The expression (ab) 4 properly appertains to a quartic; for a quadratic it may also be written (ab) 2 (cd) 2, and would denote the square of the discriminant to a factor pres.
Various artifices are employed to denote the end of the reaction.
But on the assumption that "mathematics" is to denote a science well marked out by its subject matter and its methods from other topics of thought, and that at least it is to include all topics habitually assigned to it, there is now no option but to employ "mathematics" in the general sense' of the "science concerned with the logical deduction of consequences from the general premisses of all reasoning."
Denote the distinct separates involved.
Later, they were used to denote the attendants on certain priests and priestesses, especially the flamen dialis and flaminica and the curiones.
Those words only denote a certain stage of understanding of phenomena.
Compounds were denoted by joining the symbols of the components, and by varying the manner of joining compounds of the same elements were distinguished The symbol V was used to denote a liquid, and a vertical line to denote a gas.
9 illustrates the first case: the ordinates represent specific volumes, and the abscissae denote the composition of isomorphous mixtures of ammonium and potassium dihydrogen phosphates, which mutually take one another up to the extent of 20% to form homogeneous crystals.
The term Anatomy, originally employed in biological science to denote a description of the facts of structure revealed on cutting up an organism, whether with or without the aid of lenses for the purposes of magnification, is restricted in the present article, in accordance with a common modern use, to those facts of internal structure not concerned with the constitution of the individual cell, the structural unit of which the plant is composed.
The name recurs much later, in Adamnan's Life of Columba, in the name of a wood near Londonderry, Daire-Calgaich or Roboretum Calgachi, "the wood of Calgacus": it may be Celtic and denote "the man with the sword."
During the commonwealth and empire aes grave was used to denote the old as in contradistinction to the existing depreciated coin; while aes rude was applied to the original oblong coinage of primitive times.
The word Orchis is used in a special sense to denote a particular genus of the Orchid family (Orchidaceae); very frequently, also, it is employed in a more general way to indicate any member of that large and very interesting group. It will be convenient here to use the word Orchis as applying to that particular genus which gives its name to the order or family, and to employ the term "orchid" in the less precise sense.
CAPRICORNUS (" THE Goat"), in astronomy, the tenth sign of the zodiac, represented by the symbol T-2° intended to denote the crooked horns of this animal.
" Erastianism, as a by-word, is used to denote the doctrine of the supremacy of the state in ecclesiastical causes; but the problem of the relations between church and state is one on which Erastus nowhere enters.
13, see the comm.) to denote the offspring.
The use by the Malays of artificially constructed terms to denote these things may certainly be taken to strengthen the opinion that the Malays arrived in the lands they now inhabit at a comparatively late period in their history, and at a time when they had developed considerably from the original state of primitive man.
Even in the Leiden papyrus the astronomical symbols for the sun and moon are used to denote gold and silver, and in the Meteorologica of Olympiodorus lead is attributed to Saturn, iron to Mars, copper to Venus, tin to Hermes (Mercury) and electrum to Jupiter.
"hard" or "rugged," a name sometimes used, both in earlier and in later writers, to denote the whole of the territory occupied by the Israelites eastward of Jordan, extending from the Arnon to the southern base of Hermon (Deut.
One accent only is to be used, the acute, to denote the syllable on which stress is laid.
So Beauty is by itself described as the Sensuous World, and in this capacity is called the Sacred King or simply the King, whilst Kingdom, the tenth Sephirah, which unites all the nine Sephiroth, is used to denote the Material World, and as such is denominated the Queen or the Matron.
The word denotes in very early French law the portion of lands or money given by fathers and mothers to their sons or daughters on marriage, and usually connotes a renunciation by the latter of any future inheritance; or it may denote the portion given by the eldest son to his brothers and sisters when he was sole inheritor.
Further, if DA 1 DA 2 denote successive operations of DA 1 and DA2, DX1DA2(x1X2X2...) 2 1 + b l(1) + b (12) + b 2(2) +bi (13) + b 1b2(21) + b 3(3) +...
