Denoting sentence example

denoting
  • A waitress wearing a lace cap denoting her Pennsylvania Dutch heritage seated him at a small corner table by the window.
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  • His advisors and mates dressed in well-made clothing edged with silver, denoting their rank among the shouting crowd in rags.
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  • With Descartes the use of exponents as now employed for denoting the powers of a quantity becomes systematic; and without some such step by which the homogeneity of successive powers is at once recognized, the binomial theorem could scarcely have been detected.
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  • METHODISM, a term' denoting the religious organizations which trace their origin to the evangelistic teaching of John Wesley.
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  • Toller) describes a thegn as "one engaged in a king's or a queen's service, whether in the household or in the country," and adds, "the word in this case seems gradually to acquire a technical meaning, and to become a term denoting a class, containing, however, several degrees."
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  • Typical formulae are (R denoting 0, S or NH): Isomers are possible, for the condensation may be effected on the two carbon atoms symmetrically placed to the hetero-atom; these isomers, however, are more of the nature of internal anhydrides.
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  • The plant formation may be designated in technical language ph the termination -ion added to a stem denoting the habitat.
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  • For if u, v, w be the polynomials of orders m, n, p respectively, the Jacobian is (u 1 v 2 w3), and by Euler's theorem of homogeneous functions xu i +yu 2 +zu 3 = mu xv1 +yv2 +zv3 = /IV xw 1+y w 2+ zw 3 = pw; denoting now the reciprocal determinant by (U 1 V2 W3) we obtain Jx =muUi+nvVi+pwWi; Jy=�.., Jz=..., and it appears that the vanishing of u, v, and w implies the vanishing of J.
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  • Denoting the two pairs of magnetic poles by N, S and N', S', there is attraction between N and S', and between S and N'; repulsion between N and N', and between S and S'.
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  • The figure denoting the general average yield per acre of any class of crop needs readjustment after every successive harvest.
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  • The term " futures " is used broadly and narrowly: broadly it is a generic term denoting " futures " in the Futures.
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  • If we express the pressure, volume and temperature as fractions of the critical constants, then, calling these fractions the " reduced " pressure, volume and temperature, and denoting them by 7r, 0 and 0 respectively, the characteristic equation becomes (7+3/0 2)(30-i) =80; which has the same form for all substances.
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  • - Denoting the atomic weight by W and the specific heat by s, Dulong and Petit's law states that 6.4 = Ws.
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  • The word is commonly used in the Alexandrian Greek translation of the Old Testament (Septuagint) for the Hebrew word (ger) which is derived from a root (gur) denoting to sojourn.
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  • in terms of dl, d 2, d 3, ..., products denoting successive operations, by the same law which expresses the ele mentary function a s in terms of the sums of powers s l, s 2, s3,...
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  • All symmetric functions are expressible in terms of the quantities ap g in a rational integral form; from this property they are termed elementary functions; further they are said to be single-unitary since each part of the partition denoting ap q involves but a single unit.
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  • The partitions being taken as denoting symmetric functions we have complete correspondence between the algebras of quantity and operation, and from any algebraic formula we can at once write down an operation formula.
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  • 1 Ze An Expression Which Also Enumerates The Asyzygetic Seminvariants, We May Regard The Form, Written, As Denoting The General Form Of Asyzygetic Seminvariant; A Very Important Conclusion.
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  • Denoting its mean value by Hti, and that of the demagnetizing factor by N, we have H=Ho-Hti=Ho-NI.
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  • Denoting the distance AM by d 1, BM by d2, and AB by 1, we have for the force at M due to the magnetism of the rod H P =d 12 - horizontal component (dla - d 2 3).
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  • Denoting by W the work in ergs done upon a cubic centimetre of the metal (=_fHdB or f HdI), he finds W =nips approximately, where n 47r is a number, called the hysteretic constant, depending upon the metal, and B is the maximum induction.
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  • Denoting the root by a, and the number 2222222 in this scale by N, we have N = 2222222.
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  • An expression denoting that two or more monomials are to be added or subtracted is a multinomial or polynomial, each of the monomials being a term of it.
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  • In the graphic method of representation the sign - may be taken as denoting a reversal of direction, so that, if + 3 represents a length of 3 units measured in one direction,-3 represents a length of 3 units measured in the other direction.
