, which have been thought to be derived from the Christian faith; but they are used in a heathen sense, and are explained sufficiently by the circumstance that Boetius was on intimate terms with Christians.

00Ribot, then president of the council, in the Chamber of Deputies, but the expressions he used were so vague that they did not entirely remove the prevailing doubts as to the existence of a formal treaty.

00The two following expressions are given in the Bulletin of the International Railway Congress (vol.

00The resistance found from the above expressions includes the components I, 2 and 4 of § 4.

00The curves corresponding to the above expressions are plotted in fig.

00Then a disappears from all the above expressions.

00These expressions indicate what frequent changes in the power are required as the train pursues its journey up and down gradients, against wind resistance, j ournal friction and perhaps the resistance of a badly laid track; and show how both the potential energy and kinetic energy of the train are continually changing: the first from a change in vertical position due to the gradients, the second from changes in speed.

00As a curiosity of literature Bowdler's edition, " adapted to the use of families and young persons," by the expurgation of " the indecent expressions and all allusions of an improper tendency " (5 vols.

00Literature and affairs, science and statecraft, poetry and medicine, these various expressions of human nature and activity were so harmoniously balanced that they might be found in the possession of one and the same individual.

00Its foundation was probably certain expressions lamenting Scottish interference in English affairs.

00Before the rise of Neoplaton ism proper we meet with various mystical or semimystical expressions of the same religious craving.

00But the exact meaning which he attaches to such expressions is not quite clear; and they occur, moreover, only incidentally and with the air of current phrases mechanically repeated.

00It is not surprising that with such maxims as these in his mouth, unguarded in his expressions and careless of his reputation, he should have afforded room for the circulation of many stories to his disadvantage."

00AMMONIUS GRAMMATICUS, the supposed author of a treatise entitled IIEpc 6yoLwv Kai &acaopwv (On the Di f ferences of Synonymous Expressions), of whom nothing is known.

00In the preface to the latter work he referred to Jerome as an admirer of Origen, and as having already translated some of his works with modifications of ambiguous doctrinal expressions.

00With one symbol for an unknown, it will easily be understood what scope there is foradroit assumptions, for the required numbers, of expressions in the one unknown which are at once seen to satisfy some of the conditions, leaving only one or two to be satisfied by the particular value of x to be determined.

00Evidence in support of this view is sought for in the accounts in the Anglo-Saxon Chronicle and elsewhere, where the decisions of the witan were received with loud expressions of approval or of disapproval by an assembled crowd, and it is argued that this is a survival from an earlier age, when all the freemen attended the witan.

00If we are to follow von Sybel rather than Kugler, this saga of the First Crusade found one of its earliest expressions (c. 1120) in the prose work of Albert of Aix (Historia Hierosolymitana) - genuine saga in its 1 His somewhat legendary treatise, De liberatione civitatum Orientis, was only composed about 1155.

00Expressions in Propertius (ii.

00Expressions in the Odes of Horace (ii.

00a Mahommedan, as synonymous Religion expressions.

00The Malay language abounds in idiomatic expressions, which constitute the chief difficulty in its acquisition.

00As it is rich in specific expressions for the various aspects of certain ideas, it is requisite to employ always the most appropriate term suited to the particular aspect.

00both the translation and the original were publicly burnt by the common hangman on the 5th of May 1686, as containing "expressions scandalous to His Majesty the king of France."

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.

00Alexander is said to have granted the Lydians to be " free " and " to use the laws of the ancient Lydians," whatever exactly these expressions may mean (Arr.

00The authors of rectangular maps look upon the Tabernacle as an image of the world at large, and believe that such expressions as the " four corners of the earth " (Isa.

00(b) Dittographic renderings in the Greek of the same Hebrew expression; also dittographic expressions in the Greek implying dittographs in the Hebrew.

00" If the law simply consists of ordinary expressions and narratives, such as the words of Esau, Hagar, Laban, the ass of Balaam or Balaam himself, why should it be called the law of truth, the perfect law, the true witness of God ?