While the last words, "sleeping, just sleeping," said prior to the interruption by Grasso seemed to denote failure, the earlier recorded observations suggest otherwise.
If we denote the critical volume, pressure and temperature by Vk, Pk and Tk, then it may be shown, either by considering the characteristic equation as a perfect cube in v or by using the relations that dp/dv=o, d 2 p/dv 2 =o at the critical point, that Vk = 3b, Pk= a/27b2, T ic = 8a/27b.
A simple plan is as follows - draw an outline of the country of which a map is to be produced upon a board; mark all points the altitude of which is known or can be estimated by pins or wires clipped off so as to denote the heights; mark river-courses and suitable profiles by strips of vellum and finally finish your model with the aid of a good map, in clay or wax.
Thus the rational number one, which we will denote by ' r, is not the cardinal number I; for t r is the relation I/I as defined above, and is thus a relation holding between certain pairs of cardinals.
Thus, if L denote the heat corresponding with the chemical changes associated with unit electric transfer, Le will be the heat corresponding with an electric transfer e, and will also be equal to the change in internal energy of the cell.
Is a separation of (11 1 12213 3 ...) of specification (mM'8m"`28m"`3s...), placing s under the summation sign to denote the is Zs 3s specification involved, 141t412t!p31!...
It is thus possible to study simultaneously all the theories which depend upon operations of the group. Symbolic Representation of Symmetric Functions.-Denote the s 8 s elementar symmetric function a s by al a 2 a3 ...at pleasure; then, Y y si,, si,...
Denote by brackets () and  symmetric functions of the quantities p and a respectively.
CAT,' properly the name of the well-known domesticated feline animal usually termed by naturalists Felis domestics, but in a wider sense employed to denote all the more typical members of the family Felidae.
The strict distinction between nimbus and aureole is not commonly maintained, and the latter term is most frequently used to denote the radiance round the heads of saints, angels or persons of the Godhead.
Already in the Code, when status is not concerned, it is used to denote " any one."
This word, he complains, should denote the heavenly food, the reasonable feast alone, and the Lord never used it of mere junketings.
) j1+j2+j3+..ï¿½ (J1+ j2 +j3+...-1)!/T1)?1(J2)72 (J 3)/3..., j11j2!j3!... ?.1 for the expression of Za n in terms of products of symmetric functions symbolized by separations of (n 1 1n 2 2n 3 3) Let (n) a, (n) x, (n) X denote the sums of the n th powers of quantities whose elementary symmetric functions are a l, a 2, a31ï¿½ï¿½ï¿½; x 1, x2, x31..; X1, X2, X3,...
1890, p. 490) that exp(mldl +m2d2+m3d3+...) = exp (Midi +M2d2+M3d3+...), where now the multiplications on the dexter denote successive operations, provided that pp t exp(MiE+M2 2+M3E3+...) +mlH+m2V+m3S3+..., being an undetermined algebraic quantity.
= a k; and if we wish to denote, by umbrae, a product of coefficients of degree s we employ s sets of umbrae.
Denote This Number By (W; 0, P; 0'.
(0')B Denotes A Seminvariant, If 0, 0', Be Neither Of Them Unity, For, After Operation, The Terms Destroy One Another In Pairs: When 0, Must Be Taken To Denote Ao And So For 0'.
I + is used to denote the charge on positive ions, I_ that on negative ions.
1 3p6xcv-ros, shortest, and Xpovos, time), a term invented by John Bernoulli in 1694 to denote the curve along which a body passes from one fixed point to another in the shortest time.
YOXv13Sos, lead, and was originally employed to denote many substances containing or resembling lead; ultimately the term was applied to graphite and to molybdenum sulphide.
SPIRITUALISM, a term used by philosophical writers to denote the opposite of materialism, and also used in a narrower sense to describe the belief that the spiritual world manifests itself by producing in the physical world effects inexplicable by the known laws of nature.
The French alphabet, written out with the same numerical values as the Hebrew, in which the first nine letters denote units and the others tens, will have the following significance: