# Ab sentence example

ab

- possess the invariant property, and we may write (AB) i (AC)'(BC) k ...A P E B C...
- In nonflowering plants the works usually followed are for ferns, Hooker and Baker's Synopsis filicum; for mosses, Muller's Synopsis muscorum frondosorum, Jaeger & Sauerbeck's Genera et species muscorum, and Engler & Prantl's Pflanzenfamilien; for algae, de Toni's Sylloge algarum; for hepaticae, Gottsche, Lindenberg and Nees ab Esenbeck's Synopsis hepaticarum, supplemented by Stephani's Species hepaticarum; for fungi, Saccardo's Sylloge fungorum, and for mycetozoa Lister's monograph of the group. For the members of large genera, e.g.
- A young senator (ab actis senatus) was chosen to draw up these Acta, which were kept in the imperial archives and public libraries.
- we may write (AB)i(AC)j(BC)k...
- To explain this result, chemists suppose that both changes can occur simultaneously, and that equilibrium results when the rate at which AB and CD are transformed into AD and CB is the same as the rate at which the reverse change goes on.Advertisement
- ab, g, The limpet breeds upon the southern English coast in the early part of April, but its development has not been followed.
- Thus, if the molecule of a substance in solution is represented by AB, Grotthus considered a chain of AB molecules to exist from one electrode to the other.
- In order that (ab)i(ac)j(bc)k...
- as there is a break ab, Abdominal ganglion.
- The appellatio tanquam ab abusu (appel comme d'abus) in France was an application of a like nature.Advertisement
- in the year 1147, we have the bard testifying to the supereminence of the Cid among his country's heroes: "Ipse Rodericus Mio Cid semper vocatus, De quo cantatur quod ab hostibus haud superatus, Qui domuit Mauros, comites domuit quoque nostros."
- Among these posts were various procuratorships (chief of which was that of the imperial fisc), and the offices ab epistulis, a rationibus and a libellis (secretary, accountant, receiver of petitions).
- The proportions between the four salts AB, CD, AD and CB, which exist finally in solution, are found to be the same whether we begin with the pair AB and CD or with the pair AD and CB.
- 434; quod ubique, quod semper, quod ab omnibus creditum est).
- Schurz, De mutationibus in imperio ordinando ab imp. Hadr. factis, i.Advertisement
- Some see the guarantee, or at least the indication, of infallibility in the consensus of the Church (quod semper, ubique, et ab omnibus) expressed from time to time in general councils; others see it in the special grace conferred upon St Peter and his successors, the bishops of Rome, as heads of the Church; others again see it in the inspired Scriptures, God's Word.
- It was destroyed in 1260 by Llewellyn ab Gruffydd, prince of Wales, with the supposed connivance df Mortimer, but its site was reoccupied by the earl of Lincoln in 277, and a new castle at once erected.
- Leading examples may be found in the various prosecutions of St Athanasius, in whose case also there is the germ of an appeal, tanquam ab abusu.
- (1) The taking away of all matrimonial, testamentary and ab intestate jurisdiction by 20 & 21 Vict.
- Roman Catholic writers, 4 however, have explained the prohibition to apply to matters of faith only, and in that case the Tridentine decree is little else than another form of the Vincentian canon which has been widely accepted in the Anglican communion: curandum est ut id teneamus quod ubique, quod semper, quod ab omnibus creditum est.Advertisement
- His father belonged to the class of Dihkans (the old native country families and landed proprietors of Persia, who had preserved their influence and status under the A ab rule), and possessed an estate in the neighbourhood of Cus (in Khorasan).
- I begin ab ovo.
- Philastrius, however, says: hominem autem ab angelis factum asserit, while according to Epiphanus xxiv.
- 22 by the curve AB.
- Let AB be the major axis of the orbit, B the pericentre, F the focus or centre of motion, P the position of the body.Advertisement
- ab, Abdominal ganglion or site pe, The right pedal nerve.
- ab.
- Such an expression as a l b 2 -a 2 b i, which is aa 2 ab 2 aa x 2 2 ax1' is usually written (ab) for brevity; in the same notation the determinant, whose rows are a l, a 2, a3; b2, b 2, b 3; c 1, c 2, c 3 respectively, is written (abc) and so on.
- This will be recognized as the resultant of the two linear forms. If the two linear forms be identical, the umbral sets a l, a2; b l, b 2 are alternative, are ultimately put equal to one another and (ab) vanishes.
- For the cubic (ab) 2 axbx is a covariant because each symbol a, b occurs three times; we can first of all find its real expression as a simultaneous covariant of two cubics, and then, by supposing the two cubics to merge into identity, find the expression of the quadratic covariant, of the single cubic, commonly known as the Hessian.Advertisement
- From the three equations ax = alxl+ a2x2, b.= blxl+b2x2, cx = clxi+c2x2, we find by eliminating x, and x 2 the relation a x (bc)+b x (ca) +c x (ab) =0.
- We may in any relation substitute for any pair of quantities any other cogredient pair so that writing -}-d 2, -d l for x 1 and x 2, and noting that gx then becomes (gd), the above-written identity bceomes (ad)(bc)+(bd)(ca)+(cd)(ab) = 0.
- (II.) Similarly in (I.), writing for c l, c 2 the cogredicnt pair -y2, +y1, we obtain axb5-a5bx=(ab)(xy)..
- (IV.) and herein writing d 2, -d 1 for x l, x2, 2 (ac) (bc) (ad) (bd) = (bc) 2 (ad) 2 +(ac) 2 (bd) 2 - (ab) 2 (cd) 2.
- -2 _ ab 2an-2bn-2Crz z x () x x x, Each term on the right-hand side may be shown by permutation of a, b, c to be the symbolical representation of the same covariant; they are equivalent symbolic products, and we may accordingly write 2(ac) (bc)ai -1 bi -1 cx 2 =(ab)2a:-2b:-2c:, a relation which shows that the form on the left is the product of the two covariants n (ab) ay 2 by 2 and cZ.Advertisement
- The identities are, in particular, of service in reducing symbolic products to standard forms. A symbolical expression may be always so transformed that the power of any determinant factor (ab) is even.
- (ab)(ac)bxcx = - (ab)(bc)axcx = 2(ab)c x {(ac)bx-(bc)axi = 1(ab)2ci; so that the covariant of the quadratic on the left is half the product of the quadratic itself and its only invariant.
- To obtain the corresponding theorem concerning the general form of even order we multiply throughout by (ab)2' 2c272 and obtain (ab)2m-1(ac)bxc2:^1=(ab)2mc2 Paying attention merely to the determinant factors there is no form with one factor since (ab) vanishes identically.
- For two factors the standard form is (ab) 2; for three factors (ab) 2 (ac); for four factors (ab) 4 and (ab) 2 (cd) 2; for five factors (ab) 4 (ac) and (ab) 2 (ac)(de) 2; for six factors (ab) 6, (ab) 2 (bc) 2 (ca) 2, and (ab) 2 (cd) 2 (ef) 2 .
- - We have seen that (ab) is a simultaneous invariant of the two different linear forms a x, bx, and we observe that (ab) is equivalent to where f =a x, 4)=b.Advertisement
- (a m b n) k (ab) kamkbn-k x, x - x it is clear that the k th transvectant is a simultaneous covariant of the two forms.
- We have seen that transvection is equivalent to the performance of partial differential operations upon the two forms, but, practically, we may regard the process as merely substituting (ab) k, (OW for azbx, 4x t ' respectively in the symbolic product subjected to transvection.
- The process of transvection is connected with the operations 12; for?k (a m b n) = (ab)kam-kbn-k, (x y x y or S 2 k (a x by) x = 4))k; so also is the polar process, for since f k m-k k k n - k k y = a x by, 4)y = bx by, if we take the k th transvectant of f i x; over 4 k, regarding y,, y 2 as the variables, (f k, 4)y) k (ab) ka x -kb k (f, 15)k; or the k th transvectant of the k th polars, in regard to y, is equal to the kth transvectant of the forms. Moreover, the kth transvectant (ab) k a m-k b: -k is derivable from the kth polar of ax, viz.
- Since, If F = An, 4) = By, 1 = I (Df A4) Of A?) Ab A"'^1Bz 1=, (F, Mn Ax I Ax 2 Axe Ax1) J The First Transvectant Differs But By A Numerical Factor From The Jacobian Or Functional Determinant, Of The Two Forms. We Can Find An Expression For The First Transvectant Of (F, ï¿½) 1 Over Another Form Cp. For (M N)(F,4)), =Nf.4Y Mfy.4), And F,4, F 5.4)= (Axby A Y B X) A X B X 1= (Xy)(F,4))1; (F,Ct)1=F5.D' 7,(Xy)(F4)1.
- It is (f = (ab) 2 a n-2 r7 2 =Hx - =H; unsymbolically bolically it is a numerical multiple of the determinant a2 f a2f (32 f) 2ï¿½ It is also the first transvectant of the differxi ax axa x 2 ential coefficients of the form with regard to the variables, viz.Advertisement
- For the quadratic it is the discriminant (ab) 2 and for ax2 the cubic the quadratic covariant (ab) 2 axbx.