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  • Denoting these convergents by Po/Qo, P1/Q1, P2/Q2, ...
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  • Denoting them by x, y, so that AB is axis of y and a perpendicular through A the axis of x, and rationalizing (26), we have 2 ax 2 - V 2 Xy 2 - V 2 aAy = o, which represents a hyperbola with vertices at 0 and A.
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  • - 47rb 2 dr (r / ' denoting the angle between r and z.
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  • 05v050s), a term denoting an assembly of ecclesiastical officials legally convoked to discuss and decide points of faith, discipline and morals.
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  • In this case the thrust at the lower end B must exceed the thrust at A, the upper end, by the weight of the prism of liquid; so that, denoting the cross section of the prism by a ft.
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  • (9) Turning the axes to make them coincide with the principal axes of the area A, thus making f f xydA = o, xh = - a 2 cos a, y h = - b 2 sin a, (io) where ffx2dA=Aa2, ffy 2 dA= Ab 2, (II) a and b denoting the semi-axes of the momental ellipse of the area.
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  • Suppose the ship turns about an axis through F in the water-line area, perpendicular to the plane of the paper; denoting by y the distance of an element dA if the water-line area from the axis of rotation, the change of displacement is EydA tan 8, so that there is no change of displacement if EydA = o, that is, if the axis passes through the C.G.
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  • of the fluid, equal to the weight vertically upward through the movement of a weight P through a distance c will cause the ship to heel through an angle 0 about an axis FF' through F, which is conjugate to the direction of the movement of P with respect to an ellipse, not the momental ellipse of the water-line area A, but a confocal to it, of squared semi-axes a 2 -hV/A, b 2 - hV/A, (I) h denoting the vertical height BG between C.G.
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  • The kinetic energy of the liquid inside a surface S due to the velocity function 4' f i (s given by T=2p + (d) 2+ (t) dxdydz, pff f 75 4 dS (I) by Green's transformation, dv denoting an elementary step along the normal to the exterior of the surface; so that d4ldv = o over the surface makes T = o, and then (d4 2 d4) 2 'x) + (dy) + (= O, dd?
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  • Denoting the cross-section a of a filament by dS and its mass by dm, the quantity wdS/dm is called the vorticity; this is the same at all points of a filament, and it does not change during the motion; and the vorticity is given by w cos edS/dm, if dS is the oblique section of which the normal makes an angle e with the filament, while the aggregate vorticity of a mass M inside a surface S is M - l fw cos edS.
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  • Beginning with a single body in liquid extending to infinity, and denoting by U, V, W, P, Q, R the components of linear and angular velocity with respect to axes fixed in the body, the velocity function takes the form = Ucb1+V42+W43+ P xi+Qx2+Rx3, (I) where the 0's and x's are functions of x, y, z depending on the shape of the body; interpreted dynamically, C -p0 represents the impulsive pressure required to stop the motion, or C +p4) to start it again from rest.
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  • The terms of 0 may be determined one at a time, and this problem is purely kinematical; thus to determine 4)1, the component U alone is taken to exist, and then 1, m, n, denoting the direction cosines of the normal of the surface drawn into the exterior liquid, the function 01 must be determined to satisfy the conditions v 2 0 1 = o, throughout the liquid; (ii.) ' = -1, the gradient of 0 down the normal at the surface of the moving solid; 1 =0, over a fixed boundary, or at infinity; similarly for 02 and 03.
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  • Over the ellipsoid, p denoting the length of the perpendicular from the centre on a tangent plane, px _ pv _ _ pz 1= a2+X' b +A' n c2+A p2x2 + p2y2 p2z2 I (a2 - + X)2 (b 2 +x)2 + (0+X)2, p 2 = (a2+A)12+(b2+X)m2+(c2+X)n2, = a 2 1 2 +b 2 m 2 +c 2 n 2 +X, 2p d = ds; (8) Thence d?
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  • Denoting the effective inertia of the liquid parallel to Ox by aW' the momentum aW'U = 4)0W' (24) _ U i -AO' 25) in this way the air drag was calculated by Green for an ellipsoida pendulum.
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  • These equations are proved by taking a line fixed in space, whose direction cosines are 1, then dt=mR-nQ,' d'-t = nP =lQ-mP. (5) If P denotes the resultant linear impulse or momentum in this direction P =lxl+mx2+nx3, ' dP dt xl+, d y t x2' x3 +1 dtl dt 2 +n dt3, =1 ('+m (dt2-x3P+x1R) ' +n ('-x1Q-{-x2P) ' '= IX +mY+nZ, / (7) for all values of 1, Next, taking a fixed origin and axes parallel to Ox, Oy, Oz through 0, and denoting by x, y, z the coordinates of 0, and by G the component angular momentum about 1"2 in the direction (1, G =1(yi-x2z+x3y) m 2-+xlz) n(y(y 3x 1 x3x y + x 2 x) (8) Differentiating with respect to t, and afterwards moving the fixed.
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  • The effect of an external circulation of vortex motion on the motion of a cylinder has been investigated in § 29; a similar procedure will show the influence of circulation through a hole in a solid, taking as the simplest illustration a ring-shaped figure, with uniplanar motion, and denoting by the resultant axial linear momentum of the circulation.
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  • In the second of the above books his idea of religion is somewhat of an anachronism; as he himself confessed, he " used the word in the sense which it invariably bore half a century ago," as denoting " belief in an ever-living God, a divine mind and will ruling the universe and holding moral relations with mankind."
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  • root ac-, sharp; acere, to be sour), the name loosely applied to any sour substance; in chemistry it has a more precise meaning,denoting a substance containing hydrogen which may be replaced by metals with the formation of salts.
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  • Denoting 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.
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  • Under external migration are comprised emigration and immigration, denoting simply direction from and to.
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  • In reckoning years from any fixed epoch in constant succession, the number denoting the years is necessarily always on the increase.
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  • Each of these periods, which is denominated a tsee, is subdivided into two equal portions called chung-ki and tsie-ki, the chung-ki denoting the first half of the tse, and the tsie-ki the latter half.
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  • In modern botany it is a technical term sometimes denoting the lower part of the capsule called pyxidium, attached to the flower stalk in the form of an urn.
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  • Denoting the constant ratio by fir, the area of a circle is ira 2, where a is the radius, and ir=3.14159 approximately.
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  • Denoting the areas of the three strips by A, B, and C, and introducing the middle ordinate ug, we can express A + B; B -{- C; A + B -FC; and B in terms of uo, u 1, u 2; u 1, u2, u3; uo, u, u 3; and u 1, ug, u 2 respectively.
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  • - A„L_i)4'(x„1_i), Ag5'(xm); the accents denoting the first differential coefficient.
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  • ANGEL, a general term denoting a subordinate superhuman being in monotheistic religions, e.g.
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  • Calling the radius r, and denoting by the ratio of the circumference to the diameter of a circle, the volume is 31rr 3, and the surface 41rr2.
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  • as denoting those whom history could show to have been personally connected, or at least coeval, with one or more apostles; and an effort was made, as by Cotelier, to distinguish the writings rightly and wrongly assigned to such.
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  • absolutio from absolvo, loosen, acquit), a term used in civil and ecclesiastical law, denoting the act of setting free or acquitting.
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  • Denoting the value of T at any velocity v by T (v), then (8) T(v) = sum of all the preceding values of AT plus an arbitrary constant, expressed by the notation (9) T(v) =Z(Av)/gp+ a constant, or fdv/gp+ a constant, in which p is supposed known as a function of v.
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  • Denoting by S(v) the sum of all the values of AS up to any assigned velocity v, (is) S(v) =E(OS)+ a constant, by which S(v) is calculated from AS, and then between two assigned velocities V and v, V AT, = vAv or rvvdv vgp gp' and if s feet is the advance of a shot whose ballistic coefficient is C, (17) s=C[S(V) - S(v)].
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  • Integrating (27) again, (31) y =g(zTt2t 2) = zgt(T -t); and denoting T-t by t', and taking g= 32f/s2,) y =16tt', (32 which is Colonel Sladen's formula, employed in plotting ordinates.
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  • so that Denoting dx/dt, the horizontal component of the velocity, by q, (49) v cos i =q, equation (43) becomes (50) dq/dt= -r cos i, and therefore by !(48) (51) dq _dq dt ry di - dt di-g' It is convenient to express r as a function of v in the previous notation (52) Cr = f(v), dq _vf(v) di - Cg ' an equation connecting q and i.
