Its function could determine the meaning of the symbols, since the most ancient Immortal writing is based on a complex system of symbolic context.
The opening " vision " (i.), an elaborate symbolic picture, is of the nature of a general preface, and was composed probably late in the prophet's life.
There are several symbolic acts descriptive of the siege.
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 exception of Augustus de Morgan, Boole was probably the first English mathematician since the time of John Wallis who had also written upon logic. His novel views of logical method were due to the same profound confidence in symbolic reasoning to which he had successfully trusted in mathematical investigation.
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.
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.
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.
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.
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.
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.
We cannot even outline here the process of selection by which the symbolic meanings now stereotyped in the Roman Pontifical were arrived at.
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.
Stroh, from a knowledge of the results, was able to verify and extend the results by the symbolic method.
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,...
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.
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 .
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.
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.
And we may suppose such identities between the symbols that on the whole only two, three, or more of the sets of umbrae are not equivalent; we will then obtain invariants of two, three, or more sets of binary forms. The symbolic expression of a covariant is equally simple, because we see at once that since AE, B, Ce,...
+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.
That occur in the symbolic expression; the degree in the variables (i.e.
-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.
Making the substitution in any symbolic product the only determinant factors that present themselves in the numerator are of the form (af), (bf), (cf),...and every symbol a finally appears in the form.
Such a symbolic product, if its does not vanish identically, denotes an invariant or a covariant, according as factors az, bz, cz,...