## Symbolic Sentence Examples

- 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 . **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.- 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. - Such a
**symbolic**product, if its does not vanish identically, denotes an invariant or a covariant, according as factors az, bz, cz,... - 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. - 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. - Constitutional formulae like these, in fact, are nothing more than
**symbolic**expressions of the character of the compounds which they represent, the arrangement of symbols in a certain definite manner being understood to convey certain information with regard to the compounds represented. - 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." - 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. - We cannot even outline here the process of selection by which the
**symbolic**meanings now stereotyped in the Roman Pontifical were arrived at. - The waratah or native tulip, the magnificent flowering head of which, with the kangaroo, is
**symbolic**of the country, is one of the Proteaceae. - 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. - 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. - 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.- 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. - 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. - 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. - 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,... - -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. - Among the
**symbolic**conceits in which the authors of the Brahmanas so freely indulge, there is one overshadowing all others - if indeed they do not all more or less enter into it - which may be considered as the sum and substance of these speculations, and the esoteric doctrine of the sacrifice, involved by the Brahmanical ritualists. - 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. - It consisted essentially in the adoption of Delauny's final numerical expressions for longitude, latitude and parallax, with a
**symbolic**term attached to each number, the value of which was to be determined by substitution in the equations of motion. - By
**symbolic**means," the definition, as developed by him, is one which would apply to the philosophy of Kant. - 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. - (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. **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,...