- If we have a symbolic product, which contains the symbol a only in determinant factors such as (ab), we may write x 2, -x 1 for a 1, a 2, and thus obtain a product in which (ab) is replaced by b x, (ac) by c x and so on.
- First observe that with f x =a: = b z = ï¿½ï¿½ï¿½,f1 = a l a z ', f 2 = a 2 az-', f x =f,x i +f 2 x i, we find (ab) - (a f) bx - (b f) ax.
- ukx(n-2) ï¿½ Taking the first polar with regard to y (n - k) (a f) xa x -k-l ay+ k (af) k-l ay -k (ab) (n -1) b12by n kn-2k-1 n-1 k(n-2) =k(n- 2)a u x u5+nax ayux and, writing f 2 and -f l for y1 and 3,21 (n-k)(a f) k+ta i k-1 + k (n - 1)(ab)(a f) k-1 (b f)4 1 k by-2 = (uf)u xn-2k-1?
- Moreover the second term on the left contains (a f)' c -2b z 2 = 2 (a f) k-2b x 2 - (b) /0-2a 2 ï¿½ if k be uneven, and (af)?'bx (i f) of) '-la if k be even; in either case the factor (af) bx - (bf) ax = (ab) f, and therefore (n-k),bk+1 +Mï¿½f = k(n-2)f.(uf)uxn-2k-1; and 4 ' +1 is seen to be of the form f .14+1.Advertisement
- y1 = x 15+f2n; fï¿½ y2 =x2-f?n, f .a b = ax+ (a f) n, l; n u 2 " 2 22 2 +` n) u3 n-3n3+...+U 2jnï¿½ 3 n Now a covariant of ax =f is obtained from the similar covariant of ab by writing therein x i, x 2, for yl, y2, and, since y?, Y2 have been linearly transformed to and n, it is merely necessary to form the covariants in respect of the form (u1E+u2n) n, and then division, by the proper power of f, gives the covariant in question as a function of f, u0 = I, u2, u3,...un.
- The first transvectant, (f,f') 1 = (ab) a x b x, vanishes identically.
- This can be verified by equating to zero the five coefficients of the Hessian (ab) 2 axb2.
- f= ai; the Hessian H = (ab) 2 azbx; the quartic i= (ab) 4 axb 2 x; the covariants 1= (ai) 4 ay; T = (ab)2(cb)aybyci; and the invariants A = (ab) 6; B = (ii') 4 .
- Solving the equation by the Ordinary Theory Of Linear Partial Differential Equations, We Obtain P Q 1 Independent Solutions, Of Which P Appertain To S2Au = 0, Q To 12 B U =0; The Remaining One Is Ab =Aobl A 1 Bo, The Leading Coefficient Of The Jacobian Of The Two Forms. This Constitutes An Algebraically Complete System, And, In Terms Of Its Members, All Seminvariants Can Be Rationally Expressed.
- 1 Ab' Establishing The Ground Forms Of Degrees Order (I, O; I), (O, I; I), (I, I; O), Viz: The Linear Forms Themselves And Their Jacobian J Ab.
- In the a x = aixi+a2x2, observe that a a = a2, ab = aibi +a2b2.
- then of course (AB) = (ab) the fundamental fact which appertains to the theory of the general linear substitution; now here we have additional and equally fundamental facts; for since A i = Xa i +,ia2, A2= - ï¿½ay + X a2, AA =A?-}-A2= (X2 +M 2)(a i+ a z) =aa; A B =AjBi+A2B2= (X2 +, U2)(albi+a2b2) =ab; (XA) = X i A2 - X2 Ai = (Ax i + /-Lx2) (- /-jai + Xa2) - (- / J.x i '+' Axe) (X a i +%Ga^2) = (X2 +, u 2) (x a - = showing that, in the present theory, a a, a b, and (xa) possess the invariant property.
- (ab), aa, ab, (xa), ax, xx.
- The general form of covariant is therefore (ab) h i (ac) h2 c) (b h3 a i bb2c'e3...abia?2b?3...
- X (xa) ki (xb) k2 (xc) k3...axibx2cx3...xx = (AB) hi (AC) h2 (BC) h3...A11 4 13 A1,14131 A B I ?C"' B C "' X (XA) ki (XB) k2 (XC) k3...AXB122cCk...X If this be of order e and appertain to an nie L Eke-/1+2m =e, h i+h2+ï¿½ï¿½ï¿½+221+ji+j2+ï¿½ï¿½ï¿½+kl+li =n, hi+h3+..ï¿½+222+ji+j3+ï¿½ï¿½ï¿½+k2+12 = n, h2+h3+ï¿½ï¿½ï¿½+223+j2+%3+ï¿½.ï¿½+k3+13 =n; viz., the symbols a, b, c,...
- To assist us in handling the symbolic products we have not only the identity (ab) cx + (bc) a x + (ca) bx =0, but also (ab) x x+ (b x) a + (ax) b x = 0, (ab)a+(bc)a s +(ca)a b = 0, and many others which may be derived from these in the manner which will be familiar to students of the works of Aronhold, Clebsch and Gordan.
- This is the fundamental system; we may, if we choose, replace (ab) 2 by ab =a, 2, +2a1+a2 since the identity a a b b - a, = (ab) 2 shows the syzygetic relation (74+a 2) 2 - (ao +2a +ï¿½2) = 2(aoa2 - ai).
- versions ap X ab and aXab), a Hebrew name, mentioned only once in the Old Testament (Gen.
- If 2l is the distance between the poles m and - in, d the distance from either pole to a point P on the line AB (fig.
- AB is the rod and C the middle point of its axis; NS is the magnetometer needle; AM bisects the undeflected needle NS at right angles.
- Let the distance of each pole of the rod AB from the centre of the magnetometer needle = d.
- Then, since Hp, the force at M due to m and - m, is the resultant of d, and - m2, we have (L Hp m d d2 2ml H = d3, the direction being parallel to AB.
- 8, where AB is the vertical rod and M indicates the position of the magnetometer needle, which is supposed to be perpendicular to the plane of the paper.
- 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).
- electric potential.3 If in the annexed diagram AB CD represents the metallic plate through which the current of electricity or heat flows in the E.
- - One of the Nymphonomorphous Pantopoda, Nymphon hispidum, showing the seven pairs of appendages I to 7; ab, the rudimentary opisthosoma; s, the mouth-bearing proboscis.
- The city then placed itself under the protection of the emperor .Charles V., created a magistracy of "ten conservators of the liberties of the state" (December 1524), united the different monti in one named the "monte of the reigning nobles," and, rejoicing to be rid of the last of the Petrucci, dated their public books, ab instaurata libertate year I., II., and so on.
- ï¿½ 37 (ii.)), and then says that A+B and 134-A, or AB and BA, are identical, where A and B are any multinomials.
- Thus a(b+c) and (b+c)a give the same result, though it may be written in various ways, such as abdac, ca+ab, &c. In the same way the associative law is that A(BC) and (AB)C give the same formal result.
- Let a+b denote the region made up of a and b together (the common part, if any, being reckoned only once), and let a X b or ab mean the region common to a and b.
- The sum of two weighted points aA, (3B is, by definition, the point (a+13) G, where G divides AB so that AG: GB =0: a.
- It is remarkable that Mobius employs the symbols AB, ABC, Abcd In Their Ordinary Geometrical Sense As Lengths, Areas And Volumes, Except That He Distinguishes Their Sign; Thus Ab = Ba, Abc= Acb, And So On.
- The symbol AB, from this point of view, is called the inner product of A and B, as distinguished from the outer product IAB.
- In 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.
- In ordinary algebra we have the disjunctive law that if ab = o, then either a = o or b= o.
- By the principle of energy the illumination over the entire focal plane must be equal to that over the diffracting area; and thus, in accordance with the suppositions by which (3) was obtained, its value when integrated from E= co to = -1-x, and from n = - oo to n = -1-oo should be equal to ab.
- u 2 u It will be observed that, while the total intensity is proportional to ab, the intensity at the focal point is proportional to a 2 b 2.
- 4, AB represents the axis of an optical instrument (telescope or microscope), A being a point of the object and B a point of the image.
- Let AoBo be a plane wave-surface of the light before it falls upon the prisms, AB the corresponding wave-surface for a particular part of the spectrum after the light has passed the prisms, or after it has passed the eye-piece of the observing telescope.
- The path of a ray from the wave-surface AoBo to A or B is determined by the con dition that the optical distance, µ ds, is a minimum; and, as AB is by supposition a wave-surface, this optical distance is the same for both points.
- B) - f S,u ds (along The new wave-surface is formed in such a position that the optical distance is constant; and therefore the dispersion, or the angle through which the wave-surface is turned by the change of refrangibility, is found simply by dividing (5) by the distance AB.
- If now we suppose the aperture AB to be covered by a great number of opaque strips or bars of width d, separated by transparent intervals of width a, the condition of things in the directions just spoken of is not materially changed.
- In another direction, making a small angle with the last, such that the projection of AB upon it amounts to a few wavelengths, it is easy to see that the mode of interference is the same as if there were no ruling.
- For example, when the direction is such that the projection of AB upon it amounts to one wave-length, the elementary components neutralize one another, because their phases are distributed symmetrically, though discontinuously, round the entire period.