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  • - C = C cos n [5 (u 5) - S(ue)], ' y / e 0 A =tan - C sec n [I (u 0) - S] A now denoting any finite tabular difference of the function between the initial and final (pseudo-) velocity.
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  • =0.504, the upper figure 55.01 denoting the specific volume of the charge measured in cubic inches per lb, filling the chamber in a state of gas, the product of the two numbers 55.01 and 0.504 being 2 7.73; and the chamber capacity C =1 3' 2 5 X 55.01 =730 cub.
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  • In addition to this simple meaning it has also, both in the philosophical and the colloquial speech of India a technical meaning, denoting "a person's deeds as determining his future lot."
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  • Denoting the number of units in AB by 4c, we can express BB 1j B 1 B 2,.
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  • 8 With him, apparently, began the usage of denoting by 71 the ratio of the circumference to the diameter.'
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  • The month, however, being a convenient period of time, has retained its place in the calendars of all nations; but, instead of denoting a synodic revolution of the moon, it is usually employed to denote an arbitrary number of days approaching to the twelfth part of a solar year.
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  • The general formulae of hydroxides are: M i OH, M ii (OH) 2, M il i (OH) 3, M i `'(OH) 4, &c., corresponding to the oxides M21O, M iiO, M21i103 M i °O 2, &c., the Roman index denoting the valency of the element.
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  • The name " Hebrew " is derived, through the Greek `E$3paios, from `ibhray, the Aramaic equivalent of the Old Testament word `ibhri, denoting the people who commonly spoke of themselves as Israel or Children of Israel from the name of their common ancestor (see JEws).
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  • For example, anyone studying Briinnow's List s will find the same sign denoting pages of meanings, many of which have apparently no connexion with any other meaning belonging to the sign in question.
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  • SPECIES, a term, in its general and once familiar significance, applied indiscriminately to animate and inanimate objects and to abstract conceptions or ideas, as denoting a particular phase, or sort, in which anything might appear.
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  • It is clear, however, that through Ray's work in the 17th century the common biological application of species became fixed much in its modern form, as denoting a group of animals or plants capable of interbreeding, and although not necessarily quite identical, with marked common characters.
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  • The officials were called by two names, "elders" and "bishops," the former denoting the office, the latter the function (exercising the oversight).
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  • The town of Babylon disappeared, but the strong walls of the fortress in part remain, and the name survived, " Babylon of Egypt," or " Babylon " simply, being frequently used in medieval writings as synonymous with Cairo or as denoting the successive Mahommedan dynasties of Egypt.
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  • It is probable that the verb had a special form denoting condition, as in Arabic. There was a causative form prefixing t, and ti-aces of forms resembling Piel and Niphal are observed.
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  • On the south a similar stream starting farther east, called Burgutai (denoting the position of a difficult and dangerous pass across the range) sweeps downwards towards Lake Chakmaktin, the lake of the Little Pamir, which is some 400 ft.
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  • "Doatiness," similarly, is a speckled or spotted stain denoting decay in certain varieties of timber, such as beech and some kinds of oak.
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  • 1853)4 is qualified by the warning that the real activity of thought tends to fall outside the calculus of relations and to attach rather to the subsidiary function of denoting.
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  • Denoting these limits by Pi, Pa we have P1/W=L1H/HK=sin (aX)/cos (0+X),
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  • The work which would have to be supplied by other forces, extraneous to the field, in order to bring the particle from rest in some standard position P0 to rest in any assigned position P, will depend only on the position of P; it is called the statical or potential energy of the particle with respect to the field, in the position P. Denoting this by V, we have VX~x=o, whence X=--~.
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  • Denoting this value by ~i2, we have Ax~+Hy~+Gz1 =o-,2(axi+hyi+agzi),)
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  • PT denoting the perpendicular distance of P from T.
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  • A condition equivalent to the above, and necessarily connected with it, is, that at each pair of points of contact the inclinations of the curves to their radii-vectores shall be equal and contrary; or, denoting by r1, rf the radii-vectores at any given pair of points of contact, and s the length of the equal arcs measured from a certain fixed pair of points of contact dri/ds= drm/ds; (18)
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  • Also, to find the position of the centres of curvature relatively to the pitch-circle, we have, denoting the chord of the describing circle TI bye, c=2r sin 0; and therefore For the flank, p C=2r sine ~~_r} (29) For the face, pC2r sin 8 ~-~
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  • The assembly of 1575 decided that all ministers were bishops; that of 1578 abolished the name of bishop as denoting an office in the church, and that of 1580 in spite of a royal remonstrance abolished Episcopacy, a decree to which all the bishops except five submitted.
