# Symbolic Sentence Examples

- There are several
**symbolic**acts descriptive of the siege. - It will be shown later that all invariants, single or simultaneous, are expressible in terms of
**symbolic**products. - Of the
**symbolic**factors of the form are replaced by IA others in which new variables y1, y2 replace the old variables x1, x 2 . - Given any propositions involving any number of terms, Boole showed how, by the purely
**symbolic**treatment of the premises, to draw any conclusion logically contained in those premises. - We cannot even outline here the process of selection by which the
**symbolic**meanings now stereotyped in the Roman Pontifical were arrived at. - Stroh, from a knowledge of the results, was able to verify and extend the results by the
**symbolic**method. - To express the function aoa2 - _ which is the discriminant of the binary quadratic aoxi -+-2a1x2x2-+a2x2 = ai =1, 1, in a
**symbolic**form we have 2(aoa 2 -ai) =aoa2 +aGa2 -2 a1 ï¿½ al = a;b4 -}-alb? **Symbolic**Identities.- For the purpose of manipulating**symbolic**expressions it is necessary to be in possession of certain simple identities which connect certain**symbolic**products.- And that thence every
**symbolic**product is equal to a rational function of covariants in the form of a fraction whose denominator is a power of f x. - Such a
**symbolic**product, if its does not vanish identically, denotes an invariant or a covariant, according as factors az, bz, cz,... - Early in 1886 he struck the public taste with precision in his wild
**symbolic**tale of The Strange Case of Dr Jekyll and Mr Hyde. - With the amice, "Place on my head the helmet of salvation," &c. For the
**symbolic**meanings of the various vestments see the separate articles devoted to them. - The loculi were intact and the epitaphs still in their places, so that " they form a kind of museum, in which the development, the formulae, and the
**symbolic**figures of Christian epigraphy, from its origin to the end of the 3rd or 4th century, can be notified and contemplated, not in artificial specimens as in the Lateran, but in the genuine and living reality of their original condition." - If we restrict ourselves to this set of symbols we can uniquely pass from a product of real coefficients to the
**symbolic**representations of such product, but we cannot, uniquely, from the symbols recover the real form, This is clear because we can write n-1 n-2 2 2n-3 3 a1a2 =a l a 2, a 1 a 2 = a 1 a2 while the same product of umbrae arises from n n-3 3 2n-3 3 aoa 3 = a l .a a 2 = a a 2 . **Symbolic**Identities.- For the purpose of manipulating**symbolic**expressions it is necessary to be in possession of certain simple identities which connect certain**symbolic**products.- 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. - The waratah or native tulip, the magnificent flowering head of which, with the kangaroo, is
**symbolic**of the country, is one of the Proteaceae. - That the name also prevailed as that of a god among other Semitic races (or even These sacred arks were carried in procession accompanied by
**symbolic**figures. - Two methods of treatment have been carried on in parallel lines, the unsymbolic and the
**symbolic**; both of these originated with Cayley, but he with Sylvester and the English school have in the main confined themselves to the former, whilst Aronhold, Clebsch, Gordan, and the continental schools have principally restricted themselves to the latter. - A separation is the
**symbolic**representation of a product of monomial symmetric functions. - 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,... - To find the effect of linear transformation on the
**symbolic**form of quantic we will disuse the coefficients a 111 a 12, a21, a22, and employ A1, Iï¿½1, A2, ï¿½2. - It is clear from what has been said above that the liturgical vestments possessed originally no mystic
**symbolic**meaning whatever; it was equally certain that, as their origins were forgotten, they would develop such a**symbolic**meaning. - Still more original and remarkable, however, was that part of his system, fully stated in his Laws of Thought, which formed a general
**symbolic**method of logical inference. - May be the same or different, it is necessary that every product of umbrae which arises in the expansion of the
**symbolic**product be of degree n, in a l, a 2; in the case of b,, b 2 of degree n 2; in the case of c 1, c 2 of degree n3; and so on. - Every
**symbolic**product, involving several sets of cogredient variables, can be exhibited as a sum of terms, each of which is a polar multiplied by a product of powers of the determinant factors (xy), (xz), (yz),... - 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. - It has been shown by Gordan that every
**symbolic**product is expressible as a sum of transvectants. - By
**symbolic**means," the definition, as developed by him, is one which would apply to the philosophy of Kant. - Mishawaka is the proud home of Shiojiri Niwa, one of the only Japanese strolling gardens in the state where visitors can explore rare botanicals and
**symbolic**sculptures. - Where the multiplications on the leftand right-hand sides of the equation are
**symbolic**and unsymbolic respectively, provided that m P4, M P4 are quantities which satisfy the relation exp (M14+Moir+...