- 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.
- Let P, Q denote the normal thrust across the sides bc, ca, and R the normal thrust across the base ab.
- This is proved by taking any two points A and B at the same level, and considering the equilibrium of a thin prism of liquid AB, bounded by planes at A and B perpendicular to AB.
- As gravity and the fluid pressure on the sides of the prism act at right angles to AB, the equilibrium requires the equality of thrust on the ends A and B; and as the areas are equal, the pressure must be equal at A and B; and so the pressure is the same at all points in the same horizontal plane.
- AB, p = Thus in water,.
- (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.
- (II) Thus cos 0 is the Stokes' function of a point source at 0, and Papb of a line source AB.
- 2n u (a -b.b -a')' not requiring the integration of (II) and (12) If 0=a across the end J J' of the jet, where u = oo, q= Q, b-a' a-b ch 7/2,=cos na = I, , sh 162 = i sin na = i,, a - a a-a Then a-a'+(a+a) cos 2na-[a+a'+(a-a) cos 2najcos 2110 (a-a') sin' 2na X cos 211a - cos 2110 Along the wall AB, cos nO =o, sin n0= I, a> u> b, ch n2= i sh log (q) n= i?
- m _ c Q du dO dt - rrqu 2r qu AB _ Q du L bq (u -a') +V (b -a')1,l (a -u)11/ndu) L 1,1 (a-a/),,1 (u-b), f u Along the wall Bx, cos n0 =I, sin n0 =o, b >u>o ch nSt = ch log () n=, , fb-a?, ?
- From A to B, a>u >b, 0=0, ch S2= ch log Q=cos a-i sin 2a a-b I sh S2= sh log Q= I (a u-b-a/) s i n a Q = (u-b) cos a-2(a-a') sin 2 a+1,/ (a-u.u- a')sin a (8) u-b ds _ ds d4 _ Q dw Q du - Q d 4) du q du (u-b) cos a-2(a- a') sin 2 a (a-u.0 - a') sin a (9) it j- -j' AB _f a(2b - a - a')(u-b)-2(a-b)(b-a')+2V (a - b.
- (4 a2 +A.b'-'-f-A) - a 2a b (I - V a2+A), (12) ab (.
- Sargon, who meanwhile had crushed the confederacy of the northern nations, had taken (717 B.C.) the Hittite stronghold of Carchemish and had annexed the future kingdom of Ecbatana, was now accepted as king by the Babylonian priests and his claim to be the successor of Sargon of Akkad acknowledged up to the time of his murder in 705 B.C. His son Sennacherib, who succeeded Serena- hi m on the 12th of Ab, did not possess the military or cherlb. ?
- Another castle, built in the same century, on the east bank, was held direct by the lords of Glamorgan, as the westernmost outpost of their lordship. It was frequently attacked by the Welsh, notably in 1231 when it was taken, and the town demolished by Llewelyn ab Iorwerth.
- Ab Gruffydd Llewelyn II >>
- ABC is a quadrant in which the line AB and the arc AC are divided into the same number of equal parts.
- Radii are drawn from the centre of the quadrant to the points of division of the arc, and these radii are intersected by the lines drawn parallel to BC and through the corresponding points on the radius AB.
- The castle was begun, in or about 1109, by Cadwgan ab Bleddyn ab Cynfyn (Cynvyn), and finished by Gwenwynwyn; in 1196 it was besieged, undermined and taken by Hubert, archbishop of Canterbury.
- The founda 1 It must be remembered that the Pisans and Florentines dated the beginning of the year ab incarnatione, i.e.
- 4 let AB be the axis of composition, AP be the vapour pressure of pure A, BQ the vapour pressure of pure B.
- For immiscible liquids the vapour pressure curve is the horizontal line ab, described so that aP = QB and bQ=AP. For partially miscible liquids the curve is Pa i b i Q.
- A Catholic commentator of the 16th century, Hieronymus ab Oleastro, seems to have been the first to connect the name " Jehova " with howah interpreting it contritio, sive pernicies (destruction of the Egyptians and Canaanites); Daumer, adopting the same etymology, took it in a more general sense: Yahweh, as well as Shaddai, meant " Destroyer," and fitly expressed the nature of the terrible god whom he identified with Moloch.
- 7 gives the freezing-point curve of mercury and thallium; here A and E are the melting-points of pure mercury and pure thallium, and the branches AB and ED do not cut each other, but cut an intermediate rounded branch BCD.
- Laennec, to whom we are indebted for the practice of auscultation, freely admits that the idea was suggested to him by study of Hippocrates, who, treating of the presence of morbid fluids in the thorax, gives very particular directions, by 1 " Hippocrates Cous, primus quidem ex omnibus memoria dignus, ab studio sapientiae disciplinam hanc separavit, vir et arte et facundia insignis " (Celsus, De medicina).
- One of the best methods for doing this is to charge the Ab l condenser by the known voltage of a battery, and then d e t erdischarge it through a galvanometer and repeat this minations.
- Then the potential at any point P in this ideal plane PO is equal to q/AP-q/BP=0, whilst the resultant force at P due to the two point charges is 2gAO/AP 3, and is parallel to AB or normal to PO.
- A cycle such as ABCD enclosed by parts of two isothermals, BC, AD, and two adiabatics, AB, CD, is the simplest form of cycle for theoretical purposes, since all the heat absorbed, H', is taken in during the process represented by one isothermal at the temperature o', and all the heat rejected, H", is given out during the process represented by the other at the temperature 0".
- It is not necessary in this example that AB, CD should be adiabatics, because the change of volume BC is finite.
- If we consider any short length of the stream bounded by two imaginary cross-sections A and B on either side of the plug, unit mass of the fluid in passing A has work, p'v', done on it by the fluid behind and carries its energy, E'+ U', with it into the space AB, where U' is the kinetic energy of flow.
- In passing B it does work, p"v", on the fluid in front, and carries its energy, E"+ U", with it out of the space AB.
- If there is no external loss or gain of heat through the walls of the pipe, and if the flow is steady, so that energy is not accumulating in the space AB, we must evidently have the condition E'+U'+p'v' =E'+ U"+p"v" at any two cross-sections of the stream.
- All-important, too, is the order of ceremonial and the formula of prayer: a mistake or omission or an unpropitious interruption may vitiate the whole ritual, and though such misfortunes may occasionally be expiated by the additional offering of a piaculum, in more serious cases the whole ceremony must be recommenced ab initio.
- Meanwhile Aquitaine was gradually lost; the defeat of Pembroke off La Rochelle deprived England of the command of the sea, and Sir Owen ap Thomas, a grand-nephew of Llewelyn ab Gruffyd, planned, with French help, an abortive invasion of Wales.
- Ab.
- Adjecta insuper ab eodem scholia, &c. Lyons, Melchior and Gaspar Trechsel (1 535; 2nd ed., Lyons, Hugo a Porta (1541), i.e.
- fn6 Matthew Paris gives a letter from Philip, prior of the Dominicans in Palestine, which reached the pope in 1237, and which speaks of a prelate from whom he had received several letters, "qui praeest omnibus quos Nestoriana haeresis ab ecclesia separavit (cujus praelatio per Indiam Majorem, et per regnum sacerdotis Johannis, et per regna magis proxima Orienti dilatatur)."
- AG is the axis of the bore, ab the dispart, A'DG' is parallel to AG.
- ab + a(3 + ab +43.
- Area = ab.
- Then MA'B'N is a right trapezium, whose area is equal to that of Cabd; and it is related to the latter in such a way that, if any two lines parallel to AC and BD meet AB, CD, MN, A'B', in E, G, P, E', and F, H, Q, F', respectively, the area of the piece PE'F'Q of the right trapezium 'B.
- of the base are the projections of the sides AB, BC, CD,.
- Take any point P in the latter, and form triangles by joining P to each of the sides AB, BC, ...
- ab, be, ...
- 5, the volume of the element between these planes, when h is very small, is approximately h X AB X arc PQ = h.
- AB, and OP is the distance of the middle point of either side of the rectangle from the axis.
- AB.
- Let AB (fig.
- 6) be any arc of a parabola; and suppose we require the area of the figure bounded by this arc and the chord AB.
- CV; and therefore the area of the figure bounded by AK, BL, KL and the arc AB, is KL.
- The term is also sometimes applied to the line AB along which the point P moves as Nmovesfrom K to L.
- Then it may be shown that DE is parallel to AB, and that the area of the figure between chord DE and arc DE is half the sum of the areas DHA and EJB.
- For a tetrahedron, two of whose opposite edges are AB and CD, we require the area of the section by a plane parallel to AB and CD.
- Let the distance between the parallel planes through AB and CD be h, and let a plane at distance x from the plane through AB cut the edges AC, up -f- .
- Draw the tangents at A and B, meeting at T; and through T draw a line parallel to KA and LB, meeting the arc AB in C and the chord AB in V.
- As AB moves from CD to EF it pushes forward the layer of air in contact with it.
- As AB returns from EF towards CD the layer of air next to it follows it as if it D E F were pulled back by AB.
- On the whole the air S within ABCD neither gains nor g D loses momentum, so that on the whole it receives as much through AB as it gives up to CD.