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  • Thus it is quite conceivable that they brought it with them into Western Asia: and the quarter from which it came is sufficiently indicated by the fact that the Babylonians write the word horse with a group of signs denoting ass of the East.
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  • vfUpov, nerve, and iiXryos, pain), a term denoting strictly the existence of pain in some portion or throughout the whole of the distribution of a nerve without any distinctly recognizable structural change in the nerve or nerve centres.
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  • (2) 21rT X 470 h denoting the depth of the liquid.
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  • If, as before, the frequency be p7211, and a the radius of the sphere, we have p 2 =n(n-1)(n+2)P a3, (6) n denoting the order of the spherical harmonic by which the deviation from a spherical figure is expressed.
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  • When Greek became the sole language of the East Roman Empire, imperator was rendered sometimes by Octort,Xc13 and sometimes by airroKparwp, the former word being the usual designation of a sovereign, the latter specially denoting that despotic power which the imperator held, and being in fact the official translation of imperator.
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  • It is worthy of notice that while many metals dissolve in cold dilute sulphuric acid, with the liberation of hydrogen, in accordance with the typical equation: M -{- H 2 50 4 = MSO 4 -1H2 (M denoting one atom of divalent or two atoms of a monovalent metal), there are several (copper, mercury, antimony, tin, lead and silver) which are insoluble in the cold dilute acid, but dissolve in the hot strong acid with evolution of sulphur dioxide, thus: M -}- 2H 2 250 4 = MSO 4 SO 2 + 2H 2 0.
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  • Aschan (Ber., 1902, 35, p. 33 8 9) depicts these cases by representing the plane of the carbon atoms of the ring as a straight line and denoting the substituted hydrogen atoms by the letters X, Y, Z.
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  • cannot be taken as denoting any definite concrete objects.
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  • The symbols denoting a number are called its digits.
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  • Similarly when we get to ten tens we denote them by a new representation of the figure denoting one.
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  • to the direction in which the series denoting the successive numbers one, two, three,.
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  • This system, however, would require that in passing to " double figures " the figure denoting tens should be written either above or below the figure denoting ones, e.g.
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  • The letters or symbols descriptive of each denomination are usually placed after or (in actual calculations) above the figures denoting the numbers of the corresponding units; but in a few cases, e.g.
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  • (i) A set of written symbols is sometimes read in more than one way, while on the other hand two different sets of symbols (at any rate if denoting numerical quantities) may be read in the same way.
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  • as an expression denoting a fraction or a percentage.
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  • 2 and 6, in the standard series, so that, denoting them by M, N and P, Q respectively, M will be to N in the same ratio that P is to Q.
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  • Hence, if p and n are numbers, n is sometimes regarded as denoting the result of dividing p by n, whether p and n are integral or fractional (mixed numbers being included in fractional).
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  • - Instead of regarding the 153 in 27.153 as meaning o h, we may regard the different figures in the expression as denoting numbers in the successive orders of submultiples of i on a denary scale.
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  • ., and the corresponding numbers in the second column, as denoting points between which other numbers lie, i.e.
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  • MACAQUE, a name of French origin denoting the monkeys of the mainly Asiatic genus Macacus, of which one species, the Barbary ape, inhabits North Africa and the rock of Gibraltar.
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  • Thirdly, for the double tangents; the points of contact of these are obtained as the intersections of the curve by a curve II = o, which has not as yet been geometrically defined, but which is found analytically to be of the order (m-2) (m 2 -9); the number of intersections is thus = m(rn - 2) (m 2 - 9); but if the given curve has a node then there is a diminution =4(m2 - m-6), and if it has a cusp then there is a diminution =6(m2 - m-6), where, however, it is to be noticed that the factor (m2 - m-6) is in the case of a curve having only a node or only a cusp the number of the tangents which can be drawn from the node or cusp to the curve, and is used as denoting the number of these tangents, and ceases to be the correct expression if the number of nodes and cusps is greater than unity.
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  • NONCONFORMIST, a term denoting historically (a) those persons who at the beginning of the 17th century refused to conform to certain practices, e.g.