+Mp4EpnP+...) =1+mic -Fmoif+...+mp,eng+...; where E, n are undetermined algebraic quantities. - 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. - (ab)i(ac)j(bc)k..., that the
**symbolic**product (ab)i(ac)j(bc)k..., possesses the invariant property. - The i t " power of that appertaining to a x and b x multiplied by the j t " power of that appertaining to a x and c x multiplied by &c. If any two of the linear forms, say p x, qx, be supposed identical, any
**symbolic**expression involving the factor (pq) is zero. - For these only will the
**symbolic**product be replaceable by a linear function of products of real coefficients. - = t) 1 v ...axbxcx..., and assert that the
**symbolic**product (ab)i(ac)'(bc)k...aibxc2... - +P=n1, j+k+...+T =n3, It will also be a covariant if the
**symbolic**product be factorizable into portions each of which satisfies these conditions. - -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. - In common with other sciences, economics makes use of " abstractions"; but if for some problems we employ
**symbolic**processes of reasoning, we must keep clearly in view the limits of their significance, and neither endow the symbols with attributes they can never possess, nor lose sight of the realities behind them. - 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. - Xy 2 -4z 3 +g2x 2 y+g3x 3, and also the special form axz 2 -4by 3 of the cuspidal cubic. An investigation, by non-
**symbolic**methods, is due to F. - A sort of
**symbolic**retaliation was the punishment of the offending member, seen in the cutting off the hand that struck a father or stole a trust; in cutting off the breast of a wet-nurse who substituted a changeling for the child entrusted to her; in the loss of the tongue that denied father or mother (in the Elamite contracts the same penalty was inflicted for perjury); in the loss of the eye that pried into forbidden secrets. - = exp,udl where exp denotes (by the rule over exp) that the multiplication of operators is
**symbolic**as in Taylor's theorem. **Symbolic**Form.-Restricting consideration, for the present, to binary forms in a single pair of variables, we must introduce the**symbolic**form of Aronhold, Clebsch and Gordan; they write the form Iln n n-1 n-1 n n n aixi+a2x2) = 44+(1) a l a 2 x 1 x2+...+a2.x2=az wherein al, a2 are umbrae, such that n-1 n-1 n a 1, a 1 a 2, ...a 1 a 2, a2 are**symbolical**respreentations of the real coefficients ï¿½o, ai,...**Symbolic**Form.-Restricting consideration, for the present, to binary forms in a single pair of variables, we must introduce the**symbolic**form of Aronhold, Clebsch and Gordan; they write the form Iln n n-1 n-1 n n n aixi+a2x2) = 44+(1) a l a 2 x 1 x2+...+a2.x2=az wherein al, a2 are umbrae, such that n-1 n-1 n a 1, a 1 a 2, ...a 1 a 2, a2 are**symbolical**respreentations of the real coefficients ï¿½o, ai,...- (1 + a i x) (1+ = s i z we have the
**symbolic**identity +02712+0.3x3+... - The weight of the function is bipartite and consists of the two numbers Ep and Eq; the
**symbolic**expression of the symmetric function is a partition into biparts (multiparts) of the bipartite (multipartite) number Ep, Eq. - The repetition of the process brought the same results.
- Some of them imitated the Hebrew prophets in the performance of
**symbolic**acts of denunciation, foretelling or warning, going barefoot, or in sackcloth or undress, and, in a few cases, for brief periods, altogether naked; even women in some cases distinguished themselves by extravagance of conduct. - Notice, therefore, that the
**symbolic**product (ab)i(ac)j(bc)k... - 1+Eaix+Esiy+ /al a2x 2 +Malt2xy -Z01023,2+ï¿½ï¿½ï¿½ The most general symmetric function to be considered is E 41 041 8424-3033..ï¿½ .conveniently written in the
**symbolic**form (pigi p2g2 p3go...)ï¿½ Observe that the summation is in regard to the expressions obtained by permuting then suffixes I, 2, 3, ...n. - (multiplication
**symbolic**) ?r1! ?2,ï¿½..