- If P is the undisturbed pressure and P+w the pressure at AB, the momentum entering through AB per second isJ01(P+w-+pu2)dt.
- But the values of 2 which occur successively during the second at AB exist simultaneously at the beginning of the second over the distance U behind AB.
- Or if the conditions along this distance U could be maintained constant, and we could travel back along it uniformly in one second, we should meet all the conditions actually arriving at AB and at the same intervals.
- If the train of waves is reflected, the value of p at AB will be the sum of the values for the two trains, and will, on the average, be doubled.
- 33) represent the string with the ends AB fixed.
- Then move AB from right to left with this velocity, and the disturbance remains fixed in space.
- Since the conditions in the region PQ remain always the same, the momentum perpendicular to AB entering the region at Q is equal to the momentum perpendicular to AB leaving the region at P. But, since the motion at Q is along AB, there is no momentum there perpendicular to AB.
- So also there is on the whole none in that direction leaving at P. Let the tangent at P make angle 4) with AB.
- Now keep AB fixed, and the disturbance travels with velocity U.
- In this case AB = 1)1=1 the length, and the frequency n i = U/X i = U/2l = (I/2l)1,1 (Tim).
- passes over two edges AB, which serve as the fixed ends, and then over a pulley P, being stretched by a weight W.
- The material between A and B, though continually changing, is always in the same condition, and therefore the momentum within AB is constant.
- Projecting A'F'C'B' on to the horizontal AB, take Ff =m(l-x)il, the moment at C of unit load at F.
- Set off these distances along AB and let Y1, y2,.
- run, then ab is the unit 53.
- 56) represent in magnitude and position a load W, at x from the left abutment, on a girder AB of span 1.
- Thus we shall call the first inclined line on the left hand the line AG, the line representing the first force on the top left-hand joint AB, the first horizontal member at the top left hand the line BH, &c; similarly each point requires at least three letters to denote it; the top first left-hand joint may be called Abhg, being the point where these four spaces meet.
- 67 b, superimposed and divided so that the length AX represents the load AX, the length AB the load AB, the length YX the reaction YX, and so forth.
- The line XZ consists of a series of lengths, as XA, AB ...
- All real connexion or relation, therefore, and with it all possibility of an objective system, disappears; it is, in fact, excluded by Hume ab initio, for " the mind never perceives any real connexion among distinct existences."
- 3 by the height AH, such that the rectangle Ahkb is equal to the area Apdb; and the M.E.P. multiplied by 41rd 2, the cross-section of the bore in square inches, gives in tons the mean effective thrust of the powder on the base of the shot; and multiplied again by 1, the length in inches of the travel AB of the shot up the bore, gives the work realized in inch-tons; which work is thus equal to the M.E.P. multiplied by 41+-d 2 l = B -C, the volume in cubic inches of the rifled part AB of the bore, the difference between B the total volume of the bore and C the volume of the powder-chamber.
- nunc ab omnibus receptum," and this is the origin of the name " Textus Receptus " (or T.R.) often given to the ordinary Greek Text.
- There is no evidence of any settlement on the site of the present town prior to about 1092, when Bernard Newmarch, after defeating Bleddin ab Maenarch, built here a castle which he made his residence and the chief stronghold of his new lordship. For this purpose he utilized what remained of the materials of the Roman fort, 3 m.
- The second class, referred to in inscriptions by the name of praefecti ab decurionibus creati lege Petronia, seem to have been appointed by the local senate in case of a complete absence of higher magistrates, such as would have led in Rome to the appointment of an interrex.
- AB, is a " diameter "; any other line similarly terminated, e.g.
- 36 it is seen that the line joining the points A and B is the locus of the intersection of equal tangents, for if P be any point on AB and PC and PD the tangents to the circles, then PA PB = PC 2 = PD 2, and therefore PC = PD.
- The line AB is termed the " radical axis."
- To prove this let AB, AB' be the tangents from any point on the line AX.
- 47, AB' =AO'-0B2=AX2+0X2-0P2; and OX 2 =OD 2 - DX 2 =0P 2 +PD 2 - DX 2.
- Since PD = PD', it follows that AB =AB'.
- 7 angled at C, ADB is the semicircle described on AB as diameter, AEB the circular arc described with centre C and radius CA= CB.
- 9): ACB being a semicircle whose centre is 0, and AC the arc to be rectified, he produced AB to D, making BD equal to the radius, joined DC, 1 Vieta, Opera math.
- Instead of producing AB (see fig.
- Take AB equal to one-fourth of the given line; on AB describe a square ABCD; join AC; in AC produced find, by a known process, a point C 1 such that, when C 1 B 1 is drawn perpendicular to AB produced and C 1 D 1 perpendicular to BC produced, the rectangle BC,.
- The diameter sought is the straight line from A to the limiting position of the series of B's, say the straight line AB co.
- Denoting the number of units in AB by 4c, we can express BB 1j B 1 B 2,.
- in terms of 4c, and the identity AB, =AB+BB,+B,B 2 +.
- Vulgate) ab Hebraica veritate, 1 333.
- ab, ac, ad, Three pit-like depressions in the median line of the foot supposed by some writers to be pores admitting water into the vascular system.
- indicate the course of fluid ab, Posterior, cut remnants of the from the pericardium outintestine and ventricle.
- The town derives its name from the river Avon (corrupted from Avan), which also gave its name to a medieval lordship. On the Norman conquest at Glamorgan, Caradoc, the eldest son of the defeated prince, Lestyn ab Gwrgan, continued to hold this lordship, and for the defence of the passage of the river built here a castle whose foundations are still traceable in a field near the churchyard.
- Ab 9,1 Fast, Destruction of the Temple.
- ab Iorwerth, prince of North Wales, and who died in 1236 or 1237.
- c. 900), prince of Powys, and Hywel ab Cadogan.
- He also brought out editions of the Byzantine historians, John Cinnamus and John Zonaras, as Joannis Cinnami historiarum de rebus gestis a Joanne et Manuele Comnenis (Paris, 1670) and Joannis Zonarae Annales ab exordio mundi ad mortem Alexii Comneni (Paris, 1686).
- The diagonal AD of the parallelogram, of which AB and AC are adjacent sides, will represent, both in direction and magnitude, the motion of the rain as apparent to the observer.
- 2) be a star and the s observer be carried along the line AB; let SB be perpendicular to AB.
- compluria opuscula ab Erasmo Roterodamo et Thoma Moro.
- 27-29; Anna Comnena's Life; see also Du Cange, Familiae Byzantinae; Friedrich Wilken, Rerum ab Alexio I., Joanne, Manuele et Alexio II.
- ab anno 1198 [to 156s], annotated and added to by J.
- 4 A represents the freezing point of pure water, and AB the freezing point curve showing the depression of the freezing point as phenol is added.
- At A we 66 have the freezing point of pure water, which is lowered by the gradual addition of 46 ferric chloride in the manner shown by the curve AB.
- To explain the universe Spinoza proceeds to argue that God, though undetermined ab extra, is capable of infinite self-determination.
- concentrica, Lecanora esculenta); but it can hardly be that these are really free ab initio (vide Crombie in Journ.
- ab Aitzema, Saken van spaet en oorlogh in ende om trent de Vereenigde Nederlanden (1621-1668) (15 vols., 1657-1671); continuation by Lambert van den Bos (Lambertus Sylvius) (4 vols., 1685-1699).
- If, ignoring temporarily and for simplicity the fact that part of the carbon may exist in the state of graphite, we consider the behaviour of iron in cooling from the molten state, AB and BC give the temperature at which, for any given percentage of carbon, solidification begins, and Aa, aB, and Bc that at which it ends.
- As freezing progresses, at each successive temperature reached the frozen austenite has the carbon-content of the point on Aa which that temperature abscissa cuts, and the still molten part or " mother-metal " has the carbon-content horizontally opposite this on the line AB.
- In other words, the composition of the frozen part and that of the mother-metal respectively are p and q at the beginning of the freezing, and r and t' at the end; and during freezing they slide along Aa and AB from p to r and from q to t'.
- smaller and smaller proportion of the whole, and the austenitecementite eutectic which forms at the eutectic freezing-point, 1130° (aB), increases in amount until, when the carbon-content reaches the eutectic ratio, 4 30%, there is but a single freezing-point, and the whole mass when solid is made up of this eutectic. If there is more than 4-30% of carbon, then in cooling through region 3 the excess of carbon over this ratio freezes out as " primary " cementite.
- - Section on AB through Uptake, Slag Pocket and Regenerator.
- Thus, we find Sumerian ab, " dwelling," " sea "; ab, " road," and -ab, a grammatical suffix, which words, with many others of a similar character, were perhaps originally uttered with different voice-tones.
- a secretis, ab epistulis).
- In the logic of Mill, e.g., we find much of a special character that has no counterpart in Hume, much that is introduced ab extra, from general considerations of scientific procedure, but, so far as the groundwork is concerned, the System of Logic is a mere reproduction of Hume's doctrine of knowledge.
- Working on these lines, and attaching special importance to common descent, naturalists applied the term with more and more precision, until Linnaeus, in his Philosophia botanica, gave the aphorism, "species tot sunt diversae, quot diversae formae ab initio sunt creatae" - "just so many species are to be reckoned as there were forms created at the beginning."
