## Symbolically Sentence Examples

- The contents of such a circular group are
**symbolically**(or analogically) represented by the contents of all other circles in the animal kingdom. - 1 1 where laan and di denotes, not s successive operations of d1, but the operator of order s obtained by raising d l to the s th power
**symbolically**as in Taylor's theorem in the Differential Calculus. - - If, in the identity 1 (1 +anx = 1+aiox+aoly+a20x 2 +allxy+a02y 2 +..., we multiply each side by (I -ï¿½-P.x+vy), the right-hand side becomes 1 +(aio+1.1 ') x +(a ol+ v) y +...+(a p4+/ 1a P-1,4+ va Pr4-1) xPyq - - ...; hence any rational integral function of the coefficients an, say f (al °, aol, ...) =f exp(ï¿½dlo+vdol)f d a P-1,4, dot = dapg The rule over exp will serve to denote that i udio+ vdo h is to be raised to the various powers
**symbolically**as in Taylor's theorem. - We write;L 22 = a 1 a 2 .b 1 n-2 b2s 3 n - 3 3 n-3 3 n-3 3 a 3 = a 1 a 2 .b 1 b 2 .c 1 c2, and so on whenever we require to represent a product of real coefficients
**symbolically**; we then have a one-to-one correspondence between the products of real coefficients and their symbolic forms. If we have a function of degree s in the coefficients, we may select any s sets of umbrae for use, and having made a selection we may when only one quantic is under consideration at any time permute the sets of umbrae in any manner without altering the real significance of the symbolism. - Ternary and Higher Forms.-The ternary form of order n is represented
**symbolically**by (aixl+a2x2+a3x3)' =a'; and, as usual, b, c, d,... - The Hessian is
**symbolically**(abc) 2 azbzcz = H 3, and for the canonical form (1 +2m 3)xyz-m 2 (x 3 +y 3 +z 3). - The extraordinary advantage of the transformation of S2 to association with non-unitary symmetric functions is now apparent; for we may take, as representative forms, the symmetric functions which are
**symbolically**denoted by the partitions referred to. **Symbolically**, to be the fundamental form of seminvariant of degree 0 and weight w; he observes that every form of this degree and weight is a linear lic expressions.- Franciscus Vieta (Francois Viete) named it Specious Arithmetic, on account of the species of the quantities involved, which he represented
**symbolically**by the various letters of the alphabet. - Since the weights used in conjunction with a balance are really standard masses, the word "weight" may be substituted for the word "mass" in the preceding definitions; and we may
**symbolically**express the relations thus: - If M be the weight of substance occupying a volume V, then the absolute density O = M/V; and if m, m 1 be the weights of the substance and of the standard substance which occupy the same volume, the relative density or specific gravity S = m/m l; or more generally if m i be the weight of a volume v of the substance, and m l the weight of a volume v l of the standard, then S = mv l /m l v. - Their relationship and origin from three tribes are
**symbolically**represented by the twin sisters and the two sets of three brothers. - Each sar, month and hour was represented at once visibly and
**symbolically**by a twelfth part of the " furrow " drawn by the solar Bull across the heavens. - These deities were
**symbolically**represented by three men who went round the house by night. - All Israel is represented
**symbolically**in the twelve stones with which he built the altar; and the water which he poured upon the sacrifice and into the surrounding trench was apparently designed to prevent the suspicion of fraud! - He was
**symbolically**elected to the prophetic office by Elijah some time during the reign of Ahab (1 Kings xix. - The modern name, as above-mentioned, is Merj Ibn `Amir (" the meadow-land of the son of `Amir "); in ancient times it was known as the Valley of Jezreel, of which name Esdraelon is a Greek corruption; and by another name (Har-Magedon) derived from that of the important town of Megiddo - it is referred to
**symbolically**in Rev. xvi. - The angle whose tangent is the coefficient of friction is called thf angle of repose, and is expressed
**symbolically**by 4) tan_if. - To express this
**symbolically**, let dii represent the area of a portion of a pair of rubbing surfaces at a distance r from the axis of their relative rotation; p the intensity of the normal pressure at du per unit of area; and f the coefficient of friction. - To express this
**symbolically**, let Wi, W2 be the weights of the bodies; P the effort exerted between them; S the distance through which it acts; R1, Rf the resistances opposed to the effort overcome by Wi, ~AT2 respectively; E1, Ef the shares of the whole energy E exerted upon Wi, W2 respectively. - With the capture of the capitals, the Persian war was at an end, and the atonement for the expedition of Xerxes was completea truth
**symbolically**expressed in the burning of the palace at Persepolis. - The surname "hammerer" might have been applied to Judas either as a distinctive title pure and simple or
**symbolically**as in the parallel case of Edward Scotorum ` malleus."