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  • What Humboldt terms the inner form of a language is just that mode of denoting the relations between the parts of a sentence which reflects the manner in which a particular body of men regards the world about them.
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  • ARTHROPODA, a name, denoting the possession by certain animals of jointed limbs, now applied to one of the three sub-phyla into which one of the great phyla (or primary branches) of coelomocoelous animals - the Appendiculata - is divided; the other two being respectively the Chaetopoda and the Rotifera.
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  • sairvXos, ficarbXcov), a word of Semitic origin (= bethel) denoting a sacred stone, which was supposed to be endowed with life.
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  • The unit of value was called a set, a word denoting a jewel or precious object of any kind.
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  • The term " premises " (a house, &c.), is derived loosely from the legal phase denoting that which has already been mentioned in a document, and is etymologically the same.
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  • In using the above table to find the value of E or dE/dt at any temperature or between any limits, denoting by p the value of dE/dt at 50° C., and by 2C the constant value of the second coefficient, we have the following equations :- dE/dt = p+2c(t -50), at any temperature t, Cent.
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  • (1906), who identifies Erechtheus, Erichthonius, Poseidon and Cecrops, all denoting the sacred serpent of Athena, whose cult she first contested, but then amalgamated with her own.
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  • Prefixes denoting components directly fused to the parent component are called first-order fusion prefixes.
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  • collocates twice with a word denoting a religious movement.
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  • Inland colonies of gulls, terns and great cormorants were defined by a single six figure grid reference denoting the center of the colony.
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  • Words denoting any gender shall denote all genders and words denoting persons shall include firms and corporations and vise versa.
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  • denotes are named with the initial letters denoting which array the site belongs to.
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  • The variation in z is displayed on a computer screen as a series of gray scales denoting surface protrusions.
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  • At heights from 1500 to 6000 metres his observations agreed well with the formula dV/dh= 34 - o o06 h, V denoting the potential, h the height in metres.
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  • concordatum, agreed upon, from con-, together, and cor, heart), a term originally denoting an agreement between ecclesiastical persons or secular persons, but later applied to a pact concluded between the ecclesiastical authority and the secular authority on ecclesiastical matters which concern both, and, more specially, to a pact concluded between the pope, as head of the Catholic Church, and a temporal sovereign for the regulation of ecclesiastical affairs in the territory of such sovereign.
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  • brahma), originally denoting, it would seem, "one who prays, a worshipper," perhaps also "the composer of a hymn" (brahman, n.); and the same term came subsequently to be used not only for one of the sacerdotal order generally, but also, and more commonly, as the designation of a special class of priests who officiated as superintendents during sacrificial performances, the complicated nature of which required the co-operation of a whole staff of priests, and who accordingly were expected to possess a competent knowledge of the entire course of ritual procedure, including the correct form and mystic import of the sacred texts to be repeated or chanted by the several priests.
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  • pessimus, worst), a word of modern coinage,' denoting an attitude of hopelessness towards life, a vague general opinion that pain and evil predominate in human affairs.
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  • For if u, v, w be the polynomials of orders m, n, p respectively, the Jacobian is (u 1 v 2 w3), and by Euler's theorem of homogeneous functions xu i +yu 2 +zu 3 = mu xv1 +yv2 +zv3 = /IV xw 1+y w 2+ zw 3 = pw; denoting now the reciprocal determinant by (U 1 V2 W3) we obtain Jx =muUi+nvVi+pwWi; Jy=�.., Jz=..., and it appears that the vanishing of u, v, and w implies the vanishing of J.
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  • The usual signs denoting Akkadu in the Semitic narrative inscriptions were read in the non-Semitic idiom uri-ki or ur-ki, " land of the city," which simply meant that Akkadu was the land of the city par excellence, i.e.
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  • Denoting the force at P (see fig.
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  • - (i.) An expression such as a.2.a.a.b.c.3.a.a.c, denoting that a series of multiplications is to be performed, is called a monomial; the numbers (arithmetical or algebraical) which are multiplied together being its factors.
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  • tons, (4) w denoting the density of water in tons/ft.', and W =wV, for a displacement of V ft.3 This couple, combined with the original buoyancy W through B, is equivalent to the new buoyancy through B, so that W.BB 1 =wAk 2 tan 8, (5) BM =BB 1 cot B=Ak e /V, (6) giving the radius of curvature BM of the curve of buoyancy B, in terms of the displacement V, and Ak e the moment of inertia of the water-line area about an axis through F, perpendicular to the plane of displacement.
