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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."

In other cases the impression is involuntary or less consciously sought, as in dreams, which, however, are sometimes induced, for purposes of divination, by the process known as incubation or temple sleep. Dreams are sometimes regarded as visits to or from gods or the souls of the dead, sometimes as signs to be interpreted symbolically by means of dream-books, which are found not only in Europe but in less cultured countries like Siam.

29-39), to announce symbolically the rending of the kingdom, replaces some account of a rebellion in which Jeroboam "lifted up his hand" (v.

The most important relation between the co-ordinates of a point on an ellipse is: if N be the foot of the perpendicular from a point P, then the square on PN bears a constant ratio to the product of the segments AN, NA' of the major axis, this ratio being the square of the ratio of the minor to the major axis; symbolically PN2= AN.NA'(CB/CA) 2.

It meant that the Mithraist symbolically died when he became a first grade neophyte and was born again as a crow.

Eg, the monarch symbolically chooses the prime minister, can dissolve parliament and no bill can pass into law without royal assent.

Symbolically, she represents for us the ground of the soul: that interior mirror where the divine radiance is received.

Symbolically, they can be highly resonant and emotive.

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 -Ã¯¿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 Ã‚°, aol, ...) =f exp(Ã¯¿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."

In other cases the impression is involuntary or less consciously sought, as in dreams, which, however, are sometimes induced, for purposes of divination, by the process known as incubation or temple sleep. Dreams are sometimes regarded as visits to or from gods or the souls of the dead, sometimes as signs to be interpreted symbolically by means of dream-books, which are found not only in Europe but in less cultured countries like Siam.

29-39), to announce symbolically the rending of the kingdom, replaces some account of a rebellion in which Jeroboam "lifted up his hand" (v.

The most important relation between the co-ordinates of a point on an ellipse is: if N be the foot of the perpendicular from a point P, then the square on PN bears a constant ratio to the product of the segments AN, NA' of the major axis, this ratio being the square of the ratio of the minor to the major axis; symbolically PN2= AN.NA'(CB/CA) 2.

Symbolically, she represents for us the ground of the soul: that interior mirror where the divine radiance is received.

Symbolically, they can be highly resonant and emotive.

Doorbells are symbolically charged elements that welcome the idea of opening a new door for the newlyweds.

Certain games can symbolically express a child's problems.

Overhead beams - These can create disharmony in your marriage as well as disease since they symbolically slice through the body.

Tradition: A candle burning in the window offers warmth and welcome to visitors during the holiday season with traditional connections to welcoming traveling priests or symbolically welcoming the Holy Family.

Symbolically, she represents motherhood, childbirth, knowledge, protection and justice.

Practicing hand yoga poses is a rich tradition in Hinduism and Buddhist cultures, where it continues to be used symbolically through meditation to attain spiritual growth.

London and Kelly offer sometimes biting criticism along with their comments, as the wardrobe items are symbolically tossed in a garbage can.

The word usage examples above have been gathered from various sources to reflect current and historial usage. They do not represent the opinions of YourDictionary.com.