noun
definition
The name of the Latin-script letter E.
definition
The base of the natural logarithm, 2.718281828459045…
Examples of E in a Sentence
During a small electric transfer through the cell, the external work done is Ee, where E is the electromotive force.
Q 1 The Unreduced Generating Function Which Enumerates The Covariants Of Degrees 0, 0' In The Coefficients And Order E In The Variables.
It is shown in the article on Combinatorial Analysis that (w; 0,n) is the coefficient of a e z w in the ascending expansion of the fraction 1-a.
A full account of his literary activity and ecclesiastical troubles will be found in Abbe Albert Houtin's La Question biblique au XIX e siècle (Paris, 2nd ed., 1902) and La Question biblique au XX e siècle (Paris, 1906), but the latter especially is largely unfair to the conservatives and sadly lacking in religious feeling.
The In- stituto Historico e Geographico Brazileiro, though devoted chiefly to historical research, has rendered noteworthy service in its encouragement of geographical exploration and by its publication of various scientific memoirs.
In 1586 Witherington plundered Bahia; E and i n 1591 Cavendish made an abortive attack on Santos; French in 1595 Lancaster attacked Olinda.
Pietro e Cesareo, fronting upon it, is ensconced in.a temple of Rome and Augustus, part of the side wall of which, with engaged columns, is still visible.
Mariano e Jacopo, a structure of the 12th century, with a façade, adorned with contemporary sculptures, partly restored in 1514-1550.
The government was now reconstituted under the protection of the French agents; the balia was abolished, its very name having been rendered odious by the tyranny of Spain, and was replaced by a similar magistracy styled capitani del popolo e reggimento.
In 1837 he founded the Panorama in imitation of the English Penny Magazine, and there and in Illustracdo he published the historical tales which were afterwards collected into Lendas e Narratives; in the same year he became royal librarian at the Ajuda Palace, which enabled him to continue his studies of the past.
John the Scot was still E acquainted with Greek, seeing that he translated the work of the pseudo-Dionysius; and his speculative genius achieved the fusion of Christian doctrine and Neoplatonic thought in a system of quite remarkable metaphysical completeness.
Thus, to solve the equation ax e +bx+c = o, we consider, not merely the value of x for which ax 2 +bx+c is o, but the value of ax e +bx+c for every possible value of x.
The sum and product of two quaternions are defined by the formulae mi ase + F+lases = (a s + 133) es 2arer X ZO,es = Fiarfseres, where the products e,e, are further reduced according to the following multiplication table, in which, for example, the eo e1 e2 e3 second line is to be read eieo = e1, e 1 2 = - eo, e i e 2 = es, eie3 = - e2.
Thus e 1 e 2 = - e2ei, and if q, q are any two quaternions, qq is generally different from q'q.
The symbol e 0 behaves exactly like i in ordinary algebra; Hamilton writes I, i, j, k instead of eo, el, e2, es, and in this notation all the special rules of operation may he summed up by the equalities = - I.
To multiply A 1 by a scalar, we apply the rule A = A1E = E (Eat) ea, and similarly for division by a scalar.
If A 1 = X a i e i, B i = /if i e i, the distributive law of multiplication is preserved by assuming A1B1=E(a0 i 3)eiej; it follows that A 1 B 1 = - B 1 A 1, and that A l 2 = o.
Every unit of the rth species which does not vanish is the product of r different units of the first species; two such units are independent unless they are permutations of the same set of primary units e i, in which case they are equal or opposite according to the usual rule employed in determinants.
If E is any extensive unit, there is one other unit E', and only one, such that the (progressive) product EE' =- r.
This unit is called the supplement of E, and denoted by IE.
If, in the extensive calculus of the nth category, all the units (including i and the derived units E) are taken to be homologous instead of being distributed into species, we may regard it as a (2'-I)-tuple linear algebra, which, however, is not wholly associative.
For instance, there are the symbols A, D, E used in the calculus of finite differences; Aronhold's symbolical method in the calculus of invariants; and the like.
Thus we find Paciolus calling it l'Arte Magiore; ditta dal vulgo la Regula de la Cosa over Alghebra e Almucabala.
In this they were completely successful, for they obtained general solutions for the equations ax by = c, xy = ax+by+c (since rediscovered by Leonhard Euler) and cy 2 = ax e + b.
A particular case of the last equation, namely, y 2 = ax e + 1, sorely taxed the resources of modern algebraists.
His travels and mercantile experience had led E t u eopre him to conclude that the Hindu methods of computing were in advance of those then in general use, and in 1202 he published his Liber Abaci, which treats of both algebra and arithmetic. In this work, which is of great historical interest, since it was published about two centuries before the art of printing was discovered, he adopts the Arabic notation for numbers, and solves many problems, both arithmetical and algebraical.
At the focal point (E =o, n = o) all the secondary waves agree in phase, and the intensity is easily expressed, whatever be the form of the aperture.