- We thus obtain the differential equation gk(d 2 0/dx 2) =cgdo/dt+hpo, which is satisfied by terms of the type =c" sin where a 2 -b 2 = hp/qk, and ab = urnc/k.
- He was also the author of volumes entitled De satisfactione Christi disputationes (Geneva, 1666) and De necessaria secessione nostra ab ecclesia romana (Geneva, 1687).
- "An old ruynous thinge," as the Elizabethan poet Churchyard calls it even in the 16th century, it was inhabited, apparently, about 1390, by Myfanwy Fechan of the Tudor Trevor family and beloved by the bard Howel ab Einion Llygliw, whose ode to her is still extant.
- of Llangollen, founded about 1200 by Madoc ab Gruffydd Maelor, lord of Dinas Bran and grandson of Owen Gwynedd, prince of Wales.
- the placetum regium, recursus ab abusu, nominatio regia, afid that of vetoing the nomination of personae minus gratae.
- In 1557, and again in 1559, Pope Paul IV., through the Inquisition at Rome, published what may be regarded as the first Roman Index in the modern ecclesiastical use of that term (Index auctorum et librorum qui tanquam haeretici aut suspecti aut perversi ab Officio S.
- The most generally accepted etymology of the name (ab origine), according to which they were the original inhabitants (= Gk.
- 3) consists of an ordinary pendulum diagrammatically represented by ab, connected by a universal joint to an inverted pendulum dc. The latter, which is a rod pointed at its lower end and loaded at c, would be unstable if it were not connected with b.
- These blocks were fed with sand and water to give the bite on the stone (P. Ab.
- Ab Qabus Mabmud b.
- His successor, Ab TamZm Maadd, who reigned with the title al-Mostan~ir, was also an infant at the time of his accession, being little more than seven years of age.
- Bernard himself initiated this policy by building a castle at Talgarth on the Upper Wye, but in 1091 he moved southwards, defeated the regulus of Brycheiniog, Bleddyn ab Maenarch, and his brother-in-law Rhys ap Tewdwr, the prince of south-west Wales, and with materials obtained from the Roman fort of Caer Bannau, built a castle at Brecon, which he made his caput baroniae.
- OWEN GLENDOWER (c. 1 3591415), the last to claim the title of an independent prince of Wales, more correctly described as Owain ab Gruffydd, lord of Glyndyvrdwy in Merioneth, was a man of good family, with two great houses, Sycharth and Glyndyvrdwy in the north, besides smaller estates in south Wales.
- 1, where P is a point on the curve equidistant from the fixed line AB, known as the directrix, and the fixed point F known as the focus.
- Then if a pencil be placed along B C so as to keep the string taut, and the limb AB be slid along the directrix, the A pencil will trace out the parabola.
- Some words he quoted from St Augustine influenced Newman profoundly: " Quapropter securus judicat orbis terrarum bonos non esse qui se dividunt ab orbe terrarum."
- His orations and letters were published in 1492; but his title to any measure of fame he possesses rests upon his history of Venice, De origine urbis Venetiarum rebusque ab ipsa gestis historia (1492), which was translated into Italian by Domenichi in 1545, and which at the time of its appearance was undoubtedly the best work upon the subject of which it treated.
- The axis of rotation AB bears a rigidly attached rod DBC inclined to it at an angle equal to the sun's polar distance.
- AB is the axis of rotation, BC an adjustable FIG.
- Dafydd ab Gwilym >>
- A large fire-grate (ab), having a cave (c) to facilitate stoking and stepped back at (d), is bounded on one side by a fire-bridge (e); on the other side of this, separated by an air-channel (g), there is first the proper fluxing bed (h), and behind this the "back-bed "(i) for pre-heating the charge.
- ab Aragonia (Naples, 1588); several chapters in the Storia politica d'Italia (Milan, 1875-1882); F.
- Thus the figure represents a section the (ideally simplified) uni verse cut perpendicular to C P' D the planes AB and CD between which the stars are contained, 1 This number is the 3/2th power of the ratio of the brightness of stars differing by a unit magnitude.
- Imagine this stratum to be uniformly filled with stars (of course in the actual universe instead of sharply defined boundaries AB and CD, we shall have a gradual thinning out of the stars) it follows that in the two directions SP and SP' the fewest stars will be seen; these then are the directions of the galactic poles.
- An army sent to the rescue by Ibn Zobair under the command of his brother Mus`ab was beaten in Palestine by `Amr Ashdaq.
- Mokhtar was now at the zenith of power, but Ibn Zobair, determined to get rid at all costs of so dangerous an enemy, named his brother Mus`ab governor of Basra and ordered him to march against Kufa.
- Mohallab then marched with Mus`ab against Kufa.
- Ibn Zobair, however, was occupied at Mecca with the rebuilding of the Ka`ba, and Mus`ab was harassed not only by the Kharijites, but also by a noble freebooter, Obaidallah b.
- When, in the year (69 A.H.) 689 Abdalmalik had at last encamped at Botnan Habib in the vicinity of Kinnesrin (Qinnasrin),1 with the purpose of marching against Mus`ab, his cousin `Amr Ashdaq, to whom by the treaty of Jabia, before the battle of Merj Rahit, the succession to Merwan had been promised, took advantage of his absence to lay claim to the supreme power, and to have himself proclaimed caliph by his partisans.
- Mus`ab was encamped at Bajomaira in the neighbourhood of Takrit.
- Meanwhile, Mus`ab had to curb a violent revolt in Basra, brought about by agents of Abdalmalik, and called after a place in the city the revolt of the Jofrites.
- Mus`ab's best troops were fighting under Mohallab against the Kharijites; many Basrians were secretly favourable to the Omayyads, nor were the Kufian soldiers to be trusted.
- Abdalmalik, therefore, wrote secretly to the chiefs of Mus`ab's army, and persuaded them to desert to him, with the exception of Ibrahim b.
- His death, in the beginning of the battle, decided the fate of Mus`ab, who was slain sword in hand by a Shiite of Kuf a.
- As soon as the expedition to Irak against Mus`ab had terminated, the holy war against the Greeks was renewed.
- The commentary ("Expositiones") on Dionysius' Hierarchiae caelestes appeared in the Appendix ad opera edita ab A.
- That the most important section, the list of forms of combination, was never achieved - this too was after the Baconian example while the mode of symbolization was crude with a= ab and the like - matters little.
- MELCHIOR GOLDAST AB HAIMINSFELD (1576-1635) Swiss writer, an industrious though uncritical collector of documents relating to the medieval history and Constitution of Germany, was born on the 6th of January 1576 (some say 1578), of poor Protestant parents, near Bischofszell, in the Swiss Canton of Thurgau.
- The white silver fir (abies coucola) and the silver or red fir (ab.
- AB, the fifth month of the ecclesiastical and the eleventh of the civil year of the Jews.
- Tradition ascribes the death of Aaron to the first day of Ab.
- It is therefore adequately represented, for mathematical purposes, by a straight line AB drawn in the direction in question, of length proportional (on any convenient scale) to the magnitude of the force.
- Thus if AB.
- the force exerted by a particle A on a particle B, and the force exerted by B on A, are equal and opposite in the line AB.
- Since the four co-ordinates (Cartesian or other) of these two points are connected by the relation which expresses the invariability of the length AB, it is plain that virtually three inde pendent elements are re quired and suffice to specify the position of the lamina.
- For suppose that in consequence of the displacement a point of the lamina is brought from A to B, whilst the point of the lamina which was originally at B is brought to C. Since AB, BC, are two different positions of the same line in the B C lamina they are equal, and it is evident that the rotation could have been effected by a rotation about J,
- As a special case A the three points A, B, C may be in a straight line; J is then at infinity and the displacement is equivalent to FIG 10 a pure translation, since every point of the lamina is now displaced parallel to AB through a space equal to AB.
- If, AB being held fixed, the 3 quadrilateral be slightly de formed, it is obvious that the instantaneous centre J will - be at the intersection of the - .~ straight lines AD, BC, since s the displacements of the points D, C are necessarily at right angles to AD, BC, respectively.
- Hence the locus of J relative to AB, and the locus relative to CD are equal ellipses of which A, B and C, D are respectively the foci.
- These formulae give a means of constructing the resultant by means of any transversal AB cutting the lines of action.
- When P, Q have opposite signs the point C divides AB externally on the side of the greater force.
- Let AB, AC (fig.
- of the vectors AB and AC (or BD), and of their sum AD, on a line perpendicular to AO, this is obvious.
- Again, suppose we have a bar AB resting with its ends on twc smooth inclined planes which face each other.
- If F, Q, R, be any three forces acting along BC, CA, AB, respectively, the line of action of the resultant is determined by the consideration that the sum of the moments about any point on it must vanish.
- Thus in the figure the sum of the moments about 0 is P. OAP. OB or P. AB, which is independent of the position of o 0.
- The force corresponding to AB may be replaced by the two components marked x, y; and a force corresponding to BA may be represented by the two components marked x, y.
- Thus ii AB, BC, CD represent the given loads, in the force-diagram, we construct the sides corresponding to OA, OB, OC, OD in the funicular; we then draw the closing line of the funicular polygon, and a parallel OE to it in the force diagram.