0024, the reader is left to recognize Enoch from his knowledge of the Biblical narrative.) In the second part of the book there is no expression of "messianic" hope; in the first part the picture of the national future agrees in general (if its expressions are to be taken literally) with that given in the book of Daniel: the Jews are to have dominion over the peoples (iii.

00The expressions "tribu movere" and "aerarium facere," regarded by Mommsen as identical in meaning ("to degrade from a higher tribe to a lower"), are explained by A.

00Thus the values of the expressions a 2 /(i - a /V) (Rudolphi, Zeits.

00On the analogy between this case and that of the interface between two solutions, Nernst has arrived at similar logarithmic expressions for the difference of potential, which becomes proportional to log (P 1 /P 2) where P2 is taken to mean the osmotic pressure of the cations in the solution, and P i the osmotic pressure of the cations in the substance of the metal itself.

00We may say that, in the resulting determinant, the element in the ith row and k th column is obtained by multiplying the elements in the kth row of the first determinant severally by the elements in the ith row of the second, and has the expression aklb11+ak2b12+ak3b13Ã¯¿½Ã¯¿½Ã¯¿½ +aknbin, and we obtain other expressions by transforming either or both determinants so as to read by columns as they formerly did by rows.

00Hence in all there are mn such systems. If, therefore, we have a third equation, and we substitute each system of values in it successively and form the product of the mn expressions thus formed, we obtain a function which vanishes if any one system of values, common to the first two equations, also satisfies the third.

00and therefore of the product of those expressions.

00respectively: then the result arrived at above from the logarithmic expansion may be written (n)a(n x) = (n)x, exhibiting (n) $ as an invariant of the transformation given by the expressions of X1, X2, X3...

00A table may be formed expressing the k expressions Pa l), P(2),...P(1) as linear functions of the k expressions (m"`'smÃ¯¿½2smÃ¯¿½3s...), s =1, 2, ...k, and the numbers BSc occurring therein is 2s 3s possess row and column symmetry.

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.

00When R =0, and neither of the expressions AC - B 2, 2AB -3C vanishes, the covariant a x is a linear factor of f; but, when R =AC - B 2 = 2AB -3C =0, a x also vanishes, and then f is the product of the form jx and of the Hessian of jx.

00symbolically, to be the fundamental form of seminvariant of degree 0 and weight w; he observes that every form of this degree and weight is a linear lic expressions.

00If a hollow sphere 7 of which the outer radius is R and the inner radius r is placed in a uniform field Ho, the field inside will also be uniform and in the same direction as Ho, and its value will be approximately 3 i - R 3 For a cylinder placed with its axis at right angles to the lines of force, 2 = Ho (41) 2 +4(-2)(i - R2) These expressions show that the thicker the screen and the greater its permeability o, the more effectual will be the shielding action.

00We may therefore generally substitute s/2n for tan 0 in the various expressions which have been given for I.

00Two forms of Western Aramaic survive: the Jerusalem form of the dialect, in the Aramaic portions of Daniel and Ezra; and the Galilean, in isolated expressions in the Talmud (3rd century), and in a fragmentary 5th century translation of the Bible.

00to show that both expressions agreed for every value of the variable; now it is sufficient to prove their agreement to a far less extent" [merely in certain critical points and at certain boundaries].

00It deserves to be recorded as one of the numerous coincidences of discovery that Laplace, on being made acquainted by Lagrange with his new method, produced analogous expressions, to which his independent researches had led him.

00The collected works of Hrabanus himself contain nothing new, but in some glosses on Aristotle and Porphyry, first exhumed by Cousin, there are several noteworthy expressions of opinion in a Nominalistic sense.

00Some of the expressions used by Anselm in controverting his position favour this idea.

00In the French Corps Legislatif, also, the vice-president, Forgade la Roquette, referred to his death, and warm expressions of esteem were repeated and applauded on every side.

00Logical in its derivatives and in its grammatical structure, the Magyar language is, moreover, copious in idiomatic expressions, rich in its store of words, and almost musical in its harmonious intonation.