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  • To transfer the integral equation into the differential equation of continuity, Green's transformation is required again, namely, (++) dxdydz= ff (l +mr t } ndS, (2) or individually dxdydz = f flldS, ..., (3) where the integrations extend throughout the volume and over the surface of a closed space S; 1, m, n denoting the direction cosines of the outward-drawn normal at the surface element dS, and, 77, any continuous functions of x, y, z.
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  • To determine the component acceleration of a particle, suppose F to denote any function of x, y, z, t, and investigate the time rate of F for a moving particle; denoting the change by DF/dt, DF = 1t F(x+uSt, y+vIt, z+wSt, t+St) - F(x, y, z, t) dt at = d + u dx +v dy+ w dz and D/dt is called particle differentiation, because it follows the rate of change of a particle as it leaves the point x, y, z; but dF/dt, dF/dx, dF/dy, dF/dz (2) represent the rate of change of F at the time t, at the point, x, y, z, fixed in space.
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  • Round the cylinder r=a held fixed in the U current the liquid streams past with velocity q' =2U sin 0+m/a; (2) and the loss of head due to this increase of velocity from U to q' is q' 2 -U 2 - (2U sin e to space filled with liquid, and at rest at infinity, the cylinder will experience components of force per unit length (i.) -27rpmV, 27rpmU, due to the vortex motion; 2 dU 2dV (ii.) -71-pa 2 w,, -7rpa dt, due to the kinetic reaction of the liquid; (iii.) o, -7r(a-p)a 2 g, due to gravity, taking Oy vertically upward, and denoting the density of the cylinder by a; so that the equations of motion are 71-0-a 2 - di r = - 7pa2- -- 22rpmV, (4) aa 2 - = -7rpa 2 dV +27rpmV - 7r(cr - p) a2g, (5) 7r or, putting m = a 2 w, so that the vortex velocity is due to an angular velocity w at a radius a, (o+p)dU/dt+2pwV =o, (6) (a+ p) dV /dt - 2 pwU + (v - p)g = o.
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  • At infinity U = -me a cos (i = a m b oos (3, V= -me a sin 1 3 - C7,1 sin 0, (9) a and b denoting the semi-axes of the ellipse a; so that the liquid is streaming at infinity with velocity Q = m/(a+b) in the direction of the asymptote of the hyperbola (3.
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  • (12) Along the stream line xBAPJ, t ' =0, u=ae-" c bl, n; (13) and over the jet surface JPA, where the skin velocity is Q, - q = - Q, u = ae rs Q /m = ae rs lc, (14) ds denoting the arc AP by s, starting at u = a; a ' ch nS2=cos nB= -a' u u - - a b' (15) a l a - b l u - a' a-a' u-b' co > u = ae'" S " c > a, and this gives the intrinsic equation of the jet, and of curvature ds '&1) _ i dw i dw dS2 P= - dO = Q a0 - Q as2 = Q c u-b d (u -a.u -a') _ ?
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  • Thus the capacity of a sphere in electrostatic units (E.S.U.) is the same as the number denoting its radius in centimetres.
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  • To obtain (i) and (ii) together, we show that the volume of a sphere is proportional to the volume of the cube whose edge is the diameter; denoting the constant ratio by aX, the volume of the sphere is Xa 3, and thence, by taking two concentric spheres (cf.
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  • Denoting the angle of departure and descent, measured in degrees and from the line of sight OB by ¢ and 0, the total deviation in the range OB is (fig.
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  • Starting with the exact equations of motion in a resisting medium, (43) d2t cos i = ds, d 2 y d 44 dt2 = -r sin i-g= -rds-g, and eliminating r, (45) dt - - cos z, or the equation obtained, as in (18), by resolving normally in the trajectory, but di now denoting the increment of i in the increment of time dt.
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  • apxeiov, an official building), a term (generally used in the plural "archives"), properly denoting the building in which are kept the records, charters and other papers belonging to any state, community or family, but now generally applied to the documents themselves (see Record).