- A graphical method can also be applied to find the moment of a force, or of a system of forces, about any assigned point P. Let F be a force represented by AB in the force-diagram.
- To find the pressure exerted by a bar AB on the pin A we compound with the force in AB given by the diagram a force equal to P. Conversely, to find the pressure of the pin A on the bar AB we must compound with the force given by the diagram a force equal and opposite to P. This question arises in practice in the theory of three-jointed structures; for the purpose in hand such a structure is sufficiently represented by two bars AB, BC. The right-hand figure represents a portion of the force-diagram; in particular ZX represents the pressure of AB on B
- Compounding with this XV, which represents Q1, we get the actual pressure ZV exerted by AB on B.
- ~ Three-dimensional Kinematics of a Rigid Body.The position of a rigid body is determined when we know the positions of three points A, B, C of it which are not colljnear, for the position of any other point P is then determined by the three distances PA, PB, PC. The nine co-ordinates (Cartesian or other) of A, B, C are subject to the three relations which express the invariability of the distances BC, CA, AB, and are therefote equivalent to six independent quantities.
- (usually a~ small circle of the fixed sphere), and join JA, JB, JC, AB, BC
- The spherical A isosceles triangles AJB, BJC are con gruent, and we see that AB can be brought into the position BC by a rotation about the axis OJ through an FIG.
- This is the axis of the required screw; the amount of the translation is measured by the projection of AB or BC or CD on the axis; and the angle of rotation is given, by the inclination of the aforesaid bisectors.
- An infinitely small rotation about any axis is conveniently represented geometrically by a length AB measures along the axis and proportional to the angle of rotation, with the convention that the direction from A to B shall be related to the rotation as is the direction of translation to that of rotation in a righthanded screw.
- If AB, AC represent infinitesimal rotations about intersecting axes, the consequent displacement of any point 0 in the plane BAC will be at right angles to this plane, and will be represented by twice the sum of the areas OAB, OAC, taken with proper signs.
- mon perpendicular AB in a point - - - ., -
- Let AB be the shortest distance between the lines of action, and let AA, BB
- Divide AB
- the line of intersection (B); the arms (AB,BC) will then be proportional to the respective moments.
- This product is the same whatever point on the line of action be taken, since the lengthwise components of the dispJacements of any two points A, B on a line AB are equal, to the first order of small quantities.
- To see this, let A, B be the displaced positions of A, B, and let i~ be the infinitely small angle between AB and AB.
- a, /3 be the orthogonal projections of A, B on AB, we have AaB~=ABaf3=AB(I cos~,) =4AB.~2,
- projections of AB, AC on All is equal to the projection of AD.
- It is to be noticed that All need not be in the same plane with AB, AC.
- P. JB.~=P. AB.
- 45; if AB, AB represent the two positions of a string, and T be the tension, the virtual work of the two forces ~ T at A,B is T(AnBjS), which was shown to be of the second order.
- Imagine the bar CF to be removed, and consider a deformation in which AB is fixed.
- The simplest case is that of a frame of three bars, when the three joints A, B, C fall into a straght line; a small displacement of the joint B at right angles to AC would involve changes in the lengths of AB, BC which are only of the second order of small quantities.
- 52, if an infinitesimal deformation is possible without removing the bar CF, the instantaneous centre of CF (when AB is fixed) will be at the intersection of AF and BC, and since CC, FF represent the virtual velocities of the points C, F, turned each through a right angle, CF must be parallel to CF.
- ~ the inclination to the horizontal at A or B, we have 2T~=W, AB =2p~t, approximately, where p is the radius of curvature.
- If E be the point in which the line of the string meets AB, we have pjCP, pz=EP. Many contrivances for actually drawing the resulting curves have been devised.
- But since an ellipse can always be constructed with a given centre so as to touch a given line at a given point, and to have a given value of ab(=h/-~ u) we infer that the orbit will be elliptic whatever the initial circumstances.
- (4) Since 2ATT1=B (AB)q1+C(AC)r, it appears that if A> B> C the coefficient of x2 in (4) is positive, that of Ii is negative, whilst that of y2 is positive or negative according as 2BT ~ P. Hence the polhode cone surrounds the axis of greatest or least moment according as 2BT ~ F.
- C~(AB)pq=N.
- C~=(AB)pq.
- The conditions (~) then lead to IA(AC) 2, ,2 (AC)(BC) 1 ~ tO qs B(BC)~ AB r0, C(BC) r~
- 92), when the rolling will be towards the opposite hand; and at a given instant let T be the line of coptact of the two cylindrical surfaces, which is at their commor intersection with the plane AB traversing the two axes of figure.
- The line T on the surface bbb has for the instant no velocity it a direction perpendicular to AB; becau2e for the instant it touches, without sliding, the line T on the fixed surface aaa.
- The line T on the surface bbb has also for the instant no velocity in the plane AB; for it has just ceased to move towards the fixed surface aaa, and is just about to begin to move away from that surface.
- and the path of such a point is a circle described about A with the radius AB, being for outside rolling the sum, and for inside rolling the difference, of the radii of the cylinders.
- Let a denote the angular velocity with which the plane of axes AB rotates about the fixed axis A.
- 92, AB is to be treated as negative, which will give a negative value to a, indicating that in this case the rotation of AB round A is contrary to that of the cylinder bbb.
- The angular velocity of the rolling cylinder, relatively to the plane of axes AB, is obviously given by the equation whence~=y.TA/AB 5 (7)
- Set off ab = ac = 1/2p. Draw radii bd, Ce; draw fb, cg, making angles of e 753/4 with those radii.
- The links AB and CD are equal in length and are centred respectively at A and C. The ends D and B are joined by a link DB.
- curve to a scale enlarged in the ratio ab: ac. This property of the parallelogram is utilized in the construction of the pantograph, an instrument used for obtaining a copy of a map or drawing on a different scale.
- the ratio of the distances ab and ac is constant, and the angle baa E a is constant for all positions of the FIG H
- mechanism; so that, if b is guided in any curve, the point a will describe a similar curve turned through an angle baa, the scales of the curves being in the ratio ab to cc. Sylvester called an instrument based on this property aplagiograph or a skew pantograph.
- But tile point B must also move at right angles to AB in the case under consideration.
- Hence draw a line through O in the velocity diagram at right angles to AB to cut cbi in b.
- angles to Ct; then the vector sum of these three magnitudes is Ab, and this vectol represents the acceleration of the point B.
- In the Hebrew Bible Lamentations is placed among the Cetubim or Hagiographa, usually as the middle book of the five Megilloth or Ferial Rolls (Canticles, Ruth, Lamentations, Ecclesiastes, Esther) according to the order of the days on which they are read in the Synagogue, Lamentations being read on the 9th of Ab (6th of August), when the destruction of the Temple is commemorated (Mass.
- and What Firdousi and the court-poets of Sultan Matimd Satirists, had commenced, what Ab l-Faraj Runi of Lahore and Masd b.
- Ab U IC
- The year of Ab Saids death is most likely that of the first great didactic mathnawi, the Rshan.
- For the first five centuries of the Hegira compare Eths editions and metrical translations of Rudagis Vorlhufer und Zeitgenossen, in Morgenlandische Forschungen (Leipzig, 1875); of Kisis songs, Firdousis lyrics, and Ab Said b.
- Ab l-Khairs rubis, in Sitzungsberichte der bayr.
- Modern scholars regard her as a goddess akin to Ops, Acca Larentia and Dea Dia; or as the goddess of the new year and the returning sun (according to Mommsen, ab angerendo = are) roi, ava Apeo Oat rae it Xtov).
- There exists a mid14th-century Historia do Santo Graal, and an unprinted Josep' ab Aramadia, while, though the MS. is lost, we have abundant evidence of the existence of a primitive Portuguese prose redaction of Amadis de Gaula anterior to the present Spanish text.
- If, in the rectangle Aacc, Aa= a, and AC = b, its area is S = ab, and its energy Tab.
- Hence if F is the force by which the slip BB is pulled towards AA, F =d b T ab =Ta,..
- For if in the triangle abc the side ab is taken so as to represent on a given scale the tension of the surface of contact of the fluids a and b, and if the other sides be and ca are taken so as to represent on the same scale the tensions of the surfaces between b and c and between c and a respectively, then the condition of equilibrium at 0 for the corresponding tensions R, P and Q is that the angle ROP shall be the supplement of abc, POQ of bca, and, therefore, QOR of cab.
- If four fluids, a, b, c, d, meet in a point 0, and if a tetrahedron AB CD is formed so that its edge AB represents the tension of the surface of contact of the liquids a and b, BC that of b and c, and so on; then if we place this tetrahedron so that the face ABC is normal to the tangent at 0 to the line of concourse of the fluids abc, and turn it so that the edge AB is normal to the tangent plane at 0 to the surface of contact of the fluids a and b, then the other three faces of the tetrahedron will be normal to the tangents at 0 to the other three lines of concourse of the liquids, an the other five edges of the tetrahedron will be normal to the tangent planes at 0 to the other five surfaces of contact.
- 9 represent a section through the axis Cc of a soap-bubble in the form of a Non- figure of revolution bounded by two herical circular disks AB and ab, and having sp soap- the meridian section APa.