If the image of the line be =o, the intensity at any point E, n of the diffraction pattern may be represented by ?2a2t2 S A2f2 the same law as obtains for a luminous point when horizontal directions are alone considered.
E is then the co-ordinate relatively to 0 of any focal point 0' for which the retardation is R; and the required result is obtained by simply integrating (5) with respect to from - cc to +oo.
The linear width of the band (e) is the increment of which alters p by 27r, so that e =27r /tr.
The integration of the several terms may then be effected by the formula e y dy =r(4+2)=(4 - i)(4-2)...
Since the dimensions of T are supposed to be very small in com d parison with X, the factor dy (--) is sensibly constant; so that, if Z stand for the mean value of Z over the volume T, we may write TZ y d e T ?
Its connexion with a is expressed by a =c4'/dr; so that TZ sin 05 e'(at - kr) 47b 2 where the factor e int is restored.
His comedies give a truthful and interesting picture of 18th century society, especially his best comedy, the Alec rim e Mangerona, in which he treats of the fidalgo pobre, a type fixed by Gil Vicente and Francisco Manoel de Mello.
His plays were published in the first two volumes of a collection entitled Theatro comico portuguez, which went through at least five editions in the 18th century, while the Alecrim e Mangerona appeared separately in some seven editions.
The Hexaplar text of the LXX., as reduced by Origen into greater conformity with the Hebrew by the aid of subsequent Greek versions, was further the mother (d) of the Psalterium gallicanum - that is, of Jerome's second revision of the Psalter (385) by the aid of the Hexaplar text; this edition became current in Gaul and ultimately was taken into the Vulgate; (e) of the SyroHexaplar version (published by Bugati, 1820, and in facsimile from the famous Ambrosian MS. by Ceriani, Milan, 1874).
Slippers (irepauKai) were adopted from the East by women; shoes (E e13a&ES) were worn by the poorer classes.
His name survives in the town of Mopsuestia (M6 tov `E rria) and the spring of Mopsucrene.
His Schiavitic e servaggio (Milan, 1868-1869) gave an account of the development and abolition of slavery and serfdom.
Having been appointed assistant lecturer and afterwards full lecturer at the Ecole des Hautes Etudes, it was to the town of St Omer that he devoted his first lectures and his first important work, Histoire de la vile de Saint-Omer et de ses institutions jusqu'au XI V e siecle (1877).
The substantive occurs in an inscription of the Arvalian brotherhood (Marini, Gli Atti e Monumenti de' fratelli Arvali, p. 639),but is frequent only in ecclesiastical Latin.
E is a valve in the inlet pipe opening into the cylinder; and A the piston is perforated by one or more holes, each fitted with valves opening outwards on its upper surface.
On raising the piston, the valve F remains closed and a vacuum tends to be created in the cylinder, but the pressure of the atmosphere forces the liquid up the tube D and it raises the valve E and passes into the cylinder.
On reversing the motion the valve E closes and the liquid is forced through the valve F to the upper part of the cylinder.
On raising the piston the liquid rises in the cylinder, the valve E opening and F remaining shut.
On again F J J raising the piston the valve E opens ?g G admitting more liquid whilst F re- mains closed.
The cartesian equation referred to the axis and directrix is y=c cosh (x/c) or y = Zc(e x / c +e x / c); other forms are s = c sinh (x/c) and y 2 =c 2 -1-s 2, being the arc measured from the vertex; the intrinsic equation is s = c tan The radius of curvature and normal are each equal to c sec t '.
Referring the reader to the article Elasticity for the theoretical and to the Strength Of Materials far the practical aspects of this subject, we give here a table of the "modulus of elasticity," E (column 2), for millimetre and kilogramme.
Taking the axis of x for an instant in the normal through a point on the surface H = constant, this makes u = o, = o; and in steady motion the equations reduce to dH/dv=2q-2wn = 2gco sin e, (4) where B is the angle between the stream line and vortex line; and this holds for their projection on any plane to which dv is drawn perpendicular.
When the cylinder r =a is moved with velocity U and r =b with velocity U 1 along Ox, = U b e - a,1 r +0 cos 0 - U ib2 - 2 a, (r +Q 2 ') cos 0, = - U be a2 a2 (b 2 - r) sin 0 - Uib2 b1)a, (r - ¢2 sin 0; b and similarly, with velocity components V and V 1 along Oy a 2 b2 ?= Vb,_a,(r+r) sin g -Vi b, b2 a, (r+ 2) sin 0, (17) = V b, a2 a, (b2 r) cos 0+Vi b, b, a, (r- ¢ 2) cos h; (18) and then for the resultant motion z 2zz w= (U 2 + V2)b2a a2U+Vi +b a b a2 U z Vi -(U12+V12) b2 z a2b2 Ui +VIi b 2 - a 2 U1 +Vii b 2 - a 2 z The resultant impulse of the liquid on the cylinder is given by the component, over r=a (§ 36), X =f p4 cos 0.ad0 =7rpa 2 (U b z 2 + a 2 Uib.2bz a2); (20) and over r =b Xi= fp?