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  • In Order To Adapt It To The Gregorian Calendar, We Must First Add The To Days That Were Left Out Of The Year 1582; In The Second Place We Must Add One Day For Every Century That Has Elapsed Since 1600, In Consequence Of The Secular Suppression Of The Intercalary Day; And Lastly We Must Deduct The Units Contained In A Fourth Of The Same Number, Because Every Fourth Centesimal Year Is Still A Leap Year.Q Denoting, Therefore, The Number Of The Century (Or The Date After The Two Right Hand Digits Have Been Struck Out) By C, The Value Of L Must Be Increased By 10 (C 16) (6 C L = 7M 3 X (4 X) W Io (C 16) (C 4 16) W; That Is, Since 3 To =13 Or 6 (The 7 Days Being Rejected, As They Do Not Affect The Value Of L), L=7M 6 X () W _ 16) (_ L _ 6)W; This Formula Is Perfectly General, And Easily Calculated.
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  • NAUMACHIA, the Greek word denoting a naval battle (Pais, ship, and,uaXrl, battle), used by the Romans as a term for a mimic sea-fight.
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  • The general formulae of hydroxides are: M i OH, M ii (OH) 2, M il i (OH) 3, M i `'(OH) 4, &c., corresponding to the oxides M21O, M iiO, M21i103 M i °O 2, &c., the Roman index denoting the valency of the element.
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  • we have as Leibnitz's remaining legacy to later logicians the conception of Characteristica Universalis and Ars Combinatoria, a universal denoting by symbols and a calculus working by substitutions and the like.
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  • But whilst, in its more comprehensive acceptation, the term Hinduism would thus range over the entire historical development of Brahmanical India, it is also not infrequently used in a narrower sense, as denoting more especially the modern phase of Indian social and religious institutions - from the earlier centuries of the Christian era down to our own days - as distinguished from the period dominated by the authoritative doctrine of pantheistic belief, formulated by the speculative theologians during the centuries immediately succeeding the Vedic period (see Brahmanism).
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  • This central desert is the Kir, Kej, Katz or Kash Kaian of Arabic medieval geography and a part of the ancient Kaiani kingdom; the prefix Kej or Kach always denoting lowlevel flats or valleys, in contradistinction to mountains or hills.
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  • In its more restricted connotation, denoting the district to which it is usually applied or a part thereof, it is found in Joshua xx.
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  • The petrels, all of which are placed in the family Procellariidae, were formerly associated with the Laridae (see GuLL), but they are now placed as the sole members of the suborder Tubinares (the name denoting the characteristic tubular structure of their nostrils) and of the order Procellariiformes (see Bird).
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  • In using the above table to find the value of E or dE/dt at any temperature or between any limits, denoting by p the value of dE/dt at 50° C., and by 2C the constant value of the second coefficient, we have the following equations :- dE/dt = p+2c(t -50), at any temperature t, Cent.
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  • By contrast, in other groups the older men wear penis sheaths and the young do not, denoting changing times.
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  • One foot is light, one is dark, denoting left and right.
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  • The term quilted in a handbag usually refers to the stitching pattern, which creates a quilted look, rather than denoting the use of alternating fabric squares.
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  • When you mail your application, you have to mark it with a special code denoting your region of the country.
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  • While local police forces were still wearing the same local uniforms as always, the milice had special uniforms denoting their connection with the Vichy government.
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  • The standard uniform had a beret, also in dark blue, with the milice badge (identical to the one on the breast pocket) denoting membership.
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  • The front pockets are where most patches denoting accomplishment and service go.
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  • Arnaout), denoting the people, and Arbenia or Arberia, the land, are also, though less frequently, used by the Albanians.
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  • In the more general case of the convective equilibrium of a spherical atmosphere surrounding the earth, of radius a, (1-1?-=(n+ I) Po --a 2 dr, (12) gravity varying inversely as the square of the distance r from the centre; so that, k = po/po, denoting the height of the homogeneous atmosphere at the surface, 0 is given by (n+I)k(I -9/6 0) =a(I -a/r), (13) or if c denotes the distance where 0=o, 0 _a (14) 0 r c -a' When the compressibility of water is taken into account in a deep ocean, an experimental law must be employed, such as p - po=k(P - Po), or P/po=I+(p-p0)/A, A=kpo, (15) so that A is the pressure due to a head k of the liquid at density under atmospheric pressure po; and it is the gauge pressure required on this law to double the density.
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