- But once the idea of supernatural grace going along with office as such (of which we have already a trace in the Ignatian bishop, though without the notion of actual apostolic succession) arose in connexion with successio ab apostolis, the full development of the doctrine was but a matter of time.4 Literature.
- Thus Herbert sought to do for the religion of nature what his friend Grotius was doing for natural law, - making a new application of the standard of Vincent of Lerins, Quod semper, quod ubique, quod ab omnibus.
- Its proper title was Ab urbe condita libri (also called historiae and annales).
- Ab, abdominal somites.
- Ab, abdomen.
- Over a mile south of Mold, on the right of the road to Nerquis, is the "Tower" (15th century, but perhaps restored in the 18th), where, in 1465 or 1 475, the royal chieftain, Rheinallt ab Gruffyd ad Bleddyn, hanged Robert Byrne, mayor of Chester, and subsequently burned alive some 200 Chester folk who tried to 'arrest him.
- It is generated as follows: Let ABC be a circle having AB for a diameter.
- Draw any line DE perpendicular to AB and meeting the circle in E, and take a point P on DE such that the line DP =arc BE; then the locus of P is the companion to the cycloid.
- Not, indeed, a preliminary criticism of our faculties or conceptions such as Kant himself proposed to institute, in order to determine the limits of their application; such a criticism ab extra of the nature of our experience is essentially a thing impossible.
- (For, although the term "ontology" has been as good as disused, it still remains true that the aim of philosophy must be to furnish us with an ontology or a coherent and adequate theory of the nature of reality.) But if, on the other hand, knowledge and reality be ab initio opposed to one another - if consciousness be set on one side as over against reality, and merely holding up a mirror to it - then it follows with equal naturalness that the truly real must be something which lurks unrevealed behind the subject's representation of it.
- Among his other works are his Annotationes in Biblia (1607), of which an English translation (Pious and Learned Annotations upon the Holy Bible) was published in London in 1648, and various polemical treatises, such as De fictitio Pontificiorum Purgatorio (1619); De justa secessione Reformatorum ab Ecclesia Romana (1628); De Antichristo, &c. He also published French translations of Sarpi's History of the Council of Trent, and of Edwin Sandys's Account of the State of Religion in the West.
- Juniperus the products of division of the C 16 - Ab normal Cone of Pinus rigida.
- 66), at the monastery of Palazzolo; but the position is quite unsuitable for an ancient city, and does not at all answer to Livy's description, ab situ porrectae in dorso urbis Alba longa appellata; and it is much more probable that its site is to be sought on the western side of the lake, where the modern Castel Gandolfo stands, immediately to the north of which the most important part of the archaic necropolis was situated.
- c Ab ?
- There is considerable distortion of the clay, resulting from combined shearing and tensile stress, above each of the steps of rock, and reaching its maximum at and above the highest rise ab, where it has proved sufficient to produce a dangerous line of weakness ac, the tension at a either causing actual rupture, or such increased porosity as to permit of percolation capable of keeping open the wound.
- It is clear that the greatest crushing pressure must occur, either, with the reservoir empty, near the lower part of the water face ab.
- We have hitherto considered only the horizontal overturning pressure of the water; but if from originally defective construction, or from the absence of vertical pressure due to weight of masonry towards the water edge of any horizontal bed, as at ab in fig.
- 14, water intrudes beneath that part of the masonry more readily than it can obtain egress along bc, or in any other direction towards the outer face, we shall have the uplifting and overturning pressure due to the full depth of water in the reservoir over the width ab added to the horizontal pressure, in which case all our previous calculations would be futile.
- Line ab is in such a position that the stresses.
- The vertical distance above the line ab of any point in the dotted line dc is proportional to the vertical component of the compressive stress on the line ale assumed to vary uniformly from face to face, and similarly the vertical distance of any point in the3-dot-and-dash line ae above the line ab is proportional to the vertical component of the stress determined experimentally.
- In order to increase the sensitiveness of a balance, the line AB joining the points of suspension and the centre of gravity of the balance must be brought nearer to each other.
- Io AB is the steelyard.
- The Section on AB.
- 2), with side AB =a c/2 and AD =c, is constructed, and the quadrant AEF is drawn with centre D and radius DA.
- conciliorum, quae ab episcopis rituum orientalium ab a.
- Deinde ab amicis curam ejus susceptam, domoque clauso remedia volenti nolenti adhibita, quibus jam sanitatem recuperavit ut jam rursus librum suum Principiorum Philosophiae Mathematicorum intelligere incipiat."
- It is constructed by the following method: Let AQB be a semicircle of diameter AB, produce MQ the ordinate of Q to P so that MQ: MP :: AM: AB.
- The cartesian equation, if A be taken as origin and AB (= 2a) for the axis of x, is xy 2 =4a2(2a - x).
- If a line S2 cut an arc aa at b, so that the two segments ab, ba lie on opposite sides of the line, then projecting the figure so that the line Sl goes off to infinity, the tangent at b is projected into the asymptote, and the arc ab is projected into a hyperbolic leg touching the asymptote at one extremity; the arc ba will at the same time be projected into a hyperbolic leg touching the same asymptote at the other extremity (and on the opposite side), but so that the two hyperbolic legs may or may not belong to one and the same branch.
- Next, if the line S2 touch at b the arc aa so that the two portions ab, ba lie on the same side of the line Sl, then projecting the figure as before, the tangent at b, that is, the line S2 itself, is projected to infinity; the arc ab is projected into a parabolic leg, and at the same time the arc ba is projected into a parabolic leg, having at infinity the same direction as the other leg, but so that the two legs may or may not belong to the same branch.
- (ab or the horse and the dog may be cited as instances where the single caecum is of large size, this being especially the case of the former, where it is of enormous dimensions; in human beings, on the other hand, the caecum is rudimentary, and best known in connexion with " appendicitis."
- To this new period belong Einleitung zur historic der vornehmsten Reiche and Staaten, also the Commentarium de rebus suecicis, libri XXVI., ab expeditione Gustavi Adolphi regis in Germaniam ad abdicationem usque Christinae and De rebus a Carolo Gustavo gestis.
- Bellarmine (De jejunio) distinguishes jejunium spirituale (abstinentia a vitiis), jejunium morale (parsimonia et temperantia cibi et potus), jejunium naturale (abstinentia ab omni prorsus cibo et potu, quacunque ratione sumpto), and jejunium ecclesiasticum.
- ab Eckhart, Commentarii de rebus Franciae orientalis et episcopatus Wirceburgensis (Wiirzburg, 1729); F.
- AB, Anteroposterior axis.
- Thus, for three columns, it appears by either rule that 123, 231, 312 are positive; 213, 321, 132 are negative; and the developed expression of the foregoing determinant of the third order is =ab'c" - ab "c'+a'b "c - a'bc" - a"bc' - a"b'c. 3.
- But his enemies increased in power, and about 1194 he was driven from Wales by the partisans of his half-brother Llewelyn ab Iorwerth.
- 4 represent a section of the earth through its axis AB, ECQ being a diameter of the equator.
- In this plane are a pair of cross threads or spider lines which, as the observer looks into the telescope, are seen as AB and CD (fig.
- Take a rod LMN bent at right angles at M, such that MN= AB; let the leg LM always pass through a fixed point 0 on AB produced such that OA = CA, where C is the middle point of AB, and cause N to travel along the line perpendicular to AB at C; then the midpoint of MN traces the cissoid.
- The cartesian equation, when A is the origin and AB = 2a, is y 2 (2a - x) =x 8; the polar equation is r= 2a sin 0 tan 0.
- of Aberdare, was according to tradition the scene of a battle at which Rhys ap Jewdwr, prince of Dyfed, was defeated by the allied forces of the Norman Robert Fitzhamon and Iestyn ab Gwrgan, the last prince of Glamorgan.
- The form is " A B C D, &c., are P; AB CD are all M; thus all M are P."
- 84) " Dixerat haec, adytis quum lubricus anguis ab imis Septem ingens gyros, septena volumina, traxit," and Aeneas is " Incertus, geniumne loci, famulumne parentis Esse putet."
- But that the origins of such mythical beings were, ab initio, either solar or vegetable, or, for that matter, animal, it would often be hard to prove.
- He also wrote or edited various Chinese works on geography, the celestial and terrestrial spheres, geometry and arithmetic. And the detailed history of the mission was drawn out by him, which after his death was brought home by P. Nicolas Trigault, and published at Augsburg, and later in a complete form at Lyons under the name De Expeditione Christiana apud Sinas Suscepta, ab Soc. Jesu, Ex P. Mat.
- In analytical geometry, r the equation axe+2hxy+bye+2gx+2fy+ c = o represents an ellipse when ab > h 2; if the centre of the curve be the origin, the equation is a 1 x 2 +2h 1 xy+b i y 2 =C 1, and if in addition a pair of conjugate diameters are the axes, the equation is further simplified to Ax e +By 2 = C. The simplest form is x 2 /a 2 +y 2 /b 2 = 1, in which the centre is the origin and the major and minor axes the axes of co-ordinates.
- Kal`ab: i-nau and Rindan are among the more northerly inhabited villages.