00Expressions occur in Laplace's private letters inconsistent 3 Mee.

00The expressions designated by Dr Whewell, Laplace's coefficients (see Spherical Harmonics) were definitely introduced in the memoir of 1785 on attractions above referred to.

00The 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.

00This reaction has taken the form of a return to the alliance between algebra and geometry (Ã¯¿½5), on which modern analytical geometry is based; the alliance, however, being concerned with the application of graphical methods to particular cases rather than to general expressions.

00It will be seen from Ã¯¿½ 22 that the application of algebra to equations consists in the interchange of equivalent expressions, and therefore comes under (i.) and (ii.).

00The two expressions whose equality is stated by an equation or an identity are its members.

00- The calculation of the values of simple algebraical expressions for particular values of letters involved is a useful exercise, but its tediousness is apt to make the subject repulsive.

00Another useful set of graphs comprises those which give the relation between the expressions of a length, volume, &c., on different systems of measurement.

00Let X and Y be the related quantities, their expressions in terms of selected units A and B being x and y, so that X=x.A, Y = y.

00(ii.) By means of the commutative law we can collect like terms of a monomial, numbers being regarded as like terms. Thus the above expression is equal to 6a 5 bc 2, which is, of course, equal to other expressions, such as 6ba 5 c 2.

00It must, of course, be remembered (Ã¯¿½ 23) that this is a statement of arithmetical equality; we call the statement an " identity," but we do not mean that the expressions are the same, but that, whatever the numerical values of a, b and c may be, the expressions give the same numerical result.

00is then an expression of the form a p b e c r d s, where p, q, r, s have the greatest possible values consistent with the condition that each of the given expressions shall be divisible by a p b e c r d s .

00is of the form a p b e c r d s, where p, q, r, s have the least possible values consistent with the condition that a P PC'd s shall be divisible by each of the given expressions.

00The principles of arithmetical transformation follow from those stated in Ã¯¿½Ã¯¿½ 15-18 by replacing X, A, B, m, M, x, n, a and p by any expressions involving or not involving the unknown quantity or number and representing positive numbers or (in the case of X, A, B and M) positive quantities.

00if either or both of the expressions A and B involves x, and A is arithmetically equal to B for the particular value of x which we require), and if B = C is an identity (i.e.

00if B and C are expressions involving x which are different in form but are arithmetically equal for all values of x), then the statement A = C is an equation which is true for the same value of x for which A = B is true.

00(viii.) The quadratic equation is the equation of two expressions, monomial or multinomial, none of the terms involving any power of x except x and x 2 .

00The standard form is usually taken to be ax2+bx+c =0, from which we find, by transformation, (2 ax+b) 2 =b 2 - 4ac, 4 (}b 2 -4ac} -b and thence x = 2a (ii.) In an equation of the form Q=V, the expressions P, Q, U, V are usually numerical.

00Fractional Expressions.

00The expressions obtained in this way are called the first, second,.

00Thus we arrive at the differential coefficient of f(x) as the limit of the ratio of f (x+8) - f (x) to 0 when 0 is made indefinitely small; and this gives an interpretation of nx n-1 as the derived function of xn (Ã¯¿½ 45)Ã¯¿½ This conception of a limit enables us to deal with algebraical expressions which assume such forms as -Ã‚° o for particular values of the variable (Ã¯¿½ 39 (iii.)).

00Expressions of the form b1,1 - I and a-}-b A l - I, where a and b are real numbers, are then described as imaginary and complex numbers respectively; the former being a particular case of the latter.

00In the course of reducing such expressions as (AB)C, (AB){C(DE)} and the like, where a chain of multiplications has to be performed in a certain order, the multiplications may be all progressive, or all regressive, or partly, one, partly the other.

00Its great merit consists in the complete notation and symbolism, which avoided the cumbersome expressions of the earlier algebraists, and reduced the art to a form closely resembling that of to-day.

00A fantastic and elaborate doctrine of symbolism existed which comprised all nature; witchcraft, alchemy and medicine were its practical expressions.

00

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