- of any couple, AB, for any given limits of temperature is the algebraic sum of the E.M.F.s between the same limits of temperature of the couples BC and CA formed with any other metal C. It is for this reason unnecessary to tabulate the E.M.F.s of all possible combinations of metals, since the E.M.F.
- The experimental wire AB is connected in parallel with about 2 metres of thicker wire (No.
- A lowresistance galvanometer is connected by a very fine wire (2 to 3 mils) to the centre C of the experimental wire AB, and also to the middle point D of the parallel wire so as to form a Wheatstone bridge.
- The balance is adjusted by shunting either AD or BD with a box, S, containing 20 to Ioo ohms. All the wires in the quadrilateral must be of the same metal as AB, to avoid accidental thermoelectric effects which would obscure the result.
- If the current flows from A to B there will be heat absorbed in AC and evolved in CB by the Thomson effect, if the specific heat of electricity in AB is positive as in copper.
- Nonell y Mas, Andlisis de la llnga catalana antiga comparada ab la moderna (Manresa, 1895);
- This is shown by the curve AB, and is the useless work represented by the expression (q 2 -q 1)/r.
- Sin-akhi-erba, " the Moon-god: has increased the brethren"), the son and successor of Sargon, mounted the throne on the 12th of Ab 705 B.C. His first campaign was against Babylonia, where Merodach-baladan had reappeared.
- AB - A case is reported of endometrial adenocarcinoma of the uterus in an 85-year-old patient with an unusual spreading pattern.
- AB - An acromegalic patient with a pituitary somatotroph adenoma associated with an extremely elevated plasma GHRH concentration is presented.
- AB - Pregnancy in conjunction with primary aldosteronism is an unusual occurrence.
- AB - colorectal cancer continues to be a major problem.
- AB - Sezary syndrome is a rare form of primary cutaneous T cell lymphoma.
- The GAMESS-UK Benchmark is designed to represent the typical range of calculations commonly performed by the ab initio quantum chemist.
- Most ab initio groups quickly become very close-knit since students see each other almost every day.
- AB - Many patients with multiple myeloma tend to have low serum cobalamin.
- Unsure about my new contraceptive coil Will ab toner affect the coil?
- They describe an English speaking ab initio student of German who exhibited an unusually strong tendency to use word coinage and lexical innovation.
- Doing abdominal crunches on the AB Revolutionizer is a perfect abdominal workout.
- AB - We report a case of symptomatic Rathke's cleft cyst with ossification.
- AB - The process of terminal differentiation is associated with exit from the cell cycle and loss of the proliferative potential of cells.
- AB - The prognosis of patients with HCC remains dismal.
- AB - A 77-year-old woman with hypertension was admitted to our hospital because of exertional dyspnea end peripheral edema.
- AB - OBJECTIVE: To evaluate the efficacy of adjuvant therapy for ovarian germ cell tumors.
- AB - Vancomycin-resistant Enterococcus faecium endocarditis is rare and usually occurs in immunocompromised patients.
- AB - This paper discusses several recent advances in surgical methods for treatment of cancer of the hypopharynx and cervical esophagus.
- The calories expended during ab exercises are very low.
- AB - peroxisome proliferator-activated receptor gamma (PPAR-gamma) decreases the growth of certain cancer cells.
- AB - OBJECTIVES: Helicobacter pylori infection induces gastritis, which may evolve to carcinoma or lymphoma.
- AB - BACKGROUND: Topotecan activity was evaluated for the treatment of malignant glioma.
- AB - The role of postoperative radiotherapy in patients with low grade gliomas is not established yet.
- AB - spontaneous mediastinal hematoma is rarely seen in hematologic malignancy.
- AB - A 76-year-old man was seen at this hospital for the treatment of asymptomatic gross hematuria.
- AB - The role of human herpesvirus 8 (HHV-8) in multiple myeloma (MM) remains controversial.
- homology modeling are more likely to be reliable than are results derived purely from theory (ab initio modeling ).
- AB - OBJECTIVE: To assess the place of laparoscopically assisted vaginal hysterectomy in the treatment of endometrial cancer.
- AB Mauri is ABF's international yeast and bakery ingredients division.
- AB - Recently, minimally invasive therapy has been a key word in the medical field.
- AB - Radical pelvic irradiation has constituted the definitive therapy for patients with large cervical cancers.
- AB: You need to define the statement ' extreme jeopardy ' used here.
- AB - Human glandular kallikrein (hK2) and prostate-specific antigen (PSA) are related members of the human kallikrein gene family.
- AB - The incidence of horseshoe kidney (HK) is estimated at 1 in 400 cases.
- AB - BACKGROUND: Squamous cell carcinoma of the glottic larynx is strongly related to cigarette smoking and excessive ethanol intake.
- AB - Coagulation disorders are often the reason for fatal bleeding in acute promyelocytic leukemia.
- AB - The presentation of anaplastic large cell lymphoma in bone is uncommon.
- AB - Bowel perforation in patients with primary malignant lymphoma usually occurs at the site of tumor.
- vmag The V magnitude in the AB system measured in a 3 arcsecond diameter aperture.
- AB - It is demonstrated that screening mammography programs reduce breast cancer mortality considerably.
- AB - The therapy of metastatic melanoma has not given satisfactory results.
- AB - A patient with multiple myeloma was treated with several cycles of chemotherapy and developed monoclonal IgA rheumatoid factor.
- AB - Warthin's tumors provide a unique opportunity to distinguish and compare monoclonal antibodies (mAbs) to the epithelial mucin, MUC1.
- AB - A 41-year-old male with IgG kappa multiple myeloma is described.
- AB - Early diagnosis of bladder neoplasia at the moment makes use of urinary cytology and cystoscopy.
- AB - The risk of lower genital tract neoplasia is increased in women infected with HIV.
- AB - Incomplete response to therapy may compromise the outcome of children with advanced neuroblastoma.
- AB - OBJECTIVE: Two cases of cystic neuroblastoma diagnosed by ultrasonography and CT are presented.
- AB - OBJECTIVE: Radiation optic neuropathy usually occurs months to years after exposure of the anterior visual pathways to ionizing radiation.
- Passed by voice not obligated to must be willing ab to require.
- AB - BACKGROUND: An adenoma-carcinoma sequence also applies to adenomas of the major duodenal papilla.
- AB - OBJECTIVE: Respiratory papillomas (RP) tend to recur and the difficulty in eradicating the disease makes their treatment frustrating.
- AB - Recently, several advances have been made in understanding the pathogenesis of multiple myeloma.
- AB - PURPOSE: To identify the mutation in the RB1 gene in a Syrian family showing incomplete penetrance of retinoblastoma (RB ).
- AB - BACKGROUND: tissue polypeptide specific antigen (TPS) recently was introduced as an indicator of cell proliferation in various tumors.
- AB - PURPOSE: Children with recurrent or progressive central nervous system (CNS) tumors have an unfavorable prognosis.
- AB - INTRODUCTION: Since the tumor stage has significant prognostic and therapeutic implications, accurate preoperative staging is decisive.
- AB - We report the case of a young man who presented with a clinical picture of acute pyelonephritis.
- Quod semper, quod semper, quod ubique, quod ab omnibus!
- Quod semper, quod ubique, quod semper, quod ubique, quod ab omnibus!
- AB - BACKGROUND: High rates of locoregional recurrence have been reported from surgical series of locally advanced melanoma.
- AB - PURPOSE: To evaluate the efficacy and toxicity of subconjunctival carboplatin for intraocular retinoblastoma.
- AB - Although retinoids are known to regulate gene transcription by activating retinoid receptors, the targets of retinoid receptors are largely unknown.
- Still problems with pt retrieval Some success with constituent retrievals using AB microwindows (not all MWs processed ).
- AB - A patient with essential thrombocythemia was diagnosed with pulmonary sarcoidosis after interferon alpha therapy.
- AB - BACKGROUND: Gastrointestinal stromal sarcomas are a rare group of malignancies originating in the bowel wall.
- AB - OBJECTIVE: To review cases of testicular seminoma in Down's syndrome (DS) patients.
- Patients were further subdivided into those with or without elevated quantitative serum Chlamydia trachomatis IgG antibody (Ab) titres.
- AB - More than half of the patients with testicular germ-cell cancer show impaired spermatogenesis before undergoing cytotoxic treatment.
- AB - The aim of this study was to evaluate the accuracy of dynamic CT in the preoperative staging of gastric cancer.
- AB - The prognostic importance of accurate pathological staging of oral cancer patients with established lymph node metastases is well known.
- AB - PURPOSE: Preliminary experience of radical retropubic prostatectomy using an endoscopic stapler is reported.
- Instant abs 6 second workout and lateral thigh stepper exercises, fitness & ab lounge 2.. .
- AB - Long-term outcome after laparoscopic surgery for colorectal cancer is still unknown.
- AB - An original technique for performing endoscopic thyroidectomy using a breast approach to avoid an operative scar in the neck was developed.
- AB - conventional thyroidectomy often leaves an undesirable scar on the anterior neck.
- AB - We report ten cases of carcinoid tumor of the appendix observed in children from 1988 to 1996.
- AB - We report a case of giant testicular tumor.